Mathematics ECAT Pre Engineering Chapter 10 Mathematical Inductions Online Test With Answers

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Mathematics ECAT Pre Engineering Chapter 10 Mathematical Inductions Online Test

Sr. # Questions Answers Choice
1 If the exponent in the binomial expansion is 6, then the middle term is 2nd 3rd 4th 5th
2 The first three terms in the expansion of (1 - x)-3are 1 + 3x + 6x<sup>2</sup> 1 - 3x + 6x<sup>2 </sup> -3 - 3x - 6x<sup>2</sup> 1 - 3x - 6x<sup>2</sup>
3 The first three terms in the expansion of (1 - x)-2are 1 - 2x + 3x<sup>2</sup> 1 - 2x - 3x<sup>2</sup> 1 + 2x + 3x<sup>2</sup> -2 - 2x +3x<sup>2</sup>
4 The first three terms in the expansion of (1 - x)-1are 1 + x + x<sup>2</sup> 1 - x - x<sup>2</sup> -1 -x +x<sup>2</sup> 1 - x + x<sup>2</sup>
5 The first three terms in the expansion of (1 + x)3are 1 + 3x +6x<sup>2</sup> 1- 3x + 6x<sup>2</sup>\ -3 -3x -6x<sup>2</sup> 1- 3x -6x<sup>2</sup>
6 The first three terms in the expansion of (1 + x)-2are ______ 1 - 2x + 3x<sup>2</sup> 1 - 2x - 3x<sup>2</sup> 1 + 2x + 3x<sup>2</sup> -2 -2x + 3x<sup>2</sup>
7 The first three terms in the expansion of (1 + x)-1are 1 + x + x<sup>2</sup> 1 - x - x<sup>2</sup> -1 -x + x<sup>2</sup> 1 - x + x<sup>2</sup>
8 The sum of coefficients in the binomial expansion equals to 2 2<sup>n+1</sup> 2<sup>n-1</sup> 2<sup>n</sup>
9 Even Odd Prime None of these
10 2 7 8 12
11 In the expansion of (a + x)nthe general term Tr + 1is
12 a + x is ______ A trinomial A binomial A monomial None of these
13 If n is any positive integer then n! > n2for
14 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 Integers n Positive integers n None of these
15 If n is any positive integer then n2> n + 3 for
16 If n is any positive integer then n! > 2n-1for
17 1+3x+6x2 +10x3 +....= (1+x)-3 (1-x)-2 (1-x)-3 (1+x)-2
18 The general term in the expansion of (a+x)n is (r-1)th term (r+1)th term rth term none
19 If the sum of even coefficients in the expansion of (1+x)n is 128 then n=7 n=9 n=8 None
20 The sum of first n even number is n2 n(n+1) n+1 n+2
21 The third term in the expansion of (1+2x) is -2x2 -4x2 2x2 4x2
22 If n∈Z+ then(a+x)n is a/an Finite series Convergent series Infinite series Divergent series
23 The proposition S(k+1) is true when ______ is true∀K∈N S(n) S(k) S(1) S(k-1)
24 If x+y+z+......+2n = 2n+1-1∀n∈W,then cube root of xyz is equal to 1 4 2 8
25 The exponent of x in 10th term in the expansion of (a+x)n 10 12 11 9
26 In the expansion of (x+y)n the coefficient of 5th and 12th terms are equal then n= 12 n=14 17 n=15
27 The last term of (1+2x)-2 (-1)-2 (2x)-2 (-1)-4(-2x)-2 (-1)-3(2x)-3 Does not exist
28 The no of term is the expansion of (a+x)n-1 is n+1 n-1 n n-2
29 There are two middle terms in the expansion of (a+x)n if n is Even +ve integer +ve integer Odd +ve integer All
30 The coefficient of xn in the expansion of (1-x)-1 is (-1)n2n 1 (-1)n(n+1) (n+1)
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