DPP-54-56-PC

STUDY  INNOVATIONS
STUDY INNOVATIONSEducator em Study Innovations

DAILY PRACTICE PROBLEMS Subject : Mathematics Date : DPP No. : 54 DPP No. – 01 Class : XI Course : Total Marks : 20 Max. Time : 20 min. Single choice Objective ('–1' negative marking) Q.1, 2, 3, 4 (3 marks 3 min.) [12, 12] Match the Following (no negative marking) (2 × 4) Q.5 (8 marks 8 min.) [8, 8] Ques. No. 1 2 3 4 5 Total Mark obtained 1. Difference between the maximum value of 11C and maximum value of 10C is (A) 11C (B) 10C (C) 11C (D) 10C 2. The value of 1 – 10 2nC  102 2n 103 2n   102n is 81n 81n 1 81n C2 – 81n C3 ..... 81n (A) 2 (B) 0 (C) 1/2 (D) 1 3. The coefficient of a8b4c9d9 in (abc + abd + acd + bcd)10 is (A) 10 ! (B) 10! 8! 4! 9! 9! (C) 2520 (D) none of these 4. If C = 10C for r = 1, 2, 3, ...., 10, then 1.2 C + 2.3 C + ........9.10 C = r r 1 2 9 (A) 130.28 (B) 130. 28 – 1 (C) 130. 28 + 10 (D) 130. 28 – 110 5. Match the column : Column-I Column-II (A) Last digit of (2227)2227 is (p) 1 (B) Last digit of (38)2733 is (q) 2 (C) Number of rational terms in the expansion of (r) 3 21/ 5  3 20 are (D) When 6n – 5n + 2 is divided by 25 remainder is, where n  N (s) 4 (t) 5 DPP No. – 02 Total Marks : 34 Max. Time : 36 min. Multiple choice objective ('–1' negative marking) Q.1, 2 (5 marks 4 min.) [10, 8] Subjective Questions ('–1' negative marking) Q.3, 4, 5, 6 (4 marks 5 min.) [16, 20] Match the Following (no negative marking) (2 × 4) Q.7 (8 marks 8 min.) [8, 8] Ques. No. 1 2 3 4 5 6 7 Total Mark obtained 1. For all values of , the lines represented by the equation (2 cos  + 3 sin ) x + (3 cos  – 5 sin ) y – (5 cos  – 2 sin ) = 0 (A) pass through a fixed point (B) vertex of the system is (1, 1) (C) pass through the origin if tan  = 5 2 (D) the line 3x – 4y = 3 is one of the member of the family n4 2. Let (1 + x2)2 (1 + x)n = ak xk . If a , a , a are in A.P., then a value of n is k  0 1 2 3 (A) 1 (B) 2 (C) 3 (D) 4 3. There are 6 roads between A & B and 4 roads between B & C. (i) In how many ways can one drive from A to C by way of B? (ii) In how many ways can one drive from A to C and back to A, passing through B on both trips? (iii) In how many ways can one drive the circular trip described in (ii) without using the same road more than once 4. If repetitions are not allowed (i) How many 3-digit numbers can be formed from the six digits 2, 3, 5, 6, 7 and 9. (ii) How many of these are less than 400? (iii) How many are even? (iv) How many are odd? (v) How many are multiples of 5? 5. How many car number plates can be made if each plate contains 2 different letters of english alphabet, followed by 3 different digits. 6. How many numbers divisible by 5 and lying between 4000 and 5000 can be formed from the digits 4, 5, 6, 7 and 8 (Repetition of digits is allowed). 7. Column - I Column - II  1 5 (A) If in the expansion of  x  x tan x , the ratio of 4th (p) 7 

DAILY PRACTICE PROBLEMS
Subject : Mathematics Date : DPP No. : Class : XI Course :
DPP No. – 01
Total Marks : 20 Max. Time : 20 min.
Single choice Objective ('–1' negative marking) Q.1, 2, 3, 4 (3 marks 3 min.) [12, 12]
Match the Following (no negative marking) (2 × 4) Q.5 (8 marks 8 min.) [8, 8]
Ques. No. 1 2 3 4 5 Total
Mark obtained
1. Difference between the maximum value of 11
Cp
and maximum value of 10
Cq
is
(A) 11
C4
(B) 10
C6
(C) 11
C5
(D) 10
C5
2. The value of
2 3 2n
2n 2n 2n
1 2 3
n n n n n
1 10 10 10 10
– C C – C .....
81 81 81 81 81
   is
(A) 2 (B) 0 (C) 1/2 (D) 1
3. The coefficient of a8
b4
c9
d9
in (abc + abd + acd + bcd)10
is
(A) 10 ! (B)
!
9
!
9
!
4
!
8
!
10
(C) 2520 (D) none of these
4. If Cr
= 10
Cr
for r = 1, 2, 3, ...., 10, then 1.2 C1
+ 2.3 C2
+ ........9.10 C9
=
(A) 130.28
(B) 130. 28
– 1 (C) 130. 28
+ 10 (D) 130. 28
– 110
5. Match the column :
Column-I Column-II
(A) Last digit of (2227)2227
is (p) 1
(B) Last digit of
33
27
)
38
( is (q) 2
(C) Number of rational terms in the expansion of (r) 3
 20
5
/
1
3
2  are
(D) When 6n – 5n + 2 is divided by 25 remainder is, where n  N (s) 4
(t) 5
DPP No. – 02
Total Marks : 34 Max. Time : 36 min.
Multiple choice objective ('–1' negative marking) Q.1, 2 (5 marks 4 min.) [10, 8]
Subjective Questions ('–1' negative marking) Q.3, 4, 5, 6 (4 marks 5 min.) [16, 20]
Match the Following (no negative marking) (2 × 4) Q.7 (8 marks 8 min.) [8, 8]
Ques. No. 1 2 3 4 5 6 7 Total
Mark obtained
1. For all values of , the lines represented by the equation
(2 cos + 3 sin ) x + (3 cos – 5 sin ) y – (5 cos – 2 sin ) = 0
(A) pass through a fixed point
(B) vertex of the system is (1, 1)
(C) pass through the origin if tan  =
2
5
(D) the line 3x – 4y = 3 is one of the member of the family
54
2. Let (1 + x2)2 (1 + x)n
= 


4
n
0
k
k
k x
a . If a1
, a2
, a3
are in A.P., then a value of n is
(A) 1 (B) 2 (C) 3 (D) 4
3. There are 6 roads between A & B and 4 roads between B & C.
(i) In how many ways can one drive from A to C by way of B?
(ii) In how many ways can one drive from A to C and back to A, passing through B on both trips?
(iii) In how many ways can one drive the circular trip described in (ii) without using the same road more
than once
4. If repetitions are not allowed
(i) How many 3-digit numbers can be formed from the six digits 2, 3, 5, 6, 7 and 9.
(ii) How many of these are less than 400?
(iii) Howmany are even?
(iv) How many are odd?
(v) How many are multiples of 5?
5. How many car number plates can be made if each plate contains 2 different letters of english alphabet,
followed by 3 different digits.
6. How many numbers divisible by 5 and lying between 4000 and 5000 can be formed from the digits
4, 5, 6, 7 and 8 (Repetition of digits is allowed).
7. Column - I Column - II
(A) If in the expansion of
5
x
tan
x
x
1






 , the ratio of 4th
(p) 7
term to the 2nd
term is
27
2
4
, the value of [x] can be
(where [.] is greatest integer function)
(B) The digit at 10's place of 3100
is (q) 0
(C) Let f(n) = 

n
1
k
2
k
n
2
C
.
k , then
250
)
5
(
f
= (r) 8
(D) The remainder when 22003
is divided by 17 is (s) 6
(t) 1
DPP No. – 03
Total Marks : 28 Max. Time : 32 min.
Single choice Objective ('–1' negative marking) Q.2, 3, 4, 7 (3 marks 3 min.) [12, 12]
Subjective Questions ('–1' negative marking) Q.1, 5, 6, 8 (4 marks 5 min.) [16, 20]
Ques. No. 1 2 3 4 5 6 7 8 Total
Mark obtained
1. How many 3–digit odd numbers can be formed using the digits 1, 2, 3, 4, 5, 6 if
(i) The repetition of digits is not allowed? (ii) The repetition of digits is allowed?
2. Two cards are drawn one at a time & without replacement from a pack of 52 card. The number of ways in
which the two cards can be drawn, are
(A) 2652 (B) 2704 (C) 2500 (D) none of these
3. In a class there are 30 boys and 18 girls. The teacher wants to select one boy and one girl to represent the
class for a quiz competition, the number of ways in which the teacher make this selection, are
(A) 30! × 18! (B) 48! (C) 540 (D) none of these
4. All possible three digit even numbers which can be formed with the condition that if 5 is one of the digit, then
7 is the next digit, is
(A) 5 (B) 325 (C) 345 (D) 365
5. A library has two books each having three copies and three other books each having two copies. In how
many ways can all these books be arranged in a shelf so that copies of the same book are not
seperated?
6. How many 10 digit numbers can be made with odd digits so that no two consecutive digits are same.
7. The sum of all the four digit numbers that can be formed using the digits 1, 2, 3, 4 if repetition of digits is
allowed, is
(A) 399996 (B) 388840 (C) 711040 (D) none of these
8. In how many ways can the letters of the word ‘CINEMA’ be arranged so that order of vowels do not change.
Answer Keys DPP # 54
1. B 2. D 3. C 4. D
5. (A)  (r) ; (B)  (q); (C)  (r); (D)  (r)
Answer Keys DPP # 55
1. A, B, C 2. C, D 3. (i) 24 (ii) 576 (iii) 360
4. (i) 120 (ii) 40 (iii) 40 (iv) 80 (v) 20
5. 468000 6. 25 7. (A)  (t) ; (B)  (q) ; (C)  (p) ; (D)  (r)
Answer Keys DPP # 56
1. 60, 108 2. A 3. C 4. D 5. 120
6. 5.49 7. C 8. 120
PART TEST-3 (PT-3) SYLLABUS
CHEMISTRY
• Gaseous State
• Chemical Equilibrium
• Chemical Bonding (MOT, vanderwaals force and metallic bond)
• Mole Concept-2 (Till Taught)
• DPP No. 40 to 63
MATHEMATICS
• Straight line
• Circle
• Binomial Theorem
• Permutation & Combination
• DPP No. 40 to 56
PHYSICS
• Work Power and Energy
• Circular Motion
• Centre of Mass
• Rigid Body Dynamics (up to Moment of Inertia)
• DPP No. 40 to 60

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DPP-54-56-PC

  • 1. DAILY PRACTICE PROBLEMS Subject : Mathematics Date : DPP No. : Class : XI Course : DPP No. – 01 Total Marks : 20 Max. Time : 20 min. Single choice Objective ('–1' negative marking) Q.1, 2, 3, 4 (3 marks 3 min.) [12, 12] Match the Following (no negative marking) (2 × 4) Q.5 (8 marks 8 min.) [8, 8] Ques. No. 1 2 3 4 5 Total Mark obtained 1. Difference between the maximum value of 11 Cp and maximum value of 10 Cq is (A) 11 C4 (B) 10 C6 (C) 11 C5 (D) 10 C5 2. The value of 2 3 2n 2n 2n 2n 1 2 3 n n n n n 1 10 10 10 10 – C C – C ..... 81 81 81 81 81    is (A) 2 (B) 0 (C) 1/2 (D) 1 3. The coefficient of a8 b4 c9 d9 in (abc + abd + acd + bcd)10 is (A) 10 ! (B) ! 9 ! 9 ! 4 ! 8 ! 10 (C) 2520 (D) none of these 4. If Cr = 10 Cr for r = 1, 2, 3, ...., 10, then 1.2 C1 + 2.3 C2 + ........9.10 C9 = (A) 130.28 (B) 130. 28 – 1 (C) 130. 28 + 10 (D) 130. 28 – 110 5. Match the column : Column-I Column-II (A) Last digit of (2227)2227 is (p) 1 (B) Last digit of 33 27 ) 38 ( is (q) 2 (C) Number of rational terms in the expansion of (r) 3  20 5 / 1 3 2  are (D) When 6n – 5n + 2 is divided by 25 remainder is, where n  N (s) 4 (t) 5 DPP No. – 02 Total Marks : 34 Max. Time : 36 min. Multiple choice objective ('–1' negative marking) Q.1, 2 (5 marks 4 min.) [10, 8] Subjective Questions ('–1' negative marking) Q.3, 4, 5, 6 (4 marks 5 min.) [16, 20] Match the Following (no negative marking) (2 × 4) Q.7 (8 marks 8 min.) [8, 8] Ques. No. 1 2 3 4 5 6 7 Total Mark obtained 1. For all values of , the lines represented by the equation (2 cos + 3 sin ) x + (3 cos – 5 sin ) y – (5 cos – 2 sin ) = 0 (A) pass through a fixed point (B) vertex of the system is (1, 1) (C) pass through the origin if tan  = 2 5 (D) the line 3x – 4y = 3 is one of the member of the family 54
  • 2. 2. Let (1 + x2)2 (1 + x)n =    4 n 0 k k k x a . If a1 , a2 , a3 are in A.P., then a value of n is (A) 1 (B) 2 (C) 3 (D) 4 3. There are 6 roads between A & B and 4 roads between B & C. (i) In how many ways can one drive from A to C by way of B? (ii) In how many ways can one drive from A to C and back to A, passing through B on both trips? (iii) In how many ways can one drive the circular trip described in (ii) without using the same road more than once 4. If repetitions are not allowed (i) How many 3-digit numbers can be formed from the six digits 2, 3, 5, 6, 7 and 9. (ii) How many of these are less than 400? (iii) Howmany are even? (iv) How many are odd? (v) How many are multiples of 5? 5. How many car number plates can be made if each plate contains 2 different letters of english alphabet, followed by 3 different digits. 6. How many numbers divisible by 5 and lying between 4000 and 5000 can be formed from the digits 4, 5, 6, 7 and 8 (Repetition of digits is allowed). 7. Column - I Column - II (A) If in the expansion of 5 x tan x x 1        , the ratio of 4th (p) 7 term to the 2nd term is 27 2 4 , the value of [x] can be (where [.] is greatest integer function) (B) The digit at 10's place of 3100 is (q) 0 (C) Let f(n) =   n 1 k 2 k n 2 C . k , then 250 ) 5 ( f = (r) 8 (D) The remainder when 22003 is divided by 17 is (s) 6 (t) 1 DPP No. – 03 Total Marks : 28 Max. Time : 32 min. Single choice Objective ('–1' negative marking) Q.2, 3, 4, 7 (3 marks 3 min.) [12, 12] Subjective Questions ('–1' negative marking) Q.1, 5, 6, 8 (4 marks 5 min.) [16, 20] Ques. No. 1 2 3 4 5 6 7 8 Total Mark obtained 1. How many 3–digit odd numbers can be formed using the digits 1, 2, 3, 4, 5, 6 if (i) The repetition of digits is not allowed? (ii) The repetition of digits is allowed? 2. Two cards are drawn one at a time & without replacement from a pack of 52 card. The number of ways in which the two cards can be drawn, are (A) 2652 (B) 2704 (C) 2500 (D) none of these 3. In a class there are 30 boys and 18 girls. The teacher wants to select one boy and one girl to represent the class for a quiz competition, the number of ways in which the teacher make this selection, are (A) 30! × 18! (B) 48! (C) 540 (D) none of these
  • 3. 4. All possible three digit even numbers which can be formed with the condition that if 5 is one of the digit, then 7 is the next digit, is (A) 5 (B) 325 (C) 345 (D) 365 5. A library has two books each having three copies and three other books each having two copies. In how many ways can all these books be arranged in a shelf so that copies of the same book are not seperated? 6. How many 10 digit numbers can be made with odd digits so that no two consecutive digits are same. 7. The sum of all the four digit numbers that can be formed using the digits 1, 2, 3, 4 if repetition of digits is allowed, is (A) 399996 (B) 388840 (C) 711040 (D) none of these 8. In how many ways can the letters of the word ‘CINEMA’ be arranged so that order of vowels do not change. Answer Keys DPP # 54 1. B 2. D 3. C 4. D 5. (A)  (r) ; (B)  (q); (C)  (r); (D)  (r) Answer Keys DPP # 55 1. A, B, C 2. C, D 3. (i) 24 (ii) 576 (iii) 360 4. (i) 120 (ii) 40 (iii) 40 (iv) 80 (v) 20 5. 468000 6. 25 7. (A)  (t) ; (B)  (q) ; (C)  (p) ; (D)  (r) Answer Keys DPP # 56 1. 60, 108 2. A 3. C 4. D 5. 120 6. 5.49 7. C 8. 120
  • 4. PART TEST-3 (PT-3) SYLLABUS CHEMISTRY • Gaseous State • Chemical Equilibrium • Chemical Bonding (MOT, vanderwaals force and metallic bond) • Mole Concept-2 (Till Taught) • DPP No. 40 to 63 MATHEMATICS • Straight line • Circle • Binomial Theorem • Permutation & Combination • DPP No. 40 to 56 PHYSICS • Work Power and Energy • Circular Motion • Centre of Mass • Rigid Body Dynamics (up to Moment of Inertia) • DPP No. 40 to 60