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JEE Advanced Previous Year Questions (2018 - 2025): Mathematical Induction and Binomial Theorem

2023

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

2023

7 - 3r = 5
⇒ 12 = 3r
∴ r = 4
now, 2023

2023 
⇒ b = 3/2
∴ 2b = 3

2020

Q1: For non-negative integers s and r, let 

2020

For positive integers m and n, let 

2020

where for any non-negative integer p,

2020

Then which of the following statements is/are TRUE?
(a) g(m, n) = g(n, m) for all positive integers m, n
(b) g(m, n + 1) = g(m + 1, n) for all positive integers m, n
(c) g(2m, 2n) = 2g(m, n) for all positive integers m, n
(d) g(2m, 2n) = (g(m, n))2 for all positive integers m, n     [JEE Advanced 2020 Paper 2]
Ans:
(a), (b) & (d)
Since,

2020

Since, 2020

2020

2018

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

2018

2018

Now,  2018
= 19 x 17 x 16 / 8
= 19 x 34
= 646

The document JEE Advanced Previous Year Questions (2018 - 2025): Mathematical Induction and Binomial Theorem is a part of the JEE Course Mathematics (Maths) for JEE Main & Advanced.
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