The sum of coefficients of integral powers of x in the binomial expansion of  is

If (10)⁹ +2 (11)²(10)⁷ + .....+10 (11)⁹ = K(10)⁹, then k is equal to

• 121/10

• 441/100

• 100

• 100

A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is

• 17/3⁵

• 13/3⁵

• 11/3⁵

• 11/3⁵

The term independent of  x in  is 

• 4

• 120

• 18

• 18

If n is a positive integer, then  is

• an irrational number

• an odd positive integer

• an even positive integer

• an even positive integer

The coefficient of x⁷ in the expansion of (1 - x - x² +x³)⁶ is :

• 144

• -132

• -144

• -144

The value of
(²¹C₁ – ¹⁰C₁) + (²¹C₂ – ¹⁰C₂) + (²¹C₃ – ¹⁰C₃) + (²¹C₄ – ¹⁰C₄) + .... +
(²¹C₁₀ – ¹⁰C₁₀) is

• 2²⁰ – 2¹⁰

• 2²¹ – 2¹¹

• 2²¹ – 2¹⁰

• 2²¹ – 2¹⁰

8.

• Statement −1 is false, Statement −2 is true

• Statement −1 is true, Statement −2 is true, Statement −2 is a correct explanation for Statement −1

• Statement −1 is true, Statement −2 is true; Statement −2 is not a correct explanation for Statement −1.

• Statement −1 is true, Statement −2 is true; Statement −2 is not a correct explanation for Statement −1.

In the binomial expansion of (a - b)n, n ≥ 5, the sum of 5th and 6th terms is zero, then
a/b equals

• 5/n −4

• 6 /n −5

• n -5 /6

• n -5 /6

The sum of the series ²⁰C₀ – ²⁰C₁ + ²⁰C₂ – ²⁰C₃ + …… - ….. + ²⁰C₁₀ is-

• – ²⁰C₁₀

• 

• 0

• 0