Question # 1

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

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6

3

4

8

If (1+x-2x³)⁶= 1+a₁x + a₂x²+ a₃x³+ ..... the the value of a₂+ a₄+ a₆+ .....+a₁₂will be

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32

31

64

1024

ⁿC₂= exists when n is ______

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If n∈Z+ then(a+x)n is a/an

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Finite series

Convergent series

Infinite series

Divergent series

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

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The number of terms in the expansion of (a + b)⁹is

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10

11

9

12

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

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14

12

8

4

(0.90)^1/2is equal to

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0.99

0.90

0.80

0.88

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

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If n is any positive integer then n! > n²for

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

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(1+x)-3

(1-x)-2

(1-x)-3

(1+x)-2

The middle term in the expansion of (a +x)¹²is

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7th

8th

9th

6th

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Even

Odd

Prime

None of these

If x+y+z+......+2n = 2n+1-1∀n∈W,then cube root of xyz is equal to

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1

4

2

8

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

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13

12

11

10

The middle term of (x-y)⁸is

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25 x⁴y⁴

70 x⁴y⁴

120 x⁴y⁴

97x⁴y⁴

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

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77b²/a⁵

16b²/243 a⁵

17b⁴/43a⁵

25b³/43a⁵

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The sum of even coefficient in the binomial expansion is

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2ⁿ⁺¹

2ⁿ

2^n-1

2n

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¹⁰C₆

¹⁰C₅

¹⁰C₄

None

The term involving x4 the expansion (3-2x)7 is

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217 x4

15120x4

313x4

-25x4

If n € N , then n(n+3) is always

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Multiple of 3

Multiple of 6

odd

even

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Imaginary

Rational

Irrational

Real numbers

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2 and 9

3 and 2

2/3 and 9

3/2 and 6

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

(1 - x)³= ______

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1 + 3x + 3x²+ x³

1 + x + x²+ x³

1 - x + x²- x³

1 - 3x + 3x²- x³

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

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4013 x3a13

2208a13 x12

223x7a18

38080a13 x12

The expansion (1 + x)^-3holds when

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|x| > 1

|x| < 1

x < 1

x > 1

The proposition S(n) for any n∈ N is only true if k∈ N and

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S(k +1) is true

S(1) is true and S(k+1) is true whenever S (k) is true

S(k+1) is true whenever S (k) is true

S(k) is true

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

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4th

4th and 5th

5th

6th

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

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