Question # 1

If n is any positive integer then n! > n²for

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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

If the expansion of (1 + x)²⁰, then co-efficient of rth ad (r + 4)th term are equal, then r is

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7

8

9

10

The sum of the cubes of three consecutive natural number is divisible by

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9

6

5

10

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405 / 256

504 / 259

450 / 263

None

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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 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)

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

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(1+x)-3

(1-x)-2

(1-x)-3

(1+x)-2

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

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 middle term of (x-y)⁸is

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25 x⁴y⁴

70 x⁴y⁴

120 x⁴y⁴

97x⁴y⁴

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

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

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n - 1

n + 1

n + 2

n + 3

For≥ -2 , 1+3+5+......+(2n+5)

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(n+2)²

(n-2)²

2n+1

(n+3)²

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

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217 x4

15120x4

313x4

-25x4

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

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16

30

8

32

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

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12

6

2

18

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

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

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

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10

11

9

12

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

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77b²/a⁵

16b²/243 a⁵

17b⁴/43a⁵

25b³/43a⁵

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

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If n is any positive integer then n! > 2^n-1for

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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

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

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

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4th

4th and 5th

5th

6th

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

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2nd

3rd

4th

5th

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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ab=-1

ab = 1

ab = 2

None

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

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1st term

4th term

2nd term

5th term

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

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| x | < 1

| x | < 3

| x | < 1/3

None of these

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

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| x | < 1/2

| x | < 1

| x | < 2

| x | < 3

The expansion (1 + x)^-3holds when

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|x| > 1

|x| < 1

x < 1

x > 1

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

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an even

an odd

multiple of 3

Irrational

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

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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