Question # 1

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(x³-1/2x)⁶is

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15/16 x²

2/13 x²

17/7 x²

16/15 x²

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n < 8/5

n < 5/8

|n| < 8/5

|n|>8/5

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

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The middle term(s) of (a+x)11 is

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6th term

6thor 7th

7th term

6thand7th

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ab=-1

ab = 1

ab = 2

None

The fifteenth term of (3-a)¹⁵ is

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-17a¹²

-945a¹³

-941a¹³

-515a¹²

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

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

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217x⁴

15120x⁴

313x⁴

-25x⁴

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

for n€ N, 3^{2n + 7 is divisible by}

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7

8

9

10

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)^-3are

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1 + 3x + 6x²

1 - 3x + 6x²

-3 - 3x - 6x²

1 - 3x - 6x²

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

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71

-22

27

28

If the sum of even coefficients in the expansion of (1+x)n is 128 then

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n=7

n=9

n=8

None

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 third term in the expansion of (1+2x) is

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-2x2

-4x2

2x2

4x2

(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

If n∈Z+ then(a+x)n is a/an

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Finite series

Convergent series

Infinite series

Divergent series

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

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120

1512

1250

15120

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 € N , then n(n+3) is always

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Multiple of 3

Multiple of 6

odd

even

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 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

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

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

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n! > 2ⁿ-1 is true when

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n≤ 3

n≤ 6

n≥ 4

n≤ 6

The coefficient of the second term of (a+b)⁴ is

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1

9

3

5

The proposition S(k+1) is true when ______ is true∀K∈N

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S(n)

S(k)

S(1)

S(k-1)

(1 - x)³= ______

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1 + 3x + 3x²+ x³

1 + x + x²+ x³

1 - x + x²- x³

1 - 3x + 3x²- x³

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

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