Question # 1

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ⁿC_r

ⁿ⁺¹C_r+1

ⁿC_r+1

None

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3/8

7/8

1/8

None

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 + 2x)^-2is valed if

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| x | < 1/2

| x | < 1

| x | < 2

| x | < 3

If n is any positive integer then n! > 2^n-1for

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

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12

6

2

18

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

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1700

17023

17027

17010

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 8th term of (1+2x) ^-1/2is

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-221/16 x⁷

-225/18 x⁷

-407/9 x³

-429/16 x⁷

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

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

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4th

4th and 5th

5th

6th

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

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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

There is no integer n for which 3n is

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Even

Prime

Odd

Real

The expansion (1 + x)^-3holds when

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|x| > 1

|x| < 1

x < 1

x > 1

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405 / 256

504 / 259

450 / 263

None

If n € N , then n(n+3) is always

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Multiple of 3

Multiple of 6

odd

even

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

For n€ N,2^n>2 > n is to only when

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n<2

n≤ 4

n≥ 4

The sum of the odd coefficients in the expansion of (a + x)⁴is

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14

12

8

4

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

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

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(x3-1/x)12

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295

495

395

722

If a statement S(n) is true for n = i where i is some natural number and the truth of S(n) for n = k > i implies the truth of S(n) for n = k +1 then S(n) is true for all positive integers

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The term independent of x is the expansion (x³+1/x)¹²

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295

495

395

722

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

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n - 1

n + 1

n + 2

n + 3

a + x is ______

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A trinomial

A binomial

A monomial

None of these

In the expansion of (a + x)ⁿthe general term T_{r + 1}is

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(0.90)^1/2is equal to

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0.99

0.90

0.80

0.88

The sum of first n even number is

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n2

n(n+1)

n+1

n+2

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

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32

16

8

5

(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

7²ⁿ+ 3^n-1. 2^3n-3is divisible by

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24

25

9

13

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

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1st term

4th term

2nd term

5th term

The middle term of (x-y)⁸is

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25 x⁴y⁴

70 x⁴y⁴

120 x⁴y⁴

97x⁴y⁴

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