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

(0.90)^1/2is equal to

• 0.99 A
• 0.90 B
• 0.80 C
• 0.88 D

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

• 
  A
• 
  B
• 
  C
• 
  D

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

• 2nd A
• 3rd B
• 4th C
• 5th D

If a statement S(n) is true for n = i where i is some natural number and the truth of S(n) for n = k > i implies the truth of S(n) for n = k +1 then S(n) is true for all positive integers

• 
  A
• 
  B
• 
  C
• 
  D

The coefficient of xn in the expansion of (1-x)-1 is

• (-1)n2n A
• 1 B
• (-1)n(n+1) C
• (n+1) D

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

• an even A
• an odd B
• multiple of 3 C
• Irrational 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 5th term of (3a-2b) ^-1 is

• 77b²/a⁵ A
• 16b² /243 a⁵ B
• 17b⁴/43a⁵ C
• 25b³/43a⁵ D

Number of terms in the expansion of (a+x)ⁿis

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

The middle term of (x-y)⁸is

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

• 405 / 256 A
• 504 / 259 B
• 450 / 263 C
• None 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

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

• 10 A
• 12 B
• 11 C
• 9 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

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 positive integer just greater than (1+0.0001)¹⁰⁰⁰⁰is

• 4 A
• 5 B
• 2 C
• 3 D

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

• 9 A
• 6 B
• 5 C
• 10 D

If n∈Z+ then(a+x)n is a/an

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

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

• 120 A
• 1512 B
• 1250 C
• 15120 D

n(n-1)(2n-1), for all natural numbers n, is divisible by

• 12 A
• 6 B
• 2 C
• 18 D

The expansion of (1 + 2x)^-2is valed if

• | x | < 1/2 A
• | x | < 1 B
• | x | < 2 C
• | x | < 3 D

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

• 1 A
• 9 B
• 3 C
• 5 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

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

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

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

(2.02)4 s equal to

• 16 A
• 16.6496 B
• 17 C
• 18 D

If n is any positive integer then 3 + 6 + 9 + ....+ 3n = ______

• 
  A
• 
  B
• 
  C
• 
  D

• 8 A
• 9 B
• 10 C
• 11 D

The sum of the odd coefficients in the expansion of (a + x)⁴is

• 14 A
• 12 B
• 8 C
• 4 D