Question # 1

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

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If n is any positive integer then n! > n²for

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There is no integer n for which 3n is

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Even

Prime

Odd

Real

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

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¹⁰C₆

¹⁰C₅

¹⁰C₄

None

For≥ -2 , 1+3+5+......+(2n+5)

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(n+2)²

(n-2)²

2n+1

(n+3)²

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

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217 x4

15120x4

313x4

-25x4

The fifteenth term of (3-a)¹⁵ is

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-17a¹²

-945a¹³

-941a¹³

-515a¹²

for n€ N, 3^{2n + 7 is divisible by}

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7

8

9

10

(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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8

9

10

11

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The greatest integer which divides the number 101¹⁰⁰- 1 is

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100

1000

10000

100000

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n < 8/5

n < 5/8

|n| < 8/5

|n|>8/5

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

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n+1

n-1

n

n-2

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

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1700

17023

17027

17010

If x+y+z+......+2n = 2n+1-1∀n∈W,then cube root of xyz is equal to

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1

4

2

8

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

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

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

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an even

an odd

multiple of 3

Irrational

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 middle term of (x-y)⁸is

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25 x⁴y⁴

70 x⁴y⁴

120 x⁴y⁴

97x⁴y⁴

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

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84a³ b⁶

22a³b⁶

27a⁴b⁵

28a³b⁶

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2

7

8

12

1st four terms of the expansion (1-x)^-2are

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1 + 2x + 3x²+ 4x³

3x²+ 2x + 1

1 + 3x + 4x²+ 5x³

None of these

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

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2

3

4

5

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

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32

16

8

5

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

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

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

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6

3

4

8

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

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