ECAT Pre Engineering MCQ Test With Answer for Chapter 10 Mathematics

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

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

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

If (1+x-2x³)⁶= 1+a₁x + a₂x²+ a₃x³+ ..... the the value of a₂+ a₄+ a₆+ .....+a₁₂will be

• 32 A
• 31 B
• 64 C
• 1024 D

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

• 295 A
• 495 B
• 395 C
• 722 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

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

The fifteenth term of (3-a)¹⁵ is

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

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

• 71 A
• -22 B
• 27 C
• 28 D

for n€ N, 3^{2n + 7 is divisible by}

• 7 A
• 8 B
• 9 C
• 10 D

The term involving x⁴in the expansion of (3 - 2x)⁷is

• 120 A
• 1512 B
• 1250 C
• 15120 D

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

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

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

If nis positive integers, then 2ⁿ>2n+1, only when

• n≤ 3 A
• n≥ 3 B
• n≤ 2 C
• n≤ 1 D

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

• 9 A
• 6 B
• 5 C
• 10 D

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

• 13 A
• 12 B
• 11 C
• 10 D

ⁿC₂= exists when n is ______

• 
  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

n! > 2ⁿ-1 is true when

• n≤ 3 A
• n≤ 6 B
• n≥ 4 C
• n≤ 6 D

If n is any positive integer then n! > n²for

• 
  A
• 
  B
• 
  C
• 
  D

If n is add the expansion (a + x)ⁿhas middle terms

• 2 A
• 3 B
• 4 C
• 5 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

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

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

If n∈Z+ then(a+x)n is a/an

• Finite series A
• Convergent series B
• Infinite series C
• Divergent series 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

1st four terms of the expansion (1-x)^-2are

• 1 + 2x + 3x²+ 4x³ A
• 3x²+ 2x + 1 B
• 1 + 3x + 4x²+ 5x³ C
• None of these D

The sum of coefficients in the binomial expansion equals to

• 2 A
• 2ⁿ⁺¹ B
• 2^n-1 C
• 2ⁿ 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

n² - 1 divisible by 8 when n is

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

The third term in the expansion of (1+2x) is

• -2x2 A
• -4x2 B
• 2x2 C
• 4x2 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