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

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

• 217 x4 A
• 15120x4 B
• 313x4 C
• -25x4 D

If n € N , then n(n+3) is always

• Multiple of 3 A
• Multiple of 6 B
• odd C
• even D

If n is any positive integer then n! > n²for

• 
  A
• 
  B
• 
  C
• 
  D

For every positive integers n 1+5+9+....+ (4n - 3) is

• n(2n - 1) A
• (2n - 1) B
• n - 1 C
• n D

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

• an even A
• an odd B
• multiple of 3 C
• Irrational D

• 3/8 A
• 7/8 B
• 1/8 C
• None D

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

• 6 A
• 3 B
• 4 C
• 8 D

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

• 217x⁴ A
• 15120x⁴ B
• 313x⁴ C
• -25x⁴ D

There is no integer n for which 3n is

• Even A
• Prime B
• Odd C
• Real D

The middle term of [1/x-x]¹⁰ is

• -152 A
• -252 B
• 371 C
• -421 D

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

• n=7 A
• n=9 B
• n=8 C
• None D

• 8 A
• 9 B
• 10 C
• 11 D

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

• 
  A
• 
  B
• 
  C
• 
  D

The coefficient of x¹⁰in the expansion (x³+3/x²)¹⁰is

• 1700 A
• 17023 B
• 17027 C
• 17010 D

n(n-1)(2n-1), for all natural numbers n, is divisible by

• 12 A
• 6 B
• 2 C
• 18 D

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

7²ⁿ+ 3^n-1. 2^3n-3is divisible by

• 24 A
• 25 B
• 9 C
• 13 D

If (1+x-2x³)⁶= 1+a₁x + a₂x²+ a₃x³+ ..... the the value of a₂+ a₄+ a₆+ .....+a₁₂will be

• 32 A
• 31 B
• 64 C
• 1024 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

• Imaginary A
• Rational B
• Irrational C
• Real numbers 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 third term in the expansion of (1+2x) is

• -2x2 A
• -4x2 B
• 2x2 C
• 4x2 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

• Even A
• Odd B
• Prime C
• None of these D

for n€ N, 3^{2n + 7 is divisible by}

• 7 A
• 8 B
• 9 C
• 10 D

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

• 
  A
• 
  B
• 
  C
• 
  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

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

• 
  A
• 
  B
• 
  C
• 
  D

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

• 
  A
• 
  B
• 
  C
• 
  D

n² - 1 divisible by 8 when n is

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