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Previous year question hub

Mathematical Induction And Binomial Theorem - Algebra - Mathematics Previous Year Questions

Practice Mathematical Induction And Binomial Theorem - Algebra - Mathematics previous year questions organised from real papers, with year-wise coverage and clear topic navigation.

35Papers
32Years
52Questions
1Topics

Mathematical Induction And Binomial Theorem question pattern

Every graph below is calculated only from this selection.

Questions by year

Year-wise coverage for Mathematical Induction And Binomial Theorem. Each bar uses a separate theme-derived color.

Difficulty distribution

How the classified questions are distributed by difficulty.

Medium 31 59.6%
Hard 13 25%
Easy 8 15.4%

Question type distribution

MCQ, numerical, multiple-select and other formats found in these papers.

Subjective 29 55.8%
Multiple Choices 18 34.6%
Numerical Answer Type (NAT) 5 9.6%

Subject weightage

Top subjects by unique question coverage.

Mathematics
52 Qs

Most asked topics

Top topics across the included previous year papers.

Algebra
52 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Mathematical Induction And Binomial Theorem
52 Qs

Paper coverage

Question coverage for the most populated papers. Every active PYP paper remains listed below.

JEE ADVANCED 2025 PAPER 2 ONLINE
1 Qs
JEE ADVANCED 2023 PAPER 1 ONLINE
1 Qs
JEE ADVANCED 2020 PAPER 2 OFFLINE
1 Qs
JEE ADVANCED 2018 PAPER 2 OFFLINE
1 Qs
JEE ADVANCED 2016 PAPER 1 OFFLINE
1 Qs
JEE ADVANCED 2014 PAPER 2 OFFLINE
1 Qs
JEE ADVANCED 2013 PAPER 1 OFFLINE
1 Qs
IIT JEE 2010 PAPER 2 OFFLINE
1 Qs
IIT JEE 2005 SCREENING
1 Qs
IIT JEE 2004 SCREENING
1 Qs
IIT JEE 2003
1 Qs
IIT JEE 2003 SCREENING
1 Qs
IIT JEE 2002
1 Qs
IIT JEE 2002 SCREENING
1 Qs
IIT JEE 2001 SCREENING
1 Qs
IIT JEE 2000
4 Qs
IIT JEE 2000 SCREENING
1 Qs
IIT JEE 1999
2 Qs
IIT JEE 1998
2 Qs
IIT JEE 1997
2 Qs
IIT JEE 1996
1 Qs
IIT JEE 1994
3 Qs
IIT JEE 1993
2 Qs
IIT JEE 1992
3 Qs
IIT JEE 1991
1 Qs
IIT JEE 1990
1 Qs
IIT JEE 1989
2 Qs
IIT JEE 1988
1 Qs
IIT JEE 1987
1 Qs
IIT JEE 1986
1 Qs
IIT JEE 1985
1 Qs
IIT JEE 1984
2 Qs
IIT JEE 1983
4 Qs
IIT JEE 1982
2 Qs
IIT JEE 1979
1 Qs

Included previous year papers

Newest papers appear first. Sort by year, question coverage or name.

PaperYear / sessionQuestions in this viewOpen
JEE ADVANCED 2025 PAPER 2 ONLINE20251View paper
JEE ADVANCED 2023 PAPER 1 ONLINE20231View paper
JEE ADVANCED 2020 PAPER 2 OFFLINE20201View paper
JEE ADVANCED 2018 PAPER 2 OFFLINE20181View paper
JEE ADVANCED 2016 PAPER 1 OFFLINE20161View paper
JEE ADVANCED 2014 PAPER 2 OFFLINE20141View paper
JEE ADVANCED 2013 PAPER 1 OFFLINE20131View paper
IIT JEE 2010 PAPER 2 OFFLINE20101View paper
IIT JEE 2005 SCREENING20051View paper
IIT JEE 2004 SCREENING20041View paper
IIT JEE 200320031View paper
IIT JEE 2003 SCREENING20031View paper
IIT JEE 200220021View paper
IIT JEE 2002 SCREENING20021View paper
IIT JEE 2001 SCREENING20011View paper
IIT JEE 200020004View paper
IIT JEE 2000 SCREENING20001View paper
IIT JEE 199919992View paper
IIT JEE 199819982View paper
IIT JEE 199719972View paper
IIT JEE 199619961View paper
IIT JEE 199419943View paper
IIT JEE 199319932View paper
IIT JEE 199219923View paper
IIT JEE 199119911View paper
IIT JEE 199019901View paper
IIT JEE 198919892View paper
IIT JEE 198819881View paper
IIT JEE 198719871View paper
IIT JEE 198619861View paper
IIT JEE 198519851View paper
IIT JEE 198419842View paper
IIT JEE 198319834View paper
IIT JEE 198219822View paper
IIT JEE 197919791View paper

All Mathematical Induction And Binomial Theorem previous year questions

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1
1979 · Mathematics · Algebra · Mathematical Induction And Binomial Theorem
IIT JEE 1979
Given that \({C_1} + 2{C_2}x + 3{C_3}{x^2} + ......... + 2n{C_{2n}}{x^{2n - 1}} = 2n{\left( {1 + x} \right)^{2n - 1}}\)
where \({C_r} = {{\left( {2n} \right)\,!} \over {r!\left( {2n - r} \right)!}}\,\,\,\,\,r = 0,1,2,\,............,2n\)
Prove that \({C_1}^2 - 2{C_2}^2 + 3{C_3}^2 - ............ - 2n{C_{2n}}^2 = {\left( { - 1} \right)^n}n{C_n}.\)
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2
1982 · Mathematics · Algebra · Mathematical Induction And Binomial Theorem
IIT JEE 1982
Prove that \({7^{2n}} + \left( {{2^{3n - 3}}} \right)\left( {3n - 1} \right)\) is divisible by 25 for any natural number \(n\).
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3
1982 · Mathematics · Algebra · Mathematical Induction And Binomial Theorem
IIT JEE 1982
The sum of the coefficients of the plynomial \({\left( {1 + x - 3{x^2}} \right)^{2163}}\) is ...............
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4
1983 · Mathematics · Algebra · Mathematical Induction And Binomial Theorem
IIT JEE 1983
If \({\left( {1 + x} \right)^n} = {C_0} + {C_1}x + {C_2}{x^2} + ..... + {C_n}{x^n}\) then show that the sum of the products of the \({C_i}s\) taken two at a time, represented \(\sum\limits_{0 \le i < j \le n} {\sum {{C_i}{C_j}} }\) is equal to \({2^{2n - 1}} - {{\left( {2n} \right)!} \over {2{{\left( {n!} \right)}^2}}}\)
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5
1983 · Mathematics · Algebra · Mathematical Induction And Binomial Theorem
IIT JEE 1983
The coefficient of \({x^4}\) in \({\left( {{x \over 2} - {3 \over {{x^2}}}} \right)^{10}}\) is
A
\({{{405} \over {256}}}\)
B
\({{{504} \over {259}}}\)
C
\({{{450} \over {263}}}\)
D
none of these
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6
1983 · Mathematics · Algebra · Mathematical Induction And Binomial Theorem
IIT JEE 1983
Given positive integers \(r > 1,\,n > 2\) and that the coefficient of \(\left( {3r} \right)\)th and \(\left( {r + 2} \right)\)th terms in the binomial expansion of \({\left( {1 + x} \right)^{2n}}\) are equal. Then
A
\(n = 2r\)
B
\(n = 2r + 1\)
C
\(n = 3r\)
D
none of these
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7
1983 · Mathematics · Algebra · Mathematical Induction And Binomial Theorem
IIT JEE 1983
Use mathematical Induction to prove : If \(n\) is any odd positive integer, then \(n\left( {{n^2} - 1} \right)\) is divisible by 24.
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8
1984 · Mathematics · Algebra · Mathematical Induction And Binomial Theorem
IIT JEE 1984
Given \({s_n} = 1 + q + {q^2} + ...... + {q^2};\)
$${S_n} = 1 + {{q + 1} \over 2} + {\left( {{{q + 1} \over 2}} \right)^2} + ........ + {\left( {{{q + 1} \over 2}} \right)^n}\,\,\,,q \ne 1$$
Prove that \({}^{n + 1}{C_1} + {}^{n + 1}{C_2}{s_1} + {}^{n + 1}{C_3}{s_2} + ..... + {}^{n + 1}{C_n}{s_n} = {2^n}{S_n}\)
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9
1984 · Mathematics · Algebra · Mathematical Induction And Binomial Theorem
IIT JEE 1984
If \(p\) be a natural number then prove that \({p^{n + 1}} + {\left( {p + 1} \right)^{2n - 1}}\) is divisible by \({p^2} + p + 1\) for every positive integer \(n\).
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10
1985 · Mathematics · Algebra · Mathematical Induction And Binomial Theorem
IIT JEE 1985
Use method of mathematical induction \({2.7^n} + {3.5^n} - 5\) is divisible by \(24\) for all \(n > 0\)
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11
1986 · Mathematics · Algebra · Mathematical Induction And Binomial Theorem
IIT JEE 1986
If \({C_r}\) stands for \({}^n{C_r},\) then the sum of the series \({{2\left( {{n \over 2}} \right){\mkern 1mu} !{\mkern 1mu} \left( {{n \over 2}} \right){\mkern 1mu} !} \over {n!}}\left[ {C_0^2 - 2C_1^2 + 3C_2^2 - } \right......... + {\left( { - 1} \right)^n}\left( {n + 1} \right)C_n^2\mathop ]\limits^ \sim \,,\)
where \(n\) is an even positive integer, is equal to
A
0
B
\({\left( { - 1} \right)^{n/2}}\left( {n + 1} \right)\)
C
\({\left( { - 1} \right)^{n/2}}\left( {n + 2} \right)\)
D
\({\left( { - 1} \right)^n}n\)
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12
1987 · Mathematics · Algebra · Mathematical Induction And Binomial Theorem
IIT JEE 1987
Prove by mathematical induction that \(- 5 - {{\left( {2n} \right)!} \over {{2^{2n}}{{\left( {n!} \right)}^2}}} \le {1 \over {{{\left( {3n + 1} \right)}^{1/2}}}}\) for all positive integers \(n\).
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13
1988 · Mathematics · Algebra · Mathematical Induction And Binomial Theorem
IIT JEE 1988
Let \(R\) \(= {\left( {5\sqrt 5 + 11} \right)^{2n + 1}}\) and \(f = R - \left[ R \right],\) where [ ] denotes the greatest integer function. Prove that \(Rf = {4^{2n + 4}}\)
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14
1989 · Mathematics · Algebra · Mathematical Induction And Binomial Theorem
IIT JEE 1989
Prove that
\({C_0} - {2^2}{C_1} + {3^2}{C_2}\,\, - \,..... + {\left( { - 1} \right)^n}{\left( {n + 1} \right)^2}{C_n} = 0,\,\,\,\,n > 2,\,\,\) where \({C_r} = {}^n{C_r}.\)
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15
1989 · Mathematics · Algebra · Mathematical Induction And Binomial Theorem
IIT JEE 1989
Using mathematical induction, prove that \({}^m{C_0}{}^n{C_k} + {}^m{C_1}{}^n{C_{k - 1}}\,\,\, + .....{}^m{C_k}{}^n{C_0} = {}^{\left( {m + n} \right)}{C_k},\)
where \(m,\,n,\,k\) are positive integers, and \({}^p{C_q} = 0\) for \(p < q.\)
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16
1990 · Mathematics · Algebra · Mathematical Induction And Binomial Theorem
IIT JEE 1990
Prove that \({{{n^7}} \over 7} + {{{n^5}} \over 5} + {{2{n^3}} \over 3} - {n \over {105}}\) is an integer for every positive integer \(n\)
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17
1991 · Mathematics · Algebra · Mathematical Induction And Binomial Theorem
IIT JEE 1991
Using induction or otherwise, prove that for any non-negative integers \(m\), \(n\), \(r\) and \(k\) ,
$$\sum\limits_{m = 0}^k {\left( {n - m} \right)} {{\left( {r + m} \right)!} \over {m!}} = {{\left( {r + k + 1} \right)!} \over {k!}}\left[ {{n \over {r + 1}} - {k \over {r + 2}}} \right]$$
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18
1992 · Mathematics · Algebra · Mathematical Induction And Binomial Theorem
IIT JEE 1992
If \(\sum\limits_{r = 0}^{2n} {{a_r}{{\left( {x - 2} \right)}^r}\,\, = \sum\limits_{r = 0}^{2n} {{b_r}{{\left( {x - 3} \right)}^r}} }\) and \({a_k} = 1\) for all \(k \ge n,\) then show that \({b_n} = {}^{2n + 1}{C_{n + 1}}\)
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19
1992 · Mathematics · Algebra · Mathematical Induction And Binomial Theorem
IIT JEE 1992
The expansion \({\left( {x + {{\left( {{x^3} - 1} \right)}^{{1 \over 2}}}} \right)^5} + {\left( {x - {{\left( {{x^3} - 1} \right)}^{{1 \over 2}}}} \right)^5}\) is a polynomial of degree
A
5
B
6
C
7
D
8
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20
1992 · Mathematics · Algebra · Mathematical Induction And Binomial Theorem
IIT JEE 1992
Let \(p \ge 3\) be an integer and \(\alpha\), \(\beta\) be the roots of \({x^2} - \left( {p + 1} \right)x + 1 = 0\) using mathematical induction show that \({\alpha ^n} + {\beta ^n}.\)
(i) is an integer and (ii) is not divisible by \(p\)
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