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

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

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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 sum of even coefficients in the expansion of (1+x)n is 128 then

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n=7

n=9

n=8

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 coefficient of the third term of (8a-b)^1/3, after simplification is

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-228

1/288

1/220

-1/177

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

The coefficient of x¹⁰in the expansion (x³+3/x²)¹⁰is

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1700

17023

17027

17010

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

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

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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 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

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ab=-1

ab = 1

ab = 2

None

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

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0

1

-1

None

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 expansion (1 + x)^-3holds when

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|x| > 1

|x| < 1

x < 1

x > 1

For≥ -2 , 1+3+5+......+(2n+5)

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(n+2)²

(n-2)²

2n+1

(n+3)²

The middle term(s) of (a+x)11 is

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6th term

6thor 7th

7th term

6thand7th

If (1+x-2x³)⁶= 1+a₁x + a₂x²+ a₃x³+ ..... the the value of a₂+ a₄+ a₆+ .....+a₁₂will be

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32

31

64

1024

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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¹⁰C₆

¹⁰C₅

¹⁰C₄

None

In the expansion of (x+y)n the coefficient of 5th and 12th terms are equal then n=

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12

n=14

17

n=15

(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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Even

Odd

Prime

None of these

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 3 + 6 + 9 + ....+ 3n = ______

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

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295

495

395

722

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 middle term of [1/x-x]¹⁰is

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-152

-252

371

-421

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