Question # 1

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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 sum even binomial coefficient of (3+2x)5 is ______term

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16

30

8

32

For all positive integral value of n,3ⁿ< n! , when

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n> 6

n< 6

n<11

n>11

Number of terms in the expansion of (a+x)ⁿis

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n - 1

n + 1

n + 2

n + 3

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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(0.90)^1/2is equal to

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0.99

0.90

0.80

0.88

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

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

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405 / 256

504 / 259

450 / 263

None

If the 4th term in the expansion of (px + x^-1)^mis 2.5 for all x∈ R, then

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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

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2

7

8

12

For n€ N,2^n>2 > n is to only when

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n<2

n≤ 4

n≥ 4

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ⁿC_r

ⁿ⁺¹C_r+1

ⁿC_r+1

None

The middle term of [1/x-x]¹⁰is

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-152

-252

371

-421

The expansion of (1 + 2x)^-2is valed if

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| x | < 1/2

| x | < 1

| x | < 2

| x | < 3

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

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

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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

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

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The sum of the coefficient in the expansion of (a + x)⁵is

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32

16

8

5

(1 + 2x)⁴= ______

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1 + 4x + 6x²+ 4x³+ x⁴

1 - 4x + 6x²- 4x³+ x⁴

1 - 8x + 24x²- 32x³+ 16x⁴

1 + 8x+ 24x²+ 32x³+ 16x⁴

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ab=-1

ab = 1

ab = 2

None

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

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120

1512

1250

15120

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

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217 x4

15120x4

313x4

-25x4

(1 - x)³= ______

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1 + 3x + 3x²+ x³

1 + x + x²+ x³

1 - x + x²- x³

1 - 3x + 3x²- x³

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

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

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

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