ECAT Pre Engineering MCQ Test With Answer for Chapter 10 Mathematics

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

• 8 A
• 9 B
• 10 C
• 11 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 fifth term of (a+2x3)17 is

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

The middle term of [1/x-x]¹⁰ is

• -152 A
• -252 B
• 371 C
• -421 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

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

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

The sum of even coefficient in the binomial expansion is

• 2ⁿ⁺¹ A
• 2ⁿ B
• 2^n-1 C
• 2n D

The fifteenth term of (3-a)¹⁵ is

• -17a¹² A
• -945a¹³ B
• -941a¹³ C
• -515a¹² 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

• 
  A
• 
  B
• 
  C
• 
  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

There is no integer n for which 3n is

• Even A
• Prime B
• Odd C
• Real D

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

If n is any positive integer then 2ⁿ> 2(n + 1) is true for all

• 
  A
• 
  B
• 
  C
• 
  D

n! > 2ⁿ-1 is true when

• n≤ 3 A
• n≤ 6 B
• n≥ 4 C
• n≤ 6 D

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

• 7th A
• 8th B
• 9th C
• 6th D

(x³-1/2x)⁶ is

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

The coefficient of the third term of (8a-b)^1/3, after simplification is

• -228 A
• 1/288 B
• 1/220 C
• -1/177 D

n² - 1 divisible by 8 when n is

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

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

• 295 A
• 495 B
• 395 C
• 722 D

(51)⁴is equal to

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

The middle term of (x-y)⁸is

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

For≥ -2 , 1+3+5+......+(2n+5)

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

ⁿC₂= exists when n is ______

• 
  A
• 
  B
• 
  C
• 
  D