Question # 1

In the expansion of (a + x)ⁿthe general term T_{r + 1}is

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n² - 1 divisible by 8 when n is

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an odd integer

an even integer

Irrational

Prime Number

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The positive integer just greater than (1+0.0001)¹⁰⁰⁰⁰is

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4

5

2

3

The first three terms in the expansion of (1 - x)^-3are

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1 + 3x + 6x²

1 - 3x + 6x²

-3 - 3x - 6x²

1 - 3x - 6x²

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405 / 256

504 / 259

450 / 263

None

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

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12

6

2

18

The sum of co-efficient in (1+x-3x²)⁴¹⁶³is

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0

1

-1

None

If in the expansion of (1+x)ⁿ, co-efficients of 2nd, 3rd and 4th terms are in A.P., then x=

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4

5

6

7

The 5th term of (3a-2b)^-1is

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77b²/a⁵

16b²/243 a⁵

17b⁴/43a⁵

25b³/43a⁵

a + x is ______

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A trinomial

A binomial

A monomial

None of these

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ab=-1

ab = 1

ab = 2

None

The first three terms in the expansion of (1 + x)³are

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1 + 3x +6x²

1- 3x + 6x²\

-3 -3x -6x²

1- 3x -6x²

If n is not natural number, then the expansion (1 + x)ⁿis valid for

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The middle term of [1/x-x]¹⁰is

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-152

-252

371

-421

(0.90)^1/2is equal to

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0.99

0.90

0.80

0.88

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

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S(k +1) is true

S(1) is true and S(k+1) is true whenever S (k) is true

S(k+1) is true whenever S (k) is true

S(k) is true

If n € N , then n(n+3) is always

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Multiple of 3

Multiple of 6

odd

even

If n is any positive integer ,t hen 2+4+6+......+2 n=

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2ⁿ-1

2ⁿ+1

n²+1

n(n+1)

(x³-1/2x)⁶is

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15/16 x²

2/13 x²

17/7 x²

16/15 x²

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Even

Odd

Prime

None of these

For all positive integral value of n,3ⁿ< n! , when

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n> 6

n< 6

n<11

n>11

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¹⁰C₆

¹⁰C₅

¹⁰C₄

None

The number of terms in the expansion of (a + b)⁹is

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10

11

9

12

If the exponent in the binomial expansion is 6, then the middle term is

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2nd term

3rd term

4th term

5th term

7²ⁿ+ 3^n-1. 2^3n-3is divisible by

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24

25

9

13

The greatest term in the expansion of (3+2x)⁹, when x=1 is

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4th

4th and 5th

5th

6th

The expansion of (1 - 3x)^-1is valid if

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| x | < 1

| x | < 3

| x | < 1/3

None of these

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

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(r-1)th term

(r+1)th term

rth term

none

If the exponent in the binomial expansion is 6, then the middle term is

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2nd

3rd

4th

5th

If n∈Z+ then(a+x)n is a/an

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Finite series

Convergent series

Infinite series

Divergent series

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

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