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Previous year question hub

Permutations And Combinations - Algebra - Mathematics Previous Year Questions

Practice Permutations And Combinations - Algebra - Mathematics previous year questions organised from real papers, with year-wise coverage and clear topic navigation.

36Papers
30Years
44Questions
1Topics

Permutations And Combinations question pattern

Every graph below is calculated only from this selection.

Questions by year

Year-wise coverage for Permutations And Combinations. Each bar uses a separate theme-derived color.

Difficulty distribution

How the classified questions are distributed by difficulty.

Medium 29 65.9%
Easy 10 22.7%
Hard 4 9.1%
Not classified 1 2.3%

Question type distribution

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

Multiple Choices 25 56.8%
Numerical Answer Type (NAT) 12 27.3%
Subjective 7 15.9%

Subject weightage

Top subjects by unique question coverage.

Mathematics
44 Qs

Most asked topics

Top topics across the included previous year papers.

Algebra
44 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Permutations And Combinations
44 Qs

Paper coverage

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

JEE ADVANCED 2025 PAPER 1 ONLINE
2 Qs
JEE ADVANCED 2024 PAPER 1 ONLINE
1 Qs
JEE ADVANCED 2024 PAPER 2 ONLINE
1 Qs
JEE ADVANCED 2022 PAPER 1 ONLINE
1 Qs
JEE ADVANCED 2022 PAPER 2 ONLINE
1 Qs
JEE ADVANCED 2021 PAPER 2 ONLINE
1 Qs
JEE ADVANCED 2019 PAPER 2 OFFLINE
1 Qs
JEE ADVANCED 2017 PAPER 1 OFFLINE
1 Qs
JEE ADVANCED 2016 PAPER 1 OFFLINE
1 Qs
JEE ADVANCED 2015 PAPER 1 OFFLINE
1 Qs
JEE ADVANCED 2014 PAPER 1 OFFLINE
2 Qs
JEE ADVANCED 2014 PAPER 2 OFFLINE
1 Qs
JEE ADVANCED 2013 PAPER 1 OFFLINE
1 Qs
IIT JEE 2012 PAPER 2 OFFLINE
2 Qs
IIT JEE 2012 PAPER 1 OFFLINE
1 Qs
IIT JEE 2009 PAPER 1 OFFLINE
1 Qs
IIT JEE 2009 PAPER 2 OFFLINE
1 Qs
IIT JEE 2008 PAPER 2 OFFLINE
1 Qs
IIT JEE 2007 PAPER 2 OFFLINE
1 Qs
IIT JEE 2005 SCREENING
2 Qs
IIT JEE 2005
1 Qs
IIT JEE 2004
1 Qs
IIT JEE 2002 SCREENING
1 Qs
IIT JEE 2001 SCREENING
1 Qs
IIT JEE 2000 SCREENING
1 Qs
IIT JEE 1998
1 Qs
IIT JEE 1989
1 Qs
IIT JEE 1988
2 Qs
IIT JEE 1986
1 Qs
IIT JEE 1985
2 Qs
IIT JEE 1984
1 Qs
IIT JEE 1983
1 Qs
IIT JEE 1982
3 Qs
IIT JEE 1981
1 Qs
IIT JEE 1979
1 Qs
IIT JEE 1978
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 1 ONLINE20252View paper
JEE ADVANCED 2024 PAPER 1 ONLINE20241View paper
JEE ADVANCED 2024 PAPER 2 ONLINE20241View paper
JEE ADVANCED 2022 PAPER 1 ONLINE20221View paper
JEE ADVANCED 2022 PAPER 2 ONLINE20221View paper
JEE ADVANCED 2021 PAPER 2 ONLINE20211View paper
JEE ADVANCED 2019 PAPER 2 OFFLINE20191View paper
JEE ADVANCED 2017 PAPER 1 OFFLINE20171View paper
JEE ADVANCED 2016 PAPER 1 OFFLINE20161View paper
JEE ADVANCED 2015 PAPER 1 OFFLINE20151View paper
JEE ADVANCED 2014 PAPER 1 OFFLINE20142View paper
JEE ADVANCED 2014 PAPER 2 OFFLINE20141View paper
JEE ADVANCED 2013 PAPER 1 OFFLINE20131View paper
IIT JEE 2012 PAPER 1 OFFLINE20121View paper
IIT JEE 2012 PAPER 2 OFFLINE20122View paper
IIT JEE 2009 PAPER 1 OFFLINE20091View paper
IIT JEE 2009 PAPER 2 OFFLINE20091View paper
IIT JEE 2008 PAPER 2 OFFLINE20081View paper
IIT JEE 2007 PAPER 2 OFFLINE20071View paper
IIT JEE 200520051View paper
IIT JEE 2005 SCREENING20052View paper
IIT JEE 200420041View paper
IIT JEE 2002 SCREENING20021View paper
IIT JEE 2001 SCREENING20011View paper
IIT JEE 2000 SCREENING20001View paper
IIT JEE 199819981View paper
IIT JEE 198919891View paper
IIT JEE 198819882View paper
IIT JEE 198619861View paper
IIT JEE 198519852View paper
IIT JEE 198419841View paper
IIT JEE 198319831View paper
IIT JEE 198219823View paper
IIT JEE 198119811View paper
IIT JEE 197919791View paper
IIT JEE 197819781View paper

All Permutations And Combinations previous year questions

Practice every matching question in batches of 20, with every available option.

1
1978 · Mathematics · Algebra · Permutations And Combinations
IIT JEE 1978
Six X' s have to be placed in the squares of figure below in such a way that each row contains at least one X. In how many different ways can this be done. IIT-JEE 1978 Mathematics - Permutations and Combinations Question 34 English
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2
1979 · Mathematics · Algebra · Permutations And Combinations
IIT JEE 1979
\({}^n{C_{r - 1}} = 36,{}^n{C_r} = 84\,\,and\,\,{}^n{C_{r + 1}} = 126\), then r is :
A
1
B
2
C
3
D
None of these.
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3
1981 · Mathematics · Algebra · Permutations And Combinations
IIT JEE 1981
Five balls of different colours are to be placed in there boxes of different size. Each box can hold all five. In how many different ways can be place the balls so that no box remains emply?
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4
1982 · Mathematics · Algebra · Permutations And Combinations
IIT JEE 1982
Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the numbers of words which have at least one letter repeated are
A
69760
B
30240
C
99748
D
none of these
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5
1982 · Mathematics · Algebra · Permutations And Combinations
IIT JEE 1982
Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First the women choose the chairs from amongst the chairs marked 1 to 4; and then the men select the chairs from amongst the remaining. The number of possible arrangements is
A
\({}^6{C_3} \times {}^4{C_2}\)
B
\({}^4{P_2} \times {}^4{P_3}\)
C
\({}^4{C_2} \times {}^4{P_3}\)
D
none of these
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6
1982 · Mathematics · Algebra · Permutations And Combinations
IIT JEE 1982
The value of the expression \(\,{}^{47}{C_4} + \sum\limits_{j = 1}^5 {^{52 - j}\,{C_3}}\) is equal to
A
\({}^{47}{C_5}\)
B
\({}^{52}{C_5}\)
C
\({}^{52}{C_4}\)
D
none of these
Open complete paper
7
1983 · Mathematics · Algebra · Permutations And Combinations
IIT JEE 1983
m men and n women are to be seated in a row so that no two women sit together. If \(m > n\), then show that the number of ways in which they can be seated is \(\,{{m!(m + 1)!} \over {(m - n + 1)!}}\)
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8
1984 · Mathematics · Algebra · Permutations And Combinations
IIT JEE 1984
The side AB, BC and CA of a triangle ABC have 3, 4 and 5 interior points respectively on them. The number of triangles that can be constructed using these interior points as vertices is .......................
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9
1985 · Mathematics · Algebra · Permutations And Combinations
IIT JEE 1985
The product of any r consecutive natural numbers is always divisible by r!
A
TRUE
B
FALSE
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10
1985 · Mathematics · Algebra · Permutations And Combinations
IIT JEE 1985
7 relatives of a man comprises 4 ladies and 3 gentlemen ; his wife has also 7 relatives ; 3 of them are ladies and 4 gentlemen. In how many ways can they invite a dinner party of 3 ladies and 3 gentlemen so that there are 3 of man's relatives and 3 of the wife's relatives?
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11
1986 · Mathematics · Algebra · Permutations And Combinations
IIT JEE 1986
A box contains two white balls, three black balls and four red balls. In how many ways can three balls be drawn from the box if at least one black ball is to be included in the draw?
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12
1988 · Mathematics · Algebra · Permutations And Combinations
IIT JEE 1988
There are four balls of different colours and four boxes of colours, same as those of the balls. The number of ways in which the balls, one each in a box, could be placed such that a ball does not go to a box of its own colour is.......................
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13
1988 · Mathematics · Algebra · Permutations And Combinations
IIT JEE 1988
Total number of ways in which six ' + ' and four ' - ' signs can be arranged in a line such that no two ' - ' signs occur together is.....................................
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14
1989 · Mathematics · Algebra · Permutations And Combinations
IIT JEE 1989
A five-digit numbers divisible by 3 is to be formed using the numerals 0, 1, 2, 3, 4 and 5, without repetition. The total number of ways this can be done is
A
216
B
240
C
600
D
3125
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15
1998 · Mathematics · Algebra · Permutations And Combinations
IIT JEE 1998
An n-digit number is a positive number with exactly digits. Nine hundred distinct n-digit numbers are to be formed using only the three digits 2, 5 and 7. The smallest value of n for which this is possible is
A
6
B
7
C
8
D
9
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16
2000 · Mathematics · Algebra · Permutations And Combinations
IIT JEE 2000 SCREENING
How many different nine digit numbers can be formed from the number 223355888 by rearranging its digits so that the odd digits occupy even positions?
A
16
B
36
C
60
D
180
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17
2001 · Mathematics · Algebra · Permutations And Combinations
IIT JEE 2001 SCREENING
Let \({T_n}\) denote the number of triangles which can be formed using the vertices of a regular polygon of n sides. If \({T_{n + 1}} - {T_n} = 21\), then n equals
A
5
B
7
C
6
D
4
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18
2002 · Mathematics · Algebra · Permutations And Combinations
IIT JEE 2002 SCREENING
The number of arrangements of the letters of the word BANANA in which the two N's do not appear adjacently is
A
40
B
60
C
80
D
100
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19
2004 · Mathematics · Algebra · Permutations And Combinations
IIT JEE 2004
Prove by permulation or otherwise \({{({n^2})!} \over {{{(n!)}^n}}}\) is an integer \((n \in {1^ + })\).
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20
2005 · Mathematics · Algebra · Permutations And Combinations
IIT JEE 2005
If total number of runs scored in n matches is \(\left( {{{n + 1} \over 4}} \right)\,\,({2^{n + 1}} - n - 2)\,\) where \(n > 1\), and the runs scored in the \({k^{th}}\) match are given by k. \(\,{2^{n + 1 - k}}\), where \(1 \le k \le n\). Find n.
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Showing 20 of 44 questions