Question # 1

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

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

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7th

8th

9th

6th

The number of terms in the expansion of (a + x)¹²is

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13

12

11

10

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

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The sum of co-efficient in (1+x-3x²)⁴¹⁶³is

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0

1

-1

None

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8

9

10

11

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

(1 - x)³= ______

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1 + 3x + 3x²+ x³

1 + x + x²+ x³

1 - x + x²- x³

1 - 3x + 3x²- x³

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

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217x⁴

15120x⁴

313x⁴

-25x⁴

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

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n+1

n-1

n

n-2

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

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4th

4th and 5th

5th

6th

The coefficient of the second term of (a+b)⁴ is

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1

9

3

5

The middle term of [1/x-x]¹⁰is

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-152

-252

371

-421

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

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12

6

2

18

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

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(1+x)-3

(1-x)-2

(1-x)-3

(1+x)-2

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

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an even

an odd

multiple of 3

Irrational

The greatest integer which divides the number 101¹⁰⁰- 1 is

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100

1000

10000

100000

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)

In the expansion of (a + x)ⁿthe sum of exponents of a and x in each term of the expansion is

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n + 1

n - 1

n

2n

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

If n is any positive integer then n! > n²for

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The sum of the cubes of three consecutive natural number is divisible by

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9

6

5

10

If n € N , then n(n+3) is always

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Multiple of 3

Multiple of 6

odd

even

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 (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

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 + 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

ⁿC₂= exists when n is ______

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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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