Question # 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 expansion (1 + x)^-3holds when

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|x| > 1

|x| < 1

x < 1

x > 1

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 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

a + x is ______

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A trinomial

A binomial

A monomial

None of these

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

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84a³ b⁶

22a³b⁶

27a⁴b⁵

28a³b⁶

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

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(2.02)4 s equal to

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16

16.6496

17

18

(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

The sum of even coefficient in the binomial expansion is

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2ⁿ⁺¹

2ⁿ

2^n-1

2n

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

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217 x4

15120x4

313x4

-25x4

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 coefficient of the second term of (a+b)⁴ is

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1

9

3

5

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

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0

1

-1

None

The 7th term of (3⁸ + 6⁴x)^11/4 is

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-19217/3 x⁶

189/2 6⁴x

2227/12 x³

-19712/3 x⁶

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

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an even

an odd

multiple of 3

Irrational

For≥ -2 , 1+3+5+......+(2n+5)

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(n+2)²

(n-2)²

2n+1

(n+3)²

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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If the expansion of (1 + x)²⁰, then co-efficient of rth ad (r + 4)th term are equal, then r is

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7

8

9

10

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

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9

6

5

10

The greatest integer which divides the number 101¹⁰⁰- 1 is

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100

1000

10000

100000

The middle term of [1/x-x]¹⁰is

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-152

-252

371

-421

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8

9

10

11

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

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14

12

8

4

The number of terms in the expansion of (a + x)¹²is

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13

12

11

10

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405 / 256

504 / 259

450 / 263

None

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2

7

8

12

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¹⁰C₆

¹⁰C₅

¹⁰C₄

None

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

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32

16

8

5

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

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4013 x3a13

2208a13 x12

223x7a18

38080a13 x12

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Even

Odd

Prime

None of these

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