Question # 1

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

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

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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 proposition S(n) is true∀n∈N,S(k+1) true when ______is true

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S(1)

Both a & c

S(k)

None

When we expand (a + 2b)⁵then

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a⁵+ 10a⁴b + 40a³b²+ 80a²b³+ 80ab⁴+ 32b⁵

a⁵+ a⁴b + a³b²+ a²b³+ ab⁴+ b⁵

5a⁵+ 4a⁴b + 3a³b²+ 2a²b³+ 1 ab⁴+ b⁵

None

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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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ab=-1

ab = 1

ab = 2

None

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

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a + x is ______

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A trinomial

A binomial

A monomial

None of these

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

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2nd

3rd

4th

5th

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

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n - 1

n + 1

n + 2

n + 3

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 third term in the expansion of (1+2x) is

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-2x2

-4x2

2x2

4x2

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 expansion of (1 - 3x)^-1is valid if

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| x | < 1

| x | < 3

| x | < 1/3

None of these

Digit in the unit place of the number 183! + 3¹⁸³

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7

6

3

0

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

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

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-221/16 x⁷

-225/18 x⁷

-407/9 x³

-429/16 x⁷

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

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n+1

n-1

n

n-2

(x³-1/2x)⁶is

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15/16 x²

2/13 x²

17/7 x²

16/15 x²

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

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84a³ b⁶

22a³b⁶

27a⁴b⁵

28a³b⁶

If n is any positive integer ,t hen 2+4+6+......+2 n=

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2ⁿ-1

2ⁿ+1

n²+1

n(n+1)

The term involving x⁴in the expansion of (3 - 2x)⁷is

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120

1512

1250

15120

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3/8

7/8

1/8

None

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

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217x⁴

15120x⁴

313x⁴

-25x⁴

If n is any positive integer then n²> n + 3 for

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

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6

3

4

8

for n€ N, 3^{2n + 7 is divisible by}

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7

8

9

10

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ⁿC_r

ⁿ⁺¹C_r+1

ⁿC_r+1

None

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

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6th term

6thor 7th

7th term

6thand7th

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Imaginary

Rational

Irrational

Real numbers

(1 + 2x)⁴= ______

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1 + 4x + 6x²+ 4x³+ x⁴

1 - 4x + 6x²- 4x³+ x⁴

1 - 8x + 24x²- 32x³+ 16x⁴

1 + 8x+ 24x²+ 32x³+ 16x⁴

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

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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

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