Question # 1

ⁿC₂= exists when n is ______

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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 7th term of (3⁸ + 6⁴x)^11/4 is

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-19217/3 x⁶

189/2 6⁴x

2227/12 x³

-19712/3 x⁶

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 sum of the cubes of three consecutive natural number is divisible by

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9

6

5

10

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n < 8/5

n < 5/8

|n| < 8/5

|n|>8/5

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

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14

12

8

4

The middle term of (x-y)⁸is

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25 x⁴y⁴

70 x⁴y⁴

120 x⁴y⁴

97x⁴y⁴

If a statement S(n) is true for n = i where i is some natural number and the truth of S(n) for n = k > i implies the truth of S(n) for n = k +1 then S(n) is true for all positive integers

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

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The seventh term of (x3+1/x)8is

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71

-22

27

28

7²ⁿ+ 3^n-1. 2^3n-3is divisible by

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24

25

9

13

When we expand (a + 2b)⁵then

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a⁵+ 10a⁴b + 40a³b²+ 80a²b³+ 80ab⁴+ 32b⁵

a⁵+ a⁴b + a³b²+ a²b³+ ab⁴+ b⁵

5a⁵+ 4a⁴b + 3a³b²+ 2a²b³+ 1 ab⁴+ b⁵

None

for n€ N, 3^{2n + 7 is divisible by}

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7

8

9

10

For≥ -2 , 1+3+5+......+(2n+5)

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(n+2)²

(n-2)²

2n+1

(n+3)²

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

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| x | < 1

| x | < 3

| x | < 1/3

None of these

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

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

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

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n> 6

n< 6

n<11

n>11

The middle term of the expansion (1 + 2x)⁶is ______

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1st term

4th term

2nd term

5th term

(x³-1/2x)⁶is

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15/16 x²

2/13 x²

17/7 x²

16/15 x²

If n∈Z+ then(a+x)n is a/an

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Finite series

Convergent series

Infinite series

Divergent series

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

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| x | < 1/2

| x | < 1

| x | < 2

| x | < 3

(0.90)^1/2is equal to

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0.99

0.90

0.80

0.88

If n € N , then n(n+3) is always

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Multiple of 3

Multiple of 6

odd

even

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

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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

(51)⁴is equal to

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7065201

8065201

6765201

6565201

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If n is any positive integer ,t hen 2+4+6+......+2 n=

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2ⁿ-1

2ⁿ+1

n²+1

n(n+1)

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

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 coefficient of the third term of (8a-b)^1/3, after simplification is

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-228

1/288

1/220

-1/177

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

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13

12

11

10

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

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n - 1

n + 1

n + 2

n + 3

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

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

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