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

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

• 
  A
• 
  B
• 
  C
• 
  D

The sum of even coefficient in the binomial expansion is

• 2ⁿ⁺¹ A
• 2ⁿ B
• 2^n-1 C
• 2n D

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

In the expansion of (a + x)ⁿthe sum of exponents of a and x in each term of the expansion is

• n + 1 A
• n - 1 B
• n C
• 2n D

• 3/8 A
• 7/8 B
• 1/8 C
• None D

There is no integer n for which 3ⁿ is

• Odd A
• even B
• Natural C
• Prime D

a + x is ______

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

n² - 1 divisible by 8 when n is

• an odd integer A
• an even integer B
• Irrational C
• Prime Number D

The proposition S(k+1) is true when ______ is true∀K∈N

• S(n) A
• S(k) B
• S(1) C
• S(k-1) D

(x³-1/2x)⁶ is

• 15/16 x² A
• 2/13 x² B
• 17/7 x² C
• 16/15 x² D

The coefficient of xn in the expansion of (1-2x)-1 is

• (-1)n2n A
• 2n B
• (-1)(n+1)xr C
• (n+1)2n D

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

• 2 A
• 3 B
• 4 C
• 5 D

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

• 1 A
• 9 B
• 3 C
• 5 D

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

• 10 A
• 11 B
• 9 C
• 12 D

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

• | x | < 1/2 A
• | x | < 1 B
• | x | < 2 C
• | x | < 3 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 term involving x4 the expansion (3-2x)7 is

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

The term involving x⁴ in the expansion (3-2x) is

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

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

• 
  A
• 
  B
• 
  C
• 
  D

• 28 / 81 A
• 28 / 243 B
• 81 / 28 C
• 243 / 82 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 sum of the odd coefficients in the expansion of (a + x)⁴is

• 14 A
• 12 B
• 8 C
• 4 D

• 2 A
• 7 B
• 8 C
• 12 D

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

• 13 A
• 12 B
• 11 C
• 10 D

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

• an even A
• an odd B
• multiple of 3 C
• Irrational D

(x3-1/x)12

• 295 A
• 495 B
• 395 C
• 722 D

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

If the sum of even coefficients in the expansion of (1+x)n is 128 then

• n=7 A
• n=9 B
• n=8 C
• None D