Question # 1

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

(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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3/8

7/8

1/8

None

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

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16

30

8

32

ⁿC₂= exists when n is ______

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ⁿC_r

ⁿ⁺¹C_r+1

ⁿC_r+1

None

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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

1+3x+6x2 +10x3 +....=

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(1+x)-3

(1-x)-2

(1-x)-3

(1+x)-2

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

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4013 x3a13

2208a13 x12

223x7a18

38080a13 x12

If n € N , then n(n+3) is always

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Multiple of 3

Multiple of 6

odd

even

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

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

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The sum of the even coefficients in the expansion (1 + x)ⁿis

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n²

2^n-2

2^n-1

2ⁿ

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

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Imaginary

Rational

Irrational

Real numbers

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405 / 256

504 / 259

450 / 263

None

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 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

The sum of first n even number is

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n2

n(n+1)

n+1

n+2

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

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1700

17023

17027

17010

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Even

Odd

Prime

None of these

For n€ N,2^n>2 > n is to only when

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n<2

n≤ 4

n≥ 4

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

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2nd term

3rd term

4th term

5th term

The fifteenth term of (3-a)¹⁵ is

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-17a¹²

-945a¹³

-941a¹³

-515a¹²

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 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

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