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Previous year question hub

Probability - Algebra - Mathematics Previous Year Questions

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

24Papers
21Years
25Questions
1Topics

Probability question pattern

Every graph below is calculated only from this selection.

Questions by year

Year-wise coverage for Probability. Each bar uses a separate theme-derived color.

Difficulty distribution

How the classified questions are distributed by difficulty.

Medium 16 59.3%
Easy 7 25.9%
Hard 4 14.8%

Question type distribution

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

Subjective 15 55.6%
Numerical Answer Type (NAT) 5 18.5%
Multiple Choices 4 14.8%
Fill in the blanks 3 11.1%

Subject weightage

Top subjects by unique question coverage.

Mathematics
25 Qs

Most asked topics

Top topics across the included previous year papers.

Algebra
25 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Probability
25 Qs

Paper coverage

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

JEE Advanced 2026 Paper 1 Online
1 Qs
JEE Advanced 2026 Paper 1 Online
1 Qs
JEE Advanced 2026 Paper 1 Online
1 Qs
JEE Advanced 2026 Paper 2 Online
1 Qs
JEE ADVANCED 2023 PAPER 2 ONLINE
1 Qs
JEE ADVANCED 2021 PAPER 1 ONLINE
2 Qs
JEE ADVANCED 2020 PAPER 2 OFFLINE
1 Qs
JEE ADVANCED 2017 PAPER 2 OFFLINE
1 Qs
IIT JEE 2004
1 Qs
IIT JEE 2003
1 Qs
IIT JEE 2002
1 Qs
IIT JEE 2001
2 Qs
IIT JEE 1998
2 Qs
IIT JEE 1996
1 Qs
IIT JEE 1993
1 Qs
IIT JEE 1992
1 Qs
IIT JEE 1990
1 Qs
IIT JEE 1989
1 Qs
IIT JEE 1988
1 Qs
IIT JEE 1986
1 Qs
IIT JEE 1985
1 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 2026 Paper 1 Online20261View paper
JEE Advanced 2026 Paper 1 Online20261View paper
JEE Advanced 2026 Paper 1 Online20261View paper
JEE Advanced 2026 Paper 2 Online20261View paper
JEE ADVANCED 2023 PAPER 2 ONLINE20231View paper
JEE ADVANCED 2021 PAPER 1 ONLINE20212View paper
JEE ADVANCED 2020 PAPER 2 OFFLINE20201View paper
JEE ADVANCED 2017 PAPER 2 OFFLINE20171View paper
IIT JEE 200420041View paper
IIT JEE 200320031View paper
IIT JEE 200220021View paper
IIT JEE 200120012View paper
IIT JEE 199819982View paper
IIT JEE 199619961View paper
IIT JEE 199319931View paper
IIT JEE 199219921View paper
IIT JEE 199019901View paper
IIT JEE 198919891View paper
IIT JEE 198819881View paper
IIT JEE 198619861View paper
IIT JEE 198519851View paper
IIT JEE 198119811View paper
IIT JEE 197919791View paper
IIT JEE 197819781View paper

All Probability previous year questions

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

1
1978 · Mathematics · Algebra · Probability
IIT JEE 1978
Balls are drawn one-by-one without replacement from a box containing \(2\) black, \(4\) white and \(3\) red balls till all the balls are drawn. Find the probability that the balls drawn are in the order \(2\) black, \(4\) white and \(3\) red.
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2
1979 · Mathematics · Algebra · Probability
IIT JEE 1979
Six boys and six girls sit in a row randomly. Find the probability that
(i) the six girls sit together
(ii) the boys and girls sit alternately.
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3
1981 · Mathematics · Algebra · Probability
IIT JEE 1981
For a biased die the probabilities for the different faces to turn up are given below : IIT-JEE 1981 Mathematics - Probability Question 136 English

This die tossed and you are told that either face \(1\) or face \(2\) has turned up. Then the probability that it is face \(1\) is ...............

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4
1985 · Mathematics · Algebra · Probability
IIT JEE 1985
\(P\left( {A \cup B} \right) = P\left( {A \cap B} \right)\) if and only if the relation between \(P(A)\) and \(P(B)\) is .............
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5
1986 · Mathematics · Algebra · Probability
IIT JEE 1986
If \({{1 + 3p} \over 3},\,\,\,{{1 - p} \over 4}\) and \(\,{{1 - 2p} \over 2}\) are the probabilities of three mutually exclusive events, then the set of all values of \(p\) is ..............
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6
1988 · Mathematics · Algebra · Probability
IIT JEE 1988
A box contains \(2\) fifty paise coins, \(5\) twenty five paise coins and a certain fixed number \(N\,\,\left( { \ge 2} \right)\) of ten and five paise coins. Five coins are taken out of the box at random. Find the probability that the total value of these \(5\) coins is less than one rupee and fifty paise.
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7
1989 · Mathematics · Algebra · Probability
IIT JEE 1989
Suppose the probability for A to win a game against B is \(0.4.\) If \(A\) has an option of playing either a "best of \(3\) games" or a "best of \(5\) games" match against \(B\), which option should be choose so that the probability of his winning the match is higher ? (No game ends in a draw).
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8
1990 · Mathematics · Algebra · Probability
IIT JEE 1990
A is a set containing \(n\) elements. \(A\) subset \(P\) of \(A\) is chosen at random. The set \(A\) is reconstructed by replacing the elements of \(P.\) \(A\) subset \(Q\) of \(A\) is again chosen at random. Find the probability that \(P\) and \(Q\) have no common elements.
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9
1992 · Mathematics · Algebra · Probability
IIT JEE 1992
A lot contains \(50\) defective and \(50\) non defective bulbs. Two bulbs are drawn at random, one at a time, with replacement. The events \(A, B, C\) are defined as
\(A=\) (the first bulbs is defective)
\(B=\) (the second bulbs is non-defective)
\(C=\) (the two bulbs are both defective or both non defective)
Determine whether
(i) \(\,\,\,\,\,\) \(A, B, C\) are pairwise independent
(ii)\(\,\,\,\,\,\) \(A, B, C\) are independent
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10
1993 · Mathematics · Algebra · Probability
IIT JEE 1993
Numbers are selected at random, one at a time, from the two- digit numbers \(00, 01, 02 ......, 99\) with replacement. An event \(E\) occurs if only if the product of the two digits of a selected number is \(18\). If four numbers are selected, find probability that the event \(E\) occurs at least \(3\) times.
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11
1996 · Mathematics · Algebra · Probability
IIT JEE 1996
In how many ways three girls and nine boys can be seated in two vans, each having numbered seats, \(3\) in the front and \(4\) at the back? How many seating arrangements are possible if \(3\) girls should sit together in a back row on adjacent seats? Now, if all the seating arrangements are equally likely, what is the probability of \(3\) girls sitting together in a back row on adjacent seats?
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12
1998 · Mathematics · Algebra · Probability
IIT JEE 1998
Let \({C_1}\) and \({C_2}\) be the graphs of the functions \(y = {x^2}\) and \(y = 2x,\) \(0 \le x \le 1\) respectively. Let \({C_3}\) be the graph of a function \(y=f(x),\) \(0 \le x \le 1,\) \(f(0)=0.\) For a point \(P\) on \({C_1},\) let the lines through \(P,\) parallel to the axes, meet \({C_2}\) and \({C_3}\) at \(Q\) and \(R\) respectively (see figure.) If for every position of \(P\) (on \({C_1}\) ), the areas of the shaded regions \(OPQ\) and \(ORP\) are equal, determine the function\(f(x).\) IIT-JEE 1998 Mathematics - Probability Question 37 English
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13
1998 · Mathematics · Algebra · Probability
IIT JEE 1998
Three players, \(A,B\) and \(C,\) toss a coin cyclically in that order (that is \(A, B, C, A, B, C, A, B,...\)) till a head shows. Let \(p\) be the probability that the coin shows a head. Let \(\alpha ,\,\,\,\beta\) and \(\gamma\) be, respectively, the probabilities that \(A, B\) and \(C\) gets the first head. Prove that \(\beta = \left( {1 - p} \right)\alpha\) Determine \(\alpha ,\beta\) and \(\gamma\) (in terms of \(p\)).
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14
2001 · Mathematics · Algebra · Probability
IIT JEE 2001
An unbiased die, with faces numbered \(1,2,3,4,5,6,\) is thrown \(n\) times and the list of \(n\) numbers showing up is noted. What is the probability that, among the numbers \(1,2,3,4,5,6,\) only three numbers appear in this list?
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15
2001 · Mathematics · Algebra · Probability
IIT JEE 2001
An urn contains \(m\) white and \(n\) black balls. A ball is drawn at random and is put back into the urn along with \(k\) additional balls of the same colour as that of the ball drawn. A ball is again drawn at random. What is the probability that the ball drawn now is white?
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16
2002 · Mathematics · Algebra · Probability
IIT JEE 2002
A box contains \(N\) coins, \(m\) of which are fair and the rest are biased. The probability of getting a head when a fair coin is tossed is \(1/2\), while it is \(2/3\) when a biased coin is tossed. A coin is drawn from the box at random and is tossed twice. The first time it shows head and the second time it shows tail. what is the probability that the coin drawn is fair?
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17
2003 · Mathematics · Algebra · Probability
IIT JEE 2003
For a student to qualify, he must pass at least two out of three exams. The probability that he will pass the 1st exam is \(p.\) If he fails in one of the exams then the probability of his passing in the next exam is \({p \over 2}\) otherwise it remains the same. Find the probability that he will qualify.
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18
2004 · Mathematics · Algebra · Probability
IIT JEE 2004
A box contains \(12\) red and \(6\) white balls. Balls are drawn from the box one at a time without replacement. If in \(6\) draws there are at least \(4\) white balls, find the probability that exactly one white is drawn in the next two draws. (binomial coefficients can be left as such)
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19
2017 · Mathematics · Algebra · Probability
JEE ADVANCED 2017 PAPER 2 OFFLINE
Three randomly chosen nonnegative integers x, y and z are found to satisfy the equation x + y + z = 10. Then the probability that z is even, is
A
\({1 \over {2}}\)
B
\({36 \over {55}}\)
C
\({6 \over {11}}\)
D
\({5 \over {11}}\)
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20
2020 · Mathematics · Algebra · Probability
JEE ADVANCED 2020 PAPER 2 OFFLINE
The probability that a missile hits a target successfully is 0.75. In order to destroy the target completely, at least three successful hits are required. Then the minimum number of missiles that have to be fired so that the probability of completely destroying the target is NOT less than 0.95, is ............
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Showing 20 of 25 questions