Question # 1

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

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

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6

3

4

8

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

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4013 x3a13

2208a13 x12

223x7a18

38080a13 x12

a + x is ______

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A trinomial

A binomial

A monomial

None of these

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

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1700

17023

17027

17010

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

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n+1

n-1

n

n-2

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 middle term of (x-y)⁸is

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25 x⁴y⁴

70 x⁴y⁴

120 x⁴y⁴

97x⁴y⁴

If the expansion of (1 + x)²⁰, then co-efficient of rth ad (r + 4)th term are equal, then r is

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7

8

9

10

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

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-221/16 x⁷

-225/18 x⁷

-407/9 x³

-429/16 x⁷

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

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14

12

8

4

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

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120

1512

1250

15120

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

Digit in the unit place of the number 183! + 3¹⁸³

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7

6

3

0

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

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

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-2x2

-4x2

2x2

4x2

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

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1700

17023

17027

17010

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 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

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

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4th

4th and 5th

5th

6th

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

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If the exponent in the binomial expansion is 6, then the middle term is

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2nd

3rd

4th

5th

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

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an even

an odd

multiple of 3

Irrational

n! > 2ⁿ-1 is true when

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n≤ 3

n≤ 6

n≥ 4

n≤ 6

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

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77b²/a⁵

16b²/243 a⁵

17b⁴/43a⁵

25b³/43a⁵

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

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295

495

395

722

There is no integer n for which 3n is

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Even

Prime

Odd

Real

for n€ N, 3^{2n + 7 is divisible by}

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7

8

9

10

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

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ECAT Mathematics Chapter 10 Mathematical Inductions Online Test MCQs With Answers

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