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

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

• 13 A
• 12 B
• 11 C
• 10 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

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

• | x | < 1 A
• | x | < 3 B
• | x | < 1/3 C
• None of these D

• 
  A
• 
  B
• 
  C
• 
  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

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

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

a + x is ______

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

For every positive integers n 1+5+9+....+ (4n - 3) is

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

If n is any positive integer then n! > n²for

• 
  A
• 
  B
• 
  C
• 
  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)^-2are ______

• 1 - 2x + 3x² A
• 1 - 2x - 3x² B
• 1 + 2x + 3x² C
• -2 -2x + 3x² D

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

• 
  A
• 
  B
• 
  C
• 
  D

For≥ -2 , 1+3+5+......+(2n+5)

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

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

• 1700 A
• 17023 B
• 17027 C
• 17010 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 7th term of (3⁸ + 6⁴x)^11/4 is

• -19217/3 x⁶ A
• 189/2 6⁴x B
• 2227/12 x³ C
• -19712/3 x⁶ 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 greatest integer which divides the number 101¹⁰⁰- 1 is

• 100 A
• 1000 B
• 10000 C
• 100000 D

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

• 10 A
• 12 B
• 11 C
• 9 D

The middle term of [1/x-x]¹⁰ is

• -152 A
• -252 B
• 371 C
• -421 D

• 3/8 A
• 7/8 B
• 1/8 C
• None D

The expansion (1 + x)^-3holds when

• |x| > 1 A
• |x| < 1 B
• x < 1 C
• x > 1 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

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

• 2nd term A
• 3rd term B
• 4th term C
• 5th term D

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

• 9 A
• 6 B
• 5 C
• 10 D

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

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

• 2nd A
• 3rd B
• 4th C
• 5th D