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

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

The exponent of x in 10th term in the expansion of (a+x)n

• 10 A
• 12 B
• 11 C
• 9 D

(0.90)^1/2is equal to

• 0.99 A
• 0.90 B
• 0.80 C
• 0.88 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 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 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

n² - 1 divisible by 8 when n is

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

The expansion of (1 - 3x)^-1is valid if

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

Digit in the unit place of the number 183! + 3¹⁸³

• 7 A
• 6 B
• 3 C
• 0 D

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

• 71 A
• -22 B
• 27 C
• 28 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

If the 4th term in the expansion of (px + x^-1)^mis 2.5 for all x∈ R, then

• 
  A
• 
  B
• 
  C
• 
  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 € N , then n(n+3) is always

• Multiple of 3 A
• Multiple of 6 B
• odd C
• even 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 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 in the expansion of (1+x)ⁿ, co-efficients of 2nd, 3rd and 4th terms are in A.P., then x=

• 4 A
• 5 B
• 6 C
• 7 D

The coefficient of xn in the expansion of (1-2x)-1 is

• (-1)n2n A
• 2n B
• (-1)(n+1)xr C
• (n+1)2n D

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

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

The sum of coefficients in the binomial expansion equals to

• 2 A
• 2ⁿ⁺¹ B
• 2^n-1 C
• 2ⁿ D

• Imaginary A
• Rational B
• Irrational C
• Real numbers D

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

• 9 A
• 6 B
• 5 C
• 10 D

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

• 4 A
• 5 B
• 2 C
• 3 D

• 3/8 A
• 7/8 B
• 1/8 C
• None D

• Even A
• Odd B
• Prime 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

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

For≥ -2 , 1+3+5+......+(2n+5)

• (n+2)² A
• (n-2)² B
• 2n+1 C
• (n+3)² 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