ECAT Pre General Science MCQ Test With Answer for Mathematics Chapter 10

Question # 1

The sum of even coefficient in the binomial expansion is

2ⁿ⁺¹ A
2ⁿ B
2^n-1 C
2n D

Question # 2

The sum even binomial coefficient of (3+2x)5 is ______term

16 A
30 B
8 C
32 D

Question # 3

1+3x+6x2 +10x3 +....=

(1+x)-3 A
(1-x)-2 B
(1-x)-3 C
(1+x)-2 D

Question # 4

1st four terms of the expansion (1-x)^-2are

1 + 2x + 3x²+ 4x³ A
3x²+ 2x + 1 B
1 + 3x + 4x²+ 5x³ C
None of these D

Question # 5

If n is any positive integer then n²> n + 3 for

A
B
C
D

Question # 6

The proposition S(n) is true∀n∈N,S(k+1) true when ______is true

S(1) A
Both a & c B
S(k) C
None D

Question # 7

The first three terms in the expansion of (1 + x)^-2are ______

1 - 2x + 3x² A
1 - 2x - 3x² B
1 + 2x + 3x² C
-2 -2x + 3x² D

Question # 8

If n is not natural number, then the expansion (1 + x)ⁿis valid for

A
B
C
D

Question # 9

If in the expansion of (1+x)ⁿ, co-efficients of 2nd, 3rd and 4th terms are in A.P., then x=

4 A
5 B
6 C
7 D

Question # 10

In the expansion of (a + x)ⁿthe sum of exponents of a and x in each term of the expansion is

n + 1 A
n - 1 B
n C
2n D

Question # 11

(x3-1/x)12

295 A
495 B
395 C
722 D

Question # 12

(51)⁴is equal to

7065201 A
8065201 B
6765201 C
6565201 D

Question # 13

The seventh term of (x3+1/x)8is

71 A
-22 B
27 C
28 D

Question # 14

If n is odd then the middle terms in the expansion of (a + x)ⁿare

A
B
C
D

Question # 15

The term involving x⁴in the expansion of (3 - 2x)⁷is

120 A
1512 B
1250 C
15120 D

Question # 16

For all positive integral value of n,3ⁿ< n! , when

n> 6 A
n< 6 B
n<11 C
n>11 D

Question # 17

If n is add the expansion (a + x)ⁿhas middle terms

2 A
3 B
4 C
5 D

Question # 18

Number of terms in the expansion of (a+x)ⁿis

n - 1 A
n + 1 B
n + 2 C
n + 3 D

Question # 19

The third term in the expansion of (1+2x) is

-2x2 A
-4x2 B
2x2 C
4x2 D

Question # 20

If nis positive integers, then 2ⁿ>2n+1, only when

n≤ 3 A
n≥ 3 B
n≤ 2 C
n≤ 1 D

Question # 21

The proposition S(n) for any n∈ N is only true if k∈ N and

S(k +1) is true A
S(1) is true and S(k+1) is true whenever S (k) is true B
S(k+1) is true whenever S (k) is true C
S(k) is true D

Question # 22

The middle term of [1/x-x]¹⁰is

-152 A
-252 B
371 C
-421 D

Question # 23

The coefficient of x¹⁸ in (ax⁴-bx)⁹ after expansion is

84a³ b⁶ A
22a³b⁶ B
27a⁴b⁵ C
28a³b⁶ D

Question # 24

n! > 2ⁿ-1 is true when

n≤ 3 A
n≤ 6 B
n≥ 4 C
n≤ 6 D

Question # 25

If n is any positive integer then n! > n²for

A
B
C
D

Question # 26

The general term in the expansion of (a+x)n is

(r-1)th term A
(r+1)th term B
rth term C
none D

Question # 27

If n is any positive integer ,t hen 2+4+6+......+2 n=

2ⁿ-1 A
2ⁿ+1 B
n²+1 C
n(n+1) D

Question # 28

If the exponent in the binomial expansion is 6, then the middle term is

2nd term A
3rd term B
4th term C
5th term D

Question # 29

The sum of the cubes of three consecutive natural number is divisible by

9 A
6 B
5 C
10 D

Question # 30

The fifteenth term of (3-a)¹⁵ is

-17a¹² A
-945a¹³ B
-941a¹³ C
-515a¹² D

Sr.#	Question	Answer
1	If n is any positive integer ,t hen 2+4+6+......+2 n=	A. 2ⁿ-1 B. 2ⁿ+1 C. n²+1 D. n(n+1)
2	In the expansion of (a + x)ⁿthe sum of exponents of a and x in each term of the expansion is	A. n + 1 B. n - 1 C. n D. 2n
3	The first three terms in the expansion of (1 - x)^-1are	A. 1 + x + x² B. 1 - x - x² C. -1 -x +x² D. 1 - x + x²
4		A. Imaginary B. Rational C. Irrational D. Real numbers
5	The 8th term of (1+2x) ^-1/2is	A. -221/16 x⁷ B. -225/18 x⁷ C. -407/9 x³ D. -429/16 x⁷
6	(x3-1/x)12	A. 295 B. 495 C. 395 D. 722
7	The middle term of [1/x-x]¹⁰is	A. -152 B. -252 C. 371 D. -421
8	For n€ N,2^n>2 > n is to only when	A. n<2 B. n≤ 4 C. n≥ 4
9	The term involving x4 the expansion (3-2x)7 is	A. 217 x4 B. 15120x4 C. 313x4 D. -25x4
10	If the sum of co-efficient in the expansion of (a+b)ⁿis 4096, then the greatest co-efficient in the expansion is	A. 1594 B. 792 C. 924 D. 2924

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ECAT Pre General Science MCQ Test With Answer for Mathematics Chapter 10

MCQ's Test For ECAT Mathematics Chapter 10 Mathematical Induction

ECAT Mathematics Chapter 10 Mathematical Induction

The sum of even coefficient in the binomial expansion is

The sum even binomial coefficient of (3+2x)5 is ______term

1+3x+6x2 +10x3 +....=

1st four terms of the expansion (1-x)-2are

If n is any positive integer then n2> n + 3 for

The proposition S(n) is true∀n∈N,S(k+1) true when ______is true

The first three terms in the expansion of (1 + x)-2are ______

If n is not natural number, then the expansion (1 + x)nis valid for

If in the expansion of (1+x)n, co-efficients of 2nd, 3rd and 4th terms are in A.P., then x=

In the expansion of (a + x)nthe sum of exponents of a and x in each term of the expansion is

(x3-1/x)12

(51)4is equal to

The seventh term of (x3+1/x)8is

If n is odd then the middle terms in the expansion of (a + x)nare

The term involving x4in the expansion of (3 - 2x)7is

For all positive integral value of n,3n< n! , when

If n is add the expansion (a + x)nhas middle terms

Number of terms in the expansion of (a+x)nis

The third term in the expansion of (1+2x) is

If nis positive integers, then 2n>2n+1, only when

The proposition S(n) for any n∈ N is only true if k∈ N and

The middle term of [1/x-x]10 is

The coefficient of x18 in (ax4-bx)9 after expansion is

n! > 2n-1 is true when

If n is any positive integer then n! > n2for

The general term in the expansion of (a+x)n is

If n is any positive integer ,t hen 2+4+6+......+2 n=

If the exponent in the binomial expansion is 6, then the middle term is

The sum of the cubes of three consecutive natural number is divisible by

The fifteenth term of (3-a)15 is

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