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Permutation & Combination - Past Year Questions

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Q1:

Let nn be the number of ways in which 20 identical balloons can be distributed among 5 girls and 3 boys such that everyone gets at least one balloon and no girl gets fewer balloons than a boy does. Then
Answer options
Option: 0
Correct Answer
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Q2:

The number of values of xx for which C(17−x3x+1)C \binom {17-x}{3x+1} is defined as an integer is
Answer options
Option: 4
Correct Answer
Explanation →

Q3:

The number of solutions of the equation x1+x2+x3+x4=50x_1 + x_2 + x_3 + x_4 = 50, where x1,x2,x3,x4x_1, x_2, x_3, x_4 are integers with x1≥1,x2≥2,x3≥0,x4≥0x_1 \geq 1, x_2 \geq 2, x_3 \geq 0, x_4 \geq 0 is
Answer options
Option: 3
Correct Answer
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Q4:

If 5 boys and 3 girls sit randomly around a circular table, the probability that there will be at least one boy sitting between any two girls is
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Option: 2
Correct Answer
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Q5:

A rabbit is sitting at the base of a staircase which has 10 steps. It proceeds to the top of the staircase by climbing either one step at a time or two steps at a time. The number of ways it can reach the top is
Answer options
Option: 2
Correct Answer
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Q6:

Consider an 8×88 \times 8 chessboard. The number of ways 8 rooks can be placed on the board such that no two rooks are in the same row and no two are in the same column is
Answer options
Option: 4
Correct Answer
Explanation →

Q7:

In a chess tournament, there are four groups, each containing an equal number of players. Each player plays
1. against every other player belonging to one's own group exactly once; \newline 2. against each player belonging to one of the remaining three groups exactly twice; \newline 3. against each player belonging to one of the remaining two groups exactly three times; and \newline 4. against each player belonging to the remaining group exactly four times.
If there are more than 1000 matches being played in the tournament, the minimum possible number of players in each group is
8
Correct Answer
Explanation →

Q8:

The total number of positive integer solutions of 21≤a+b+c≤2521 ≤ a + b + c ≤ 25 is
1160
Correct Answer
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Q9:

In how many ways can the letters of the word MANAGEMENT be arranged such that no two vowels appear together?
Answer options
Option: 3
Correct Answer
Explanation →

Q10:

The number of triangles that can be formed by choosing points from 7 points on a line and 5 points on another parallel line is _________.
175
Correct Answer
Explanation →

Q11:

Mrs and Mr Sharma, and Mrs and Mr Ahuja along with four other persons are to be seated at a round table for dinner. If Mrs and Mr Sharma are to be seated next to each other, and Mrs and Mr Ahuja are not to be seated next to each other, then the total number of seating arrangements is _________.
960
Correct Answer
Explanation →

Q12:

The number of 5-digit numbers consisting of distinct digits that can be formed such that only odd digits occur at odd places is
Answer options
Option: 3
Correct Answer
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Q13:

There are 10 points in the plane, of which 5 points are collinear and no three among the remaining are collinear. Then the number of distinct straight lines that can be formed out of these 10 points is
Answer options
Option: 4
Correct Answer
Explanation →

Q14:

There are 5 parallel lines on the plane. On the same plane, there are nn other lines that are perpendicular to the 5 parallel lines. If the number of distinct rectangles formed by these lines is 360, what is the value of nn?
9
Correct Answer
Explanation →

Q15:

Out of 13 objects, 4 are indistinguishable and the rest are distinct. The number of ways we can choose 4 objects out of 13 objects is __________.
256
Correct Answer
Explanation →

Q16:

How many different numbers can be formed by using only the digits 1 and 3 which are smaller than 3000000?
Answer options
Option: 3
Correct Answer
Explanation →

Q17:

Five racquets needs to be placed in three boxes. Each box can hold all the five racquets. In how many ways can the racquets be placed in the boxes so that no box can be empty if all racquets are different but all boxes are identical?
Answer options
Option: 2
Correct Answer
Explanation →

Q18:

How many signposts can be made using 6 different coloured symbols when any number of them can be posted at a time?
Answer options
Option: 4
Correct Answer
Explanation →

Q19:

There are 12 copies of Beetles CDs, 7 copies of Pink Floyd CDs, 3 different CDs of Michael Jackson, and 2 different CDs of Madonna. Find the number of ways in which one or more than one CD can be selected?
Answer options
Option: 4
Correct Answer
Explanation →

Q20:

Please calculate in how many ways can a platoon of sixteen soldiers be chosen out of a total of twenty soldiers for a surgical strike?
Answer options
Option: 1
Correct Answer
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Q21:

A box contains 2 white shirts, 3 black shirts, and 4 red shirts. In how many ways can 3 shirts be drawn from the box, if at least one black shirt is to be included in the draw?
Answer options
Option: 3
Correct Answer
Explanation →

Q22:

Can you calculate in how many ways can 7 tennis players can be seated in a circular order?
Answer options
Option: 3
Correct Answer
Explanation →

Q23:

Please calculate in how many ways can a set of five players be formed out of a total of ten players such that two particular players should be involved in each set?
Answer options
Option: 3
Correct Answer
Explanation →

Permutation & Combination - Past Year Questions (Free PDF Download)

Practice with our comprehensive collection of Permutation & Combination Past Year Questions (PYQs of IPMAT Indore, IPMAT Rohtak & JIPMAT) with detailed solutions. These questions are carefully curated from previous year papers to help you understand the exam pattern and improve your preparation.

Our free resources include handwritten solutions for all questions, making it easier to understand the concepts and approach. Use these PYQs to assess your preparation level and identify areas that need more focus. No login required. Compilation of IPMAT Indore, IPMAT Rohtak & JIPMAT Questions!