Practice Test: Binomial Theorem, Class 11, Mathematics JEE Notes | EduRev

JEE : Practice Test: Binomial Theorem, Class 11, Mathematics JEE Notes | EduRev

 Page 1


 
 
 
BINOMIAL  THEOREM 
(WORKSHEET) 
OBJECTIVE 
1. If the (r + 1)th term in the expansion of 
21
3
3
a
b
b
a
?
?
?
?
?
?
?
?
+ has the same power of a and b, then the 
value 
(A) 9 (B) 10 
(C) 8 (D) 6 
2. In the expansion of 
6
x
1
x ?
?
?
?
?
?
- , the constant term is 
(A) – 20 (B) 20 
(C) 30 (D) – 30 
3. In the expansion of 
10
2
x
3
2
x
?
?
?
?
?
?
- , the coefficient of x
4
 is 
(A) 
256
405
 (B) 
259
504
 
(C) 
263
450
 (D) None of these 
4. If in the expansion of (1 + x)
m
 (1 – x)
n
, the coefficient of x and x
2
 are 3 & – 6 respectively, then m is 
(A) 6 (B) 9 
(C) 12 (D) 24 
5. Coefficients of x
r
 [0 = r = (n – 1)] in the expansion of 
(x + 3)
n – 1
 + (x + 3)
n – 2
 (x + 2) + (x + 3)
n – 3
 (x + 2)
2
 + …… + (x + 2)
n – 1
 
(A) 
n
C
r
 (3
r
 – 2
n
) (B) 
n
C
r
 (3
n – r
 – 2
n – r
) 
(C) 
n
C
r
 (3
r
 + 2
n – r
) (D) None of these 
6. Find the value of 
64 32 . 3 . 6 16 . 9 . 15 8 . 27 . 20 4 . 81 . 15 2 . 243 . 6 3
) 25 . 7 . 18 . 3 7 18 (
6
3 3
+ + + + + +
+ +
 
(A) 1 (B) 5 
(C) 25 (D) 100 
7. The expression 
1 x 4
1
+
 
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
+ +
7
2
1 x 4 1
 – 
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
+ -
7
2
1 x 4 1
 is a polynomial in x of degree 
GIITJEE (GURUS  FOR  IITJEE) SCO 382, Sector 37–D, Chandigarh, Ph. 0172–2628810, 2628811, 2628820 P – 1 
 
Page 2


 
 
 
BINOMIAL  THEOREM 
(WORKSHEET) 
OBJECTIVE 
1. If the (r + 1)th term in the expansion of 
21
3
3
a
b
b
a
?
?
?
?
?
?
?
?
+ has the same power of a and b, then the 
value 
(A) 9 (B) 10 
(C) 8 (D) 6 
2. In the expansion of 
6
x
1
x ?
?
?
?
?
?
- , the constant term is 
(A) – 20 (B) 20 
(C) 30 (D) – 30 
3. In the expansion of 
10
2
x
3
2
x
?
?
?
?
?
?
- , the coefficient of x
4
 is 
(A) 
256
405
 (B) 
259
504
 
(C) 
263
450
 (D) None of these 
4. If in the expansion of (1 + x)
m
 (1 – x)
n
, the coefficient of x and x
2
 are 3 & – 6 respectively, then m is 
(A) 6 (B) 9 
(C) 12 (D) 24 
5. Coefficients of x
r
 [0 = r = (n – 1)] in the expansion of 
(x + 3)
n – 1
 + (x + 3)
n – 2
 (x + 2) + (x + 3)
n – 3
 (x + 2)
2
 + …… + (x + 2)
n – 1
 
(A) 
n
C
r
 (3
r
 – 2
n
) (B) 
n
C
r
 (3
n – r
 – 2
n – r
) 
(C) 
n
C
r
 (3
r
 + 2
n – r
) (D) None of these 
6. Find the value of 
64 32 . 3 . 6 16 . 9 . 15 8 . 27 . 20 4 . 81 . 15 2 . 243 . 6 3
) 25 . 7 . 18 . 3 7 18 (
6
3 3
+ + + + + +
+ +
 
(A) 1 (B) 5 
(C) 25 (D) 100 
7. The expression 
1 x 4
1
+
 
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
+ +
7
2
1 x 4 1
 – 
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
+ -
7
2
1 x 4 1
 is a polynomial in x of degree 
GIITJEE (GURUS  FOR  IITJEE) SCO 382, Sector 37–D, Chandigarh, Ph. 0172–2628810, 2628811, 2628820 P – 1 
 
(A) 7 (B) 5 
(C) 4 (D) 3 
8. The coefficients of three successive terms in the expansion of (1 + x)
n
 are 165, 330 and 462 
respectively, then the value of n will be 
(A) 11 (B) 10 
(C) 12 (D) 8 
9. If T
0
, T
1
, T
2
, ……, T
n
 represent the terms in the expansion of (x + a)
n
, then 
(T
0
 – T
2
 + T
4
 – ….)
2
 + (T
1
 – T
3
 + T
5
 – …..)
2
 = 
(A) (x
2
 + a
2
) (B) (x
2
 + a
2
)
n
 
(C) (x
2
 + a
2
)
1/n
 (D) (x
2
 + a
2
)
– 1/n
 
10. 
10
C
1
 + 
10
C
3
 + 
10
C
5
 + 
10
C
7
 + 
10
C
9
 = 
(A) 2
9
 (B) 2
10
 
(C) 2
10
 – 1 (D) None of these 
11. 
! ) 1 n ( ! 1
1
-
 + 
! ) 3 n ( ! 3
1
-
 + 
! ) 5 n ( ! 5
1
-
 + ….. = 
(A) 
! n
2
n
 ; for all even values of n 
(B) 
! n
2
1 n -
 ; for all values of n i.e. all even odd values 
(C) 0      (D) None of these 
12. 
?
=
10
0 k
k
20
C = 
(A) 2
19
 + 
2
1
 
20
C
10
 (B) 2
19
 
(C) 
20
C
10
 (D) None of these 
13. The sum of all the coefficients in the binomial expansion of (x
2
 + x – 3)
319
 is 
(A) 1 (B) 2 
(C) – 1 (D) 0 
14. If the sum of the coefficients in the expansion of (x – 2y + 3z)
n
 is 128, then the greatest coefficient in 
the expansion of (1 + x)
n
 is 
(A) 35 (B) 20 
(C) 10 (D) None of these 
GIITJEE (GURUS  FOR  IITJEE) SCO 382, Sector 37–D, Chandigarh, Ph. 0172–2628810, 2628811, 2628820 P – 2 
 
Page 3


 
 
 
BINOMIAL  THEOREM 
(WORKSHEET) 
OBJECTIVE 
1. If the (r + 1)th term in the expansion of 
21
3
3
a
b
b
a
?
?
?
?
?
?
?
?
+ has the same power of a and b, then the 
value 
(A) 9 (B) 10 
(C) 8 (D) 6 
2. In the expansion of 
6
x
1
x ?
?
?
?
?
?
- , the constant term is 
(A) – 20 (B) 20 
(C) 30 (D) – 30 
3. In the expansion of 
10
2
x
3
2
x
?
?
?
?
?
?
- , the coefficient of x
4
 is 
(A) 
256
405
 (B) 
259
504
 
(C) 
263
450
 (D) None of these 
4. If in the expansion of (1 + x)
m
 (1 – x)
n
, the coefficient of x and x
2
 are 3 & – 6 respectively, then m is 
(A) 6 (B) 9 
(C) 12 (D) 24 
5. Coefficients of x
r
 [0 = r = (n – 1)] in the expansion of 
(x + 3)
n – 1
 + (x + 3)
n – 2
 (x + 2) + (x + 3)
n – 3
 (x + 2)
2
 + …… + (x + 2)
n – 1
 
(A) 
n
C
r
 (3
r
 – 2
n
) (B) 
n
C
r
 (3
n – r
 – 2
n – r
) 
(C) 
n
C
r
 (3
r
 + 2
n – r
) (D) None of these 
6. Find the value of 
64 32 . 3 . 6 16 . 9 . 15 8 . 27 . 20 4 . 81 . 15 2 . 243 . 6 3
) 25 . 7 . 18 . 3 7 18 (
6
3 3
+ + + + + +
+ +
 
(A) 1 (B) 5 
(C) 25 (D) 100 
7. The expression 
1 x 4
1
+
 
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
+ +
7
2
1 x 4 1
 – 
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
+ -
7
2
1 x 4 1
 is a polynomial in x of degree 
GIITJEE (GURUS  FOR  IITJEE) SCO 382, Sector 37–D, Chandigarh, Ph. 0172–2628810, 2628811, 2628820 P – 1 
 
(A) 7 (B) 5 
(C) 4 (D) 3 
8. The coefficients of three successive terms in the expansion of (1 + x)
n
 are 165, 330 and 462 
respectively, then the value of n will be 
(A) 11 (B) 10 
(C) 12 (D) 8 
9. If T
0
, T
1
, T
2
, ……, T
n
 represent the terms in the expansion of (x + a)
n
, then 
(T
0
 – T
2
 + T
4
 – ….)
2
 + (T
1
 – T
3
 + T
5
 – …..)
2
 = 
(A) (x
2
 + a
2
) (B) (x
2
 + a
2
)
n
 
(C) (x
2
 + a
2
)
1/n
 (D) (x
2
 + a
2
)
– 1/n
 
10. 
10
C
1
 + 
10
C
3
 + 
10
C
5
 + 
10
C
7
 + 
10
C
9
 = 
(A) 2
9
 (B) 2
10
 
(C) 2
10
 – 1 (D) None of these 
11. 
! ) 1 n ( ! 1
1
-
 + 
! ) 3 n ( ! 3
1
-
 + 
! ) 5 n ( ! 5
1
-
 + ….. = 
(A) 
! n
2
n
 ; for all even values of n 
(B) 
! n
2
1 n -
 ; for all values of n i.e. all even odd values 
(C) 0      (D) None of these 
12. 
?
=
10
0 k
k
20
C = 
(A) 2
19
 + 
2
1
 
20
C
10
 (B) 2
19
 
(C) 
20
C
10
 (D) None of these 
13. The sum of all the coefficients in the binomial expansion of (x
2
 + x – 3)
319
 is 
(A) 1 (B) 2 
(C) – 1 (D) 0 
14. If the sum of the coefficients in the expansion of (x – 2y + 3z)
n
 is 128, then the greatest coefficient in 
the expansion of (1 + x)
n
 is 
(A) 35 (B) 20 
(C) 10 (D) None of these 
GIITJEE (GURUS  FOR  IITJEE) SCO 382, Sector 37–D, Chandigarh, Ph. 0172–2628810, 2628811, 2628820 P – 2 
 
15. If (1 + x – 2x
2
)
6
 = 1 + a
1
x + a
2
x
2
 + …… + a
12
x
12
, then the expression a
2
 + a
4
 + a
6
 + …. + a
12
 has the 
value 
(A) 32 (B) 63 
(C) 64 (D) 31 
16. If the sum of the coefficients in the expansion of ( a
2
x
2
 – 2ax + 1)
51
 vanishes, then the value of a is 
(A) 2 (B) – 1 
(C) 1 (D) – 2 
17. The value of the sum of the series 3 . 
n
C
0
 – 8 
n
C
1
 + 13 
n
C
2
 – 18 
n
C
3
 + ….. 
(A) 0 (B) 3
n
 
(C) 5
n
 (D) None of these 
18. The value of  2C
0
 + 
2
2
2
 C
1
 + 
3
2
3
 C
2
 + 
4
2
4
 C
3
 + ….. + 
11
2
11
 C
10
  is 
(A) 
11
1 3
11
-
 (B) 
11
1 2
11
-
 
(C) 
11
1 11
3
-
 (D) 
11
1 11
2
-
 
19. If x + y = 1, then 
?
=
n
0 r
r 
n
C
r
 x
r
 y
n – r
  equals 
(A) 1 (B) n 
(C) nx (D) ny 
20. The coefficient of x
5
 in the expansion of (1 + x)
21
 + (1 + x)
22
 + ….. + (1 + x)
30
 is 
(A) 
51
C
5
 (B) 
9
C
5
 
(C) 
31
C
6
 – 
21
C
6
 (D) 
30
C
5
 + 
20
C
5
 
21. The coefficient of t
24
 in the expansion of (1 + t
2
)
12
 (1 + t
12
) (1 + t
24
) is 
(A) 
12
C
6
 + 2 (B) 
12
C
5
 
(C) 
12
C
6
 (D) 
12
C
7
 
22. The sum of the coefficients of even power of x in the expansion of (1 + x + x
2
 + x
3
)
5
 is 
(A) 256 (B) 128 
(C) 512 (D) 64 
23. If C
0
, C
1
, C
2
, …..,C
n
 are the binomial coefficients, then 2.C
1
 + 2
3
.C
3
 + 2
5
 C
5
 + ….. equals 
(A) 
2
) 1 ( 3
n n
- +
 (B) 
2
) 1 ( 3
n n
- -
 
GIITJEE (GURUS  FOR  IITJEE) SCO 382, Sector 37–D, Chandigarh, Ph. 0172–2628810, 2628811, 2628820 P – 3 
 
Page 4


 
 
 
BINOMIAL  THEOREM 
(WORKSHEET) 
OBJECTIVE 
1. If the (r + 1)th term in the expansion of 
21
3
3
a
b
b
a
?
?
?
?
?
?
?
?
+ has the same power of a and b, then the 
value 
(A) 9 (B) 10 
(C) 8 (D) 6 
2. In the expansion of 
6
x
1
x ?
?
?
?
?
?
- , the constant term is 
(A) – 20 (B) 20 
(C) 30 (D) – 30 
3. In the expansion of 
10
2
x
3
2
x
?
?
?
?
?
?
- , the coefficient of x
4
 is 
(A) 
256
405
 (B) 
259
504
 
(C) 
263
450
 (D) None of these 
4. If in the expansion of (1 + x)
m
 (1 – x)
n
, the coefficient of x and x
2
 are 3 & – 6 respectively, then m is 
(A) 6 (B) 9 
(C) 12 (D) 24 
5. Coefficients of x
r
 [0 = r = (n – 1)] in the expansion of 
(x + 3)
n – 1
 + (x + 3)
n – 2
 (x + 2) + (x + 3)
n – 3
 (x + 2)
2
 + …… + (x + 2)
n – 1
 
(A) 
n
C
r
 (3
r
 – 2
n
) (B) 
n
C
r
 (3
n – r
 – 2
n – r
) 
(C) 
n
C
r
 (3
r
 + 2
n – r
) (D) None of these 
6. Find the value of 
64 32 . 3 . 6 16 . 9 . 15 8 . 27 . 20 4 . 81 . 15 2 . 243 . 6 3
) 25 . 7 . 18 . 3 7 18 (
6
3 3
+ + + + + +
+ +
 
(A) 1 (B) 5 
(C) 25 (D) 100 
7. The expression 
1 x 4
1
+
 
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
+ +
7
2
1 x 4 1
 – 
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
+ -
7
2
1 x 4 1
 is a polynomial in x of degree 
GIITJEE (GURUS  FOR  IITJEE) SCO 382, Sector 37–D, Chandigarh, Ph. 0172–2628810, 2628811, 2628820 P – 1 
 
(A) 7 (B) 5 
(C) 4 (D) 3 
8. The coefficients of three successive terms in the expansion of (1 + x)
n
 are 165, 330 and 462 
respectively, then the value of n will be 
(A) 11 (B) 10 
(C) 12 (D) 8 
9. If T
0
, T
1
, T
2
, ……, T
n
 represent the terms in the expansion of (x + a)
n
, then 
(T
0
 – T
2
 + T
4
 – ….)
2
 + (T
1
 – T
3
 + T
5
 – …..)
2
 = 
(A) (x
2
 + a
2
) (B) (x
2
 + a
2
)
n
 
(C) (x
2
 + a
2
)
1/n
 (D) (x
2
 + a
2
)
– 1/n
 
10. 
10
C
1
 + 
10
C
3
 + 
10
C
5
 + 
10
C
7
 + 
10
C
9
 = 
(A) 2
9
 (B) 2
10
 
(C) 2
10
 – 1 (D) None of these 
11. 
! ) 1 n ( ! 1
1
-
 + 
! ) 3 n ( ! 3
1
-
 + 
! ) 5 n ( ! 5
1
-
 + ….. = 
(A) 
! n
2
n
 ; for all even values of n 
(B) 
! n
2
1 n -
 ; for all values of n i.e. all even odd values 
(C) 0      (D) None of these 
12. 
?
=
10
0 k
k
20
C = 
(A) 2
19
 + 
2
1
 
20
C
10
 (B) 2
19
 
(C) 
20
C
10
 (D) None of these 
13. The sum of all the coefficients in the binomial expansion of (x
2
 + x – 3)
319
 is 
(A) 1 (B) 2 
(C) – 1 (D) 0 
14. If the sum of the coefficients in the expansion of (x – 2y + 3z)
n
 is 128, then the greatest coefficient in 
the expansion of (1 + x)
n
 is 
(A) 35 (B) 20 
(C) 10 (D) None of these 
GIITJEE (GURUS  FOR  IITJEE) SCO 382, Sector 37–D, Chandigarh, Ph. 0172–2628810, 2628811, 2628820 P – 2 
 
15. If (1 + x – 2x
2
)
6
 = 1 + a
1
x + a
2
x
2
 + …… + a
12
x
12
, then the expression a
2
 + a
4
 + a
6
 + …. + a
12
 has the 
value 
(A) 32 (B) 63 
(C) 64 (D) 31 
16. If the sum of the coefficients in the expansion of ( a
2
x
2
 – 2ax + 1)
51
 vanishes, then the value of a is 
(A) 2 (B) – 1 
(C) 1 (D) – 2 
17. The value of the sum of the series 3 . 
n
C
0
 – 8 
n
C
1
 + 13 
n
C
2
 – 18 
n
C
3
 + ….. 
(A) 0 (B) 3
n
 
(C) 5
n
 (D) None of these 
18. The value of  2C
0
 + 
2
2
2
 C
1
 + 
3
2
3
 C
2
 + 
4
2
4
 C
3
 + ….. + 
11
2
11
 C
10
  is 
(A) 
11
1 3
11
-
 (B) 
11
1 2
11
-
 
(C) 
11
1 11
3
-
 (D) 
11
1 11
2
-
 
19. If x + y = 1, then 
?
=
n
0 r
r 
n
C
r
 x
r
 y
n – r
  equals 
(A) 1 (B) n 
(C) nx (D) ny 
20. The coefficient of x
5
 in the expansion of (1 + x)
21
 + (1 + x)
22
 + ….. + (1 + x)
30
 is 
(A) 
51
C
5
 (B) 
9
C
5
 
(C) 
31
C
6
 – 
21
C
6
 (D) 
30
C
5
 + 
20
C
5
 
21. The coefficient of t
24
 in the expansion of (1 + t
2
)
12
 (1 + t
12
) (1 + t
24
) is 
(A) 
12
C
6
 + 2 (B) 
12
C
5
 
(C) 
12
C
6
 (D) 
12
C
7
 
22. The sum of the coefficients of even power of x in the expansion of (1 + x + x
2
 + x
3
)
5
 is 
(A) 256 (B) 128 
(C) 512 (D) 64 
23. If C
0
, C
1
, C
2
, …..,C
n
 are the binomial coefficients, then 2.C
1
 + 2
3
.C
3
 + 2
5
 C
5
 + ….. equals 
(A) 
2
) 1 ( 3
n n
- +
 (B) 
2
) 1 ( 3
n n
- -
 
GIITJEE (GURUS  FOR  IITJEE) SCO 382, Sector 37–D, Chandigarh, Ph. 0172–2628810, 2628811, 2628820 P – 3 
 
(C) 
2
1 3
n
+
 (D) 
2
1 3
n
-
 
24. The value of 
?
?
?
?
?
?
?
?
0
30
 
?
?
?
?
?
?
?
?
10
30
 – 
?
?
?
?
?
?
?
?
1
30
?
?
?
?
?
?
?
?
11
30
 + 
?
?
?
?
?
?
?
?
2
30
?
?
?
?
?
?
?
?
12
30
 + ….. + 
?
?
?
?
?
?
?
?
20
30
?
?
?
?
?
?
?
?
30
30
 
(A) 
60
C
20
 (B) 
30
C
10
 
(C) 
60
C
30
 (D) 
40
C
30
 
25. The value of 
20
C
0
 + 
20
C
1
 + 
20
C
2
 + 
20
C
3
 + 
20
C
4
 + 
20
C
12
 + 
20
C
13
 + 
20
C
14
 + 
20
C
15
 equal to 
(A) 2
19
 – 
2
) C C (
9
20
10
20
+
 (B) 2
19
 – 
2
) C 2 C (
9
20
10
20
× +
 
(C) 2
19
 – 
2
C
10
20
 (D) None of these 
 
 
ANSWERS 
(OBJECTIVE) 
1. A 
2. A 
3. A 
4. C 
5. B 
6. A 
7. D 
8. A 
9. B 
10. A 
11. B 
12. A 
13. C 
14. A 
15. D 
16. C 
17. A 
18. A 
19. C 
20. C 
21. A 
22. C 
23. B 
24. B 
25. B 
 
GIITJEE (GURUS  FOR  IITJEE) SCO 382, Sector 37–D, Chandigarh, Ph. 0172–2628810, 2628811, 2628820 P – 4 
 
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