ECAT Pre Engineering Mathematic MCQ Test With Answer for Chapter 10 (Mathematical Inductions)

MCQ's Test For ECAT (Pre-Eng) Mathematics Chapter 10 Mathematical Inductions

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ECAT (Pre-Eng) Mathematics Chapter 10 Mathematical Inductions

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Question # 1

The sum of first n even number is

Question # 2

There are two middle terms in the expansion of (a+x)n if n is

Question # 3

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

Question # 4

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

Question # 5

(x3-1/x)12

Question # 6

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

Question # 7

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

Question # 8

The sum of coefficients in the binomial expansion equals to

Question # 9

(1 - x)3= ______

Question # 10

(0.90)1/2is equal to

Question # 11

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

Question # 12

The sum of the even coefficients in the expansion (1 + x)nis

Question # 13

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

Question # 14

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

Question # 15

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

Question # 16

The coefficient of xn in the expansion of (1-2x)-1 is

Question # 17

If | x | < 1, then the first two terms of (1 - x)1/2are

Question # 18

The expansion of (1 + 2x)-2is valed if

Question # 19

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

Question # 20

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

Question # 21

(2.02)4 s equal to

Question # 22

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

Question # 23

If the 4th term in the expansion of (px + x-1)mis 2.5 for all x∈ R, then

Question # 24

72n+ 3n-1. 23n-3is divisible by

Question # 25

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

Question # 26

for n€ N, 32n + 7 is divisible by

Question # 27

If n∈Z+ then(a+x)n is a/an

Question # 28

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

Question # 29

The exponent of x in 10th term in the expansion of (a+x)n

Question # 30

If (1+x-2x3)6= 1+a1x + a2x2+ a3x3+ ..... the the value of a2+ a4+ a6+ .....+a12will be

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Sr.# Question Answer
1 The sum of the cubes of three consecutive natural number is divisible by
A. 9
B. 6
C. 5
D. 10
2
Question Image
3 If n is any positive integer then 2n> 2(n + 1) is true for all
4 The general term in the expansion of (a+x)n is
A. (r-1)th term
B. (r+1)th term
C. rth term
D. none
5 (51)4is equal to
A. 7065201
B. 8065201
C. 6765201
D. 6565201
6 n(n-1)(2n-1), for all natural numbers n, is divisible by
A. 12
B. 6
C. 2
D. 18
7 1+3x+6x2 +10x3 +....=
A. (1+x)-3
B. (1-x)-2
C. (1-x)-3
D. (1+x)-2
8 The middle term in the expansion of (a +x)12is
A. 7th
B. 8th
C. 9th
D. 6th
9 The sum of co-efficient in (1+x-3x2)4163is
A. 0
B. 1
C. -1
D. None
10 The last term of (1+2x)-2
A. (-1)-2 (2x)-2
B. (-1)-4(-2x)-2
C. (-1)-3(2x)-3
D. Does not exist

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