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

MCQ's Test For ECAT Mathematics Chapter 10 Mathematical Induction

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ECAT Mathematics Chapter 10 Mathematical Induction

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Question # 1

The no of term is the expansion of (a+x)n-1 is

Question # 2

The coefficient of xn in the expansion of (1-x)-1 is

Question # 3

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

Question # 4

n! > 2n-1 is true when

Question # 5

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

Question # 6

If n is any positive integer then 2n> 2(n + 1) is true for all

Question # 7

(0.90)1/2is equal to

Question # 8

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

Question # 9

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

Question # 10

If n is any positive integer then n! > n2for

Question # 11

If the sum of even coefficients in the expansion of (1+x)n is 128 then

Question # 12

n(n-1)(2n-1), for all natural numbers n, is divisible by

Question # 13

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

Question # 14

In the expansion of (a + x)nthe general term Tr + 1is

Question # 15

The number of terms in the expansion of (a + x)12is

Question # 16

nC2= exists when n is ______

Question # 17

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

Question # 18

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

Question # 19

The greatest term in the expansion of (3+2x)9, when x=1 is

Question # 20

The expansion (1 + x)-3holds when

Question # 21

The term independent of x is the expansion (x3+1/x)12

Question # 22

(1 + 2x)4= ______

Question # 23

The sum of co-efficient in (1+x-3x2)4163is

Question # 24

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

Question # 25

The sum of coefficients in the binomial expansion equals to

Question # 26

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

Question # 27

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

Question # 28

If a statement S(n) is true for n = i where i is some natural number and the truth of S(n) for n = k > i implies the truth of S(n) for n = k +1 then S(n) is true for all positive integers

Question # 29

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

Question # 30

If the expansion of (1 + x)20, then co-efficient of rth ad (r + 4)th term are equal, then r is

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ECAT Mathematics Chapter 10 Important MCQ's

Sr.# Question Answer
1
Question Image
A. 2
B. 7
C. 8
D. 12
2 When we expand (a + 2b)5then
A. a5+ 10a4b + 40a3b2+ 80a2b3+ 80ab4+ 32b5
B. a5+ a4b + a3b2+ a2b3+ ab4+ b5
C. 5a5+ 4a4b + 3a3b2+ 2a2b3+ 1 ab4+ b5
D. None
3 If | x | < 1, then the first two terms of (1 - x)1/2are
4 nC2= exists when n is ______
5 The proposition S(n) is true∀n∈N,S(k+1) true when ______is true
A. S(1)
B. Both a & c
C. S(k)
D. None
6 1+3x+6x2 +10x3 +....=
A. (1+x)-3
B. (1-x)-2
C. (1-x)-3
D. (1+x)-2
7 The sum of even coefficient in the binomial expansion is
A. 2n+1
B. 2n
C. 2n-1
D. 2n
8 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
A. Real numbers n
B. Integers n
C. Positive integers n
D. None of these
9 The middle term of the expansion (1 + 2x)6is ______
A. 1st term
B. 4th term
C. 2nd term
D. 5th term
10 The term involving x4 in the expansion (3-2x) is
A. 217x4
B. 15120x4
C. 313x4
D. -25x4

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