Question # 1

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

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4th

4th and 5th

5th

6th

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

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

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217x⁴

15120x⁴

313x⁴

-25x⁴

(x3-1/x)12

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295

495

395

722

The coefficient of the second term of (a+b)⁴ is

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1

9

3

5

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

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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 greatest integer which divides the number 101¹⁰⁰- 1 is

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100

1000

10000

100000

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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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

7²ⁿ+ 3^n-1. 2^3n-3is divisible by

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24

25

9

13

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

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77b²/a⁵

16b²/243 a⁵

17b⁴/43a⁵

25b³/43a⁵

If n € N , then n(n+3) is always

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Multiple of 3

Multiple of 6

odd

even

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

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

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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

a + x is ______

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A trinomial

A binomial

A monomial

None of these

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

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

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-2x2

-4x2

2x2

4x2

n² - 1 divisible by 8 when n is

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an odd integer

an even integer

Irrational

Prime Number

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

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

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295

495

395

722

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

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| x | < 1/2

| x | < 1

| x | < 2

| x | < 3

n(n-1)(2n-1), for all natural numbers n, is divisible by

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12

6

2

18

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

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2 and 9

3 and 2

2/3 and 9

3/2 and 6

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

ⁿC₂= exists when n is ______

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The no of term is the expansion of (a+x)n-1 is

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n+1

n-1

n

n-2

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

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| x | < 1

| x | < 3

| x | < 1/3

None of these

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ECAT Mathematics Chapter 10 Mathematical Inductions Online Test MCQs With Answers

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