JEE Main Mathematics: Permutation & Combination Practice Questions

15 questions with answers and step-by-step solutions. Tap any question to see the full worked solution.

Q1.
$If nC2 = 10, what is the value of n?$
Easy
Q2.
$In how many ways can a committee of 3 members be selected from a group of 6 people?$
Easy
Q3.
$How many different 3-digit numbers can be formed using the digits 1, 2, 3, 4, and 5 if repetition of digits is not allowed?$
Easy
Q4.
$How many ways can 4 students be seated in a row of 4 chairs?$
Easy
Q5.
$How many ways can the letters of the word APPLE be arranged?$
Easy
Q6.
$How many 4-digit numbers can be formed using the digits 1, 2, 3, 4, 5 if repetition of digits is allowed?$
Medium
Q7.
$In how many ways can 6 different books be distributed among 3 students such that each student receives at least one book?$
Medium
Q8.
$A committee of 5 members is to be formed from 6 men and 4 women such that it contains at least one woman. How many such committees can be formed?$
Medium
Q9.
$The number of diagonals in a polygon with 10 sides is?$
Medium
Q10.
$Find the number of ways to arrange the letters of the word MISSISSIPPI such that no two I's are together.$
Medium
Q11.
$There are 10 points in a plane, no three of which are collinear, except for 4 points which are collinear. How many distinct triangles can be formed?$
Hard
Q12.
$Find the number of ways to arrange the letters of the word 'MATHEMATICS' such that the vowels are always together.$
Hard
Q13.
$Find the number of ways to distribute 10 distinct balls into 3 distinct boxes such that no box is empty.$
Hard
Q14.
$How many 6-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5 such that the digits are not repeated and the number is divisible by 6?$
Hard
Q15.
$A committee of 5 is to be formed from 6 men and 4 women such that at least one woman is included. How many ways can this be done?$
Hard

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