Question # 1

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

7²ⁿ+ 3^n-1. 2^3n-3is divisible by

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24

25

9

13

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ⁿC_r

ⁿ⁺¹C_r+1

ⁿC_r+1

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 x⁴in the expansion of (3 - 2x)⁷is

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120

1512

1250

15120

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

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12

6

2

18

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28 / 81

28 / 243

81 / 28

243 / 82

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

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

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n - 1

n + 1

n + 2

n + 3

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

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

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n≤ 3

n≥ 3

n≤ 2

n≤ 1

(1 - x)³= ______

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1 + 3x + 3x²+ x³

1 + x + x²+ x³

1 - x + x²- x³

1 - 3x + 3x²- x³

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

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-2x2

-4x2

2x2

4x2

For n€ N,2^n>2 > n is to only when

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n<2

n≤ 4

n≥ 4

If n is any positive integer then 4ⁿ>3ⁿ+ 4 is true for all

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The middle term of [1/x-x]¹⁰is

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-152

-252

371

-421

The sum of the even coefficients in the expansion (1 + x)ⁿis

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n²

2^n-2

2^n-1

2ⁿ

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

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

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

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n < 8/5

n < 5/8

|n| < 8/5

|n|>8/5

The fifth term of (a+2x3)17 is

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4013 x3a13

2208a13 x12

223x7a18

38080a13 x12

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

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0

1

-1

None

For all positive integral value of n,3ⁿ< n! , when

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n> 6

n< 6

n<11

n>11

The greatest integer which divides the number 101¹⁰⁰- 1 is

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100

1000

10000

100000

The coefficient of the third term of (8a-b)^1/3, after simplification is

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-228

1/288

1/220

-1/177

The sum of coefficients in the binomial expansion equals to

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2

2ⁿ⁺¹

2^n-1

2ⁿ

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

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1st term

4th term

2nd term

5th term

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

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7

6

3

0

The fifteenth term of (3-a)¹⁵ is

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-17a¹²

-945a¹³

-941a¹³

-515a¹²

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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Imaginary

Rational

Irrational

Real numbers

If in the expansion of (1+x)ⁿ, co-efficients of 2nd, 3rd and 4th terms are in A.P., then x=

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4

5

6

7

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

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6

3

4

8

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ab=-1

ab = 1

ab = 2

None

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

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