Question # 1

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

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

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an even

an odd

multiple of 3

Irrational

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ⁿC_r

ⁿ⁺¹C_r+1

ⁿC_r+1

None

If n € N , then n(n+3) is always

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Multiple of 3

Multiple of 6

odd

even

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

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| x | < 1

| x | < 3

| x | < 1/3

None of these

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

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1st term

4th term

2nd term

5th term

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28 / 81

28 / 243

81 / 28

243 / 82

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

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0

1

-1

None

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3/8

7/8

1/8

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

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

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

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12

6

2

18

The 5th term of (3a-2b)^-1is

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77b²/a⁵

16b²/243 a⁵

17b⁴/43a⁵

25b³/43a⁵

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

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32

16

8

5

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

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217x⁴

15120x⁴

313x⁴

-25x⁴

For≥ -2 , 1+3+5+......+(2n+5)

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(n+2)²

(n-2)²

2n+1

(n+3)²

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

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7

6

3

0

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

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6

3

4

8

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 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

The middle term(s) of (a+x)11 is

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6th term

6thor 7th

7th term

6thand7th

If n is any positive integer then n! > n²for

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

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295

495

395

722

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

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1700

17023

17027

17010

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

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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

If the sum of co-efficient in the expansion of (a+b)ⁿis 4096, then the greatest co-efficient in the expansion is

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1594

792

924

2924

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

(0.90)^1/2is equal to

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0.99

0.90

0.80

0.88

If the sum of co-efficient in the expansion of (a+b)ⁿis 4096, then the greatest co-efficient in the expansion is

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1594

792

924

2924

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

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10

11

9

12

The middle term of (x-y)⁸is

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25 x⁴y⁴

70 x⁴y⁴

120 x⁴y⁴

97x⁴y⁴

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n < 8/5

n < 5/8

|n| < 8/5

|n|>8/5

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

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