Question # 1

If a statement S(n) is true for n = 1 and the truth of S(n) for n = k implies the truth of S(n) for = k + 1, then S(n) is true for all

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Real numbers n

Integers n

Positive integers n

None of these

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

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13

12

11

10

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 add the expansion (a + x)ⁿhas middle terms

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2

3

4

5

The exponent of x in 10th term in the expansion of (a+x)n

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10

12

11

9

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

The sum of first n even number is

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n2

n(n+1)

n+1

n+2

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

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n < 8/5

n < 5/8

|n| < 8/5

|n|>8/5

The sum of even coefficient in the binomial expansion is

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2ⁿ⁺¹

2ⁿ

2^n-1

2n

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)

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

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

The middle term of [1/x-x]¹⁰is

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-152

-252

371

-421

If nis positive integers, then 2ⁿ>2n+1, only when

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n≤ 3

n≥ 3

n≤ 2

n≤ 1

(1 - x)³= ______

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1 + 3x + 3x²+ x³

1 + x + x²+ x³

1 - x + x²- x³

1 - 3x + 3x²- x³

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¹⁰C₆

¹⁰C₅

¹⁰C₄

None

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

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n> 6

n< 6

n<11

n>11

If n∈Z+ then(a+x)n is a/an

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Finite series

Convergent series

Infinite series

Divergent series

The fifth term of (a+2x3)17 is

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4013 x3a13

2208a13 x12

223x7a18

38080a13 x12

For n€ N,2^n>2 > n is to only when

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n<2

n≤ 4

n≥ 4

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

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n - 1

n + 1

n + 2

n + 3

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

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2nd

3rd

4th

5th

The sum even binomial coefficient of (3+2x)5 is ______term

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16

30

8

32

The term independent of x is the expansion (x³+1/x)¹²

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295

495

395

722

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)

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

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If n is any positive integer then n! > n²for

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

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n+1

n-1

n

n-2

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

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4

5

2

3

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