Permutations and Combinations – Most Repeated PYQs for JEE Main 2026

Permutations & Combinations – JEE Main PYQ Quiz

Permutations and Combinations is a high-scoring chapter in JEE Main Mathematics. Most questions are based on counting, arrangements, selections, restrictions and distribution concepts. Practising PYQs ensures accuracy and speed.

Q1. Line L₁ of slope 2 and line L₂ of slope 1/2 intersect at origin. In first quadrant, P₁…P₁₂ are on L₁ and Q₁…Q₉ on L₂. Total number of triangles formed using O, Pᵢ, Qⱼ is:
1026
1188
1134
1080
Q2. Number of 3-digit numbers divisible by 2 and 3, but not divisible by 4 and 9 is:
Correct Answer: 125
Q3. Number of permutations of digits 1 to 7 without repetition which neither contain string 153 nor 2467 is:
Correct Answer: 4898
Q4. All six-digit numbers x₁x₂x₃x₄x₅x₆ (0<x₁<…<x₆) are arranged. Find sum of digits of the 72nd number:
Correct Answer: 32
Q5. Number of ways of giving 20 distinct oranges to 3 children such that each child gets at least one orange is:
Correct Answer: 3483638676
Q6. Number of integers greater than 7000 formed using digits 3,5,6,7,8 without repetition is:
48
120
168
220
Q7. Number of ways in which 21 identical apples can be distributed among 3 children such that each gets at least 2 apples:
130
136
142
406
Q8. If (n+1)C(r+1) : nCr : (n−1)C(r−1) = 55 : 35 : 21, then value of (2n + 5r) is:
62
60
55
50
Q9. Number of 5-digit numbers greater than 40000 and divisible by 5 formed using digits 0,1,3,5,7,9 without repetition is:
132
72
120
96
Q10. Group A has 4 men and 5 women, Group B has 5 men and 4 women. If 4 persons are selected from each group, number of ways of selecting 4 men and 4 women is:
Correct Answer: 5626
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