Question # 1

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

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(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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405 / 256

504 / 259

450 / 263

None

The 7th term of (3⁸ + 6⁴x)^11/4 is

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-19217/3 x⁶

189/2 6⁴x

2227/12 x³

-19712/3 x⁶

If the expansion of (1 + x)²⁰, then co-efficient of rth ad (r + 4)th term are equal, then r is

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7

8

9

10

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2

7

8

12

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 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 fifth term of (a+2x3)17 is

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4013 x3a13

2208a13 x12

223x7a18

38080a13 x12

The expansion (1 + x)^-3holds when

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|x| > 1

|x| < 1

x < 1

x > 1

7²ⁿ+ 3^n-1. 2^3n-3is divisible by

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24

25

9

13

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 xn in the expansion of (1-2x)-1 is

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(-1)n2n

2n

(-1)(n+1)xr

(n+1)2n

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 term involving x⁴ in the expansion (3-2x) is

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217x⁴

15120x⁴

313x⁴

-25x⁴

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 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

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

The sum of the coefficient in the expansion of (a + x)⁵is

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32

16

8

5

The middle term of (x-y)⁸is

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25 x⁴y⁴

70 x⁴y⁴

120 x⁴y⁴

97x⁴y⁴

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

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10

11

9

12

The coefficient of the second term of (a+b)⁴ is

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1

9

3

5

If the 4th term in the expansion of (px + x^-1)^mis 2.5 for all x∈ R, then

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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

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2 and 9

3 and 2

2/3 and 9

3/2 and 6

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

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1st term

4th term

2nd term

5th term

If n is any positive integer then n! > n²for

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The sum of the odd coefficients in the expansion of (a + x)⁴is

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14

12

8

4

The seventh term of (x3+1/x)8is

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71

-22

27

28

ⁿC₂= exists when n is ______

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