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

The sum of first n even number is

• n2 A
• n(n+1) B
• n+1 C
• n+2 D

In the expansion of (x+y)n the coefficient of 5th and 12th terms are equal then n=

• 12 A
• n=14 B
• 17 C
• n=15 D

7²ⁿ+ 3^n-1. 2^3n-3is divisible by

• 24 A
• 25 B
• 9 C
• 13 D

(x3-1/x)12

• 295 A
• 495 B
• 395 C
• 722 D

The sum of the odd coefficients in the expansion of (a + x)⁴is

• 14 A
• 12 B
• 8 C
• 4 D

(x³-1/2x)⁶ is

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

If the exponent in the binomial expansion is 6, then the middle term is

• 2nd A
• 3rd B
• 4th C
• 5th D

• ¹⁰C₆ A
• ¹⁰C₅ B
• ¹⁰C₄ C
• None D

The proposition S(n) for any n∈ N is only true if k∈ N and

• S(k +1) is true A
• S(1) is true and S(k+1) is true whenever S (k) is true B
• S(k+1) is true whenever S (k) is true C
• S(k) is true D

(51)⁴is equal to

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

• 3/8 A
• 7/8 B
• 1/8 C
• None D

• ⁿC_r A
• ⁿ⁺¹C_r+1 B
• ⁿC_r+1 C
• None D

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

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

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

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

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

There is no integer n for which 3n is

• Even A
• Prime B
• Odd C
• Real 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

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

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

• 1st term A
• 4th term B
• 2nd term C
• 5th term 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)^-1are

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

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

• 
  A
• 
  B
• 
  C
• 
  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 n is any positive integer then 2ⁿ> 2(n + 1) 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

a + x is ______

• A trinomial A
• A binomial B
• A monomial C
• None of these 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 the exponent in the binomial expansion is 6, then the middle term is

• 2nd term A
• 3rd term B
• 4th term C
• 5th term D

The middle term of (x-y)⁸is

• 25 x⁴y⁴ A
• 70 x⁴y⁴ B
• 120 x⁴y⁴ C
• 97x⁴y⁴ D

The sum of the coefficient in the expansion of (a + x)⁵is

• 32 A
• 16 B
• 8 C
• 5 D