SlideShare uma empresa Scribd logo
1 de 42
Baixar para ler offline
SSC Higher Secondary Exam
www.jagranjosh.com
                        (Preparation Booklet)
TABLE OF CONTENTS
 Introduction ................................................................................................................................ 4

 General Intelligence .................................................................................................................... 6

    Analogy ................................................................................................................................... 6

    Classification ........................................................................................................................... 6

    Series ....................................................................................................................................... 6

    Coding-Decoding ..................................................................................................................... 7

    Sequence ................................................................................................................................. 7

    Direction Test .......................................................................................................................... 7

    Puzzles ..................................................................................................................................... 8

    Mathematical Puzzles ............................................................................................................. 9

    Syllogism ............................................................................................................................... 10

    Non-Verbal ............................................................................................................................ 11

 Quantitative Aptitude ............................................................................................................... 14

    HCF & LCM ............................................................................................................................ 14

    Ratio & Proportion ................................................................................................................ 15

    Percentage ............................................................................................................................ 16

    Average ................................................................................................................................. 17

    Surds and Indices .................................................................................................................. 18

    Profit & Loss .......................................................................................................................... 18

    Interest Calculation ............................................................................................................... 19

    Time, Speed & Distance ........................................................................................................ 22

    Time & Work ......................................................................................................................... 23

    Elementary Algebra .............................................................................................................. 24

    Geometry .............................................................................................................................. 26
Mensuration.......................................................................................................................... 28

   Trigonometry ........................................................................................................................ 30

   Data Interpretation ............................................................................................................... 32

English Language ....................................................................................................................... 35

   Synonyms .............................................................................................................................. 35

   Antonyms .............................................................................................................................. 35

   Idioms and phrases ............................................................................................................... 36

   One Word Substitution ......................................................................................................... 36

   Spelling Test .......................................................................................................................... 38

   Incorrect Sentences .............................................................................................................. 38

   Sentence Reconstruction ...................................................................................................... 39

   Spotting the Error ................................................................................................................. 39

   Cloze Test .............................................................................................................................. 40
INTRODUCTION
SSC Combined Higher Secondary Level (10+2) Examination 2012 will be conducted by Staff
Selection Commission (SSC) for the recruitment to the posts of Data Entry Operators and Lower
Division Clerk. SSC Combined Higher Secondary Level (10+2) Examination 2012 is going to be
conducted on 21 October 2012 & 28 October 2012. To be eligible for SSC Combined Higher
Secondary Level (10+2) Examination 2012, the candidate must have passed 12th Standard or
equivalent or higher examination from a recognized Board or University. In addition, the
candidate’s minimum age should be 18 years and maximum age should be 27 years.

The selection will be based on basis of 2 hours written examination carrying 200 marks, which is
followed by Data Entry Skill Test/ Typing Test of shortlisted candidates. The written
examination consists of objective type paper including 4 parts that are as follows:

   General Intelligence (50 Questions)
   English Language (50 Questions)
   Quantitative Aptitude (50 Questions)
   General Awareness (50 Questions)

The question will be set in both Hindi and English Language for Part I, II, and IV. There will be
negative marking of 0.25 marks for each wrong answer.

Syllabus for Objective Paper

General Intelligence

Semantic Analogy, Symbolic operation, Symbolic/Number Analogy, Trends, Figural Analogy,
Space Orientation, Semantic Classification, Venn Diagrams, Symbolic/Number Classification,
Drawing inferences, Figural Classification, Punched hole/pattern-folding & unfolding, Semantic
Series, Figural Pattern – folding and completion, Number Series, Embedded figures, Figural
Series, Critical Thinking, Problem Solving, Emotional Intelligence, Word Building, Social
Intelligence, Coding and de-coding, Numerical operations

English Language

Spot the Error, Fill in the Blanks, Synonyms/Homonyms, Antonyms, Spellings/Detecting Mis-
spelt words, Idioms & Phrases, One word substitution, Improvement of Sentences,
Active/Passive Voice of Verbs, Conversion into Direct/Indirect narration, Shuffling of Sentence
parts, Shuffling of Sentences in a passage, Cloze Passage, Comprehension Passage

Quantitative Aptitude

1. Arithmetic

Number Systems: Computation of Whole Number, Decimal and Fractions, Relationship
between numbers
Fundamental Arithmetical Operations: Percentage, Ratio and Proportion, Square roots,
Averages, Interest (Simple and Compound), Profit and Loss, Discount, Partnership Business,
Mixture and Alligation, Time and distance, Time and work

2. Algebra

Basic algebraic identities of School Algebra (and their simple applications) e.g. Formulas for
(a + b) 2, (a - b) 2, (a + b)3, (a - b)3 , a3 - b3, a3 + b3, a2 - b2; if a + b + c=0, then a3 + b3 + c3 = 3abc
etc. and Elementary surds (simple problems), and Graphs of Linear Equations

3. Geometry

Familiarity with elementary geometric figures and facts:

Triangle and its various kinds of centres viz. Centroid, In-centre, Orthocentre, Circumcentre
Congruence and similarity of triangles

Circle and its chords, tangents, angles subtended by chords of a circle, common tangents to two
or more circles

4. Mensuration

Triangle, Quadrilaterals, Regular Polygons (sum of the internal angles of a polygon), Circle, Right
Prism, Right Circular Cone, Right Circular Cylinder, Sphere, Hemispheres, Rectangular
Parallelepiped, Regular Right Pyramid with triangular or square Base

5. Trigonometry

Trigonometry (for acute angles 0 with 0≤0≤90): Trigonometric ratios, Degree and Radian
Measures, Standard Identities like sin20 + Cos20=1 etc

Complementary Angles, Heights and Distances (simple problems only)

6. Statistical Charts

Use of Tables and Graphs: Histogram, Frequency polygon, Bar-diagram, and Pie-chart

General Awareness

History, Culture Geography, Economic Scene, General policy and Scientific Research
GENERAL INTELLIGENCE

ANALOGY
Analogy: In this type of questions the students are required to identify the previous relation
and find out the best suitable relation for the other term. These questions are asked in the form
of proportion where two related terms are given and the next matching missing term can be
asked. The questions of the analogy can be in the form of words, numbers, letters and coded
letters etc. with any relation.

For Example, Cricket : Pitch :: Tennis :: ?

     (a)   Arena
     (b)   Course
     (c)   Court
     (d)   Rink

Answer: - (c) Court. Here Cricket is played at Pitch and Tennis is played at Court.

CLASSIFICATION
Classification: In this type of questions the students are required to identify the item which
does not belong to a group. It means the other items in the group are similar with respect to
certain logic but one is different. The students can get questions on word group, number group,
letter group, coded letter group and numeral pair group etc.

For Examples

1.
   (a) 36
   (b) 125
   (c) 144
   (d) 121
Answers: - (b) All except 125 are squares.

SERIES
Series: It can be understood as a sequence of numerical, alphabetical and alphanumerical terms
which follows a fixed pattern. The students are required to identify the missing term or wrong
term in the series.
For Example

1. 6, 11, 18, 27, 38, ?.
   (a) 49                                                (c) 51
   (b) 50                                                (d) 52
Answer: - (c) The series is +5, +7, +9……

CODING-DECODING
Coding: Coding is a process by which certain information is written into another form of
information on the basis of certain principles.

Decoding: Decoding is used to infer the right information from the coded information.

For Example, In a certain code language, BOOK is written as 2151511. In the same language
how PEN be written?

Answer:- In the above example the letters of BOOK is coded on the basis of their position in the
English alphabet. The letters B=2, O = 15, K = 11. In the same way we can encode PEN as 16514.

SEQUENCE
The question on this topic can be of following types;

1. Ascertaining meaningful word sequence.
2. Ascertaining similar numerical sequence.
3. Finding a position in a sequence.

For Example,

Find the meaningful order of the following words in ascending order.

1.   Line
2.   Angle
3.   Pentagon
4.   Rectangle
5.   Triangle

Answer: - The right order for these words will be Line – Angle – Triangle – Rectangle –
Pentagon. Therefore the answer is 1, 2, 5, 4, and 3.

DIRECTION TEST
In this unit, the problems are generally formulated with successive follow-up of the directions
and the candidates are required to find the final direction, the final position with respect to the
initial position or the distance between the final position and initial position.
On paper, we can draw the directions as;
(Here, N = North, NE = North-East, E = East, SE = South-East, S = South, SW = South-West,

W = West, NW = North-West)

Example: If a person is going to the east of his home and turning to his left after that turning to
his right.                                                         His final position

We can draw his path as;
                       His Home

For Example, A starts walking towards East, turns right, again turn right, turns left, again turns
left, turns left, again turns left. In which direction is A walking now?

     (a)   East
     (b)   West
     (c)   North
     (d)   South

Answer:- (b)

PUZZLES
The Puzzle questions can be in the form of following types;

1.   Blood Relation Problems
2.   Height and Position Related Problems
3.   Cube and Blocks Related Problems
4.   Embedded Words & Unscrambled Words Related Problem.

Examples;

1. P and Q are brothers. R and S are sisters. P’s son is S’s brother. How is Q related to R?
                                                                                    (SSC 2011)

Answer: In the question P’s son is S’s brother means P is the father of S and similarly P is the
father of R because S and R are sisters. Therefore Q is the uncle of R. because Q is the father’s
brother of R.

2. There are five friends - Satish, Kishore, Mohan, Anil and Rajesh. Mohan is the tallest. Satish is
   shorter than Kishore but taller than Rajesh. Anil is little shorter than Kishore but little taller
   than Satish. Who is taller than Rajesh but shorter than Anil?                     (SSC 2011)
Answer: It is given that Kishore>Satish>Rajesh and Kishore>Anil>Satish. It means the sequence
of height is Mohan>Kishore>Anil>Satish> Rajesh. Therefore, the person who is taller than
Rajesh but shorter than Anil is Satish.

MATHEMATICAL PUZZLES
Introduction: In this unit we will study various types of questions based on the basic
mathematical and logical concepts. These types of questions are regularly asked in the SSC
exams. After analyzing previous papers, it is clear that in the exam you can get 5 to 8 questions
from this unit.

The question types

1. Arrangement of correct mathematical operations.
2. Filling the correct mathematical operations.
3. Mathematical-Logical problems

When you are solving these questions you should follow basic mathematical operations in a
correct sequence. The correct sequence of solving mathematical problems is known by
“BODMAS Rule” or “VBODMAS Rule”.

V – Vinculum B – Brackets O – Of D – Division       M – Multiplication     A – Addition

S – Subtraction.

For Examples

1. Which interchange of signs will make the following equation correct?

   25 − 5 + 32 ÷ 4 × 6 = 13.

   (a)   − and ÷
   (b)   × and ÷
   (c)   – and +
   (d)   × and –

Answer:- (a)

2. Select the correct combination of mathematical signs to replace the * signs and to balance
   the given equation.

   5 * 5 * 3 * 4 * 64 * 4.

   (a)   ÷×−= +
   (b)   ×−= +÷
   (c)   +×−=÷
   (d)   ×−=÷+

Answer:- (c)
3. Some equations are solved on the basis of certain system on the same basis find out the
   correct answer for the unsolved equation.

   1 × 2 × 5 = 125, 2 × 1 × 6 = 216,

   3×4×3=?

   (a)   125
   (b)   216
   (c)   512
   (d)   343

Answer:- (d)

SYLLOGISM
Syllogism: The literal meaning of syllogism is ‘Conclusion’ or ‘inference’. The questions in the
syllogism are in the form of statements (premises) followed by Conclusion (proposition) and the
students are asked to find the correct conclusion on the basis of the statements.

The general form of statements and conclusions in the syllogism is;

 All As are Bs.
 Some As are Bs.
 No A is a B.

The graphical representation of the statements

1. All As are Bs.




2. Some As are Bs.




3. No A is a B.
For Example

Direction (Q. 1 – 2): In each questions below there are two/three statements followed by two
conclusions I and II. Assuming both the statements true, you have to decide which of the two
conclusions logically follows the statements and then give your answer

(a)   If only conclusion I follows.
(b)   If only conclusion II follows.
(c)   If either conclusion I or conclusion II follows.
(d)   If neither conclusion I nor conclusion II follows.
(e)   If both conclusion I and conclusion II follow.

1. Statements:           Some pens are pencils.

                         Some pencils are books.

      Conclusions:       I. Some pens are books.

                         II. All books are pens.

Answer:- (d)

2. Statements:           All bottles are bags.

                         All bags are buses.

      Conclusions:       I. Some bags are bottles.

                         II. All bags are bottles.

Answer:- (a)

NON-VERBAL
The questions from this unit can be of following types;

1.    Pictorial pattern based questions.
2.    Embedded figure questions.
3.    Mirror Image questions.
4.    Paper Cutting problems.
5.    Relationship based problems.
For Example

1. Which answer figure will complete the pattern in the question figure?         (SSC 2011)

   Question figure:




   Answer figures:




Answer: (D) will complete the pattern

2. Which of the answer figures is exactly the mirror image of the question figure, when the
   mirror is held on the line MN?                                                (SSC 2002)

   Question figure:




   (a)                       (b)                      (c)                       (d)
Answer: (d)

3. Select the answer figure in which the question figure is hidden/embedded.

         Question figure:




   (a)                       (b)                      (c)                       (d)
Answer: (d)
QUANTITATIVE APTITUDE

HCF & LCM
Some Important concepts

Factors and Multiples: If a number m divides the number n with remainder = 0, then m is called
the factor of n and n is called multiple of m.

Highest Common Factor (HCF): The HCF is the highest common factor for two or more
numbers.

For Example, if we have two numbers 30 and 20, then the factors of 30 are 1, 2, 3, 5, 6, 10, 15
and 30. And the factors of 20 are 1, 2, 4, 5, 10 and 20. Here 10 is the highest common factor.

Least Common Multiple (LCM): The LCM is the lowest number which is exactly divisible by the
given two or more than two numbers. For example, if we have two numbers 20 and 30, then
the multiples of 20 are 20, 40, 60, 80………. And the multiples of 30 are 30, 60, 90, 120………..
Here 60 is the lowest number which is exactly divisible by both 20 and 30. Therefore 60 is the
required LCM.

        Product of two numbers = Product of their LCM and HCF

        For example, the LCM for 20 and 30 is 60 and HCF for 20 and 30 is 10. Here 20 × 30 = 60
        × 10 = 600.

Co-primes: Two numbers are co-primes if their HCF = 1.

HCF and LCM of Fraction:
         𝐇𝐂𝐅 𝐨𝐟 𝐧𝐮𝐦𝐞𝐫𝐚𝐭𝐨𝐫𝐬                𝐋𝐂𝐌 𝐨𝐟 𝐧𝐮𝐦𝐞𝐫𝐚𝐭𝐨𝐫𝐬
HCF =   𝐋𝐂𝐌 𝐨𝐟 𝐃𝐞𝐧𝐨𝐦𝐢𝐧𝐚𝐭𝐨𝐫𝐬
                              and LCM =   𝐇𝐂𝐅 𝐨𝐟 𝐃𝐞𝐧𝐨𝐦𝐢𝐧𝐚𝐭𝐨𝐫𝐬

For Example

The L.C.M. of two numbers is 189 and H.C.F. of two numbers is 9.If one of the number is 63
then other number is:

   (a) 27
   (b) 28
   (c) 29
   (d) 30
Answer:- (a)
RATIO & PROPORTION
Ratio: A ratio is a comparison of two numbers (quantity in the same unit). It is written as, a: b =
a
  = a ÷ b, where a and b are two number (quantity).
b

In a ratio a : b, a and b are the terms of the ratio; ‘a’ is called the antecedent and ‘b’ is called the
consequent.

The word ‘antecedent’ literally means ‘that which goes before’ and the word consequent
literally means ‘that which goes after’.

Compound Ratio: Compounded ratio is a product of two or more ratios.

Example: Find the ratio compounded of the three ratios:

2 : 3, 3 : 4 and 7 : 11
                                      2 × 3 ×7   7
Solution: the required ratio is =3 ×4 ×11 = 22 .
                                                 1   1
Inverse Ratio: If a : b is a given ratio, then a ∶ b or b : a is called its inverse ratio or reciprocal
ratio.

1. If the antecedent (a) = the consequent (b), the ratio is called the ratio of equality, such as
   2 : 2.
2. If the antecedent (a) > the consequent (b), the ratio is called the ratio of greater inequality,
   such as 3 : 2.
3. If the antecedent (a) < the consequent (b), the ratio is called the ratio of less inequality,
   such as 2 : 3.
                                                                           a   c
Proportion: A proportion expresses the equality of two ratios. e.g. b = d

Or a : b = c : d or a : b :: c : d.

In a proportion in the form of a : b :: c : d the first and the last terms are called the extremes
and the second and the third terms or the middle terms are called as the mean terms. When
four quantities are in proportion, we can write it in the mathematical form as a : b :: c : d 
a    c
  = d  ad = bc
b
For Example,
                                                                            2             1
If Rs. 510 be divided among A, B, C in such a way that A gets 3 of what B gets and B gets 4 of
what C gets, then their shares are respectively :

   (a) Rs. 120, Rs. 240, Rs. 150
   (b) Rs. 60, Rs. 90, Rs. 360
   (c) Rs. 150, Rs. 300, Rs. 60
   (d) None of these
Answer:- (b)

PERCENTAGE
Percentage: The term “per cent” means “for every hundred”. A fraction whose denominators is
100 is called a percentage and the numerator of the fraction is called the rate per cent. It is
denoted by the symbol %.
           x                              10        1
Here x % =100 . For example 10% =100 = 10 .

Similarly, fraction can be changed in the form of percentage when we multiply them by 100.
               1      1
For Example 4 = 4 × 100 = 25%.

To decrease a number by a given %:
                                              𝟏𝟎𝟎−𝐑𝐚𝐭𝐞
Multiply the numbers by the factor               𝟏𝟎𝟎

To find the % increase of a number:
               𝐓𝐨𝐭𝐚𝐥 𝐢𝐧𝐜𝐫𝐞𝐚𝐬𝐞                  𝐅𝐢𝐧𝐚𝐥 𝐯𝐚𝐥𝐮𝐞−𝐈𝐧𝐢𝐭𝐢𝐚𝐥 𝐯𝐚𝐥𝐮𝐞
% increase =                        × 𝟏𝟎𝟎 =                                × 𝟏𝟎𝟎
                   𝐈𝐧𝐢𝐭𝐢𝐚𝐥 𝐯𝐚𝐥𝐮𝐞                       𝐈𝐧𝐢𝐭𝐢𝐚𝐥 𝐯𝐚𝐥𝐮𝐞

To find the % decrease of a number:
                   𝐓𝐨𝐭𝐚𝐥 𝐝𝐞𝐜𝐫𝐞𝐚𝐬𝐞               𝐅𝐢𝐧𝐚𝐥 𝐯𝐚𝐥𝐮𝐞−𝐅𝐢𝐧𝐚𝐥 𝐯𝐚𝐥𝐮𝐞
% decrease =                        × 𝟏𝟎𝟎 =                                × 𝟏𝟎𝟎
                    𝐈𝐧𝐢𝐭𝐢𝐚𝐥 𝐯𝐚𝐥𝐮𝐞                       𝐈𝐧𝐢𝐭𝐢𝐚𝐥 𝐯𝐚𝐥𝐮𝐞

For Example

1. In an election between two candidates, 75% of the voters casted their votes, out of which
   2% of the votes were declared invalid. A candidate got 9261 votes which were 75% of the
   total valid votes. Find the total number of votes enrolled in that election. (SSC 2003)

   (a) 15000                                                            (c) 16800
   (b) 16000                                                            (d) 17000
Answer:- (c) Let the total enrolled votes are x. Then, Number of votes cast = 75 % of x. Valid
votes = 98 % of (75 % of x) ∴ 75 % 0f [98 % of (75 % of x)] = 9261

2. If 50% of (x – y) = 30% of (x + y), then what percent of x is y?
   (a) 25 %
   (b) 50 %
   (c) 75 %
   (d) 100 %
                                                     50                      30
Answer:- (a) here 50% of (x – y) = 30% of (x + y)  100 x − y = 100 (x + y)
                                                               1
 10(x – y) = 6(x + y)  10x – 6x = 6y + 10y  4x = 16y  4 x = y  25 % of x = y.
        1
Because4 = 25%

AVERAGE
Average is defined as the sum of n different numerical values divided by n.
            𝐒𝐮𝐦 𝐨𝐟 𝐧 𝐝𝐢𝐟𝐟𝐞𝐫𝐞𝐧𝐭 𝐍𝐮𝐦𝐞𝐫𝐢𝐜𝐚𝐥 𝐕𝐚𝐥𝐮𝐞
Average =                    𝐧

                    𝐓𝐨𝐭𝐚𝐥 𝐃𝐢𝐬𝐭𝐚𝐧𝐜𝐞
Average Speed =      𝐓𝐨𝐭𝐚𝐥 𝐒𝐩𝐞𝐞𝐝

If a person covers half of his journey at a speed of x km/h and the next half at the speed of y
                                                                   𝟐𝒙𝒚
km/h, then the average speed during the whole journey is                     .
                                                                   𝒙+ 𝒚

                                                          𝒘𝟏𝒙𝟏 + 𝒘𝟐𝒙𝟐
Weighted Average of x1, x2 where weight is w1, w2 =                      .
                                                            𝒘𝟏 + 𝒘𝟐

Average of different groups

If the average of a group of n items is a and the average of another group of m items is m, then
                          𝐧𝐚 + 𝐦𝐛
the combined average = 𝐧 + 𝐦 .

For Example

1. The average of a non-zero number and its square is 5 times the number. The number is:
                                                                              (SSC 2003)
   (a) 9
   (b) 17
   (c) 29
   (d) 295

Answer:- (a) Let the number be x. Then
x2+ x
        = 5x  x 2 + x = 10x  x 2 + x − 10x = 0  x x − 9 = 0 ∴ x = 9.
 2




SURDS AND INDICES

Laws of Indices:

     (a) am × an = am + n
           am
     (b) a n = am – n
     (c) (am) n = a m n
     (d) (a b)m = a m b m
               a m              am
     (e) b     = bm
          0
     (f) a = 1

Laws of Surds:
                            1                                                          n       n
     (a)
           n
               a = an                                                            (d)       a       =a
           n          n n                                                              m   n       mn
     (b)       ab = a × b                                                        (e)        a=          a
                        n                                                              n    m       n
     (c)
           n    a
                    =   n
                            a                                                    (f)       a =          am
                b           b

For Example,
                                             1

1. Find the value of ( 81) 4 .
   (a) 3
   (b) 3
   (c) 9
       3
   (d) 3
                                     1
                                                                 1       1   1   1         1
Answer: - (b) ( 81) 4 = (3 × 3 × 3 × 3 )2 × 4 = (34 )2 × 4 = (3)2 = 3.
            1 −4
2. (−         ) 3       =?
           64
   (a)     254
   (b)     -254
   (c)     256
   (d)     -256
                                 1 −4         1       (−4)
                                                                     1
Answer:- (c) (−                    ) 3   = (− 4)3 ×     3    = (− 4)−4 = (−4)4 = 256.
                                64


PROFIT & LOSS
Some important terms for Profit and Loss:

Cost Price: It is the price at which an article is purchased. The cost price is generally abbreviated
as C.P.

Selling Price: It is the price at which an article is sold. The selling price is generally abbreviated
as S.P.

Profit or Loss: It is the difference of selling price (SP) and cost price (CP). If the difference is
positive, then it is called a profit and if the difference is negative, then it is called a loss.

Important Formulae

1. SP = CP + Profit = CP – Loss
                Gain × 100
2. Gain % =         C.P.
                Loss × 100
3. Loss % =         C.P.
          (100 + Gain %)            (100 − Loss %)
4. SP =                    × CP =                    × CP
               100                       100
               100                       100
5. CP = (100 + Gain        × SP = (100 −Loss         × SP
                      %)                       %)

For Example

1. Arjun buys an old car for Rs 1, 12, 000 and spends 8000 on its repairs. If he sells the Car for
   Rs 1,80,000, his gain percent is:

    (a) 50                                                              (c) 52
    (b) 51                                                              (d) 53

Answer:- (a) C.P. = Rs. (1,12,000 + 8,000) = Rs. 1,20,000, S.P = 1,80,000,
             60,000
Gain % = ( 1,20,000 × 100) =50%

2. If loss is 1/4 of S.P., the loss percentage is:
   (a) 25%
   (b) 20%
   (c) 35%
   (d) 40%
                                                     a   5a                  a       4
Answer:- (b) S.P. = a, Loss = a/4, CP. =a + 4 =                  Loss% =(       ×        × 100) % = 20%
                                                            4                4       5a



INTEREST CALCULATION
Important Facts and Formulae related to Interest calculation
Principal: It is the money which is borrowed or lend out for certain period. Generally, Principal
is denoted with P.

Interest: It is the cost of holding others money for a certain period of time.

Rate of Interest: It is the rate at which the interest is calculated. The rate of interest is the
amount of interest which is calculated at every Rs. 100 for a fixed period. Generally for 1 year.
                            P ×R ×T              S.I.× 100              S.I.× 100         S.I.× 100
Simple Interest (S. I.) =              ,P=                       ,R=                ,T=
                                 100              R×T                    P×T               P×R

                                             R    n
Compound Interest (C. I.) = P 1 + 100                 −P                (When interest is compounded annually)

                                             R     2n
                                             2
Compound Interest (C. I.) = P 1 + 100                   −P              (When interest is compounded Half yearly)

When rates of interest are different for different years, for example R1%, R2% and R3% for 1st,
2nd and 3rd year respectively.
                                1        R               2   R              R3
Then Compound Interest =P 1 + 100                  1 + 100             1 + 100 − P.

For Example

1. Find the compound interest on Rs. 160, 000 in 2 years at 10 % per annum. The interest
   being compounded half yearly.

    (a)   32000
    (b)   33000
    (c)   34000
    (d)   34481
                                                                  10    2×2
                                                                   2
Answer:- (d) The required C.I. = 160, 000 1 +                                 − 160, 000
                                                                 100

               21   21      21    21
= 160, 000                             − 160, 000 = 194, 481 − 160, 000 = 34, 481
               20   20      20    20

2. The difference between the compound interest and simple interest on a certain sum at 10%
   per annum for 2 years is Rs. 200. Find the principal.

    (a)   Rs. 10, 000
    (b)   Rs. 15, 000
    (c)   Rs. 20, 000
    (d)   Rs. 25, 000

Answer:- (c) Let the required principal be P. then
10   2         P × 10 × 2               121        1               1
P 1 + 100       −P−                = 200  P         − 1 − 5 = 200  P         = 200
                         100                   100                       100

Therefore, P = 20, 000
TIME, SPEED & DISTANCE
Important facts and formulae

Distance = (Speed × Time)
          Distance
Speed =     Time

         Distance
Time =    Speed

                       5
x km/h = x × 18 m/s

                  18
x m/s = x ×                km/h
                  5

                           Total Distance
Average Speed =                Total Speed

If a person covers half of his journey at a speed of x km/h and the next half at the speed of y
                                                              𝟐𝒙𝒚
km/h, then the average speed during the whole journey is             .
                                                              𝒙+ 𝒚

In water, the direction along the stream is called downstream. And the direction against the
stream is called upstream.

If the speed of a boat in still water is a km/h and the speed of the stream is b km/h, then:

Speed downstream = (a + b) km/h

Speed upstream = (a + b) km/h

If the speed downstream is p km/h and the speed upstream is b km/h, then:
                                   𝟏
Speed in still water = 𝟐 (𝐚 + 𝐛) km/h
                           𝟏
Rate of stream = 𝟐 (𝐚 − 𝐛) km/h

For Example

1. A man travelled from the village to the post-office at the rate of 25km/h and walked back at
   the rate of 4 km/h. If the whole journey took 5 hours 48 minutes. Find the distance of the
   post-office from the village.                                                 (SSC, 2004)

   (a) 10 km                                             (c) 20 km
   (b) 15 km                                             (d) 25 km
2 × 25 × 4       200
Answer: - (c) The average speed for the whole journey =                                   =         km/h. the total time is
                                                                              25 + 4          29
 48      4      29                               200           29
5 60 = 5 5 =         h. ∴ the total distance =             ×        = 40 km. Therefore the distance from village
                5                                    29        5
                         40
to the post office =          = 20 km.
                         2

2. In what time will a train 100 m long, cross an electric pole, if its speed be 144 km/h?

   (a) 2.5 seconds                                                          (c) 3.5 seconds
   (b) 3 seconds                                                            (d) 4 seconds
                                                 5
Answer: - (a) The speed in m/s = 144 × 18 = 40 m/s and the train has to cross its own length to
                                                                                                        100
cross a pole. The length of the train is 100 m. therefore the required time is                                = 2.5 s
                                                                                                         40


TIME & WORK
Some Important Facts and Formulae

1. If m persons can complete a work in p days, then the same work will be completed by n
              m
   persons in n × p days.
                                                                                                    1
2. If P can complete a piece of work in A days, then P’s one day work = A of the complete work
                        1
   and if P can do A of work in 1 day, then P can complete the work in A days.
3. If A can complete a piece of work in m days and B can complete the same work in n days,
                                                                        1     1       m+n
   then the 1 day work of both of them together =                           +n =              of the work and both of
                                                                       m               mn
                                                      mn
   them together complete the work in m+n .
4. If A is twice as good a workman as B, then ratio of work done by A and B = 2 : 1 and the ratio
   of times taken by both of them to finish the work = 1 : 2.

For Example

1. Aryan takes 5 hours to do a job, and Aryaman takes 6 hours to do the same job. How long
   should it take if both Aryan and Aryaman, working together but independently, to do the
   same job?
                                                                                  9
   (a) 3 days                                                               (c) 211 days
         8
   (b) 211 days                                                             (d) 4 days

Answer: - (b)
1
2. A can finish a work in 12 days and B can do the same work in 3 the time taken by A. Then,
   working together, what part of same work they can finish in a day?
            1                                                         1
      (a)                                                       (c)
            5                                                         3
            1                                                         1
      (b)                                                       (d)
            4                                                         2

Answer:- (c)


ELEMENTARY ALGEBRA
Below are some important formulae which are very useful to solve questions.

1.  (a + b)2 = a2 + b2 + 2ab
2.  (a – b)2 = a2 + b2 – 2ab
3.  a2 – b2 = (a + b)(a – b)
4.  (a + b)3 = a3 + 3a2b + 3ab2 + b3
5.  (a − b)3 = a3 − 3a2b + 3ab2 − b3
6.  a3 + b3 = (a + b)(a2 – ab + b2)
7.  a3 − b3 = (a − b)(a2 + ab + b2)
8.  a3 + b3 + c3 – 3abc = (a + b + c)(a2 + b2 + c2 – ab – bc – ca)
                                1
                              = 2(a + b + c)[(a – b)2 + (b – c)2 + (c – a)2]
9. (a + b + c)3 = a3 +b3 + c3 + 3(a + b)(b + c)(c + a)
10. If (a + b + c) = 0 or a = b = c, then a3 + b3 + c3 = 3abc.
11. am × an = am + n
12. (am)n = am n
13. (a b)m = a m b m
      𝑎 𝑚
14.         = x m – n.
      𝑎𝑛

The questions in the SSC exam are generally based on the addition, subtraction, multiplication
and division of algebraic expressions. Some questions are also asked from quadratic equations.

For Example,

1. If for two real constants a and b, the expression ax3 + 3x2 – 8x + b is exactly divisible by (x +
   2) and (x – 2). Find the value of a and b.

Answer: - the expression is exactly divisible by (x + 2) and (x – 2). Therefore

a(−2)3 + 3(−2)2 – 8(−2) + b = 0  −8a + 3×4 + 16 + b = 0  8a – b = 28                ………(1)

Again, a(2)3 + 3(2)2 – 8(2) + b = 0  8a + 3×4 − 16 + b = 0  8a + b = 4              ………(2)
After adding (1) and (2)

8a – b + 8a + b = 28 + 4  16a = 32 ∴ a = 2.

After putting the value of a in (1)

8 × 2 – b = 28  16 – 28 = b ∴ b = − 12.

Hence, a = 2 and b = −12.
           1                             4a
2. If a + a = 2, find the value of 3a 2 + 4a − 3.

    (a)   0
    (b)   1
    (c)   2
    (d)   −1
                          1                              4a
Answer: - (b) Solve a + a = 2 and put the value in 3a 2 + 4a − 3.


3. If a2 + b2 + 2b + 1 = 0, then find the value of a34 + b38.
   (a) 1
   (b) 0
   (c) −1
   (d) 2

Answer: - (a) Here a = 0 and b = −1, then a34 + b38 = 1
GEOMETRY
Concepts

Triangles: Triangle is a polygon which has three sides. The sum of all the angles of a triangle is
180°.

Types of Triangles:

1. Acute angle triangle: It is a triangle in which all the angles are less than 90°.
2. Obtuse angle triangle: It is a triangle in which one angle is greater than 90°.
3. Right angle triangle: It is a triangle in which one angle is equal to 90°.
4. Equilateral triangle: It is a triangle in which all the sides are equal and the all angles are
   equal to 60°.
5. Isosceles triangle: It is a triangle in which two sides are equal and angle opposite the equal
   sides are also equal.
6. Scalene triangle: It is a triangle in which all the sides are unequal.

General Properties of Triangles:

1. Sum of the length of any two sides of a triangle is always greater than the third side.
2. Difference between the lengths of any two sides of a triangle is always less than the third
   side.
3. The side opposite to the greatest angle will be the greatest similarly the side opposite to the
   smallest angle will be the smallest.
                              a      b       c
4. Sine rule in a triangle: sinA = sinB = sinC = 2R, where a, b and c are the side of a triangle
   and A, B and C are the corresponding angles of the side. R is the circum radius.
5. Cosine rule in a triangle: a2 = b2 + c2 – 2bc cosA.
6. The exterior angle is equal to the sum of two interior angles which are not adjacent to it.


Important terms

1. Median: A line joining the mid-point of a side of a triangle to the
   opposite vertex is called a median. The median divides a triangle
   into two parts of equal area and the point where all the medians
   meet is called the centroid of the triangle. The centroid divides
   each median in the ratio
   2 : 1.

2. Altitudes: Altitudes are the perpendiculars drawn from any
   vertex to the opposite sides. All the altitudes meet at the
   orthocentre of the triangle. The angle made by any side at
   the orthocentre and vertical angle is together equal to 180°.
   Here,  A +  BOC = 180°.
3. Perpendicular Bisectors: It is a line which bisects
   a side and at the same time perpendicular to the
   side. The point at which the perpendicular
   bisectors of the sides meet is called the
   circumcentre of the triangle. The circumcentre
   of a triangle circumscribes the triangle and the
   circle is unique for the triangle. The angle made
   by a side of a triangle at the circumcentre is
   double to the opposite angle.
        Here, 2  A =  BOC.


Circles: A circle is a set of points in a plane which are equidistant from a point O. The point O is
called centre of the circle and the distance from the centre O is called radius which is generally
represented as r.

Properties

1. There can be only one circle passing through three or more non-collinear points in a plane.
2. If two circles intersect in two points then the line through the centres is the perpendicular
   bisector of the common chord.

For Example

1. ABCD is a square. M is the midpoint of AB and N is the mid-point of BC. DM and AN are
   joined and they meet at O. Then which of the following is correct?

   (a)   OA : OM = 1 : 2
   (b)   AN = MD
   (c)    ADM =  ANB
   (d)    AMD =  BAN
Answer: - (b)

2. AB = 8 cm and CD = 6 cm are two parallel chords on the same side of the centre of a circle.
   The distance between them is 1 cm. The radius of the circle (in cm) is               (SSC)

   (a)   5
   (b)   4
   (c)   3
   (d)   2

Answer: - (a)
3. The circumcentre of a triangle ABC is O. If  BAC = 85° and  BCA = 75°, then the value of
    OAC is
     (a)   40°
     (b)   60°
     (c)   70°
     (d)   90°

Answer: - (a)

4. AB is a chord of a circle of radius 7 cm. The chord subtends a right angle at the centre of the
                                                                22
   circle. Find the area of the minor segment in sq cm. Use 𝛑 = 7 .

     (a)   7
     (b)   24.5
     (c)   14
     (d)   38.5

Answer:- (c)

MENSURATION
Below are some important formulae which are very useful to solve questions.

1.   Area of a rectangle = Length × Breadth
2.   In a rectangle, (Diagonal)2 = (Length)2 + (Breadth)2.
3.   Perimeter of a rectangle = 2(Length + Breadth).
                                1
4.   Area of square = (Side)2 = 2 (Diagonal)2.
5.   Perimeter of a square = 4 × Side.
6.   Area of 4 walls of a room = 2(Length + Breadth) × height
7.   Area of a parallelogram = Base × Height.
                           1
8.   Area of a rhombus = 2 (Product of Diagonals).
                                       3
9. Area of an equilateral triangle = 4 (Side)2.
10. Perimeter of an equilateral triangle = 3(Side).
                                                                 a +b +c
11. Area of a triangle = s s − a s − b s − c , where s = 2 .
12. Area of a circle = 𝛑r2, where r is the radius of the circle.
13. Circumference of a circle = 2𝛑r
                         2πrθ
14. Arc AB on a circle = 360° , where AOB = 𝛉 and O is the centre.
                          πr 2 θ
15. Area of sector AOB = 360° .
16. Volume of a cube = a3, where a is a side or edge.
17. Whole suface area of a cube = 6a2.
18. Diagonal of a cube = √3 a.
19. Volume of a cuboid = lbh, where l = length, b = breadth and h = height.
20. Whole suface area of a cuboid = 2(lb + bh + hl).
21. Diagonal of a cuboid = l2 + b 2 + h2 .
22. Volume of a cylinder = 𝛑r2h.
23. Curved surface area of a cylinder = 2𝛑rh.
24. Total surface area of a cylinder = (2𝛑rh + 𝛑r2).
                           4
25. Volume of a sphere = 3 πr 3 .
26. Surface area of a sphere = 4𝛑r2.
                                 2
27. Volume of a hemisphere = 3 πr 3 .
28. Curved surface area of a hemisphere = 2𝛑r2.
29. Whole surface area of a hemisphere = 3𝛑r2.
30. Right circular Cone,
  I. Slant height l = r 2 + h2 , where r = radius of base and h = height.
                             1
 II.    Volume of a cone = 3 πr 2 h.
 III.   Curved surface area of a cone = 𝛑rl = 𝛑r r 2 + h2 .
 IV. Total surface area of a cone = (𝛑rl + 𝛑r2).
                                      1
31. Slant surface area of a pyramid = 2 (Perimeter of the base)×(Slant height).
                                              1
32. Total surface are of a pyramid = 2 (Perimeter of the base)×(Slant height) + area of base.
                                   area of the base
33. Volume of pyramid =                               ×Height.
                                          3

For Example

1. There is a pyramid on a base which is a regular hexagon of side 2a cm. If every slant edge of
                             5a
   this pyramid is of length 2 cm, then the volume of this pyramid is                     (SSC)

   (a) 3a3 cm3
   (b) 3 2a3 cm3
   (c) 3 3a3 cm3
   (d) 6a3 cm3

                                                3                                 5a 2
Answer:- (c) Here area of base = 6 × 4 (2a)2 = 6 3a2 and height =                        − 2a   2   =
                                                                                  2
 25a 2             9a 2       3a                                      6 3a2 × 3a =
         − 4a2 =          =        , then the volume of a pyramid =                   3 3a.
   4                4         2                                         3     2

2. The area of the four walls of a room is 660 m2 and its length is twice its breadth. If the
   height of the room is 11 m, then the area of its floor (in m2) is

   (a) 120                                                       (c) 200
   (b) 150                                                       (d) 330
Answer:- (c) Let b be the Breadth, l be the Length and h be the Height of the room. 2 × (l + b) ×
h =660  2 × (2b + b) × 11 = 660  2 × 3b × 11 = 660  66b = 660 ∴ b = 10, then l = 200.

Therefore, area of the floor = 20 × 10 = 200.

3. A cylindrical rod of iron whose height is five times its radius is melted and cast into spherical
   balls each of half the radius of the cylinder. the number of such spherical balls is

        (a)      5
        (b)      30
        (c)      10
        (d)      25

Answer:- (b) Let the given radius of the cylinder be r and the height be 5r then the volume of
                                                                                                  r   4   r 3
the cylinder =  r2(5r) = 5  r3. Again the volume of one sphere whose radius is 2 = 3 π                  2
                                                                                                                  =
4       r3       πr 3                                                              5πr 3
    π        =          . Therefore the number of spheres in the volume 5  r3 =   πr 3
                                                                                           = 30
3       8         6
                                                                                    6



TRIGONOMETRY
Pythagoras Theorem: In a right-angled triangle,

h2 = p2 + b2 Here, h is the hypotenuse, p is the perpendicular and b is the base of the right
angled

Trigonometric Ratios: the trigonometric ratios are calculated according to the angles. The
hypotenuse is the largest side of a right angled triangle, the perpendicular is the opposite side
of the angle and the base is the adjacent side.

For example,

Here, for angle  R, PR = hypotenuse, PQ = perpendicular and QR = base.

                            P

                            Q                   R
                 A
The Trigonometric ratios are
     Sin Ѳ            p                             Tan Ѳ            p                Sec Ѳ                   h
                      h                                              b                                        b
            Cos Ѳ                   b               Cot Ѳ            b              Cosec Ѳ                   h
                                    h                                p                                        p
The important values of Trigonometric ratios
     Ѳ           Sin           Cos           Tan                   Cot             Sec        Cosec

     30®              1                3                  1        √3               2          2
                      2               2                    3                         3
     45®              1               1                   1         1              √2          √2
                       2               2
     60®               3              1                   √3        1               2          2
                      2               2                              3                          3


Some important formulae
           1               1                1
Sin Ѳ = cosec Ѳ, cos Ѳ = sec Ѳ, tan Ѳ = cot Ѳ, sin (90® - Ѳ) = cos Ѳ, tan (90®- Ѳ) = cot Ѳ,

Sec (90® - Ѳ) = cosec Ѳ, cos(90®- Ѳ) = sin Ѳ, cot (90® - Ѳ) = tan Ѳ,

Cosec (90® - Ѳ) = sec Ѳ, Sin2Ѳ + Cos2Ѳ = 1, Sec2Ѳ – Tan2Ѳ = 1, Cosec2Ѳ – Cot2Ѳ = 1.

Angle of Elevation: If a person looking at an object which
is placed above the line of his eye. Then, the angle which
is the made by the object’s line with the eye and the
horizontal line is called the angle of elevation.




Angle of Depression: If a person looking down at an
object which is placed below the level of his eye. Then,
the angle which is made at his eye by the object’s line
with the horizontal line of his eye is called the angle of
depression.



For Example
               3                          5sin Ѳ+2cos Ѳ
1. If tan Ѳ = 4, then the value of 4 cos 2 Ѳ−3 sin 2 Ѳ is

    (a) 1
    (b) 0
        115
    (c) 37
110
     (d)   23

                           3              3             4
Answer:- (c) Here tan 𝛉 = 4, then sin 𝛉 = 5 and cos 𝛉 = 5 from the Pythagoras Theorem.

2. The value of tan 5°. tan 15°. tan 35°. tan 55°. tan 75°. tan 85° is
   (a) 1
   (b) 0
   (c) 0.5
   (d) 0.75

Answer:- (a) Here we can change tan 5° = tan (90° − 85°) = cot 85° and tan 𝛉 × cot 𝛉 = 1.

3. A ladder leaning against a wall makes an angle of 60° with the ground. If the length of the
   ladder is 30m, find the height of the wall up to the ladder.
   (a) 15
   (b) 15√3
   (c) 30
   (d) 30√3

Answer:- (b) The diagram can be,




DATA INTERPRETATION
The questions in this unit can be asked from four different types of data.

1.   Histogram
2.   Frequency polygon
3.   Bar-diagram
4.   Pie-chart

For Example

Question (1 to 5): The line diagram shows the cost of production and profit of five companies
for the year 2011-12. (The figures are in '000').
500

       400

       300
                                                                               COST OF PRODUCTION
       200
                                                                               PROFIT
       100

         0
                  A           B           C            D                E


1. The ratio of profits of company B to D is:

     (a) 2:3                                               (c) 4:3
     (b) 3:4                                               (d) 3:2

2. The profit of company C is what percentage of the cost of production of company E?

     (a) 20%                                               (c) 30%
     (b) 25%                                               (d) 35%

3. The cost of production of company B is how many times of company C profit?

     (a) 2.5                                               (c) 3.5
     (b) 3                                                 (d) 4

4. Which company has the maximum percentage of profit?

     (a) A                                                 (c) C
     (b) B                                                 (d) D

5. What is the average profit of all the companies?

     (a) 50,000                                            (c) 70,000
     (b) 60,000                                            (d) 80,000

Answers:-

1.   The profit of B is 50,000 and D is 75,000 therefore the ratio is 2:3.
2.   The profit of C is 1,00,000 which is 25% of E's cost of production which is 4,00,000.
3.   The cost of B is 3,50,000 which 3.5 times the profit of C' profit which is 50,000.
4.   The company C has a 40% profit.
5.   The total profit of all the companies are 75,000+50,000+1,00,000+75,000+1,00,000 =
     4,00,000, therefore the average will be (4,00,000)/5= 80,000.
ENGLISH LANGUAGE

SYNONYMS
Synonyms: The word comes from ancient Greek words ‘syn’ and ‘onoma’ where ‘syn’ means
‘with’ and ‘onoma’ means ‘name’. Synonyms are the word which has similar meanings.

Two words are said to be synonymous when they have similar meanings. The words caste and
class is synonymous because both the words have similar meaning.

For Example,

Q. Find the word which is synonymous to Deny.                                 (SSC 2011)

   (a)   Regain
   (b)   Refuse
   (c)   Repair
   (d)   Reduce

Answer: The synonyms for Deny are Contradict, Refuse, Reject etc. here we have Refuse as an
option, which means the right answer is (b).

Q. Find the word which is synonymous to Deposit.

   (a)   Degrade
   (b)   Dethrone
   (c)   Place
   (d)   Removal

Answer:- (c)


ANTONYMS
Antonyms: The word “antonym “comes from ancient Greek words ‘anti’ and ‘onoma’ where
‘anti’ means opposite and ‘onoma’ means name. The literal meaning of antonyms is the
opposite name which means the word which has opposite meaning. For example; Day – Night,
Long – Short, Up – Down, Small – Large, etc.

For Example

Q. Find the opposite word to Concur.                                             (SSC 2011)

   (a) Disagree                                      (c) Disarrange
   (b) Disappear                                     (d) Discourage
Answer: The synonyms for Concur are agree, cooperate, combine etc. Therefore the antonym
for ‘agree’ is ‘disagree’. Hence right answer is (a).

Q. Find the opposite word to Condensation.

   (a) Abridgment                                      (c) Compression
   (b) Broadening                                      (d) Concentration
Answer: - (b)

IDIOMS AND PHRASES
Idioms and phrases refer to commonly used groups of words in English. They are used in
specific situations and often used in an idiomatic, rather than a figurative sense. Idioms are
often full sentences. Phrases, however, are usually made up of a few words and are used as a
grammatical unit in a sentence.

For Example,

1. Ram used very ugly words against his kind uncle; he threw down the gauntlet before him.
   (a) he abused and insulted him
   (b) he threw the challenge
   (c) he behaved as if he was a very great and important person
   (d) he put several conditions for negotiation

Answer: - (b)

2. He always cuts both ends
   (a) Work for both sides
   (b) Inflicts injuries on others
   (c) Argues in support of both sides of the issue
   (d) Behaves dishonestly

Answer: - (c)

ONE WORD SUBSTITUTION
One word substitution is the words that replace a group of words or sentences without creating
or changing the exact meaning of sentences. These words generally bring compression in any
kind of writing.

There are lots of words in English language that can be used effectively in place of complex
sentences or words to make writing to the point without losing the meaning of the context.

For Example,
1. One who eats too much
   (a) Foodie
   (b) Glutton
   (c) Eater
   (d) Food loving

Answer: - (b) glutton

2. A book published after the death of its author
   (a) Posthumous
   (b) Anonymous
   (c) Synonymous
   (d) Mysterious

Answer: - (a) Posthumous
SPELLING TEST
Spelling test is basically devised to test the vocabulary power and the candidate ability to write
the words with correct spellings.

Question asked is such section generally required to choose the correct spelt word or the mis-
spelt out of the alternatives given.

For Example, find the mis – spelt word.

1.
     (a)   Comission
     (b)   Commisson
     (c)   Comession
     (d)   Commission

Answer: (d)

2.
     (a)   Liutenenat
     (b)   Lieutanent
     (c)   Lieutenant
     (d)   Leiutanent

Answer: (c)

INCORRECT SENTENCES
Directions: In questions no. 1 to 2, a part of the sentence is underlined. Below are given
alternatives to the underlined part at (a), (b) and (c) which may improve the sentence. Choose
the correct alternative. In case no correction is needed, your answer is (d).

1. All the allegations levelled against him were found to be baseless.
     (a)   levelled for
     (b)   level with
     (c)   level against
     (d)   no correction

Answer:- (c)

2. Last Sunday I went to the market and bought spectacles.
   (a) two spectacles
   (b) a pair of spectacles
   (c) a spectacle
   (d) no correction

Answer:- (b)
SENTENCE RECONSTRUCTION
Sentence reconstruction is the grammatical arrangement of words in sentences, phrase
structure, and syntax. The sentences are presented in a jumbled manner and the students are
supposed to arrange it chronologically.

Here we are giving some examples. Students are advised to go through it carefully.

1. There is a fashion now-a-days

   P.    as an evil
   Q.    who is born with a silver spoon
   R.    to bewail poverty
   S.    and to pity the youngman

   in his mouth

   (a)   PSRQ
   (b)   RPSQ
   (c)   RSQP
   (d)   SPRQ

Answer:- (b)

2. Though the government claims
   P. it has failed to arrest
   Q. the rate of inflation is down
   R. or the decrease
   S. the rise in prices
   6. in the per capita income
   (a) PQRS
   (b) PQSR
   (c) PSQR
   (d) QPSR

Answer:- (d)

SPOTTING THE ERROR
Directions: Read each sentence to find out whether there is any grammatical mistake/error in
it. The error if any will be in one part of the sentence. Mark the number of the part with error
as your answer. If there is no error, mark the last option.

1. (a) My brother lived at the top / (b) of an old house / (c) which attic had been / (d)
   converted into a flat. / (e) No error.

Answer: - (c) Replace ‘which’ by ‘whose’.
2. (a) All companies must / (b) send its annual report to/ (c) its shareholders twenty one days /
   (d) before the annual general meeting./ (e) No error.

Answer: - (a) Use ‘every’ in place of ‘all’.

3. (a) They agreed / (b) to repair the damage / (c)freely of charge / (d)No error

Answer: - (c)

4. (a) Radha was trying for admission / (b) in the Science College / (c) even though her parents
   wanted/ (d) her to take up medicine. / (e) No error.

Answer: - (c) Use ‘had wanted’ in place of ‘wanted’.

5. (a) My younger sister and / (b) I am interested / (c) in mathematics./ (d) No error

Answer: - (b) Use ‘are’ in place of ‘am’.

6. (a) You should purchase/ (b) this insurance policy/ (c) as the company/ (d) offers many
   benefits./ (e) No error.

Answer: - (e) No error.

7. (a) Having acquired some experience/(b) she is no longer/ (c) one of those who believes/ (d)
   every explanation she is given./(e) No error

Answer: - (d) Replace ‘is’ with ‘has’

CLOZE TEST
Cloze test is the test of the ability to comprehend text in which the reader has to supply the
missing words that have been removed from the text at regular intervals.

It is basically a test for diagnosing reading ability; words are generally deleted from a prose
passage and the reader is required to fill in the blanks.

Directions (Q. 1-1O): In the following passage there arc blanks, each of which has been
numbered. These numbers are printed below the passage and against each, five words are
suggested, one of which fits the blank appropriately. Find out the appropriate word in each
case.

Raju was orphaned at a very (1) age. He lost (2) of his parents because his family was (3) poor to
afford any treatment. He was deeply affected by this. He decided to work hard and (4) on his
own feet. Along with his studies he (5) part-time in a restaurant and earned enough money in
order to (6) his studies. Being a brilliant student, he earned scholarships and later managed to
get admission in a good medical college. He is now a (7) doctor and helps poor patient for (8).
This shows that one can survive every (9) condition. Determine and hard work (10) to success in
life.
1. (a) youth (b) early         (c) childhood (d) childish      (e) recent
2. (a) any     (b) few         (c) either       (d) couple     (e) both
3. (a) little (b) so           (c) too          (d) some       (e) ample
4. (a) balance(b) establish (c) stand           (d) erect      (e) talk
5. (a) worked (b) employed (c) busy             (d) established(e) functioned
6. (a) done (b) practice (c) follow             (d) pursue     (e) proceed
7. (a) recognise        (b) know        (c) respected          (d) worth      (e) merit
8. (a) favour (b) less         (c) penny        (d) subsidy    (e) free
9. (a) failed (b) adverse (c) worse             (c) evil       (e) tragedy
10. (a) result (b) follow      (c) excel        (d) lead       (e) urge

Answers:

1. (b)               3. (c)                5. (a)                7. (c)                   9. (b)
2. (e)               4. (c)                6. (d)                8. (e)                   10. (d)
Josh magazine-ssc-higher-secondary-exam-2012-booklet-1

Mais conteúdo relacionado

Semelhante a Josh magazine-ssc-higher-secondary-exam-2012-booklet-1

SYLLABUS JUNIOR EXECUTIVE (COMMON CADRE) Advt. No. 03-2023.pdf
SYLLABUS JUNIOR EXECUTIVE (COMMON CADRE) Advt. No. 03-2023.pdfSYLLABUS JUNIOR EXECUTIVE (COMMON CADRE) Advt. No. 03-2023.pdf
SYLLABUS JUNIOR EXECUTIVE (COMMON CADRE) Advt. No. 03-2023.pdf08115SakshiTewari
 
basic statistics
basic statisticsbasic statistics
basic statisticsrosedelle
 
Karen Tsang (2016) - Perceived Glass Ceilings
Karen Tsang (2016) - Perceived Glass CeilingsKaren Tsang (2016) - Perceived Glass Ceilings
Karen Tsang (2016) - Perceived Glass CeilingsKaren Tsang
 
(Textbooks in mathematics) hodge, jonathan k. schlicker, steven sundstrom,...
(Textbooks in mathematics) hodge, jonathan k.  schlicker,  steven  sundstrom,...(Textbooks in mathematics) hodge, jonathan k.  schlicker,  steven  sundstrom,...
(Textbooks in mathematics) hodge, jonathan k. schlicker, steven sundstrom,...META GUNAWAN
 
LafargeHolcim good application tips
LafargeHolcim good application tipsLafargeHolcim good application tips
LafargeHolcim good application tipsClaudia Balan
 
Guidelines for effective reading discussion
Guidelines for effective reading discussionGuidelines for effective reading discussion
Guidelines for effective reading discussionEva F. Andrianarivo
 
An Introduction to Statistical Learning R Fourth Printing.pdf
An Introduction to Statistical Learning R Fourth Printing.pdfAn Introduction to Statistical Learning R Fourth Printing.pdf
An Introduction to Statistical Learning R Fourth Printing.pdfDanielMondragon15
 
life-after-high-school
life-after-high-schoollife-after-high-school
life-after-high-schoolSamantha Salas
 
5065946.pdf
5065946.pdf5065946.pdf
5065946.pdfshinco1
 
Taylor john garnier_ rowan-understanding mathematical proof-taylor &amp; fr...
Taylor  john  garnier_ rowan-understanding mathematical proof-taylor &amp; fr...Taylor  john  garnier_ rowan-understanding mathematical proof-taylor &amp; fr...
Taylor john garnier_ rowan-understanding mathematical proof-taylor &amp; fr...Vidi Al Imami
 

Semelhante a Josh magazine-ssc-higher-secondary-exam-2012-booklet-1 (20)

Basic calculus
Basic calculusBasic calculus
Basic calculus
 
Grammar1
Grammar1Grammar1
Grammar1
 
SYLLABUS JUNIOR EXECUTIVE (COMMON CADRE) Advt. No. 03-2023.pdf
SYLLABUS JUNIOR EXECUTIVE (COMMON CADRE) Advt. No. 03-2023.pdfSYLLABUS JUNIOR EXECUTIVE (COMMON CADRE) Advt. No. 03-2023.pdf
SYLLABUS JUNIOR EXECUTIVE (COMMON CADRE) Advt. No. 03-2023.pdf
 
Pg cb thandbook2011-12
Pg cb thandbook2011-12Pg cb thandbook2011-12
Pg cb thandbook2011-12
 
edu
eduedu
edu
 
Basic calculus
Basic calculusBasic calculus
Basic calculus
 
basic statistics
basic statisticsbasic statistics
basic statistics
 
Karen Tsang (2016) - Perceived Glass Ceilings
Karen Tsang (2016) - Perceived Glass CeilingsKaren Tsang (2016) - Perceived Glass Ceilings
Karen Tsang (2016) - Perceived Glass Ceilings
 
(Textbooks in mathematics) hodge, jonathan k. schlicker, steven sundstrom,...
(Textbooks in mathematics) hodge, jonathan k.  schlicker,  steven  sundstrom,...(Textbooks in mathematics) hodge, jonathan k.  schlicker,  steven  sundstrom,...
(Textbooks in mathematics) hodge, jonathan k. schlicker, steven sundstrom,...
 
ACT_RR2015-4
ACT_RR2015-4ACT_RR2015-4
ACT_RR2015-4
 
LafargeHolcim good application tips
LafargeHolcim good application tipsLafargeHolcim good application tips
LafargeHolcim good application tips
 
Seofs2011 free
Seofs2011 freeSeofs2011 free
Seofs2011 free
 
Guidelines for effective reading discussion
Guidelines for effective reading discussionGuidelines for effective reading discussion
Guidelines for effective reading discussion
 
An Introduction to Statistical Learning R Fourth Printing.pdf
An Introduction to Statistical Learning R Fourth Printing.pdfAn Introduction to Statistical Learning R Fourth Printing.pdf
An Introduction to Statistical Learning R Fourth Printing.pdf
 
life-after-high-school
life-after-high-schoollife-after-high-school
life-after-high-school
 
Cds exam syllabus 2012
Cds exam syllabus 2012Cds exam syllabus 2012
Cds exam syllabus 2012
 
5065946.pdf
5065946.pdf5065946.pdf
5065946.pdf
 
rosario_phd_thesis
rosario_phd_thesisrosario_phd_thesis
rosario_phd_thesis
 
Taylor john garnier_ rowan-understanding mathematical proof-taylor &amp; fr...
Taylor  john  garnier_ rowan-understanding mathematical proof-taylor &amp; fr...Taylor  john  garnier_ rowan-understanding mathematical proof-taylor &amp; fr...
Taylor john garnier_ rowan-understanding mathematical proof-taylor &amp; fr...
 
Understanding Mathematical Proof
Understanding Mathematical ProofUnderstanding Mathematical Proof
Understanding Mathematical Proof
 

Mais de GIO

Gio.in
Gio.inGio.in
Gio.inGIO
 
Great indian outdoors gio.in
Great indian outdoors gio.inGreat indian outdoors gio.in
Great indian outdoors gio.inGIO
 
Presentation1 himalayanecolodges
Presentation1 himalayanecolodgesPresentation1 himalayanecolodges
Presentation1 himalayanecolodgesGIO
 
Binsar to jageshwar ideal short treks of indian himalayas
Binsar to jageshwar ideal short treks of indian himalayasBinsar to jageshwar ideal short treks of indian himalayas
Binsar to jageshwar ideal short treks of indian himalayasGIO
 
Know the relation between fun at work and company output
Know the relation between fun at work and company outputKnow the relation between fun at work and company output
Know the relation between fun at work and company outputGIO
 
Kausani bestowed with natural beauty
Kausani bestowed with natural beautyKausani bestowed with natural beauty
Kausani bestowed with natural beautyGIO
 
With team building events bring positive attitude among employees
With team building events  bring positive attitude among employeesWith team building events  bring positive attitude among employees
With team building events bring positive attitude among employeesGIO
 
Adding fun at work to motivate employees
Adding fun at work to motivate employeesAdding fun at work to motivate employees
Adding fun at work to motivate employeesGIO
 
Experience awesome journey to gangorti
Experience awesome journey to gangortiExperience awesome journey to gangorti
Experience awesome journey to gangortiGIO
 
Increases your company output through corporate training
Increases your company output through corporate trainingIncreases your company output through corporate training
Increases your company output through corporate trainingGIO
 
Auli is a perfect destination for every skii lovers
Auli is a perfect destination for every skii loversAuli is a perfect destination for every skii lovers
Auli is a perfect destination for every skii loversGIO
 
Auli an ultimate magical tourist destination
Auli an ultimate magical tourist destinationAuli an ultimate magical tourist destination
Auli an ultimate magical tourist destinationGIO
 
4 important outdoor adventure activities of garhwal himalayas
4 important outdoor adventure activities of garhwal himalayas4 important outdoor adventure activities of garhwal himalayas
4 important outdoor adventure activities of garhwal himalayasGIO
 
Pragmatic role of company offsite events
Pragmatic role of company offsite eventsPragmatic role of company offsite events
Pragmatic role of company offsite eventsGIO
 
Know how leadership program can help your business
Know how leadership program can help your businessKnow how leadership program can help your business
Know how leadership program can help your businessGIO
 
Know why team activities is highly valued in most company
Know why team activities is highly valued in most companyKnow why team activities is highly valued in most company
Know why team activities is highly valued in most companyGIO
 
Unearth chamba the fascinating hill station by anima sharma
Unearth chamba the fascinating hill station by anima sharmaUnearth chamba the fascinating hill station by anima sharma
Unearth chamba the fascinating hill station by anima sharmaGIO
 
Valley of flower
Valley of flowerValley of flower
Valley of flowerGIO
 

Mais de GIO (18)

Gio.in
Gio.inGio.in
Gio.in
 
Great indian outdoors gio.in
Great indian outdoors gio.inGreat indian outdoors gio.in
Great indian outdoors gio.in
 
Presentation1 himalayanecolodges
Presentation1 himalayanecolodgesPresentation1 himalayanecolodges
Presentation1 himalayanecolodges
 
Binsar to jageshwar ideal short treks of indian himalayas
Binsar to jageshwar ideal short treks of indian himalayasBinsar to jageshwar ideal short treks of indian himalayas
Binsar to jageshwar ideal short treks of indian himalayas
 
Know the relation between fun at work and company output
Know the relation between fun at work and company outputKnow the relation between fun at work and company output
Know the relation between fun at work and company output
 
Kausani bestowed with natural beauty
Kausani bestowed with natural beautyKausani bestowed with natural beauty
Kausani bestowed with natural beauty
 
With team building events bring positive attitude among employees
With team building events  bring positive attitude among employeesWith team building events  bring positive attitude among employees
With team building events bring positive attitude among employees
 
Adding fun at work to motivate employees
Adding fun at work to motivate employeesAdding fun at work to motivate employees
Adding fun at work to motivate employees
 
Experience awesome journey to gangorti
Experience awesome journey to gangortiExperience awesome journey to gangorti
Experience awesome journey to gangorti
 
Increases your company output through corporate training
Increases your company output through corporate trainingIncreases your company output through corporate training
Increases your company output through corporate training
 
Auli is a perfect destination for every skii lovers
Auli is a perfect destination for every skii loversAuli is a perfect destination for every skii lovers
Auli is a perfect destination for every skii lovers
 
Auli an ultimate magical tourist destination
Auli an ultimate magical tourist destinationAuli an ultimate magical tourist destination
Auli an ultimate magical tourist destination
 
4 important outdoor adventure activities of garhwal himalayas
4 important outdoor adventure activities of garhwal himalayas4 important outdoor adventure activities of garhwal himalayas
4 important outdoor adventure activities of garhwal himalayas
 
Pragmatic role of company offsite events
Pragmatic role of company offsite eventsPragmatic role of company offsite events
Pragmatic role of company offsite events
 
Know how leadership program can help your business
Know how leadership program can help your businessKnow how leadership program can help your business
Know how leadership program can help your business
 
Know why team activities is highly valued in most company
Know why team activities is highly valued in most companyKnow why team activities is highly valued in most company
Know why team activities is highly valued in most company
 
Unearth chamba the fascinating hill station by anima sharma
Unearth chamba the fascinating hill station by anima sharmaUnearth chamba the fascinating hill station by anima sharma
Unearth chamba the fascinating hill station by anima sharma
 
Valley of flower
Valley of flowerValley of flower
Valley of flower
 

Josh magazine-ssc-higher-secondary-exam-2012-booklet-1

  • 1. SSC Higher Secondary Exam www.jagranjosh.com (Preparation Booklet)
  • 2. TABLE OF CONTENTS Introduction ................................................................................................................................ 4 General Intelligence .................................................................................................................... 6 Analogy ................................................................................................................................... 6 Classification ........................................................................................................................... 6 Series ....................................................................................................................................... 6 Coding-Decoding ..................................................................................................................... 7 Sequence ................................................................................................................................. 7 Direction Test .......................................................................................................................... 7 Puzzles ..................................................................................................................................... 8 Mathematical Puzzles ............................................................................................................. 9 Syllogism ............................................................................................................................... 10 Non-Verbal ............................................................................................................................ 11 Quantitative Aptitude ............................................................................................................... 14 HCF & LCM ............................................................................................................................ 14 Ratio & Proportion ................................................................................................................ 15 Percentage ............................................................................................................................ 16 Average ................................................................................................................................. 17 Surds and Indices .................................................................................................................. 18 Profit & Loss .......................................................................................................................... 18 Interest Calculation ............................................................................................................... 19 Time, Speed & Distance ........................................................................................................ 22 Time & Work ......................................................................................................................... 23 Elementary Algebra .............................................................................................................. 24 Geometry .............................................................................................................................. 26
  • 3. Mensuration.......................................................................................................................... 28 Trigonometry ........................................................................................................................ 30 Data Interpretation ............................................................................................................... 32 English Language ....................................................................................................................... 35 Synonyms .............................................................................................................................. 35 Antonyms .............................................................................................................................. 35 Idioms and phrases ............................................................................................................... 36 One Word Substitution ......................................................................................................... 36 Spelling Test .......................................................................................................................... 38 Incorrect Sentences .............................................................................................................. 38 Sentence Reconstruction ...................................................................................................... 39 Spotting the Error ................................................................................................................. 39 Cloze Test .............................................................................................................................. 40
  • 4. INTRODUCTION SSC Combined Higher Secondary Level (10+2) Examination 2012 will be conducted by Staff Selection Commission (SSC) for the recruitment to the posts of Data Entry Operators and Lower Division Clerk. SSC Combined Higher Secondary Level (10+2) Examination 2012 is going to be conducted on 21 October 2012 & 28 October 2012. To be eligible for SSC Combined Higher Secondary Level (10+2) Examination 2012, the candidate must have passed 12th Standard or equivalent or higher examination from a recognized Board or University. In addition, the candidate’s minimum age should be 18 years and maximum age should be 27 years. The selection will be based on basis of 2 hours written examination carrying 200 marks, which is followed by Data Entry Skill Test/ Typing Test of shortlisted candidates. The written examination consists of objective type paper including 4 parts that are as follows:  General Intelligence (50 Questions)  English Language (50 Questions)  Quantitative Aptitude (50 Questions)  General Awareness (50 Questions) The question will be set in both Hindi and English Language for Part I, II, and IV. There will be negative marking of 0.25 marks for each wrong answer. Syllabus for Objective Paper General Intelligence Semantic Analogy, Symbolic operation, Symbolic/Number Analogy, Trends, Figural Analogy, Space Orientation, Semantic Classification, Venn Diagrams, Symbolic/Number Classification, Drawing inferences, Figural Classification, Punched hole/pattern-folding & unfolding, Semantic Series, Figural Pattern – folding and completion, Number Series, Embedded figures, Figural Series, Critical Thinking, Problem Solving, Emotional Intelligence, Word Building, Social Intelligence, Coding and de-coding, Numerical operations English Language Spot the Error, Fill in the Blanks, Synonyms/Homonyms, Antonyms, Spellings/Detecting Mis- spelt words, Idioms & Phrases, One word substitution, Improvement of Sentences, Active/Passive Voice of Verbs, Conversion into Direct/Indirect narration, Shuffling of Sentence parts, Shuffling of Sentences in a passage, Cloze Passage, Comprehension Passage Quantitative Aptitude 1. Arithmetic Number Systems: Computation of Whole Number, Decimal and Fractions, Relationship between numbers
  • 5. Fundamental Arithmetical Operations: Percentage, Ratio and Proportion, Square roots, Averages, Interest (Simple and Compound), Profit and Loss, Discount, Partnership Business, Mixture and Alligation, Time and distance, Time and work 2. Algebra Basic algebraic identities of School Algebra (and their simple applications) e.g. Formulas for (a + b) 2, (a - b) 2, (a + b)3, (a - b)3 , a3 - b3, a3 + b3, a2 - b2; if a + b + c=0, then a3 + b3 + c3 = 3abc etc. and Elementary surds (simple problems), and Graphs of Linear Equations 3. Geometry Familiarity with elementary geometric figures and facts: Triangle and its various kinds of centres viz. Centroid, In-centre, Orthocentre, Circumcentre Congruence and similarity of triangles Circle and its chords, tangents, angles subtended by chords of a circle, common tangents to two or more circles 4. Mensuration Triangle, Quadrilaterals, Regular Polygons (sum of the internal angles of a polygon), Circle, Right Prism, Right Circular Cone, Right Circular Cylinder, Sphere, Hemispheres, Rectangular Parallelepiped, Regular Right Pyramid with triangular or square Base 5. Trigonometry Trigonometry (for acute angles 0 with 0≤0≤90): Trigonometric ratios, Degree and Radian Measures, Standard Identities like sin20 + Cos20=1 etc Complementary Angles, Heights and Distances (simple problems only) 6. Statistical Charts Use of Tables and Graphs: Histogram, Frequency polygon, Bar-diagram, and Pie-chart General Awareness History, Culture Geography, Economic Scene, General policy and Scientific Research
  • 6. GENERAL INTELLIGENCE ANALOGY Analogy: In this type of questions the students are required to identify the previous relation and find out the best suitable relation for the other term. These questions are asked in the form of proportion where two related terms are given and the next matching missing term can be asked. The questions of the analogy can be in the form of words, numbers, letters and coded letters etc. with any relation. For Example, Cricket : Pitch :: Tennis :: ? (a) Arena (b) Course (c) Court (d) Rink Answer: - (c) Court. Here Cricket is played at Pitch and Tennis is played at Court. CLASSIFICATION Classification: In this type of questions the students are required to identify the item which does not belong to a group. It means the other items in the group are similar with respect to certain logic but one is different. The students can get questions on word group, number group, letter group, coded letter group and numeral pair group etc. For Examples 1. (a) 36 (b) 125 (c) 144 (d) 121 Answers: - (b) All except 125 are squares. SERIES Series: It can be understood as a sequence of numerical, alphabetical and alphanumerical terms which follows a fixed pattern. The students are required to identify the missing term or wrong term in the series.
  • 7. For Example 1. 6, 11, 18, 27, 38, ?. (a) 49 (c) 51 (b) 50 (d) 52 Answer: - (c) The series is +5, +7, +9…… CODING-DECODING Coding: Coding is a process by which certain information is written into another form of information on the basis of certain principles. Decoding: Decoding is used to infer the right information from the coded information. For Example, In a certain code language, BOOK is written as 2151511. In the same language how PEN be written? Answer:- In the above example the letters of BOOK is coded on the basis of their position in the English alphabet. The letters B=2, O = 15, K = 11. In the same way we can encode PEN as 16514. SEQUENCE The question on this topic can be of following types; 1. Ascertaining meaningful word sequence. 2. Ascertaining similar numerical sequence. 3. Finding a position in a sequence. For Example, Find the meaningful order of the following words in ascending order. 1. Line 2. Angle 3. Pentagon 4. Rectangle 5. Triangle Answer: - The right order for these words will be Line – Angle – Triangle – Rectangle – Pentagon. Therefore the answer is 1, 2, 5, 4, and 3. DIRECTION TEST In this unit, the problems are generally formulated with successive follow-up of the directions and the candidates are required to find the final direction, the final position with respect to the initial position or the distance between the final position and initial position. On paper, we can draw the directions as;
  • 8. (Here, N = North, NE = North-East, E = East, SE = South-East, S = South, SW = South-West, W = West, NW = North-West) Example: If a person is going to the east of his home and turning to his left after that turning to his right. His final position We can draw his path as; His Home For Example, A starts walking towards East, turns right, again turn right, turns left, again turns left, turns left, again turns left. In which direction is A walking now? (a) East (b) West (c) North (d) South Answer:- (b) PUZZLES The Puzzle questions can be in the form of following types; 1. Blood Relation Problems 2. Height and Position Related Problems 3. Cube and Blocks Related Problems 4. Embedded Words & Unscrambled Words Related Problem. Examples; 1. P and Q are brothers. R and S are sisters. P’s son is S’s brother. How is Q related to R? (SSC 2011) Answer: In the question P’s son is S’s brother means P is the father of S and similarly P is the father of R because S and R are sisters. Therefore Q is the uncle of R. because Q is the father’s brother of R. 2. There are five friends - Satish, Kishore, Mohan, Anil and Rajesh. Mohan is the tallest. Satish is shorter than Kishore but taller than Rajesh. Anil is little shorter than Kishore but little taller than Satish. Who is taller than Rajesh but shorter than Anil? (SSC 2011)
  • 9. Answer: It is given that Kishore>Satish>Rajesh and Kishore>Anil>Satish. It means the sequence of height is Mohan>Kishore>Anil>Satish> Rajesh. Therefore, the person who is taller than Rajesh but shorter than Anil is Satish. MATHEMATICAL PUZZLES Introduction: In this unit we will study various types of questions based on the basic mathematical and logical concepts. These types of questions are regularly asked in the SSC exams. After analyzing previous papers, it is clear that in the exam you can get 5 to 8 questions from this unit. The question types 1. Arrangement of correct mathematical operations. 2. Filling the correct mathematical operations. 3. Mathematical-Logical problems When you are solving these questions you should follow basic mathematical operations in a correct sequence. The correct sequence of solving mathematical problems is known by “BODMAS Rule” or “VBODMAS Rule”. V – Vinculum B – Brackets O – Of D – Division M – Multiplication A – Addition S – Subtraction. For Examples 1. Which interchange of signs will make the following equation correct? 25 − 5 + 32 ÷ 4 × 6 = 13. (a) − and ÷ (b) × and ÷ (c) – and + (d) × and – Answer:- (a) 2. Select the correct combination of mathematical signs to replace the * signs and to balance the given equation. 5 * 5 * 3 * 4 * 64 * 4. (a) ÷×−= + (b) ×−= +÷ (c) +×−=÷ (d) ×−=÷+ Answer:- (c)
  • 10. 3. Some equations are solved on the basis of certain system on the same basis find out the correct answer for the unsolved equation. 1 × 2 × 5 = 125, 2 × 1 × 6 = 216, 3×4×3=? (a) 125 (b) 216 (c) 512 (d) 343 Answer:- (d) SYLLOGISM Syllogism: The literal meaning of syllogism is ‘Conclusion’ or ‘inference’. The questions in the syllogism are in the form of statements (premises) followed by Conclusion (proposition) and the students are asked to find the correct conclusion on the basis of the statements. The general form of statements and conclusions in the syllogism is;  All As are Bs.  Some As are Bs.  No A is a B. The graphical representation of the statements 1. All As are Bs. 2. Some As are Bs. 3. No A is a B.
  • 11. For Example Direction (Q. 1 – 2): In each questions below there are two/three statements followed by two conclusions I and II. Assuming both the statements true, you have to decide which of the two conclusions logically follows the statements and then give your answer (a) If only conclusion I follows. (b) If only conclusion II follows. (c) If either conclusion I or conclusion II follows. (d) If neither conclusion I nor conclusion II follows. (e) If both conclusion I and conclusion II follow. 1. Statements: Some pens are pencils. Some pencils are books. Conclusions: I. Some pens are books. II. All books are pens. Answer:- (d) 2. Statements: All bottles are bags. All bags are buses. Conclusions: I. Some bags are bottles. II. All bags are bottles. Answer:- (a) NON-VERBAL The questions from this unit can be of following types; 1. Pictorial pattern based questions. 2. Embedded figure questions. 3. Mirror Image questions. 4. Paper Cutting problems. 5. Relationship based problems.
  • 12. For Example 1. Which answer figure will complete the pattern in the question figure? (SSC 2011) Question figure: Answer figures: Answer: (D) will complete the pattern 2. Which of the answer figures is exactly the mirror image of the question figure, when the mirror is held on the line MN? (SSC 2002) Question figure: (a) (b) (c) (d) Answer: (d) 3. Select the answer figure in which the question figure is hidden/embedded. Question figure: (a) (b) (c) (d) Answer: (d)
  • 13.
  • 14. QUANTITATIVE APTITUDE HCF & LCM Some Important concepts Factors and Multiples: If a number m divides the number n with remainder = 0, then m is called the factor of n and n is called multiple of m. Highest Common Factor (HCF): The HCF is the highest common factor for two or more numbers. For Example, if we have two numbers 30 and 20, then the factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30. And the factors of 20 are 1, 2, 4, 5, 10 and 20. Here 10 is the highest common factor. Least Common Multiple (LCM): The LCM is the lowest number which is exactly divisible by the given two or more than two numbers. For example, if we have two numbers 20 and 30, then the multiples of 20 are 20, 40, 60, 80………. And the multiples of 30 are 30, 60, 90, 120……….. Here 60 is the lowest number which is exactly divisible by both 20 and 30. Therefore 60 is the required LCM. Product of two numbers = Product of their LCM and HCF For example, the LCM for 20 and 30 is 60 and HCF for 20 and 30 is 10. Here 20 × 30 = 60 × 10 = 600. Co-primes: Two numbers are co-primes if their HCF = 1. HCF and LCM of Fraction: 𝐇𝐂𝐅 𝐨𝐟 𝐧𝐮𝐦𝐞𝐫𝐚𝐭𝐨𝐫𝐬 𝐋𝐂𝐌 𝐨𝐟 𝐧𝐮𝐦𝐞𝐫𝐚𝐭𝐨𝐫𝐬 HCF = 𝐋𝐂𝐌 𝐨𝐟 𝐃𝐞𝐧𝐨𝐦𝐢𝐧𝐚𝐭𝐨𝐫𝐬 and LCM = 𝐇𝐂𝐅 𝐨𝐟 𝐃𝐞𝐧𝐨𝐦𝐢𝐧𝐚𝐭𝐨𝐫𝐬 For Example The L.C.M. of two numbers is 189 and H.C.F. of two numbers is 9.If one of the number is 63 then other number is: (a) 27 (b) 28 (c) 29 (d) 30 Answer:- (a)
  • 15. RATIO & PROPORTION Ratio: A ratio is a comparison of two numbers (quantity in the same unit). It is written as, a: b = a = a ÷ b, where a and b are two number (quantity). b In a ratio a : b, a and b are the terms of the ratio; ‘a’ is called the antecedent and ‘b’ is called the consequent. The word ‘antecedent’ literally means ‘that which goes before’ and the word consequent literally means ‘that which goes after’. Compound Ratio: Compounded ratio is a product of two or more ratios. Example: Find the ratio compounded of the three ratios: 2 : 3, 3 : 4 and 7 : 11 2 × 3 ×7 7 Solution: the required ratio is =3 ×4 ×11 = 22 . 1 1 Inverse Ratio: If a : b is a given ratio, then a ∶ b or b : a is called its inverse ratio or reciprocal ratio. 1. If the antecedent (a) = the consequent (b), the ratio is called the ratio of equality, such as 2 : 2. 2. If the antecedent (a) > the consequent (b), the ratio is called the ratio of greater inequality, such as 3 : 2. 3. If the antecedent (a) < the consequent (b), the ratio is called the ratio of less inequality, such as 2 : 3. a c Proportion: A proportion expresses the equality of two ratios. e.g. b = d Or a : b = c : d or a : b :: c : d. In a proportion in the form of a : b :: c : d the first and the last terms are called the extremes and the second and the third terms or the middle terms are called as the mean terms. When four quantities are in proportion, we can write it in the mathematical form as a : b :: c : d  a c = d  ad = bc b
  • 16. For Example, 2 1 If Rs. 510 be divided among A, B, C in such a way that A gets 3 of what B gets and B gets 4 of what C gets, then their shares are respectively : (a) Rs. 120, Rs. 240, Rs. 150 (b) Rs. 60, Rs. 90, Rs. 360 (c) Rs. 150, Rs. 300, Rs. 60 (d) None of these Answer:- (b) PERCENTAGE Percentage: The term “per cent” means “for every hundred”. A fraction whose denominators is 100 is called a percentage and the numerator of the fraction is called the rate per cent. It is denoted by the symbol %. x 10 1 Here x % =100 . For example 10% =100 = 10 . Similarly, fraction can be changed in the form of percentage when we multiply them by 100. 1 1 For Example 4 = 4 × 100 = 25%. To decrease a number by a given %: 𝟏𝟎𝟎−𝐑𝐚𝐭𝐞 Multiply the numbers by the factor 𝟏𝟎𝟎 To find the % increase of a number: 𝐓𝐨𝐭𝐚𝐥 𝐢𝐧𝐜𝐫𝐞𝐚𝐬𝐞 𝐅𝐢𝐧𝐚𝐥 𝐯𝐚𝐥𝐮𝐞−𝐈𝐧𝐢𝐭𝐢𝐚𝐥 𝐯𝐚𝐥𝐮𝐞 % increase = × 𝟏𝟎𝟎 = × 𝟏𝟎𝟎 𝐈𝐧𝐢𝐭𝐢𝐚𝐥 𝐯𝐚𝐥𝐮𝐞 𝐈𝐧𝐢𝐭𝐢𝐚𝐥 𝐯𝐚𝐥𝐮𝐞 To find the % decrease of a number: 𝐓𝐨𝐭𝐚𝐥 𝐝𝐞𝐜𝐫𝐞𝐚𝐬𝐞 𝐅𝐢𝐧𝐚𝐥 𝐯𝐚𝐥𝐮𝐞−𝐅𝐢𝐧𝐚𝐥 𝐯𝐚𝐥𝐮𝐞 % decrease = × 𝟏𝟎𝟎 = × 𝟏𝟎𝟎 𝐈𝐧𝐢𝐭𝐢𝐚𝐥 𝐯𝐚𝐥𝐮𝐞 𝐈𝐧𝐢𝐭𝐢𝐚𝐥 𝐯𝐚𝐥𝐮𝐞 For Example 1. In an election between two candidates, 75% of the voters casted their votes, out of which 2% of the votes were declared invalid. A candidate got 9261 votes which were 75% of the total valid votes. Find the total number of votes enrolled in that election. (SSC 2003) (a) 15000 (c) 16800 (b) 16000 (d) 17000
  • 17. Answer:- (c) Let the total enrolled votes are x. Then, Number of votes cast = 75 % of x. Valid votes = 98 % of (75 % of x) ∴ 75 % 0f [98 % of (75 % of x)] = 9261 2. If 50% of (x – y) = 30% of (x + y), then what percent of x is y? (a) 25 % (b) 50 % (c) 75 % (d) 100 % 50 30 Answer:- (a) here 50% of (x – y) = 30% of (x + y)  100 x − y = 100 (x + y) 1  10(x – y) = 6(x + y)  10x – 6x = 6y + 10y  4x = 16y  4 x = y  25 % of x = y. 1 Because4 = 25% AVERAGE Average is defined as the sum of n different numerical values divided by n. 𝐒𝐮𝐦 𝐨𝐟 𝐧 𝐝𝐢𝐟𝐟𝐞𝐫𝐞𝐧𝐭 𝐍𝐮𝐦𝐞𝐫𝐢𝐜𝐚𝐥 𝐕𝐚𝐥𝐮𝐞 Average = 𝐧 𝐓𝐨𝐭𝐚𝐥 𝐃𝐢𝐬𝐭𝐚𝐧𝐜𝐞 Average Speed = 𝐓𝐨𝐭𝐚𝐥 𝐒𝐩𝐞𝐞𝐝 If a person covers half of his journey at a speed of x km/h and the next half at the speed of y 𝟐𝒙𝒚 km/h, then the average speed during the whole journey is . 𝒙+ 𝒚 𝒘𝟏𝒙𝟏 + 𝒘𝟐𝒙𝟐 Weighted Average of x1, x2 where weight is w1, w2 = . 𝒘𝟏 + 𝒘𝟐 Average of different groups If the average of a group of n items is a and the average of another group of m items is m, then 𝐧𝐚 + 𝐦𝐛 the combined average = 𝐧 + 𝐦 . For Example 1. The average of a non-zero number and its square is 5 times the number. The number is: (SSC 2003) (a) 9 (b) 17 (c) 29 (d) 295 Answer:- (a) Let the number be x. Then
  • 18. x2+ x = 5x  x 2 + x = 10x  x 2 + x − 10x = 0  x x − 9 = 0 ∴ x = 9. 2 SURDS AND INDICES Laws of Indices: (a) am × an = am + n am (b) a n = am – n (c) (am) n = a m n (d) (a b)m = a m b m a m am (e) b = bm 0 (f) a = 1 Laws of Surds: 1 n n (a) n a = an (d) a =a n n n m n mn (b) ab = a × b (e) a= a n n m n (c) n a = n a (f) a = am b b For Example, 1 1. Find the value of ( 81) 4 . (a) 3 (b) 3 (c) 9 3 (d) 3 1 1 1 1 1 1 Answer: - (b) ( 81) 4 = (3 × 3 × 3 × 3 )2 × 4 = (34 )2 × 4 = (3)2 = 3. 1 −4 2. (− ) 3 =? 64 (a) 254 (b) -254 (c) 256 (d) -256 1 −4 1 (−4) 1 Answer:- (c) (− ) 3 = (− 4)3 × 3 = (− 4)−4 = (−4)4 = 256. 64 PROFIT & LOSS
  • 19. Some important terms for Profit and Loss: Cost Price: It is the price at which an article is purchased. The cost price is generally abbreviated as C.P. Selling Price: It is the price at which an article is sold. The selling price is generally abbreviated as S.P. Profit or Loss: It is the difference of selling price (SP) and cost price (CP). If the difference is positive, then it is called a profit and if the difference is negative, then it is called a loss. Important Formulae 1. SP = CP + Profit = CP – Loss Gain × 100 2. Gain % = C.P. Loss × 100 3. Loss % = C.P. (100 + Gain %) (100 − Loss %) 4. SP = × CP = × CP 100 100 100 100 5. CP = (100 + Gain × SP = (100 −Loss × SP %) %) For Example 1. Arjun buys an old car for Rs 1, 12, 000 and spends 8000 on its repairs. If he sells the Car for Rs 1,80,000, his gain percent is: (a) 50 (c) 52 (b) 51 (d) 53 Answer:- (a) C.P. = Rs. (1,12,000 + 8,000) = Rs. 1,20,000, S.P = 1,80,000, 60,000 Gain % = ( 1,20,000 × 100) =50% 2. If loss is 1/4 of S.P., the loss percentage is: (a) 25% (b) 20% (c) 35% (d) 40% a 5a a 4 Answer:- (b) S.P. = a, Loss = a/4, CP. =a + 4 =  Loss% =( × × 100) % = 20% 4 4 5a INTEREST CALCULATION Important Facts and Formulae related to Interest calculation
  • 20. Principal: It is the money which is borrowed or lend out for certain period. Generally, Principal is denoted with P. Interest: It is the cost of holding others money for a certain period of time. Rate of Interest: It is the rate at which the interest is calculated. The rate of interest is the amount of interest which is calculated at every Rs. 100 for a fixed period. Generally for 1 year. P ×R ×T S.I.× 100 S.I.× 100 S.I.× 100 Simple Interest (S. I.) = ,P= ,R= ,T= 100 R×T P×T P×R R n Compound Interest (C. I.) = P 1 + 100 −P (When interest is compounded annually) R 2n 2 Compound Interest (C. I.) = P 1 + 100 −P (When interest is compounded Half yearly) When rates of interest are different for different years, for example R1%, R2% and R3% for 1st, 2nd and 3rd year respectively. 1 R 2 R R3 Then Compound Interest =P 1 + 100 1 + 100 1 + 100 − P. For Example 1. Find the compound interest on Rs. 160, 000 in 2 years at 10 % per annum. The interest being compounded half yearly. (a) 32000 (b) 33000 (c) 34000 (d) 34481 10 2×2 2 Answer:- (d) The required C.I. = 160, 000 1 + − 160, 000 100 21 21 21 21 = 160, 000 − 160, 000 = 194, 481 − 160, 000 = 34, 481 20 20 20 20 2. The difference between the compound interest and simple interest on a certain sum at 10% per annum for 2 years is Rs. 200. Find the principal. (a) Rs. 10, 000 (b) Rs. 15, 000 (c) Rs. 20, 000 (d) Rs. 25, 000 Answer:- (c) Let the required principal be P. then
  • 21. 10 2 P × 10 × 2 121 1 1 P 1 + 100 −P− = 200  P − 1 − 5 = 200  P = 200 100 100 100 Therefore, P = 20, 000
  • 22. TIME, SPEED & DISTANCE Important facts and formulae Distance = (Speed × Time) Distance Speed = Time Distance Time = Speed 5 x km/h = x × 18 m/s 18 x m/s = x × km/h 5 Total Distance Average Speed = Total Speed If a person covers half of his journey at a speed of x km/h and the next half at the speed of y 𝟐𝒙𝒚 km/h, then the average speed during the whole journey is . 𝒙+ 𝒚 In water, the direction along the stream is called downstream. And the direction against the stream is called upstream. If the speed of a boat in still water is a km/h and the speed of the stream is b km/h, then: Speed downstream = (a + b) km/h Speed upstream = (a + b) km/h If the speed downstream is p km/h and the speed upstream is b km/h, then: 𝟏 Speed in still water = 𝟐 (𝐚 + 𝐛) km/h 𝟏 Rate of stream = 𝟐 (𝐚 − 𝐛) km/h For Example 1. A man travelled from the village to the post-office at the rate of 25km/h and walked back at the rate of 4 km/h. If the whole journey took 5 hours 48 minutes. Find the distance of the post-office from the village. (SSC, 2004) (a) 10 km (c) 20 km (b) 15 km (d) 25 km
  • 23. 2 × 25 × 4 200 Answer: - (c) The average speed for the whole journey = = km/h. the total time is 25 + 4 29 48 4 29 200 29 5 60 = 5 5 = h. ∴ the total distance = × = 40 km. Therefore the distance from village 5 29 5 40 to the post office = = 20 km. 2 2. In what time will a train 100 m long, cross an electric pole, if its speed be 144 km/h? (a) 2.5 seconds (c) 3.5 seconds (b) 3 seconds (d) 4 seconds 5 Answer: - (a) The speed in m/s = 144 × 18 = 40 m/s and the train has to cross its own length to 100 cross a pole. The length of the train is 100 m. therefore the required time is = 2.5 s 40 TIME & WORK Some Important Facts and Formulae 1. If m persons can complete a work in p days, then the same work will be completed by n m persons in n × p days. 1 2. If P can complete a piece of work in A days, then P’s one day work = A of the complete work 1 and if P can do A of work in 1 day, then P can complete the work in A days. 3. If A can complete a piece of work in m days and B can complete the same work in n days, 1 1 m+n then the 1 day work of both of them together = +n = of the work and both of m mn mn them together complete the work in m+n . 4. If A is twice as good a workman as B, then ratio of work done by A and B = 2 : 1 and the ratio of times taken by both of them to finish the work = 1 : 2. For Example 1. Aryan takes 5 hours to do a job, and Aryaman takes 6 hours to do the same job. How long should it take if both Aryan and Aryaman, working together but independently, to do the same job? 9 (a) 3 days (c) 211 days 8 (b) 211 days (d) 4 days Answer: - (b)
  • 24. 1 2. A can finish a work in 12 days and B can do the same work in 3 the time taken by A. Then, working together, what part of same work they can finish in a day? 1 1 (a) (c) 5 3 1 1 (b) (d) 4 2 Answer:- (c) ELEMENTARY ALGEBRA Below are some important formulae which are very useful to solve questions. 1. (a + b)2 = a2 + b2 + 2ab 2. (a – b)2 = a2 + b2 – 2ab 3. a2 – b2 = (a + b)(a – b) 4. (a + b)3 = a3 + 3a2b + 3ab2 + b3 5. (a − b)3 = a3 − 3a2b + 3ab2 − b3 6. a3 + b3 = (a + b)(a2 – ab + b2) 7. a3 − b3 = (a − b)(a2 + ab + b2) 8. a3 + b3 + c3 – 3abc = (a + b + c)(a2 + b2 + c2 – ab – bc – ca) 1 = 2(a + b + c)[(a – b)2 + (b – c)2 + (c – a)2] 9. (a + b + c)3 = a3 +b3 + c3 + 3(a + b)(b + c)(c + a) 10. If (a + b + c) = 0 or a = b = c, then a3 + b3 + c3 = 3abc. 11. am × an = am + n 12. (am)n = am n 13. (a b)m = a m b m 𝑎 𝑚 14. = x m – n. 𝑎𝑛 The questions in the SSC exam are generally based on the addition, subtraction, multiplication and division of algebraic expressions. Some questions are also asked from quadratic equations. For Example, 1. If for two real constants a and b, the expression ax3 + 3x2 – 8x + b is exactly divisible by (x + 2) and (x – 2). Find the value of a and b. Answer: - the expression is exactly divisible by (x + 2) and (x – 2). Therefore a(−2)3 + 3(−2)2 – 8(−2) + b = 0  −8a + 3×4 + 16 + b = 0  8a – b = 28 ………(1) Again, a(2)3 + 3(2)2 – 8(2) + b = 0  8a + 3×4 − 16 + b = 0  8a + b = 4 ………(2)
  • 25. After adding (1) and (2) 8a – b + 8a + b = 28 + 4  16a = 32 ∴ a = 2. After putting the value of a in (1) 8 × 2 – b = 28  16 – 28 = b ∴ b = − 12. Hence, a = 2 and b = −12. 1 4a 2. If a + a = 2, find the value of 3a 2 + 4a − 3. (a) 0 (b) 1 (c) 2 (d) −1 1 4a Answer: - (b) Solve a + a = 2 and put the value in 3a 2 + 4a − 3. 3. If a2 + b2 + 2b + 1 = 0, then find the value of a34 + b38. (a) 1 (b) 0 (c) −1 (d) 2 Answer: - (a) Here a = 0 and b = −1, then a34 + b38 = 1
  • 26. GEOMETRY Concepts Triangles: Triangle is a polygon which has three sides. The sum of all the angles of a triangle is 180°. Types of Triangles: 1. Acute angle triangle: It is a triangle in which all the angles are less than 90°. 2. Obtuse angle triangle: It is a triangle in which one angle is greater than 90°. 3. Right angle triangle: It is a triangle in which one angle is equal to 90°. 4. Equilateral triangle: It is a triangle in which all the sides are equal and the all angles are equal to 60°. 5. Isosceles triangle: It is a triangle in which two sides are equal and angle opposite the equal sides are also equal. 6. Scalene triangle: It is a triangle in which all the sides are unequal. General Properties of Triangles: 1. Sum of the length of any two sides of a triangle is always greater than the third side. 2. Difference between the lengths of any two sides of a triangle is always less than the third side. 3. The side opposite to the greatest angle will be the greatest similarly the side opposite to the smallest angle will be the smallest. a b c 4. Sine rule in a triangle: sinA = sinB = sinC = 2R, where a, b and c are the side of a triangle and A, B and C are the corresponding angles of the side. R is the circum radius. 5. Cosine rule in a triangle: a2 = b2 + c2 – 2bc cosA. 6. The exterior angle is equal to the sum of two interior angles which are not adjacent to it. Important terms 1. Median: A line joining the mid-point of a side of a triangle to the opposite vertex is called a median. The median divides a triangle into two parts of equal area and the point where all the medians meet is called the centroid of the triangle. The centroid divides each median in the ratio 2 : 1. 2. Altitudes: Altitudes are the perpendiculars drawn from any vertex to the opposite sides. All the altitudes meet at the orthocentre of the triangle. The angle made by any side at the orthocentre and vertical angle is together equal to 180°. Here,  A +  BOC = 180°.
  • 27. 3. Perpendicular Bisectors: It is a line which bisects a side and at the same time perpendicular to the side. The point at which the perpendicular bisectors of the sides meet is called the circumcentre of the triangle. The circumcentre of a triangle circumscribes the triangle and the circle is unique for the triangle. The angle made by a side of a triangle at the circumcentre is double to the opposite angle. Here, 2  A =  BOC. Circles: A circle is a set of points in a plane which are equidistant from a point O. The point O is called centre of the circle and the distance from the centre O is called radius which is generally represented as r. Properties 1. There can be only one circle passing through three or more non-collinear points in a plane. 2. If two circles intersect in two points then the line through the centres is the perpendicular bisector of the common chord. For Example 1. ABCD is a square. M is the midpoint of AB and N is the mid-point of BC. DM and AN are joined and they meet at O. Then which of the following is correct? (a) OA : OM = 1 : 2 (b) AN = MD (c)  ADM =  ANB (d)  AMD =  BAN Answer: - (b) 2. AB = 8 cm and CD = 6 cm are two parallel chords on the same side of the centre of a circle. The distance between them is 1 cm. The radius of the circle (in cm) is (SSC) (a) 5 (b) 4 (c) 3 (d) 2 Answer: - (a)
  • 28. 3. The circumcentre of a triangle ABC is O. If  BAC = 85° and  BCA = 75°, then the value of  OAC is (a) 40° (b) 60° (c) 70° (d) 90° Answer: - (a) 4. AB is a chord of a circle of radius 7 cm. The chord subtends a right angle at the centre of the 22 circle. Find the area of the minor segment in sq cm. Use 𝛑 = 7 . (a) 7 (b) 24.5 (c) 14 (d) 38.5 Answer:- (c) MENSURATION Below are some important formulae which are very useful to solve questions. 1. Area of a rectangle = Length × Breadth 2. In a rectangle, (Diagonal)2 = (Length)2 + (Breadth)2. 3. Perimeter of a rectangle = 2(Length + Breadth). 1 4. Area of square = (Side)2 = 2 (Diagonal)2. 5. Perimeter of a square = 4 × Side. 6. Area of 4 walls of a room = 2(Length + Breadth) × height 7. Area of a parallelogram = Base × Height. 1 8. Area of a rhombus = 2 (Product of Diagonals). 3 9. Area of an equilateral triangle = 4 (Side)2. 10. Perimeter of an equilateral triangle = 3(Side). a +b +c 11. Area of a triangle = s s − a s − b s − c , where s = 2 . 12. Area of a circle = 𝛑r2, where r is the radius of the circle. 13. Circumference of a circle = 2𝛑r 2πrθ 14. Arc AB on a circle = 360° , where AOB = 𝛉 and O is the centre. πr 2 θ 15. Area of sector AOB = 360° . 16. Volume of a cube = a3, where a is a side or edge. 17. Whole suface area of a cube = 6a2.
  • 29. 18. Diagonal of a cube = √3 a. 19. Volume of a cuboid = lbh, where l = length, b = breadth and h = height. 20. Whole suface area of a cuboid = 2(lb + bh + hl). 21. Diagonal of a cuboid = l2 + b 2 + h2 . 22. Volume of a cylinder = 𝛑r2h. 23. Curved surface area of a cylinder = 2𝛑rh. 24. Total surface area of a cylinder = (2𝛑rh + 𝛑r2). 4 25. Volume of a sphere = 3 πr 3 . 26. Surface area of a sphere = 4𝛑r2. 2 27. Volume of a hemisphere = 3 πr 3 . 28. Curved surface area of a hemisphere = 2𝛑r2. 29. Whole surface area of a hemisphere = 3𝛑r2. 30. Right circular Cone, I. Slant height l = r 2 + h2 , where r = radius of base and h = height. 1 II. Volume of a cone = 3 πr 2 h. III. Curved surface area of a cone = 𝛑rl = 𝛑r r 2 + h2 . IV. Total surface area of a cone = (𝛑rl + 𝛑r2). 1 31. Slant surface area of a pyramid = 2 (Perimeter of the base)×(Slant height). 1 32. Total surface are of a pyramid = 2 (Perimeter of the base)×(Slant height) + area of base. area of the base 33. Volume of pyramid = ×Height. 3 For Example 1. There is a pyramid on a base which is a regular hexagon of side 2a cm. If every slant edge of 5a this pyramid is of length 2 cm, then the volume of this pyramid is (SSC) (a) 3a3 cm3 (b) 3 2a3 cm3 (c) 3 3a3 cm3 (d) 6a3 cm3 3 5a 2 Answer:- (c) Here area of base = 6 × 4 (2a)2 = 6 3a2 and height = − 2a 2 = 2 25a 2 9a 2 3a 6 3a2 × 3a = − 4a2 = = , then the volume of a pyramid = 3 3a. 4 4 2 3 2 2. The area of the four walls of a room is 660 m2 and its length is twice its breadth. If the height of the room is 11 m, then the area of its floor (in m2) is (a) 120 (c) 200 (b) 150 (d) 330
  • 30. Answer:- (c) Let b be the Breadth, l be the Length and h be the Height of the room. 2 × (l + b) × h =660  2 × (2b + b) × 11 = 660  2 × 3b × 11 = 660  66b = 660 ∴ b = 10, then l = 200. Therefore, area of the floor = 20 × 10 = 200. 3. A cylindrical rod of iron whose height is five times its radius is melted and cast into spherical balls each of half the radius of the cylinder. the number of such spherical balls is (a) 5 (b) 30 (c) 10 (d) 25 Answer:- (b) Let the given radius of the cylinder be r and the height be 5r then the volume of r 4 r 3 the cylinder =  r2(5r) = 5  r3. Again the volume of one sphere whose radius is 2 = 3 π 2 = 4 r3 πr 3 5πr 3 π = . Therefore the number of spheres in the volume 5  r3 = πr 3 = 30 3 8 6 6 TRIGONOMETRY Pythagoras Theorem: In a right-angled triangle, h2 = p2 + b2 Here, h is the hypotenuse, p is the perpendicular and b is the base of the right angled Trigonometric Ratios: the trigonometric ratios are calculated according to the angles. The hypotenuse is the largest side of a right angled triangle, the perpendicular is the opposite side of the angle and the base is the adjacent side. For example, Here, for angle  R, PR = hypotenuse, PQ = perpendicular and QR = base. P Q R A The Trigonometric ratios are Sin Ѳ p Tan Ѳ p Sec Ѳ h h b b Cos Ѳ b Cot Ѳ b Cosec Ѳ h h p p
  • 31. The important values of Trigonometric ratios Ѳ Sin Cos Tan Cot Sec Cosec 30® 1 3 1 √3 2 2 2 2 3 3 45® 1 1 1 1 √2 √2 2 2 60® 3 1 √3 1 2 2 2 2 3 3 Some important formulae 1 1 1 Sin Ѳ = cosec Ѳ, cos Ѳ = sec Ѳ, tan Ѳ = cot Ѳ, sin (90® - Ѳ) = cos Ѳ, tan (90®- Ѳ) = cot Ѳ, Sec (90® - Ѳ) = cosec Ѳ, cos(90®- Ѳ) = sin Ѳ, cot (90® - Ѳ) = tan Ѳ, Cosec (90® - Ѳ) = sec Ѳ, Sin2Ѳ + Cos2Ѳ = 1, Sec2Ѳ – Tan2Ѳ = 1, Cosec2Ѳ – Cot2Ѳ = 1. Angle of Elevation: If a person looking at an object which is placed above the line of his eye. Then, the angle which is the made by the object’s line with the eye and the horizontal line is called the angle of elevation. Angle of Depression: If a person looking down at an object which is placed below the level of his eye. Then, the angle which is made at his eye by the object’s line with the horizontal line of his eye is called the angle of depression. For Example 3 5sin Ѳ+2cos Ѳ 1. If tan Ѳ = 4, then the value of 4 cos 2 Ѳ−3 sin 2 Ѳ is (a) 1 (b) 0 115 (c) 37
  • 32. 110 (d) 23 3 3 4 Answer:- (c) Here tan 𝛉 = 4, then sin 𝛉 = 5 and cos 𝛉 = 5 from the Pythagoras Theorem. 2. The value of tan 5°. tan 15°. tan 35°. tan 55°. tan 75°. tan 85° is (a) 1 (b) 0 (c) 0.5 (d) 0.75 Answer:- (a) Here we can change tan 5° = tan (90° − 85°) = cot 85° and tan 𝛉 × cot 𝛉 = 1. 3. A ladder leaning against a wall makes an angle of 60° with the ground. If the length of the ladder is 30m, find the height of the wall up to the ladder. (a) 15 (b) 15√3 (c) 30 (d) 30√3 Answer:- (b) The diagram can be, DATA INTERPRETATION The questions in this unit can be asked from four different types of data. 1. Histogram 2. Frequency polygon 3. Bar-diagram 4. Pie-chart For Example Question (1 to 5): The line diagram shows the cost of production and profit of five companies for the year 2011-12. (The figures are in '000').
  • 33. 500 400 300 COST OF PRODUCTION 200 PROFIT 100 0 A B C D E 1. The ratio of profits of company B to D is: (a) 2:3 (c) 4:3 (b) 3:4 (d) 3:2 2. The profit of company C is what percentage of the cost of production of company E? (a) 20% (c) 30% (b) 25% (d) 35% 3. The cost of production of company B is how many times of company C profit? (a) 2.5 (c) 3.5 (b) 3 (d) 4 4. Which company has the maximum percentage of profit? (a) A (c) C (b) B (d) D 5. What is the average profit of all the companies? (a) 50,000 (c) 70,000 (b) 60,000 (d) 80,000 Answers:- 1. The profit of B is 50,000 and D is 75,000 therefore the ratio is 2:3. 2. The profit of C is 1,00,000 which is 25% of E's cost of production which is 4,00,000. 3. The cost of B is 3,50,000 which 3.5 times the profit of C' profit which is 50,000. 4. The company C has a 40% profit. 5. The total profit of all the companies are 75,000+50,000+1,00,000+75,000+1,00,000 = 4,00,000, therefore the average will be (4,00,000)/5= 80,000.
  • 34.
  • 35. ENGLISH LANGUAGE SYNONYMS Synonyms: The word comes from ancient Greek words ‘syn’ and ‘onoma’ where ‘syn’ means ‘with’ and ‘onoma’ means ‘name’. Synonyms are the word which has similar meanings. Two words are said to be synonymous when they have similar meanings. The words caste and class is synonymous because both the words have similar meaning. For Example, Q. Find the word which is synonymous to Deny. (SSC 2011) (a) Regain (b) Refuse (c) Repair (d) Reduce Answer: The synonyms for Deny are Contradict, Refuse, Reject etc. here we have Refuse as an option, which means the right answer is (b). Q. Find the word which is synonymous to Deposit. (a) Degrade (b) Dethrone (c) Place (d) Removal Answer:- (c) ANTONYMS Antonyms: The word “antonym “comes from ancient Greek words ‘anti’ and ‘onoma’ where ‘anti’ means opposite and ‘onoma’ means name. The literal meaning of antonyms is the opposite name which means the word which has opposite meaning. For example; Day – Night, Long – Short, Up – Down, Small – Large, etc. For Example Q. Find the opposite word to Concur. (SSC 2011) (a) Disagree (c) Disarrange (b) Disappear (d) Discourage
  • 36. Answer: The synonyms for Concur are agree, cooperate, combine etc. Therefore the antonym for ‘agree’ is ‘disagree’. Hence right answer is (a). Q. Find the opposite word to Condensation. (a) Abridgment (c) Compression (b) Broadening (d) Concentration Answer: - (b) IDIOMS AND PHRASES Idioms and phrases refer to commonly used groups of words in English. They are used in specific situations and often used in an idiomatic, rather than a figurative sense. Idioms are often full sentences. Phrases, however, are usually made up of a few words and are used as a grammatical unit in a sentence. For Example, 1. Ram used very ugly words against his kind uncle; he threw down the gauntlet before him. (a) he abused and insulted him (b) he threw the challenge (c) he behaved as if he was a very great and important person (d) he put several conditions for negotiation Answer: - (b) 2. He always cuts both ends (a) Work for both sides (b) Inflicts injuries on others (c) Argues in support of both sides of the issue (d) Behaves dishonestly Answer: - (c) ONE WORD SUBSTITUTION One word substitution is the words that replace a group of words or sentences without creating or changing the exact meaning of sentences. These words generally bring compression in any kind of writing. There are lots of words in English language that can be used effectively in place of complex sentences or words to make writing to the point without losing the meaning of the context. For Example,
  • 37. 1. One who eats too much (a) Foodie (b) Glutton (c) Eater (d) Food loving Answer: - (b) glutton 2. A book published after the death of its author (a) Posthumous (b) Anonymous (c) Synonymous (d) Mysterious Answer: - (a) Posthumous
  • 38. SPELLING TEST Spelling test is basically devised to test the vocabulary power and the candidate ability to write the words with correct spellings. Question asked is such section generally required to choose the correct spelt word or the mis- spelt out of the alternatives given. For Example, find the mis – spelt word. 1. (a) Comission (b) Commisson (c) Comession (d) Commission Answer: (d) 2. (a) Liutenenat (b) Lieutanent (c) Lieutenant (d) Leiutanent Answer: (c) INCORRECT SENTENCES Directions: In questions no. 1 to 2, a part of the sentence is underlined. Below are given alternatives to the underlined part at (a), (b) and (c) which may improve the sentence. Choose the correct alternative. In case no correction is needed, your answer is (d). 1. All the allegations levelled against him were found to be baseless. (a) levelled for (b) level with (c) level against (d) no correction Answer:- (c) 2. Last Sunday I went to the market and bought spectacles. (a) two spectacles (b) a pair of spectacles (c) a spectacle (d) no correction Answer:- (b)
  • 39. SENTENCE RECONSTRUCTION Sentence reconstruction is the grammatical arrangement of words in sentences, phrase structure, and syntax. The sentences are presented in a jumbled manner and the students are supposed to arrange it chronologically. Here we are giving some examples. Students are advised to go through it carefully. 1. There is a fashion now-a-days P. as an evil Q. who is born with a silver spoon R. to bewail poverty S. and to pity the youngman in his mouth (a) PSRQ (b) RPSQ (c) RSQP (d) SPRQ Answer:- (b) 2. Though the government claims P. it has failed to arrest Q. the rate of inflation is down R. or the decrease S. the rise in prices 6. in the per capita income (a) PQRS (b) PQSR (c) PSQR (d) QPSR Answer:- (d) SPOTTING THE ERROR Directions: Read each sentence to find out whether there is any grammatical mistake/error in it. The error if any will be in one part of the sentence. Mark the number of the part with error as your answer. If there is no error, mark the last option. 1. (a) My brother lived at the top / (b) of an old house / (c) which attic had been / (d) converted into a flat. / (e) No error. Answer: - (c) Replace ‘which’ by ‘whose’.
  • 40. 2. (a) All companies must / (b) send its annual report to/ (c) its shareholders twenty one days / (d) before the annual general meeting./ (e) No error. Answer: - (a) Use ‘every’ in place of ‘all’. 3. (a) They agreed / (b) to repair the damage / (c)freely of charge / (d)No error Answer: - (c) 4. (a) Radha was trying for admission / (b) in the Science College / (c) even though her parents wanted/ (d) her to take up medicine. / (e) No error. Answer: - (c) Use ‘had wanted’ in place of ‘wanted’. 5. (a) My younger sister and / (b) I am interested / (c) in mathematics./ (d) No error Answer: - (b) Use ‘are’ in place of ‘am’. 6. (a) You should purchase/ (b) this insurance policy/ (c) as the company/ (d) offers many benefits./ (e) No error. Answer: - (e) No error. 7. (a) Having acquired some experience/(b) she is no longer/ (c) one of those who believes/ (d) every explanation she is given./(e) No error Answer: - (d) Replace ‘is’ with ‘has’ CLOZE TEST Cloze test is the test of the ability to comprehend text in which the reader has to supply the missing words that have been removed from the text at regular intervals. It is basically a test for diagnosing reading ability; words are generally deleted from a prose passage and the reader is required to fill in the blanks. Directions (Q. 1-1O): In the following passage there arc blanks, each of which has been numbered. These numbers are printed below the passage and against each, five words are suggested, one of which fits the blank appropriately. Find out the appropriate word in each case. Raju was orphaned at a very (1) age. He lost (2) of his parents because his family was (3) poor to afford any treatment. He was deeply affected by this. He decided to work hard and (4) on his own feet. Along with his studies he (5) part-time in a restaurant and earned enough money in order to (6) his studies. Being a brilliant student, he earned scholarships and later managed to get admission in a good medical college. He is now a (7) doctor and helps poor patient for (8). This shows that one can survive every (9) condition. Determine and hard work (10) to success in life.
  • 41. 1. (a) youth (b) early (c) childhood (d) childish (e) recent 2. (a) any (b) few (c) either (d) couple (e) both 3. (a) little (b) so (c) too (d) some (e) ample 4. (a) balance(b) establish (c) stand (d) erect (e) talk 5. (a) worked (b) employed (c) busy (d) established(e) functioned 6. (a) done (b) practice (c) follow (d) pursue (e) proceed 7. (a) recognise (b) know (c) respected (d) worth (e) merit 8. (a) favour (b) less (c) penny (d) subsidy (e) free 9. (a) failed (b) adverse (c) worse (c) evil (e) tragedy 10. (a) result (b) follow (c) excel (d) lead (e) urge Answers: 1. (b) 3. (c) 5. (a) 7. (c) 9. (b) 2. (e) 4. (c) 6. (d) 8. (e) 10. (d)