Question # 1

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

for n€ N, 3^{2n + 7 is divisible by}

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7

8

9

10

There is no integer n for which 3n is

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Even

Prime

Odd

Real

n! > 2ⁿ-1 is true when

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n≤ 3

n≤ 6

n≥ 4

n≤ 6

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

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14

12

8

4

For≥ -2 , 1+3+5+......+(2n+5)

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(n+2)²

(n-2)²

2n+1

(n+3)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

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Even

Odd

Prime

None of these

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ab=-1

ab = 1

ab = 2

None

(x³-1/2x)⁶is

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15/16 x²

2/13 x²

17/7 x²

16/15 x²

The fifth term of (a+2x3)17 is

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4013 x3a13

2208a13 x12

223x7a18

38080a13 x12

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8

9

10

11

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

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2 and 9

3 and 2

2/3 and 9

3/2 and 6

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

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217x⁴

15120x⁴

313x⁴

-25x⁴

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

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¹⁰C₆

¹⁰C₅

¹⁰C₄

None

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

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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 last term of (1+2x)-2

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(-1)-2 (2x)-2

(-1)-4(-2x)-2

(-1)-3(2x)-3

Does not exist

If in the expansion of (1+x)ⁿ, co-efficients of 2nd, 3rd and 4th terms are in A.P., then x=

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4

5

6

7

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

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295

495

395

722

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405 / 256

504 / 259

450 / 263

None

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

The sum of first n even number is

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n2

n(n+1)

n+1

n+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 n € N , then n(n+3) is always

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Multiple of 3

Multiple of 6

odd

even

The middle term(s) of (a+x)11 is

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6th term

6thor 7th

7th term

6thand7th

If n is any positive integer then 4ⁿ>3ⁿ+ 4 is true for all

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(0.90)^1/2is equal to

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0.99

0.90

0.80

0.88

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