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

(1 + 2x)⁴= ______

• 1 + 4x + 6x²+ 4x³+ x⁴ A
• 1 - 4x + 6x²- 4x³+ x⁴ B
• 1 - 8x + 24x²- 32x³+ 16x⁴ C
• 1 + 8x+ 24x²+ 32x³+ 16x⁴ 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

• ab=-1 A
• ab = 1 B
• ab = 2 C
• None D

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

• 9 A
• 6 B
• 5 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 the exponent in the binomial expansion is 6, then the middle term is

• 2nd A
• 3rd B
• 4th C
• 5th D

n! > 2ⁿ-1 is true when

• n≤ 3 A
• n≤ 6 B
• n≥ 4 C
• n≤ 6 D

The positive integer just greater than (1+0.0001)¹⁰⁰⁰⁰is

• 4 A
• 5 B
• 2 C
• 3 D

(x³-1/2x)⁶ is

• 15/16 x² A
• 2/13 x² B
• 17/7 x² C
• 16/15 x² D

The no of term is the expansion of (a+x)n-1 is

• n+1 A
• n-1 B
• n C
• n-2 D

• 8 A
• 9 B
• 10 C
• 11 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 expansion of (1 - 3x)^-1is valid if

• | x | < 1 A
• | x | < 3 B
• | x | < 1/3 C
• None of these D

The sum of first n even number is

• n2 A
• n(n+1) B
• n+1 C
• n+2 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

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

• 
  A
• 
  B
• 
  C
• 
  D

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

If n € N , then n(n+3) is always

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

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

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

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

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

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

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

• 295 A
• 495 B
• 395 C
• 722 D

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

• 
  A
• 
  B
• 
  C
• 
  D

The sum of coefficients in the binomial expansion equals to

• 2 A
• 2ⁿ⁺¹ B
• 2^n-1 C
• 2ⁿ 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 sum of co-efficient in the expansion of (a+b)ⁿis 4096, then the greatest co-efficient in the expansion is

• 1594 A
• 792 B
• 924 C
• 2924 D

(x3-1/x)12

• 295 A
• 495 B
• 395 C
• 722 D

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

• 71 A
• -22 B
• 27 C
• 28 D