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

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

• 12 A
• 6 B
• 2 C
• 18 D

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

• 6 A
• 3 B
• 4 C
• 8 D

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

• 7th A
• 8th B
• 9th C
• 6th D

(2.02)4 s equal to

• 16 A
• 16.6496 B
• 17 C
• 18 D

• Even A
• Odd B
• Prime C
• None of these D

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

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

• 13 A
• 12 B
• 11 C
• 10 D

• 3/8 A
• 7/8 B
• 1/8 C
• None 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 fifteenth term of (3-a)¹⁵ is

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

7²ⁿ+ 3^n-1. 2^3n-3is divisible by

• 24 A
• 25 B
• 9 C
• 13 D

• 
  A
• 
  B
• 
  C
• 
  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

If n∈Z+ then(a+x)n is a/an

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

(x3-1/x)12

• 295 A
• 495 B
• 395 C
• 722 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

If n € N , then n(n+3) is always

• Multiple of 3 A
• Multiple of 6 B
• odd C
• even 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

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

• 2 A
• 3 B
• 4 C
• 5 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

(51)⁴is equal to

• 7065201 A
• 8065201 B
• 6765201 C
• 6565201 D

(0.90)^1/2is equal to

• 0.99 A
• 0.90 B
• 0.80 C
• 0.88 D

The middle term of [1/x-x]¹⁰ is

• -152 A
• -252 B
• 371 C
• -421 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

• 
  A
• 
  B
• 
  C
• 
  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

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

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

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

• 2nd A
• 3rd B
• 4th C
• 5th D

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

• 10 A
• 12 B
• 11 C
• 9 D

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

• 32 A
• 16 B
• 8 C
• 5 D