Question # 1

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 | x | < 1, then the first two terms of (1 - x)^1/2are

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

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1700

17023

17027

17010

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

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32

16

8

5

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28 / 81

28 / 243

81 / 28

243 / 82

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3/8

7/8

1/8

None

(0.90)^1/2is equal to

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0.99

0.90

0.80

0.88

(x³-1/2x)⁶is

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15/16 x²

2/13 x²

17/7 x²

16/15 x²

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 a statement S(n) is true for n = i where i is some natural number and the truth of S(n) for n = k > i implies the truth of S(n) for n = k +1 then S(n) is true for all positive integers

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(2.02)4 s equal to

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16

16.6496

17

18

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

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n - 1

n + 1

n + 2

n + 3

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

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n+1

n-1

n

n-2

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

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12

6

2

18

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

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6

3

4

8

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

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2nd

3rd

4th

5th

ⁿC₂= exists when n is ______

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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 greatest integer which divides the number 101¹⁰⁰- 1 is

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100

1000

10000

100000

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

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84a³ b⁶

22a³b⁶

27a⁴b⁵

28a³b⁶

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

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If n is not natural number, then the expansion (1 + x)ⁿis valid for

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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

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)³are

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1 + 3x +6x²

1- 3x + 6x²\

-3 -3x -6x²

1- 3x -6x²

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

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217x⁴

15120x⁴

313x⁴

-25x⁴

The middle term of (x-y)⁸is

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25 x⁴y⁴

70 x⁴y⁴

120 x⁴y⁴

97x⁴y⁴

for n€ N, 3^{2n + 7 is divisible by}

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7

8

9

10

a + x is ______

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A trinomial

A binomial

A monomial

None of these

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

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295

495

395

722

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2

7

8

12

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

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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

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