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 For each natural number n, n (n+1) is an even an odd multiple of 3 Irrational
2 There is no integer n for which 3n is Odd even Natural Prime
3 If n is add the expansion (a + x)nhas middle terms 2 3 4 5
4 The middle term of the expansion (1 + 2x)6is ______ 1st term 4th term 2nd term 5th term
5 The expansion (1 + x)-3holds when |x| > 1 |x| < 1 x < 1 x > 1
6 1st four terms of the expansion (1-x)-2are 1 + 2x + 3x<sup>2</sup>+ 4x<sup>3</sup> 3x<sup>2</sup>+ 2x + 1 1 + 3x + 4x<sup>2</sup>+ 5x<sup>3</sup> None of these
7 nC2= exists when n is ______
8 n &lt; 8/5 n &lt; 5/8 |n| &lt; 8/5 |n|&gt;8/5
9 Number of terms in the expansion of (a+x)nis n - 1 n + 1 n + 2 n + 3
10 Imaginary Rational Irrational Real numbers
11 (0.90)1/2is equal to 0.99 0.90 0.80 0.88
12
13 (0.90)1/2is equal to 0.99 0.90 0.80 0.88
14 The term involving x4in the expansion of (3 - 2x)7is 120 1512 1250 15120
15 (51)4is equal to 7065201 8065201 6765201 6565201
16 72n+ 3n-1. 23n-3is divisible by 24 25 9 13
17 (2.02)4 s equal to 16 16.6496 17 18
18 When we expand (a + 2b)5then a<sup>5</sup>+ 10a<sup>4</sup>b + 40a<sup>3</sup>b<sup>2</sup>+ 80a<sup>2</sup>b<sup>3</sup>+ 80ab<sup>4</sup>+ 32b<sup>5</sup> a<sup>5</sup>+ a<sup>4</sup>b + a<sup>3</sup>b<sup>2</sup>+ a<sup>2</sup>b<sup>3</sup>+ ab<sup>4</sup>+ b<sup>5</sup> 5a<sup>5</sup>+ 4a<sup>4</sup>b + 3a<sup>3</sup>b<sup>2</sup>+ 2a<sup>2</sup>b<sup>3</sup>+ 1 ab<sup>4</sup>+ b<sup>5</sup> None
19 For every positive integers n 1+5+9+....+ (4n - 3) is n(2n - 1) (2n - 1) n - 1 n
20 3/8 7/8 1/8 None
21 <sup>n</sup>C<sub>r</sub> <sup>n+1</sup>C<sub>r+1</sub> <sup>n</sup>C<sub>r+1</sub> None
22 If (1+x-2x3)6= 1+a1x + a2x2+ a3x3+ ..... the the value of a2+ a4+ a6+ .....+a12will be 32 31 64 1024
23 The greatest integer which divides the number 101100- 1 is 100 1000 10000 100000
24 If (1+x)n=C0+ C1x +C2x2+ ......+Cnx1then C0C2+ C1C3+ C2C4+ .....+Cn-2Cn=
25 ab=-1 ab = 1 ab = 2 None
26 If the 4th term in the expansion of (px + x-1)mis 2.5 for all x∈ R, then
27 The greatest term in the expansion of (3+2x)9, when x=1 is 4th 4th and 5th 5th 6th
28 The sum of co-efficient in (1+x-3x2)4163is 0 1 -1 None
29 Digit in the unit place of the number 183! + 3183 7 6 3 0
30 If the expansion of (1 + x)20, then co-efficient of rth ad (r + 4)th term are equal, then r is 7 8 9 10
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