ECAT Pre Engineering Mathematic MCQ Test With Answer for Chapter 10 (Mathematical Inductions)

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

• 6th term A
• 6thor 7th B
• 7th term C
• 6thand7th D

There is no integer n for which 3n is

• Even A
• Prime B
• Odd C
• Real D

• 28 / 81 A
• 28 / 243 B
• 81 / 28 C
• 243 / 82 D

n² - 1 divisible by 8 when n is

• an odd integer A
• an even integer B
• Irrational C
• Prime Number D

(x3-1/x)12

• 295 A
• 495 B
• 395 C
• 722 D

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

• 
  A
• 
  B
• 
  C
• 
  D

The sum of co-efficient in (1+x-3x²)⁴¹⁶³is

• 0 A
• 1 B
• -1 C
• None D

The general term in the expansion of (a+x)n is

• (r-1)th term A
• (r+1)th term B
• rth term C
• none D

The last term of (1+2x)-2

• (-1)-2 (2x)-2 A
• (-1)-4(-2x)-2 B
• (-1)-3(2x)-3 C
• Does not exist D

(51)⁴is equal to

• 7065201 A
• 8065201 B
• 6765201 C
• 6565201 D

If the expansion of (1 + x)²⁰, then co-efficient of rth ad (r + 4)th term are equal, then r is

• 7 A
• 8 B
• 9 C
• 10 D

• 3/8 A
• 7/8 B
• 1/8 C
• None D

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

• 13 A
• 12 B
• 11 C
• 10 D

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

• 7th A
• 8th B
• 9th C
• 6th D

If n is not natural number, then the expansion (1 + x)ⁿis valid for

• 
  A
• 
  B
• 
  C
• 
  D

a + x is ______

• A trinomial A
• A binomial B
• A monomial C
• None of these D

(0.90)^1/2is equal to

• 0.99 A
• 0.90 B
• 0.80 C
• 0.88 D

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

• 2ⁿ-1 A
• 2ⁿ+1 B
• n²+1 C
• n(n+1) D

The first three terms in the expansion of (1 - x)^-3are

• 1 + 3x + 6x² A
• 1 - 3x + 6x² B
• -3 - 3x - 6x² C
• 1 - 3x - 6x² D

The term independent of x is the expansion (x³+1/x)¹²

• 295 A
• 495 B
• 395 C
• 722 D

7²ⁿ+ 3^n-1. 2^3n-3is divisible by

• 24 A
• 25 B
• 9 C
• 13 D

• n < 8/5 A
• n < 5/8 B
• |n| < 8/5 C
• |n|>8/5 D

Digit in the unit place of the number 183! + 3¹⁸³

• 7 A
• 6 B
• 3 C
• 0 D

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

• | x | < 1/2 A
• | x | < 1 B
• | x | < 2 C
• | x | < 3 D

If n∈Z+ then(a+x)n is a/an

• Finite series A
• Convergent series B
• Infinite series C
• Divergent series D

The sum of the even coefficients in the expansion (1 + x)ⁿis

• n² A
• 2^n-2 B
• 2^n-1 C
• 2ⁿ D

The first three terms in the expansion of (1 - x)^-2are

• 1 - 2x + 3x² A
• 1 - 2x - 3x² B
• 1 + 2x + 3x² C
• -2 - 2x +3x² D

The sum of even coefficient in the binomial expansion is

• 2ⁿ⁺¹ A
• 2ⁿ B
• 2^n-1 C
• 2n D

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

• 9 A
• 6 B
• 5 C
• 10 D

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

• |x| > 1 A
• |x| < 1 B
• x < 1 C
• x > 1 D