Question # 1

There is no integer n for which 3ⁿis

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Odd

even

Natural

Prime

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2

7

8

12

For each even natural number n (n²-1) is divisible by

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6

3

4

8

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2 and 9

3 and 2

2/3 and 9

3/2 and 6

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

The middle term of the expansion (1 + 2x)⁶is ______

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1st term

4th term

2nd term

5th term

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ⁿC_r

ⁿ⁺¹C_r+1

ⁿC_r+1

None

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Even

Odd

Prime

None of these

for n€ N, 3^{2n + 7 is divisible by}

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7

8

9

10

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

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12

6

2

18

If the sum of co-efficient in the expansion of (a+b)ⁿis 4096, then the greatest co-efficient in the expansion is

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1594

792

924

2924

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

If n is any positive integer then n²> n + 3 for

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If n is any positive integer then n! > n²for

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The last term of (1+2x)-2

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(-1)-2 (2x)-2

(-1)-4(-2x)-2

(-1)-3(2x)-3

Does not exist

There are two middle terms in the expansion of (a+x)n if n is

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Even +ve integer

+ve integer

Odd +ve integer

All

The first three terms in the expansion of (1 + x)^-2are ______

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1 - 2x + 3x²

1 - 2x - 3x²

1 + 2x + 3x²

-2 -2x + 3x²

The greatest integer which divides the number 101¹⁰⁰- 1 is

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100

1000

10000

100000

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

Number of terms in the expansion of (a+x)ⁿis

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n - 1

n + 1

n + 2

n + 3

If n is add the expansion (a + x)ⁿhas middle terms

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2

3

4

5

1st four terms of the expansion (1-x)^-2are

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1 + 2x + 3x²+ 4x³

3x²+ 2x + 1

1 + 3x + 4x²+ 5x³

None of these

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

ⁿC₂= exists when n is ______

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If n∈Z+ then(a+x)n is a/an

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Finite series

Convergent series

Infinite series

Divergent series

In the expansion of (a + x)ⁿthe sum of exponents of a and x in each term of the expansion is

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n + 1

n - 1

n

2n

If (1+x)ⁿ=C₀+ C₁x +C₂x²+ ......+C_nx¹then C₀C₂+ C₁C₃+ C₂C₄+ .....+C_n-2C_n=

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The number of terms in the expansion of (a + x)¹²is

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13

12

11

10

The expansion of (1 + 2x)^-2is valed if

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| x | < 1/2

| x | < 1

| x | < 2

| x | < 3

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

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