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

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

If n is any positive integer then n! > n²for

• 
  A
• 
  B
• 
  C
• 
  D

The coefficient of x¹⁸ in (ax⁴-bx)⁹ after expansion is

• 84a³ b⁶ A
• 22a³b⁶ B
• 27a⁴b⁵ C
• 28a³b⁶ D

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

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

• 2 A
• 7 B
• 8 C
• 12 D

The sum of coefficients in the binomial expansion equals to

• 2 A
• 2ⁿ⁺¹ B
• 2^n-1 C
• 2ⁿ D

n² - 1 divisible by 8 when n is

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

If a statement S(n) is true for n = 1 and the truth of S(n) for n = k implies the truth of S(n) for = k + 1, then S(n) is true for all

• Real numbers n A
• Integers n B
• Positive integers n C
• None of these 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

The number of terms in the expansion of (a + b)⁹is

• 10 A
• 11 B
• 9 C
• 12 D

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

• 71 A
• -22 B
• 27 C
• 28 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

(2.02)4 s equal to

• 16 A
• 16.6496 B
• 17 C
• 18 D

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

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

• 405 / 256 A
• 504 / 259 B
• 450 / 263 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

If n € N , then n(n+3) is always

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

• ¹⁰C₆ A
• ¹⁰C₅ B
• ¹⁰C₄ C
• None D

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

• 13 A
• 12 B
• 11 C
• 10 D

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

• -228 A
• 1/288 B
• 1/220 C
• -1/177 D

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

• 
  A
• 
  B
• 
  C
• 
  D

The fifth term of (a+2x3)17 is

• 4013 x3a13 A
• 2208a13 x12 B
• 223x7a18 C
• 38080a13 x12 D

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

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

• 
  A
• 
  B
• 
  C
• 
  D

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

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

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

• 
  A
• 
  B
• 
  C
• 
  D

1st four terms of the expansion (1-x)^-2are

• 1 + 2x + 3x²+ 4x³ A
• 3x²+ 2x + 1 B
• 1 + 3x + 4x²+ 5x³ C
• None of these D