Question # 1

If n € N , then n(n+3) is always

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Multiple of 3

Multiple of 6

odd

even

The proposition S(n) for any n∈ N is only true if k∈ N and

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S(k +1) is true

S(1) is true and S(k+1) is true whenever S (k) is true

S(k+1) is true whenever S (k) is true

S(k) is true

For n€ N,2^n>2 > n is to only when

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n<2

n≤ 4

n≥ 4

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

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1700

17023

17027

17010

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Even

Odd

Prime

None of these

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

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

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295

495

395

722

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

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84a³ b⁶

22a³b⁶

27a⁴b⁵

28a³b⁶

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

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

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an even

an odd

multiple of 3

Irrational

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

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

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

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n - 1

n + 1

n + 2

n + 3

The middle term of (x-y)⁸is

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25 x⁴y⁴

70 x⁴y⁴

120 x⁴y⁴

97x⁴y⁴

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

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n(2n - 1)

(2n - 1)

n - 1

n

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405 / 256

504 / 259

450 / 263

None

If (1+x)ⁿ=C₀+ C₁x +C₂x²+ ......+C_nx¹then C₀C₂+ C₁C₃+ C₂C₄+ .....+C_n-2C_n=

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28 / 81

28 / 243

81 / 28

243 / 82

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

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217 x4

15120x4

313x4

-25x4

ⁿC₂= exists when n is ______

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(2.02)4 s equal to

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16

16.6496

17

18

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

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

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

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14

12

8

4

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 positive integer just greater than (1+0.0001)¹⁰⁰⁰⁰is

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4

5

2

3

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n < 8/5

n < 5/8

|n| < 8/5

|n|>8/5

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¹⁰C₆

¹⁰C₅

¹⁰C₄

None

The sum of the even coefficients in the expansion (1 + x)ⁿis

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n²

2^n-2

2^n-1

2ⁿ

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