ECAT Pre General Science Mathematics Chapter 10 Mathematical Induction Online Test With Answers

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ECAT Pre General Science Mathematics Chapter 10 Mathematical Induction Online Test

Sr. # Questions Answers Choice
1 If the sum of co-efficient in the expansion of (a+b)nis 4096, then the greatest co-efficient in the expansion is 1594 792 924 2924
2 If the sum of co-efficient in the expansion of (a+b)nis 4096, then the greatest co-efficient in the expansion is 1594 792 924 2924
3 The positive integer just greater than (1+0.0001)10000is 4 5 2 3
4
5 2 and 9 3 and 2 2/3 and 9 3/2 and 6
6 28 / 81 28 / 243 81 / 28 243 / 82
7 405 / 256 504 / 259 450 / 263 None
8 <sup>10</sup>C<sub>6</sub> <sup>10</sup>C<sub>5</sub> <sup>10</sup>C<sub>4</sub> None
9 If in the expansion of (1+x)n, co-efficients of 2nd, 3rd and 4th terms are in A.P., then x= 4 5 6 7
10 The expansion of (1 - 3x)-1is valid if | x | &lt; 1 | x | &lt; 3 | x | &lt; 1/3 None of these
11 The expansion of (1 + 2x)-2is valed if | x | &lt; 1/2 | x | &lt; 1 | x | &lt; 2 | x | &lt; 3
12 If | x | < 1, then the first two terms of (1 - x)1/2are
13 8 9 10 11
14 If n is not natural number, then the expansion (1 + x)nis valid for
15 The sum of the even coefficients in the expansion (1 + x)nis n<sup>2</sup> 2<sup>n-2</sup> 2<sup>n-1</sup> 2<sup>n</sup>
16 If the exponent in the binomial expansion is 6, then the middle term is 2nd term 3rd term 4th term 5th term
17 The number of terms in the expansion of (a + x)12is 13 12 11 10
18 (1 - x)3= ______ 1 + 3x + 3x<sup>2</sup>+ x<sup>3</sup> 1 + x + x<sup>2</sup>+ x<sup>3</sup> 1 - x + x<sup>2</sup>- x<sup>3</sup> 1 - 3x + 3x<sup>2</sup>- x<sup>3</sup>
19 (1 + 2x)4= ______ 1 + 4x + 6x<sup>2</sup>+ 4x<sup>3</sup>+ x<sup>4</sup> 1 - 4x + 6x<sup>2</sup>- 4x<sup>3</sup>+ x<sup>4</sup> 1 - 8x + 24x<sup>2</sup>- 32x<sup>3</sup>+ 16x<sup>4</sup> 1 + 8x+ 24x<sup>2</sup>+ 32x<sup>3</sup>+ 16x<sup>4</sup>
20 If n is any positive integer then 2n> 2(n + 1) is true for all
21 If n is any positive integer then 4n>3n+ 4 is true for all
22 If n is any positive integer then 3 + 6 + 9 + ....+ 3n = ______
23 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
24 The middle term in the expansion of (a +x)12is 7th 8th 9th 6th
25 The sum of the coefficient in the expansion of (a + x)5is 32 16 8 5
26 The sum of the odd coefficients in the expansion of (a + x)4is 14 12 8 4
27 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
28 If n is odd then the middle terms in the expansion of (a + x)nare
29 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
30 The number of terms in the expansion of (a + b)9is 10 11 9 12
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