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

Question # 1

The coefficient of x¹⁰in the expansion (x³+3/x²)¹⁰is

1700 A
17023 B
17027 C
17010 D

Question # 2

The middle term in the expansion of (a +x)¹²is

7th A
8th B
9th C
6th D

Question # 3

If n € N , then n(n+3) is always

Multiple of 3 A
Multiple of 6 B
odd C
even D

Question # 4

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 # 5

For≥ -2 , 1+3+5+......+(2n+5)

(n+2)² A
(n-2)² B
2n+1 C
(n+3)² D

Question # 6

If a statement S(n) is true for n = 1 and the truth of S(n) for n = k implies the truth of S(n) for = k + 1, then S(n) is true for all

Real numbers n A
Integers n B
Positive integers n C
None of these D

Question # 7

ⁿC₂= exists when n is ______

A
B
C
D

Question # 8

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

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

Question # 9

The 7th term of (3⁸ + 6⁴x)^11/4 is

-19217/3 x⁶ A
189/2 6⁴x B
2227/12 x³ C
-19712/3 x⁶ D

Question # 10

If the sum of co-efficient in the expansion of (a+b)ⁿis 4096, then the greatest co-efficient in the expansion is

1594 A
792 B
924 C
2924 D

Question # 11

The expansion (1 + x)^-3holds when

|x| > 1 A
|x| < 1 B
x < 1 C
x > 1 D

Question # 12

When we expand (a + 2b)⁵then

a⁵+ 10a⁴b + 40a³b²+ 80a²b³+ 80ab⁴+ 32b⁵ A
a⁵+ a⁴b + a³b²+ a²b³+ ab⁴+ b⁵ B
5a⁵+ 4a⁴b + 3a³b²+ 2a²b³+ 1 ab⁴+ b⁵ C
None D

Question # 13

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

84a³ b⁶ A
22a³b⁶ B
27a⁴b⁵ C
28a³b⁶ D

Question # 14

The first three terms in the expansion of (1 + x)³are

1 + 3x +6x² A
1- 3x + 6x²\ B
-3 -3x -6x² C
1- 3x -6x² D

Question # 15

The middle term(s) of (a+x)11 is

6th term A
6thor 7th B
7th term C
6thand7th D

Question # 16

For every positive integers n 1+5+9+....+ (4n - 3) is

n(2n - 1) A
(2n - 1) B
n - 1 C
n D

Question # 17

In the expansion of (x+y)n the coefficient of 5th and 12th terms are equal then n=

12 A
n=14 B
17 C
n=15 D

Question # 18

If n is any positive integer then n! > 2^n-1for

A
B
C
D

Question # 19

The 8th term of (1+2x) ^-1/2is

-221/16 x⁷ A
-225/18 x⁷ B
-407/9 x³ C
-429/16 x⁷ D

Question # 20

(0.90)^1/2is equal to

0.99 A
0.90 B
0.80 C
0.88 D

Question # 21

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

A
B
C
D

Question # 22

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

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

Question # 23

For each natural number n, n (n+1) is

an even A
an odd B
multiple of 3 C
Irrational D

Question # 24

The middle term of [1/x-x]¹⁰is

-152 A
-252 B
371 C
-421 D

Question # 25

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

A
B
C
D

Question # 26

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 # 27

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 # 28

The last term of (1+2x)-2

(-1)-2 (2x)-2 A
(-1)-4(-2x)-2 B
(-1)-3(2x)-3 C
Does not exist D

Question # 29

If (1+x)ⁿ=C₀+ C₁x +C₂x²+ ......+C_nx¹then C₀C₂+ C₁C₃+ C₂C₄+ .....+C_n-2C_n=

A
B
C
D

Question # 30

The term involving x⁴ in the expansion (3-2x) is

217x⁴ A
15120x⁴ B
313x⁴ C
-25x⁴ D

Sr.#	Question	Answer
1	If n € N , then n(n+3) is always	A. Multiple of 3 B. Multiple of 6 C. odd D. even
2	(51)⁴is equal to	A. 7065201 B. 8065201 C. 6765201 D. 6565201
3	The 8th term of (1+2x) ^-1/2is	A. -221/16 x⁷ B. -225/18 x⁷ C. -407/9 x³ D. -429/16 x⁷
4	(x³-1/2x)⁶is	A. 15/16 x² B. 2/13 x² C. 17/7 x² D. 16/15 x²
5		A. 2 and 9 B. 3 and 2 C. 2/3 and 9 D. 3/2 and 6
6	The term involving x⁴ in the expansion (3-2x) is	A. 217x⁴ B. 15120x⁴ C. 313x⁴ D. -25x⁴
7	The number of terms in the expansion of (a + x)¹²is	A. 13 B. 12 C. 11 D. 10
8	The sum of the coefficient in the expansion of (a + x)⁵is	A. 32 B. 16 C. 8 D. 5
9	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
10	If \| x \| < 1, then the first two terms of (1 - x)^1/2are

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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 coefficient of x10in the expansion (x3+3/x2)10is

The middle term in the expansion of (a +x)12is

If n € N , then n(n+3) is always

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

For≥ -2 , 1+3+5+......+(2n+5)

If a statement S(n) is true for n = 1 and the truth of S(n) for n = k implies the truth of S(n) for = k + 1, then S(n) is true for all

nC2= exists when n is ______

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

The 7th term of (38 + 64x)11/4 is

If the sum of co-efficient in the expansion of (a+b)nis 4096, then the greatest co-efficient in the expansion is

The expansion (1 + x)-3holds when

When we expand (a + 2b)5then

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

The first three terms in the expansion of (1 + x)3are

The middle term(s) of (a+x)11 is

For every positive integers n 1+5+9+....+ (4n - 3) is

In the expansion of (x+y)n the coefficient of 5th and 12th terms are equal then n=

If n is any positive integer then n! > 2n-1for

The 8th term of (1+2x) -1/2is

(0.90)1/2is equal to

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

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

For each natural number n, n (n+1) is

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

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

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

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

The last term of (1+2x)-2

If (1+x)n=C0+ C1x +C2x2+ ......+Cnx1then C0C2+ C1C3+ C2C4+ .....+Cn-2Cn=

The term involving x4 in the expansion (3-2x) is

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