ECAT Pre General Science MCQ Test With Answer for Mathematics Chapter 10

(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

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

The proposition S(k+1) is true when ______ is true∀K∈N

• S(n) A
• S(k) B
• S(1) C
• S(k-1) 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

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

(x³-1/2x)⁶ is

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

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

• 10 A
• 11 B
• 9 C
• 12 D

(51)⁴is equal to

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

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

• 9 A
• 6 B
• 5 C
• 10 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

For all positive integral value of n,3ⁿ< n! , when

• n> 6 A
• n< 6 B
• n<11 C
• n>11 D

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

If n is any positive integer then 3 + 6 + 9 + ....+ 3n = ______

• 
  A
• 
  B
• 
  C
• 
  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 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

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 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

If x+y+z+......+2n = 2n+1-1∀n∈W,then cube root of xyz is equal to

• 1 A
• 4 B
• 2 C
• 8 D

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

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

If a statement S(n) is true for n = i where i is some natural number and the truth of S(n) for n = k > i implies the truth of S(n) for n = k +1 then S(n) is true for all positive integers

• 
  A
• 
  B
• 
  C
• 
  D

The proposition S(n) is true∀n∈N,S(k+1) true when ______is true

• S(1) A
• Both a & c B
• S(k) C
• None 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

If n∈Z+ then(a+x)n is a/an

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

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

• 7th A
• 8th B
• 9th C
• 6th D

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

• 
  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 n€ N, 3^{2n + 7 is divisible by}

• 7 A
• 8 B
• 9 C
• 10 D

If n € N , then n(n+3) is always

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

• 2 and 9 A
• 3 and 2 B
• 2/3 and 9 C
• 3/2 and 6 D