Question # 1

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

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

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7

6

3

0

If the sum of even coefficients in the expansion of (1+x)n is 128 then

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n=7

n=9

n=8

None

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

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13

12

11

10

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

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

If the 4th term in the expansion of (px + x^-1)^mis 2.5 for all x∈ R, then

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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

For every positive integers n 1+5+9+....+ (4n - 3) is

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n(2n - 1)

(2n - 1)

n - 1

n

If (1+x-2x³)⁶= 1+a₁x + a₂x²+ a₃x³+ ..... the the value of a₂+ a₄+ a₆+ .....+a₁₂will be

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32

31

64

1024

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

If n € N , then n(n+3) is always

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Multiple of 3

Multiple of 6

odd

even

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

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The proposition S(k+1) is true when ______ is true∀K∈N

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S(n)

S(k)

S(1)

S(k-1)

The seventh term of (x3+1/x)8is

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71

-22

27

28

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

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| x | < 1/2

| x | < 1

| x | < 2

| x | < 3

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

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2nd

3rd

4th

5th

For n€ N,2^n>2 > n is to only when

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n<2

n≤ 4

n≥ 4

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

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-221/16 x⁷

-225/18 x⁷

-407/9 x³

-429/16 x⁷

For all positive integral value of n,3ⁿ< n! , when

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n> 6

n< 6

n<11

n>11

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

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| x | < 1

| x | < 3

| x | < 1/3

None of these

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

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ⁿC_r

ⁿ⁺¹C_r+1

ⁿC_r+1

None

The general term in the expansion of (a+x)n is

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(r-1)th term

(r+1)th term

rth term

none

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

(x³-1/2x)⁶is

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15/16 x²

2/13 x²

17/7 x²

16/15 x²

If n is any positive integer then n! > n²for

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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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28 / 81

28 / 243

81 / 28

243 / 82

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

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

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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

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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 proposition S(n) is true∀n∈N,S(k+1) true when ______is true

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S(1)

Both a & c

S(k)

None

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