My dear Friends/students Wishing you all happy sankranti and happy wishes to Ugadi in advance. As I have uploaded a New pattern (NCERT + PUC BOARD GUIDELINES) Model question paper of MATHEMATICS for all the science students (For the classes XI, XII-PUC1 AND PUC2) Who are writing Annual exam -2014.I designed this model paper according to latest syllabus.I request all science students to make use of this question paper to secure maximum score in their Annual exam 2014.And also I request all my friends and students to help other students by sharing this model question paper. Wish you all the best for Annual exam-2014. From: NAGARAJ DIRECTOR & FACULTY SHREE SUSHEELA TUTORIALS BAGALKOT-587101 CONTACT: 9845222682 EMAIL: edulation@gmail.com

1. A. Nagaraj’S Trin : 9845222682
I P.U.C.MATHEMATICS- ANNUAL EXAM-2014
Max. Marks:100
PART-A
ANSWER ALL THE QUESTIONS
10X1=10
1. If A = {1, 2} then Find the number of elements of P(A).
2. Let A = {1, 2,3, 4,5, 6} .Define R from A to A by R=
3. Find the Radian measure of 22 30′ . (OR) If cot x =
4. Find the Additive inverse of (−i ) .
{( x, y ) : y=
x + 1}. Write the elements of R.
3
and x lies in IIIrd Quadrant then find cos x .
4
(OR)
Write the conjugate of (-1/ i ).
5. A coin is tossed 3 times and the outcomes are recorded. How many possible outcomes are there?
6. Write the first Five terms of the Sequence, whose nth terms is given by an =
2n − 3
.
6
7. Find the equation of the line through (-2,3) With slope -4.
8. Evaluate lim 1 + x + x 2 + ......... + x10  .

x →−1 
9. Write the Negation of “All triangles are not Equilateral triangle”.
10. Define simple event. Also write the sample space of tossing the coin Twice.
PART-B
Answer any Ten question
10x2=20
11. In a School there are 20 Teachers who teach mathematics or Physics . Of these 12 teach Mathematics and
4 Teach both Physics and Mathematics. How many teach Physics?
=
12. Let f
{(1,1) , ( 2,3) , ( 0, −1) , ( −1, −3)} be a linear function from Z to Z .Find
f ( x) .
13. The Minute hand of a watch is 1.5 cm long. How far does its tip move in 40 minutes?
14. Prove that
cos 7 x + cos 5 x
= cot x .
sin 7 x − sin 5 x
15. Express (−1 − i ) in Polar form (OR) Solve : x 2 + 3 x + 5 =.
0
16. Solve 7 x + 3 < 5 x + 9 . Show the Graph of the solutions on Number line.
17. Find a Point on the X-axis, Which is equidistant from the points (7,6) and (3,4).
18. Find the equation of the line Parallel to the line 3 x − 4 y + 2 = and Passing through the Point (-2,3).
0
19. Find the Coordinates of the Point which divides the line joining the points (-2,3,5) and (1,-4,6) internally

2. A. Nagaraj’S Trin : 9845222682
in the ratio 2:3.

x 4 − 81 
.
2
 2 x − 5x − 3 
20. Evaluate lim 
x →3
21. Write Converse and Contra positive of the Statement “If x is a Prime number ,then x is Odd”.
22. Coefficient of Variation of distribution are 60 and the standard deviation is 21. What is the arithmetic
Mean of the distribution?
23.A committee of two persons is selected from two men and two women. What is the Probability that the
committee will have no man?
24. If U = {1, 2,3, 4,5, 6, 7,8,9} , A = {2, 4, 6,8} and B = {2,3,5, 7} Verify that ( A ∪ B )′ =A′ ∩ B ′ .
PART – C
Answer any Ten questions.
10x3=30
25. In a Group of 70 People, 37 like Coffee, 52 like Tea and each person likes at least one of the two drinks,
How many People like both Coffee and Tea?
26. Let A = {1, 2,3, 4, 6} . Let R be the relation on A defined by {(a, b) : a, b ∈ A, b is exactly divisibleby a}
i) Write R in Roster form ii) Find the domain and Range of R.
27. Prove that cos 4 x = 1 − 8sin 2 x cos 2 x .
a + ib
, Prove that x 2 + y 2 =
1.
a − ib
28. If x + iy =
29. Find the modulus and argument of
1
.
1+ i
30. In how many Ways can the letters of the word “PERMUTATIONS”. Be arranged if the (i) Words start
with P and end with S. (ii) Vowels are all together
(iii) There are always 4 letters between P and S?
7

x3 
31. Find the middle terms in the expansion of  3 −
 .
6 

32. Insert 6 arithmetic means between 3 and 24.
33. Find the three numbers are in G.P. their sum is 13/12 and their product is (-1).
34. Find the equation of the circle,passing through the point (2,3) and radius 5,also whose centre lies on X-axis.
35. Find the Derivative of "cos x " w.r.t. x .From first principle.
36. Verify by the method of Contradiction that
2 is irrational.

3. A. Nagaraj’S Trin : 9845222682
37. Two dice are thrown and the sum of the numbers which come up on the dice is noted.Let us consider the
following events associated with this experiment A: ‘the sum is even’. B: ‘the sum is a multiple of 3’.
C: ‘the sum is less than 4’. D: ‘the sum is greater than 11’. Which pairs of these events are mutually
exclusive?
38. Find the Probability that when a hand of 7 cards is drawn from a well shuffled deck of 52 cards,it contains
(i) all Kings
(ii) 3 Kings
(iii) atleast 3 Kings.
6×5 =
30
PART - D
Answer any SIX questions
1 − x, x < 0

= = 0 Draw the graph of f ( x) .
x
39. The Function f is defined by f ( x) 1,
 x + 1, x > 0

 ta n θ 
 sin θ 

 = 1, Where θ measured in Radians .by using this Evaluate lim 
θ →0
 θ 
 θ 
40. Prove that lim 
θ →0
41.Prove by Mathematical induction
1
1
1
1
n
+
+
+ ........................... +
= .
2 ⋅ 5 5 ⋅ 8 8 ⋅ 11
(3n − 1) ⋅ (3n + 2) 6n + 4
42. Solve the following system of inequalities Graphically
x + 2 y ≤ 8; 2 x + y ≤ 8; x ≥ 0; an d y ≥ 0 .
43. A Group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the
team has (i) no girl? (ii) at least one boy and one girl? (iii) at least 3 girls?
44. State and Prove Binomial theorem for Positive integral values of its exponent.
45. Derive the equation of the line having slope ' m ' and whose Y-intercept is ' c ' .
46. Find the coordinates of the point which divides the line joining the points ( x1 , y1 , z1 ) and ( x2 , y2 , z2 )
internally in the ratio m : n .
a + bx, x < 1

= = 1
x
47. Suppose f ( x)  4,
b − ax, x > 1

and if lim f ( x) = f (1) What are Possible values of a and b ? .
x →1
48. Find the mean deviation about the mean for the following data:
xi
2
5
6
8
10
12
fi
2
8
10
7
8
5

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Part- E
Answer any One question
1x10=10
49. (a) Prove that sin( A + B ) sin A cos B + cos A sin B ,Geometrically.
=
(b) Find the Derivative of
50.
x + cos x
w.r.t.x .
tan x
(a) Define equation of an ellipse as a locus .Also Derive standard equation of Ellipse in the form
x2 y 2
1.
+
=
a 2 b2
(b) Find the Sum to n terms of the series 3 × 12 + 5 × 22 + 7 × 32 + ................. . .
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Thought for the day:
 “Talk about your blessing more than you talk about your problems”.
“If you Always do your best, you will be free from regrets”.

 “Pleasure in the job puts Perfection in the work”.
 “Life is like a coin.Pleasure and pain are the two sides .Only one side is visible
at a time.But remember other side is waiting for its turn”.
 “Pray not for things,but for wisdom and courage”.
Attention!!!!.
Vacation classes start from
10-March-2014 .
Last Date to take Admission only for Mathematics is 25-jan-2014.


And last date to take Admission for P.C.M.B. is

Syllabus will be completed in 3 months.

Study materials will be provided to all students.

25-jan-2014.
Only limited seats for vacation batch.



FREE C.E.T.&JEE COACHING
C.E.T&JEE coaching will be Free For all Vacation batch students who
take admission before 15-jan-2014.
------------We Wish you all the best for your Annual Exams-----From:
A. Nagaraj
Shree susheela tutorials,