Question # 1

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

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n> 6

n< 6

n<11

n>11

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

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The third term in the expansion of (1+2x) is

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-2x2

-4x2

2x2

4x2

The greatest integer which divides the number 101¹⁰⁰- 1 is

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100

1000

10000

100000

(1 - x)³= ______

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1 + 3x + 3x²+ x³

1 + x + x²+ x³

1 - x + x²- x³

1 - 3x + 3x²- x³

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

a + x is ______

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A trinomial

A binomial

A monomial

None of these

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Imaginary

Rational

Irrational

Real numbers

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

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

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(1+x)-3

(1-x)-2

(1-x)-3

(1+x)-2

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

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77b²/a⁵

16b²/243 a⁵

17b⁴/43a⁵

25b³/43a⁵

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n < 8/5

n < 5/8

|n| < 8/5

|n|>8/5

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

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n(2n - 1)

(2n - 1)

n - 1

n

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 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

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

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217 x4

15120x4

313x4

-25x4

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If n € N , then n(n+3) is always

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Multiple of 3

Multiple of 6

odd

even

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

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

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n - 1

n + 1

n + 2

n + 3

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

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|x| > 1

|x| < 1

x < 1

x > 1

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

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4

5

2

3

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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If n is any positive integer then n²> n + 3 for

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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

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2 and 9

3 and 2

2/3 and 9

3/2 and 6

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)

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Even

Odd

Prime

None of these

For each even natural number n (n²-1) is divisible by

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6

3

4

8

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