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

If nis positive integers, then 2ⁿ>2n+1, only when

• n≤ 3 A
• n≥ 3 B
• n≤ 2 C
• n≤ 1 D

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

• 1 A
• 9 B
• 3 C
• 5 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

In the expansion of (a + x)ⁿthe sum of exponents of a and x in each term of the expansion is

• n + 1 A
• n - 1 B
• n C
• 2n D

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

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

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

• 6 A
• 3 B
• 4 C
• 8 D

(2.02)4 s equal to

• 16 A
• 16.6496 B
• 17 C
• 18 D

The sum even binomial coefficient of (3+2x)5 is ______term

• 16 A
• 30 B
• 8 C
• 32 D

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

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

(0.90)^1/2is equal to

• 0.99 A
• 0.90 B
• 0.80 C
• 0.88 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

• 405 / 256 A
• 504 / 259 B
• 450 / 263 C
• None D

(0.90)^1/2is equal to

• 0.99 A
• 0.90 B
• 0.80 C
• 0.88 D

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

• 1st term A
• 4th term B
• 2nd term C
• 5th term D

The sum of even coefficient in the binomial expansion is

• 2ⁿ⁺¹ A
• 2ⁿ B
• 2^n-1 C
• 2n D

There is no integer n for which 3ⁿ is

• Odd A
• even B
• Natural C
• Prime D

If n is any positive integer then n! > n²for

• 
  A
• 
  B
• 
  C
• 
  D

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

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

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

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

If n is any positive integer then 4ⁿ>3ⁿ+ 4 is true for all

• 
  A
• 
  B
• 
  C
• 
  D

for n€ N, 3^{2n + 7 is divisible by}

• 7 A
• 8 B
• 9 C
• 10 D

There are two middle terms in the expansion of (a+x)n if n is

• Even +ve integer A
• +ve integer B
• Odd +ve integer C
• All D

If | x | < 1, then the first two terms of (1 - x)^1/2are

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

The 8th term of (1+2x) ^-1/2is

• -221/16 x⁷ A
• -225/18 x⁷ B
• -407/9 x³ C
• -429/16 x⁷ D

• 3/8 A
• 7/8 B
• 1/8 C
• None D

• 8 A
• 9 B
• 10 C
• 11 D

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

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

The greatest term in the expansion of (3+2x)⁹, when x=1 is

• 4th A
• 4th and 5th B
• 5th C
• 6th D

• 
  A
• 
  B
• 
  C
• 
  D