Question # 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

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n < 8/5

n < 5/8

|n| < 8/5

|n|>8/5

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

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n(2n - 1)

(2n - 1)

n - 1

n

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

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

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1700

17023

17027

17010

The 8th term of (1+2x) ^-1/2is

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-221/16 x⁷

-225/18 x⁷

-407/9 x³

-429/16 x⁷

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ⁿC_r

ⁿ⁺¹C_r+1

ⁿC_r+1

None

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

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1700

17023

17027

17010

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

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16

30

8

32

The middle term of (x-y)⁸is

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25 x⁴y⁴

70 x⁴y⁴

120 x⁴y⁴

97x⁴y⁴

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

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

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217x⁴

15120x⁴

313x⁴

-25x⁴

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

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

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32

16

8

5

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

For n€ N,2^n>2 > n is to only when

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n<2

n≤ 4

n≥ 4

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

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

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n> 6

n< 6

n<11

n>11

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

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

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

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

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The coefficient of xn in the expansion of (1-x)-1 is

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(-1)n2n

1

(-1)n(n+1)

(n+1)

n! > 2ⁿ-1 is true when

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n≤ 3

n≤ 6

n≥ 4

n≤ 6

(x³-1/2x)⁶is

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15/16 x²

2/13 x²

17/7 x²

16/15 x²

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 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 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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