Question # 1

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

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9

6

5

10

The fifteenth term of (3-a)¹⁵ is

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-17a¹²

-945a¹³

-941a¹³

-515a¹²

The exponent of x in 10th term in the expansion of (a+x)n

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10

12

11

9

The first three terms in the expansion of (1 - x)^-2are

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1 - 2x + 3x²

1 - 2x - 3x²

1 + 2x + 3x²

-2 - 2x +3x²

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

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n - 1

n + 1

n + 2

n + 3

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

(0.90)^1/2is equal to

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0.99

0.90

0.80

0.88

If n is any positive integer then n! > n²for

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The number of terms in the expansion of (a + b)⁹is

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10

11

9

12

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

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

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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

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

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1700

17023

17027

17010

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

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0

1

-1

None

The middle term of [1/x-x]¹⁰is

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-152

-252

371

-421

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Even

Odd

Prime

None of these

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Imaginary

Rational

Irrational

Real numbers

The proposition S(k+1) is true when ______ is true∀K∈N

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S(n)

S(k)

S(1)

S(k-1)

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

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(1+x)-3

(1-x)-2

(1-x)-3

(1+x)-2

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

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)

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ⁿC_r

ⁿ⁺¹C_r+1

ⁿC_r+1

None

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

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1st term

4th term

2nd term

5th term

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

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n+1

n-1

n

n-2

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

ⁿC₂= exists when n is ______

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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

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405 / 256

504 / 259

450 / 263

None

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

7²ⁿ+ 3^n-1. 2^3n-3is divisible by

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24

25

9

13

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