Question # 1

(x³-1/2x)⁶is

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15/16 x²

2/13 x²

17/7 x²

16/15 x²

The middle term of (x-y)⁸is

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25 x⁴y⁴

70 x⁴y⁴

120 x⁴y⁴

97x⁴y⁴

The sum of coefficients in the binomial expansion equals to

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2

2ⁿ⁺¹

2^n-1

2ⁿ

n² - 1 divisible by 8 when n is

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an odd integer

an even integer

Irrational

Prime Number

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 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

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Even

Odd

Prime

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

The sum of co-efficient in (1+x-3x²)⁴¹⁶³is

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0

1

-1

None

ⁿC₂= exists when n is ______

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There is no integer n for which 3n is

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Even

Prime

Odd

Real

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

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1

9

3

5

For≥ -2 , 1+3+5+......+(2n+5)

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(n+2)²

(n-2)²

2n+1

(n+3)²

If n∈Z+ then(a+x)n is a/an

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Finite series

Convergent series

Infinite series

Divergent series

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 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

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

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

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| x | < 1

| x | < 3

| x | < 1/3

None of these

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

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

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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 fifth term of (a+2x3)17 is

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4013 x3a13

2208a13 x12

223x7a18

38080a13 x12

The fifteenth term of (3-a)¹⁵ is

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-17a¹²

-945a¹³

-941a¹³

-515a¹²

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 is any positive integer then n! > n²for

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

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an even

an odd

multiple of 3

Irrational

(51)⁴is equal to

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7065201

8065201

6765201

6565201

There is no integer n for which 3ⁿis

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Odd

even

Natural

Prime

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

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120

1512

1250

15120

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Mathematics ECAT Pre Engineering Chapter 10 Mathematical Inductions Online Test MCQs With Answers

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