Question # 1

There is no integer n for which 3n is

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Even

Prime

Odd

Real

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

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

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6th term

6thor 7th

7th term

6thand7th

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

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

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1st term

4th term

2nd term

5th term

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

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1700

17023

17027

17010

for n€ N, 3^{2n + 7 is divisible by}

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7

8

9

10

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Imaginary

Rational

Irrational

Real numbers

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

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6

3

4

8

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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ⁿC₂= exists when n is ______

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

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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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28 / 81

28 / 243

81 / 28

243 / 82

(1 - x)³= ______

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1 + 3x + 3x²+ x³

1 + x + x²+ x³

1 - x + x²- x³

1 - 3x + 3x²- x³

(0.90)^1/2is equal to

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0.99

0.90

0.80

0.88

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

For each natural number n, n (n+1) is

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an even

an odd

multiple of 3

Irrational

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

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

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77b²/a⁵

16b²/243 a⁵

17b⁴/43a⁵

25b³/43a⁵

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 sum of coefficients in the binomial expansion equals to

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2

2ⁿ⁺¹

2^n-1

2ⁿ

7²ⁿ+ 3^n-1. 2^3n-3is divisible by

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24

25

9

13

The sum of first n even number is

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n2

n(n+1)

n+1

n+2

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

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| x | < 1/2

| x | < 1

| x | < 2

| x | < 3

The greatest integer which divides the number 101¹⁰⁰- 1 is

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100

1000

10000

100000

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)

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

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405 / 256

504 / 259

450 / 263

None

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

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ECAT Mathematics Chapter 10 Mathematical Inductions Online Test MCQs With Answers

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