Question # 1

If in the expansion of (1+x)ⁿ, co-efficients of 2nd, 3rd and 4th terms are in A.P., then x=

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4

5

6

7

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

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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

n² - 1 divisible by 8 when n is

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an odd integer

an even integer

Irrational

Prime Number

a + x is ______

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A trinomial

A binomial

A monomial

None of these

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28 / 81

28 / 243

81 / 28

243 / 82

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

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

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

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n> 6

n< 6

n<11

n>11

(51)⁴is equal to

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7065201

8065201

6765201

6565201

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

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| x | < 1/2

| x | < 1

| x | < 2

| x | < 3

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

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an even

an odd

multiple of 3

Irrational

(0.90)^1/2is equal to

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0.99

0.90

0.80

0.88

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

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n < 8/5

n < 5/8

|n| < 8/5

|n|>8/5

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

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(1+x)-3

(1-x)-2

(1-x)-3

(1+x)-2

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

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| x | < 1

| x | < 3

| x | < 1/3

None of these

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

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ⁿC_r

ⁿ⁺¹C_r+1

ⁿC_r+1

None

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 4ⁿ>3ⁿ+ 4 is true for all

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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 € N , then n(n+3) is always

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Multiple of 3

Multiple of 6

odd

even

(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

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

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6

3

4

8

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

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10

11

9

12

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2 and 9

3 and 2

2/3 and 9

3/2 and 6

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Even

Odd

Prime

None of these

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

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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)

The fifteenth term of (3-a)¹⁵ is

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-17a¹²

-945a¹³

-941a¹³

-515a¹²

The greatest integer which divides the number 101¹⁰⁰- 1 is

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100

1000

10000

100000

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

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n - 1

n + 1

n + 2

n + 3

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

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