ECAT Mathematics MCQ's Test For Full Book With Answers

ECAT Mathematics MCQ's Test For Full Book

Sr. # Questions Answers Choice
1 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
2 The middle term in the expansion of (a +x)12is 7th 8th 9th 6th
3 The sum of the coefficient in the expansion of (a + x)5is 32 16 8 5
4 The sum of the odd coefficients in the expansion of (a + x)4is 14 12 8 4
5 The sum of even coefficient in the binomial expansion is 2<sup>n+1</sup> 2<sup>n</sup> 2<sup>n-1</sup> 2n
6 If n is odd then the middle terms in the expansion of (a + x)nare
7 In the expansion of (a + x)nthe sum of exponents of a and x in each term of the expansion is n + 1 n - 1 n 2n
8 The number of terms in the expansion of (a + b)9is 10 11 9 12
9 If the exponent in the binomial expansion is 6, then the middle term is 2nd 3rd 4th 5th
10 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>
11 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>
12 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>
13 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>
14 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>
15 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>
16 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>
17 Even Odd Prime None of these
18 2 7 8 12
19 In the expansion of (a + x)nthe general term Tr + 1is
20 a + x is ______ A trinomial A binomial A monomial None of these
21 If n is any positive integer then n! > n2for
22 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
23 If n is any positive integer then n2> n + 3 for
24 If n is any positive integer then n! > 2n-1for
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27 5 10 20 30
28
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30 The probability to get an odd number in a dice thrown once is 1/2 1/6 1/3 2
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