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JEE Advanced Previous Year Questions (2018 - 2023): Mathematical Induction and Binomial Theorem | Mathematics (Maths) for JEE Main & Advanced PDF Download

2023

Q1: Let a and b be two nonzero real numbers. If the coefficient of x5 in the expansion of JEE Advanced Previous Year Questions (2018 - 2023): Mathematical Induction and Binomial Theorem | Mathematics (Maths) for JEE Main & Advanced is equal to the coefficient of x−5 in the expansion of JEE Advanced Previous Year Questions (2018 - 2023): Mathematical Induction and Binomial Theorem | Mathematics (Maths) for JEE Main & Advanced , then the value of 2b is :               [JEE Advanced 2023 Paper 1]
Ans: 
3
JEE Advanced Previous Year Questions (2018 - 2023): Mathematical Induction and Binomial Theorem | Mathematics (Maths) for JEE Main & Advanced
here 8 - 3r = 5
8 - 5 = 3r
∴ r = 1

JEE Advanced Previous Year Questions (2018 - 2023): Mathematical Induction and Binomial Theorem | Mathematics (Maths) for JEE Main & Advanced

7 - 3r = 5
⇒ 12 = 3r
∴ r = 4
now, JEE Advanced Previous Year Questions (2018 - 2023): Mathematical Induction and Binomial Theorem | Mathematics (Maths) for JEE Main & Advanced

JEE Advanced Previous Year Questions (2018 - 2023): Mathematical Induction and Binomial Theorem | Mathematics (Maths) for JEE Main & Advanced 
⇒ b = 3/2
∴ 2b = 3

2020

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

JEE Advanced Previous Year Questions (2018 - 2023): Mathematical Induction and Binomial Theorem | Mathematics (Maths) for JEE Main & Advanced

For positive integers m and n, let 

JEE Advanced Previous Year Questions (2018 - 2023): Mathematical Induction and Binomial Theorem | Mathematics (Maths) for JEE Main & Advanced

where for any non-negative integer p,

JEE Advanced Previous Year Questions (2018 - 2023): Mathematical Induction and Binomial Theorem | Mathematics (Maths) for JEE Main & Advanced

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,

JEE Advanced Previous Year Questions (2018 - 2023): Mathematical Induction and Binomial Theorem | Mathematics (Maths) for JEE Main & Advanced

Since, JEE Advanced Previous Year Questions (2018 - 2023): Mathematical Induction and Binomial Theorem | Mathematics (Maths) for JEE Main & Advanced

JEE Advanced Previous Year Questions (2018 - 2023): Mathematical Induction and Binomial Theorem | Mathematics (Maths) for JEE Main & Advanced

2018

Q1: Let JEE Advanced Previous Year Questions (2018 - 2023): Mathematical Induction and Binomial Theorem | Mathematics (Maths) for JEE Main & Advanced where JEE Advanced Previous Year Questions (2018 - 2023): Mathematical Induction and Binomial Theorem | Mathematics (Maths) for JEE Main & Advanced denote binomial coefficients. Then, the value of JEE Advanced Previous Year Questions (2018 - 2023): Mathematical Induction and Binomial Theorem | Mathematics (Maths) for JEE Main & Advanced is _____.            [JEE Advanced 2018 Paper 2]
Ans:
646
JEE Advanced Previous Year Questions (2018 - 2023): Mathematical Induction and Binomial Theorem | Mathematics (Maths) for JEE Main & Advanced

JEE Advanced Previous Year Questions (2018 - 2023): Mathematical Induction and Binomial Theorem | Mathematics (Maths) for JEE Main & Advanced

JEE Advanced Previous Year Questions (2018 - 2023): Mathematical Induction and Binomial Theorem | Mathematics (Maths) for JEE Main & Advanced

Now,  JEE Advanced Previous Year Questions (2018 - 2023): Mathematical Induction and Binomial Theorem | Mathematics (Maths) for JEE Main & Advanced
= 19 x 17 x 16 / 8
= 19 x 34
= 646

The document JEE Advanced Previous Year Questions (2018 - 2023): Mathematical Induction and Binomial Theorem | Mathematics (Maths) for JEE Main & Advanced is a part of the JEE Course Mathematics (Maths) for JEE Main & Advanced.
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