Question # 1

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

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The sum of even coefficient in the binomial expansion is

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2ⁿ⁺¹

2ⁿ

2^n-1

2n

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

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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

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

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1700

17023

17027

17010

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

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0

1

-1

None

The middle term of [1/x-x]¹⁰is

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-152

-252

371

-421

If n is any positive integer ,t hen 2+4+6+......+2 n=

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2ⁿ-1

2ⁿ+1

n²+1

n(n+1)

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

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| x | < 1/2

| x | < 1

| x | < 2

| x | < 3

For≥ -2 , 1+3+5+......+(2n+5)

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(n+2)²

(n-2)²

2n+1

(n+3)²

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405 / 256

504 / 259

450 / 263

None

The sum of first n even number is

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n2

n(n+1)

n+1

n+2

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¹⁰C₆

¹⁰C₅

¹⁰C₄

None

There is no integer n for which 3n is

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Even

Prime

Odd

Real

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

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n(2n - 1)

(2n - 1)

n - 1

n

n! > 2ⁿ-1 is true when

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n≤ 3

n≤ 6

n≥ 4

n≤ 6

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

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295

495

395

722

(x³-1/2x)⁶is

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15/16 x²

2/13 x²

17/7 x²

16/15 x²

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 greatest term in the expansion of (3+2x)⁹, when x=1 is

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4th

4th and 5th

5th

6th

(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 term involving x⁴in the expansion of (3 - 2x)⁷is

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120

1512

1250

15120

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

ⁿC₂= exists when n is ______

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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

The middle term of (x-y)⁸is

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25 x⁴y⁴

70 x⁴y⁴

120 x⁴y⁴

97x⁴y⁴

n² - 1 divisible by 8 when n is

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an odd integer

an even integer

Irrational

Prime Number

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

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10

11

9

12

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