Question # 1

ⁿC₂= exists when n is ______

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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

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

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(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

(1 - x)³= ______

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1 + 3x + 3x²+ x³

1 + x + x²+ x³

1 - x + x²- x³

1 - 3x + 3x²- x³

The middle term of (x-y)⁸is

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25 x⁴y⁴

70 x⁴y⁴

120 x⁴y⁴

97x⁴y⁴

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 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

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

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| x | < 1

| x | < 3

| x | < 1/3

None of these

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

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10

12

11

9

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

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If the exponent in the binomial expansion is 6, then the middle term is

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2nd

3rd

4th

5th

(0.90)^1/2is equal to

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0.99

0.90

0.80

0.88

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

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9

6

5

10

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Even

Odd

Prime

None of these

The fifteenth term of (3-a)¹⁵ is

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-17a¹²

-945a¹³

-941a¹³

-515a¹²

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8

9

10

11

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

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1700

17023

17027

17010

The sum even binomial coefficient of (3+2x)5 is ______term

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16

30

8

32

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

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

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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

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

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n+1

n-1

n

n-2

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

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12

6

2

18

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

The positive integer just greater than (1+0.0001)¹⁰⁰⁰⁰is

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4

5

2

3

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

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1700

17023

17027

17010

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

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7

6

3

0

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2

7

8

12

a + x is ______

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A trinomial

A binomial

A monomial

None of these

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