Q1: Let a and b be two nonzero real numbers. If the coefficient of x5 in the expansion of
is equal to the coefficient of x-5 in the expansion of
, then the value of 2b is : [JEE Advanced 2023 Paper 1]
Ans: 3
here 8 - 3r = 5
8 - 5 = 3r
∴ r = 1

7 - 3r = 5
⇒ 12 = 3r
∴ r = 4
now, 
⇒ b = 3/2
∴ 2b = 3
Q1: For non-negative integers s and r, let

For positive integers m and n, let

where for any non-negative integer p,


Since, 

Q1: Let
where
denote binomial coefficients. Then, the value of
is _____. [JEE Advanced 2018 Paper 2]
Ans: 646


Now, 
= 19 x 17 x 16 / 8
= 19 x 34
= 646