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

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

• 14 A
• 12 B
• 8 C
• 4 D

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

• 2nd A
• 3rd B
• 4th C
• 5th D

The fifteenth term of (3-a)¹⁵ is

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

Digit in the unit place of the number 183! + 3¹⁸³

• 7 A
• 6 B
• 3 C
• 0 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

7²ⁿ+ 3^n-1. 2^3n-3is divisible by

• 24 A
• 25 B
• 9 C
• 13 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

• 
  A
• 
  B
• 
  C
• 
  D

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

• 10 A
• 12 B
• 11 C
• 9 D

If in the expansion of (1+x)ⁿ, co-efficients of 2nd, 3rd and 4th terms are in A.P., then x=

• 4 A
• 5 B
• 6 C
• 7 D

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

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

• 
  A
• 
  B
• 
  C
• 
  D

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

• 7th A
• 8th B
• 9th C
• 6th D

In the expansion of (x+y)n the coefficient of 5th and 12th terms are equal then n=

• 12 A
• n=14 B
• 17 C
• n=15 D

The sum of coefficients in the binomial expansion equals to

• 2 A
• 2ⁿ⁺¹ B
• 2^n-1 C
• 2ⁿ 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

For n€ N,2^n>2 > n is to only when

• n<2 A
• n≤ 4 B
• n≥ 4 C

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

• 71 A
• -22 B
• 27 C
• 28 D

(2.02)4 s equal to

• 16 A
• 16.6496 B
• 17 C
• 18 D

1+3x+6x2 +10x3 +....=

• (1+x)-3 A
• (1-x)-2 B
• (1-x)-3 C
• (1+x)-2 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 middle term of [1/x-x]¹⁰ is

• -152 A
• -252 B
• 371 C
• -421 D

• 2 A
• 7 B
• 8 C
• 12 D

• Imaginary A
• Rational B
• Irrational C
• Real numbers D

for n€ N, 3^{2n + 7 is divisible by}

• 7 A
• 8 B
• 9 C
• 10 D

The sum of even coefficient in the binomial expansion is

• 2ⁿ⁺¹ A
• 2ⁿ B
• 2^n-1 C
• 2n D

If n∈Z+ then(a+x)n is a/an

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

If n is any positive integer then n! > 2^n-1for

• 
  A
• 
  B
• 
  C
• 
  D

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

• 295 A
• 495 B
• 395 C
• 722 D