Question # 1

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

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14

12

8

4

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

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-2x2

-4x2

2x2

4x2

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)

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

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13

12

11

10

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

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2

3

4

5

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n < 8/5

n < 5/8

|n| < 8/5

|n|>8/5

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

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n+1

n-1

n

n-2

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 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

There is no integer n for which 3ⁿis

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Odd

even

Natural

Prime

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

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7

6

3

0

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Even

Odd

Prime

None of these

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

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an even

an odd

multiple of 3

Irrational

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

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4013 x3a13

2208a13 x12

223x7a18

38080a13 x12

(1 - x)³= ______

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1 + 3x + 3x²+ x³

1 + x + x²+ x³

1 - x + x²- x³

1 - 3x + 3x²- x³

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

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6th term

6thor 7th

7th term

6thand7th

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2

7

8

12

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

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1st term

4th term

2nd term

5th term

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

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)

For≥ -2 , 1+3+5+......+(2n+5)

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(n+2)²

(n-2)²

2n+1

(n+3)²

ⁿC₂= exists when n is ______

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

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

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1700

17023

17027

17010

(x³-1/2x)⁶is

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15/16 x²

2/13 x²

17/7 x²

16/15 x²

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

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

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(1+x)-3

(1-x)-2

(1-x)-3

(1+x)-2

The last term of (1+2x)-2

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(-1)-2 (2x)-2

(-1)-4(-2x)-2

(-1)-3(2x)-3

Does not exist

The middle term of [1/x-x]¹⁰is

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-152

-252

371

-421

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ab=-1

ab = 1

ab = 2

None

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

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The sum of coefficients in the binomial expansion equals to

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2

2ⁿ⁺¹

2^n-1

2ⁿ

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 sum of first n even number is

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n2

n(n+1)

n+1

n+2

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

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ECAT Pre General Science Mathematics Chapter 10 Mathematical Induction Online Test MCQs With Answers

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