Question # 1

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

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9

6

5

10

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

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| x | < 1

| x | < 3

| x | < 1/3

None of these

If n is any positive integer then n! > n²for

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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

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

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an even

an odd

multiple of 3

Irrational

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

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The middle term of [1/x-x]¹⁰is

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-152

-252

371

-421

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

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0

1

-1

None

If x+y+z+......+2n = 2n+1-1∀n∈W,then cube root of xyz is equal to

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1

4

2

8

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

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217x⁴

15120x⁴

313x⁴

-25x⁴

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

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

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n> 6

n< 6

n<11

n>11

The sum of even coefficient in the binomial expansion is

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2ⁿ⁺¹

2ⁿ

2^n-1

2n

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

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Imaginary

Rational

Irrational

Real numbers

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Even

Odd

Prime

None of these

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

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1700

17023

17027

17010

(0.90)^1/2is equal to

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0.99

0.90

0.80

0.88

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

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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 7th term of (3⁸ + 6⁴x)^11/4 is

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-19217/3 x⁶

189/2 6⁴x

2227/12 x³

-19712/3 x⁶

a + x is ______

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A trinomial

A binomial

A monomial

None of these

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

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14

12

8

4

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

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If n∈Z+ then(a+x)n is a/an

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Finite series

Convergent series

Infinite series

Divergent series

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

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2

7

8

12

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

The middle term of (x-y)⁸is

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25 x⁴y⁴

70 x⁴y⁴

120 x⁴y⁴

97x⁴y⁴

If n € N , then n(n+3) is always

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Multiple of 3

Multiple of 6

odd

even

The fifteenth term of (3-a)¹⁵ is

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-17a¹²

-945a¹³

-941a¹³

-515a¹²

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8

9

10

11

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

The sum of first n even number is

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n2

n(n+1)

n+1

n+2

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

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n²

2^n-2

2^n-1

2ⁿ

The sum of coefficients in the binomial expansion equals to

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2

2ⁿ⁺¹

2^n-1

2ⁿ

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