Statement 1: If n is even, then ^ 2n C_1+ ^ 2n C_3+ + ^ 2n C_ n-1 =2^ 2n-1 . Statement 2: ^ 2n C_1+ ^ 2n C_3+ + ^ 2n C_ 2n-1 =2^ 2n-1 .

JEE Main Mathematics question

Statement 1: If is even, then . Statement 2: .

(A)Assertion is True, Reason is True; Reason is correct explanation for Assertion
(B)Assertion is True, Reason is True; Reason is not correct explanation for Assertion
(C)Assertion is True, Reason is False
(D)Assertion is False, Reason is TrueCorrect

Answer: (D)

Solution

Statement 2: the sum of the odd-indexed binomial coefficients of is half of , i.e. , so it is true. Statement 1 stops at index , which is only half of the odd

See the full step-by-step solution

Create a free account to read the complete working, and practise questions like this in a timed test.

Create a free account

Question ID VK-021103