Mathematical Induction and Binomial Theorem PYQs - Last 10 Years
JEE Advanced / Mathematics / Algebra / 5 recent questions
MathematicsAlgebra2016-2025
Practice 5 JEE Advanced Mathematics questions from Mathematical Induction and Binomial Theorem. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.
5
PYQs on Page
Mathematics / Algebra
2016-2025
Year Range
Based on indexed question metadata
2
Last 5 Years
2021-2025
5
Last 10 Years
2016-2025
Recent Year Trend
2016
2018
2020
2023
2025Latest year
20161 max PYQs/year2025
Question Types
5PYQs
INTEGER80%
MCQM20%
Difficulty Mix
#1 Medium3
#2 Hard2
2 in last 5 years5 in last 10 years
Last 10 Years Mathematical Induction and Binomial Theorem Questions
Showing 5 of 5 filtered questions.
1Mathematical Induction And Binomial Theorem
Let $a_0, a_1, \ldots, a_{23}$ be real numbers such that
\(\left(1+\frac{2}{5} x\right)^{23}=\sum\limits_{i=0}^{23} a_i x^i\)
for every real number $x$. Let $a_r$ be the largest among the numbers $a_j$ for $0 \leq j \leq 23$. Then the val...
\(\left(1+\frac{2}{5} x\right)^{23}=\sum\limits_{i=0}^{23} a_i x^i\)
for every real number $x$. Let $a_r$ be the largest among the numbers $a_j$ for $0 \leq j \leq 23$. Then the val...
INTEGER+4 / -02025
2Mathematical Induction And Binomial Theorem
Let $a$ and $b$ be two nonzero real numbers. If the coefficient of $x^5$ in the expansion of $\left(a x^2+\frac{70}{27 b x}\right)^4$ is equal to the coefficient of $x^{-5}$ in the expansion of $\left(a x-\frac{1}{b x^2}\right)^7$, then the...
INTEGER+4 / -02023
3Mathematical Induction And Binomial Theorem
For non-negative integers s and r, let\(\left( {\matrix{
s \cr
r \cr
} } \right) = \left\{ {\matrix{
{{{s!} \over {r!(s - r)!}}} & {if\,r \le \,s,} \cr
0 & {if\,r\, > \,s} \cr
} } \right.\)For positive integers m and...
MCQM+4 / -22020
4Mathematical Induction And Binomial Theorem
Let \(X = {({}^{10}{C_1})^2} + 2{({}^{10}{C_2})^2} + 3{({}^{10}{C_3})^2} + ... + 10{({}^{10}{C_{10}})^2}\), where \({}^{10}{C_r}\), r \(\in\){1, 2, ..., 10} denote binomial coefficients. Then, the value of \({1 \over {1430}}X\) is ..........
INTEGER+3 / -02018
5Mathematical Induction And Binomial Theorem
Let \(m\) be the smallest positive integer such that the coefficient of \({x^2}\) in the expansion of $${\left( {1 + x} \right)^2} + {\left( {1 + x} \right)^3} + ........ + {\left( {1 + x} \right)^{49}} + {\left( {1 + mx} \right)^{50}}\,\,$...
INTEGER+3 / -02016