Question # 1

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

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4013 x3a13

2208a13 x12

223x7a18

38080a13 x12

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

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

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16

30

8

32

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¹⁰C₆

¹⁰C₅

¹⁰C₄

None

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ⁿC_r

ⁿ⁺¹C_r+1

ⁿC_r+1

None

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

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1+3x+6x2 +10x3 +....=

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(1+x)-3

(1-x)-2

(1-x)-3

(1+x)-2

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

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n - 1

n + 1

n + 2

n + 3

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

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

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1st term

4th term

2nd term

5th term

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

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217x⁴

15120x⁴

313x⁴

-25x⁴

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

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The expansion of (1 + 2x)^-2is valed if

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| x | < 1/2

| x | < 1

| x | < 2

| x | < 3

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

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1700

17023

17027

17010

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

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77b²/a⁵

16b²/243 a⁵

17b⁴/43a⁵

25b³/43a⁵

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

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-221/16 x⁷

-225/18 x⁷

-407/9 x³

-429/16 x⁷

(0.90)^1/2is equal to

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0.99

0.90

0.80

0.88

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

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If a statement S(n) is true for n = 1 and the truth of S(n) for n = k implies the truth of S(n) for = k + 1, then S(n) is true for all

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Real numbers n

Integers n

Positive integers n

None of these

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

If n is odd then the middle terms in the expansion of (a + x)ⁿare

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for n€ N, 3^{2n + 7 is divisible by}

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7

8

9

10

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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405 / 256

504 / 259

450 / 263

None

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

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n≤ 3

n≥ 3

n≤ 2

n≤ 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

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Imaginary

Rational

Irrational

Real numbers

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

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13

12

11

10

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

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6th term

6thor 7th

7th term

6thand7th

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

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0

1

-1

None

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

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2

7

8

12

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 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 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 fifteenth term of (3-a)¹⁵ is

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-17a¹²

-945a¹³

-941a¹³

-515a¹²

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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