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

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

• 7 A
• 6 B
• 3 C
• 0 D

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

a + x is ______

• A trinomial A
• A binomial B
• A monomial C
• None of these D

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

• 2nd A
• 3rd B
• 4th C
• 5th 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

(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

• 2 A
• 7 B
• 8 C
• 12 D

(1 - x)³= ______

• 1 + 3x + 3x²+ x³ A
• 1 + x + x²+ x³ B
• 1 - x + x²- x³ C
• 1 - 3x + 3x²- x³ D

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

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

• 4013 x3a13 A
• 2208a13 x12 B
• 223x7a18 C
• 38080a13 x12 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 term involving x⁴in the expansion of (3 - 2x)⁷is

• 120 A
• 1512 B
• 1250 C
• 15120 D

If n is odd then the middle terms in the expansion of (a + x)ⁿare

• 
  A
• 
  B
• 
  C
• 
  D

The fifteenth term of (3-a)¹⁵ is

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

(0.90)^1/2is equal to

• 0.99 A
• 0.90 B
• 0.80 C
• 0.88 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

For≥ -2 , 1+3+5+......+(2n+5)

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

for n€ N, 3^{2n + 7 is divisible by}

• 7 A
• 8 B
• 9 C
• 10 D

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

• 295 A
• 495 B
• 395 C
• 722 D

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

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

• 7th A
• 8th B
• 9th C
• 6th D

ⁿC₂= exists when n is ______

• 
  A
• 
  B
• 
  C
• 
  D

For each even natural number n (n²-1) is divisible by

• 6 A
• 3 B
• 4 C
• 8 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

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

• 71 A
• -22 B
• 27 C
• 28 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

The coefficient of x¹⁸ in (ax⁴-bx)⁹ after expansion is

• 84a³ b⁶ A
• 22a³b⁶ B
• 27a⁴b⁵ C
• 28a³b⁶ D

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

• 13 A
• 12 B
• 11 C
• 10 D

n! > 2ⁿ-1 is true when

• n≤ 3 A
• n≤ 6 B
• n≥ 4 C
• n≤ 6 D

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

• 
  A
• 
  B
• 
  C
• 
  D