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

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

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

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

The sum of co-efficient in (1+x-3x²)⁴¹⁶³is

• 0 A
• 1 B
• -1 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

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

• 13 A
• 12 B
• 11 C
• 10 D

For each natural number n, n (n+1) is

• an even A
• an odd B
• multiple of 3 C
• Irrational D

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

• 2nd A
• 3rd B
• 4th C
• 5th D

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

• 14 A
• 12 B
• 8 C
• 4 D

7²ⁿ+ 3^n-1. 2^3n-3is divisible by

• 24 A
• 25 B
• 9 C
• 13 D

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

• 1st term A
• 4th term B
• 2nd term C
• 5th term D

The sum of first n even number is

• n2 A
• n(n+1) B
• n+1 C
• n+2 D

• 2 A
• 7 B
• 8 C
• 12 D

The greatest term in the expansion of (3+2x)⁹, when x=1 is

• 4th A
• 4th and 5th B
• 5th C
• 6th D

For n€ N,2^n>2 > n is to only when

• n<2 A
• n≤ 4 B
• n≥ 4 C

If n € N , then n(n+3) is always

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

If the sum of even coefficients in the expansion of (1+x)n is 128 then

• n=7 A
• n=9 B
• n=8 C
• None D

The 7th term of (3⁸ + 6⁴x)^11/4 is

• -19217/3 x⁶ A
• 189/2 6⁴x B
• 2227/12 x³ C
• -19712/3 x⁶ D

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

• 10 A
• 12 B
• 11 C
• 9 D

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

• 3/8 A
• 7/8 B
• 1/8 C
• None D

If n is any positive integer then n²> n + 3 for

• 
  A
• 
  B
• 
  C
• 
  D

n(n-1)(2n-1), for all natural numbers n, is divisible by

• 12 A
• 6 B
• 2 C
• 18 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 coefficient of xn in the expansion of (1-x)-1 is

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

(51)⁴is equal to

• 7065201 A
• 8065201 B
• 6765201 C
• 6565201 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 term involving x⁴ in the expansion (3-2x) is

• 217x⁴ A
• 15120x⁴ B
• 313x⁴ C
• -25x⁴ D

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

for n€ N, 3^{2n + 7 is divisible by}

• 7 A
• 8 B
• 9 C
• 10 D

(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