Question # 1

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)

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

There is no integer n for which 3ⁿis

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Odd

even

Natural

Prime

If n is any positive integer then n! > 2^n-1for

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The greatest term in the expansion of (3+2x)⁹, when x=1 is

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4th

4th and 5th

5th

6th

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

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1st term

4th term

2nd term

5th term

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

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| x | < 1

| x | < 3

| x | < 1/3

None of these

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

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295

495

395

722

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405 / 256

504 / 259

450 / 263

None

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

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(1+x)-3

(1-x)-2

(1-x)-3

(1+x)-2

The sum of even coefficient in the binomial expansion is

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2ⁿ⁺¹

2ⁿ

2^n-1

2n

The term involving x4 the expansion (3-2x)7 is

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217 x4

15120x4

313x4

-25x4

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 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

If n is odd then the middle terms in the expansion of (a + x)ⁿare

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There is no integer n for which 3n is

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Even

Prime

Odd

Real

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

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12

6

2

18

If nis positive integers, then 2ⁿ>2n+1, only when

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n≤ 3

n≥ 3

n≤ 2

n≤ 1

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

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

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32

16

8

5

If n is add the expansion (a + x)ⁿhas middle terms

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2

3

4

5

For each natural number n, n (n+1) is

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an even

an odd

multiple of 3

Irrational

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

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7

6

3

0

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

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1700

17023

17027

17010

If n is any positive integer then 3 + 6 + 9 + ....+ 3n = ______

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The middle term in the expansion of (a +x)¹²is

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7th

8th

9th

6th

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

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71

-22

27

28

The sum of coefficients in the binomial expansion equals to

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2

2ⁿ⁺¹

2^n-1

2ⁿ

(x³-1/2x)⁶is

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15/16 x²

2/13 x²

17/7 x²

16/15 x²

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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