Question # 1

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

The proposition S(k+1) is true when ______ is true∀K∈N

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S(n)

S(k)

S(1)

S(k-1)

The greatest integer which divides the number 101¹⁰⁰- 1 is

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100

1000

10000

100000

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

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

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13

12

11

10

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3/8

7/8

1/8

None

The no of term is the expansion of (a+x)n-1 is

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n+1

n-1

n

n-2

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

(1 + 2x)⁴= ______

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1 + 4x + 6x²+ 4x³+ x⁴

1 - 4x + 6x²- 4x³+ x⁴

1 - 8x + 24x²- 32x³+ 16x⁴

1 + 8x+ 24x²+ 32x³+ 16x⁴

Digit in the unit place of the number 183! + 3¹⁸³

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7

6

3

0

The coefficient of x¹⁸ in (ax⁴-bx)⁹ after expansion is

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84a³ b⁶

22a³b⁶

27a⁴b⁵

28a³b⁶

If x+y+z+......+2n = 2n+1-1∀n∈W,then cube root of xyz is equal to

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1

4

2

8

If n is any positive integer then 2ⁿ> 2(n + 1) is true for all

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

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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

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

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n - 1

n + 1

n + 2

n + 3

The proposition S(n) is true∀n∈N,S(k+1) true when ______is true

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S(1)

Both a & c

S(k)

None

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

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The sum of even coefficient in the binomial expansion is

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2ⁿ⁺¹

2ⁿ

2^n-1

2n

(x3-1/x)12

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295

495

395

722

For every positive integers n 1+5+9+....+ (4n - 3) is

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n(2n - 1)

(2n - 1)

n - 1

n

If n is odd then the middle terms in the expansion of (a + x)ⁿare

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¹⁰C₆

¹⁰C₅

¹⁰C₄

None

If n is any positive integer then 4ⁿ>3ⁿ+ 4 is true for all

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If n is any positive integer then n! > 2^n-1for

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

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1 + x + x²

1 - x - x²

-1 -x + x²

1 - x + x²

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

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2

7

8

12

If n € N , then n(n+3) is always

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Multiple of 3

Multiple of 6

odd

even

For each natural number n, n (n+1) is

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an even

an odd

multiple of 3

Irrational

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Mathematics ECAT Pre Engineering Chapter 10 Mathematical Inductions Online Test MCQs With Answers

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