Question # 1

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

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14

12

8

4

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

There are two middle terms in the expansion of (a+x)n if n is

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Even +ve integer

+ve integer

Odd +ve integer

All

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

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(51)⁴is equal to

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7065201

8065201

6765201

6565201

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

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

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|x| > 1

|x| < 1

x < 1

x > 1

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

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n²

2^n-2

2^n-1

2ⁿ

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

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1700

17023

17027

17010

The coefficient of xn in the expansion of (1-x)-1 is

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(-1)n2n

1

(-1)n(n+1)

(n+1)

The fifteenth term of (3-a)¹⁵ is

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-17a¹²

-945a¹³

-941a¹³

-515a¹²

(2.02)4 s equal to

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16

16.6496

17

18

The middle term in the expansion of (a +x)¹²is

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7th

8th

9th

6th

If n € N , then n(n+3) is always

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Multiple of 3

Multiple of 6

odd

even

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

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0

1

-1

None

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

The number of terms in the expansion of (a + x)¹²is

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13

12

11

10

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

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405 / 256

504 / 259

450 / 263

None

The 8th term of (1+2x) ^-1/2is

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-221/16 x⁷

-225/18 x⁷

-407/9 x³

-429/16 x⁷

a + x is ______

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A trinomial

A binomial

A monomial

None of these

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

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77b²/a⁵

16b²/243 a⁵

17b⁴/43a⁵

25b³/43a⁵

The proposition S(k+1) is true when ______ is true∀K∈N

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S(n)

S(k)

S(1)

S(k-1)

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

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| x | < 1

| x | < 3

| x | < 1/3

None of these

The exponent of x in 10th term in the expansion of (a+x)n

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10

12

11

9

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

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| x | < 1/2

| x | < 1

| x | < 2

| x | < 3

The seventh term of (x3+1/x)8is

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71

-22

27

28

If (1+x-2x³)⁶= 1+a₁x + a₂x²+ a₃x³+ ..... the the value of a₂+ a₄+ a₆+ .....+a₁₂will be

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32

31

64

1024

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ⁿC_r

ⁿ⁺¹C_r+1

ⁿC_r+1

None

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ab=-1

ab = 1

ab = 2

None

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

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6

3

4

8

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

(x³-1/2x)⁶is

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15/16 x²

2/13 x²

17/7 x²

16/15 x²

n! > 2ⁿ-1 is true when

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n≤ 3

n≤ 6

n≥ 4

n≤ 6

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

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n - 1

n + 1

n + 2

n + 3

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

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6th term

6thor 7th

7th term

6thand7th

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