Question # 1

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

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1st term

4th term

2nd term

5th term

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

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10

11

9

12

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¹⁰C₆

¹⁰C₅

¹⁰C₄

None

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The middle term of [1/x-x]¹⁰is

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-152

-252

371

-421

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

If n is any positive integer then n! > n²for

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

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for n€ N, 3^{2n + 7 is divisible by}

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7

8

9

10

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)

If n∈Z+ then(a+x)n is a/an

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Finite series

Convergent series

Infinite series

Divergent series

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

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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)

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

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

If n € N , then n(n+3) is always

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Multiple of 3

Multiple of 6

odd

even

n² - 1 divisible by 8 when n is

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an odd integer

an even integer

Irrational

Prime Number

There is no integer n for which 3n is

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Even

Prime

Odd

Real

a + x is ______

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A trinomial

A binomial

A monomial

None of these

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

If n is add the expansion (a + x)ⁿhas middle terms

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2

3

4

5

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

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4th

4th and 5th

5th

6th

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

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

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| x | < 1

| x | < 3

| x | < 1/3

None of these

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

In the expansion of (x+y)n the coefficient of 5th and 12th terms are equal then n=

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12

n=14

17

n=15

If n is odd then the middle terms in the expansion of (a + x)ⁿare

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

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| x | < 1/2

| x | < 1

| x | < 2

| x | < 3

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

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

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16

30

8

32

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

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The term involving x⁴in the expansion of (3 - 2x)⁷is

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120

1512

1250

15120

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

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217x⁴

15120x⁴

313x⁴

-25x⁴

For n€ N,2^n>2 > n is to only when

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n<2

n≤ 4

n≥ 4

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

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

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(1+x)-3

(1-x)-2

(1-x)-3

(1+x)-2

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