ECAT Pre Engineering MCQ Test With Answer for Chapter 10 Mathematics

• 
  A
• 
  B
• 
  C
• 
  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 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

There is no integer n for which 3n is

• Even A
• Prime B
• Odd C
• Real 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

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

When we expand (a + 2b)⁵then

• a⁵+ 10a⁴b + 40a³b²+ 80a²b³+ 80ab⁴+ 32b⁵ A
• a⁵+ a⁴b + a³b²+ a²b³+ ab⁴+ b⁵ B
• 5a⁵+ 4a⁴b + 3a³b²+ 2a²b³+ 1 ab⁴+ b⁵ C
• None 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

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 greatest integer which divides the number 101¹⁰⁰- 1 is

• 100 A
• 1000 B
• 10000 C
• 100000 D

If n is not natural number, then the expansion (1 + x)ⁿis valid for

• 
  A
• 
  B
• 
  C
• 
  D

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

• 13 A
• 12 B
• 11 C
• 10 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

The coefficient of the second term of (a+b)⁴ is

• 1 A
• 9 B
• 3 C
• 5 D

If n is any positive integer then 4ⁿ>3ⁿ+ 4 is true for all

• 
  A
• 
  B
• 
  C
• 
  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

• 
  A
• 
  B
• 
  C
• 
  D

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

• 
  A
• 
  B
• 
  C
• 
  D

If the 4th term in the expansion of (px + x^-1)^mis 2.5 for all x∈ R, then

• 
  A
• 
  B
• 
  C
• 
  D

• ¹⁰C₆ A
• ¹⁰C₅ B
• ¹⁰C₄ C
• None 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 coefficient of x¹⁸ in (ax⁴-bx)⁹ after expansion is

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

The expansion of (1 - 3x)^-1is valid if

• | x | < 1 A
• | x | < 3 B
• | x | < 1/3 C
• None of these 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 term involving x⁴ in the expansion (3-2x) is

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

The number of terms in the expansion of (a + b)⁹is

• 10 A
• 11 B
• 9 C
• 12 D

ⁿC₂= exists when n is ______

• 
  A
• 
  B
• 
  C
• 
  D

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

• 32 A
• 16 B
• 8 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