Question # 1

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

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

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2nd term

3rd term

4th term

5th term

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

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120

1512

1250

15120

(51)⁴is equal to

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7065201

8065201

6765201

6565201

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¹⁰C₆

¹⁰C₅

¹⁰C₄

None

(x³-1/2x)⁶is

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15/16 x²

2/13 x²

17/7 x²

16/15 x²

If n € N , then n(n+3) is always

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Multiple of 3

Multiple of 6

odd

even

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

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4th

4th and 5th

5th

6th

for n€ N, 3^{2n + 7 is divisible by}

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7

8

9

10

(0.90)^1/2is equal to

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0.99

0.90

0.80

0.88

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

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

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1700

17023

17027

17010

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

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The sum of the even coefficients in the expansion (1 + x)ⁿis

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n²

2^n-2

2^n-1

2ⁿ

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Even

Odd

Prime

None of these

The fifteenth term of (3-a)¹⁵ is

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-17a¹²

-945a¹³

-941a¹³

-515a¹²

(x3-1/x)12

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295

495

395

722

If n∈Z+ then(a+x)n is a/an

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Finite series

Convergent series

Infinite series

Divergent series

For every positive integers n 1+5+9+....+ (4n - 3) is

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n(2n - 1)

(2n - 1)

n - 1

n

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The general term in the expansion of (a+x)n is

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(r-1)th term

(r+1)th term

rth term

none

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2

7

8

12

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

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For≥ -2 , 1+3+5+......+(2n+5)

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(n+2)²

(n-2)²

2n+1

(n+3)²

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

If (1+x)ⁿ=C₀+ C₁x +C₂x²+ ......+C_nx¹then C₀C₂+ C₁C₃+ C₂C₄+ .....+C_n-2C_n=

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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

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

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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(s) of (a+x)11 is

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6th term

6thor 7th

7th term

6thand7th

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ECAT Mathematics Chapter 10 Mathematical Inductions Online Test MCQs With Answers

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