Permutations and Combinations
Numerical Question Bank for JEE Main
Numerical Question Bank for JEE Main
Permutations and Combinations – Questions
1. A question paper is divided into two parts A and B and each part contains 5 questions. The number of
ways in which a candidate can answer 6 questions selecting at least two questions from each part is
M. Find M/40.
2. Number of numbers lying between 10 and 1000 can be formed from the digits 1, 2, 3, 4, 5, 6, 7, 8, 9
(repetition is allowed) are N. Find N/10.
3. The number of ways in which the letters of the word TRIANGLE can be arranged such that two
vowels do not occur together is N. Find value of √𝑁/10.
4. Ten different letters of an alphabet are given. Words with five letters are formed from these given
letters. Then the number of words which have at least one letter repeated is A. Find sum of digits in
A.
5. A five-digit number divisible by 3 has to be formed using the numerals 0, 1, 2, 3, 4 and 5 without
repetition. The total number of ways in which this can be done is N 3. Find N.
6. In a certain test there are n questions. In the test 2 n−i students gave wrong answers to at least i
questions, where i = 1, 2, ...... n . If the total number of wrong answers given is 2047, then n is equal to
7. Ten persons, amongst whom are A, B and C to speak at a function. The number of ways in which it
can be done if A wants to speak before B and B wants to speak before C is (10!)/M. Find M.
8. The number of ways in which an examiner can assign 30 marks to 8 questions, awarding not less
than 2 marks to any question is
A
C B Find A + 2B.
9. Five balls of different colors are to be placed in three boxes of different sizes. Each box can hold all
five balls. Number of ways in which we place the balls so that no box remains empty is 10 x N. Find
N.
10. The exponent of 6 in 100 ! is
11. The total number of different combinations of one or more letters which can be made from the letters
of the word ‘MISSISSIPPI’ is
12. A person goes in for an examination in which there are four papers with a maximum of m marks from
each paper. The number of ways in which one can get 2m marks is 1 (m + A)( Bm 2 + Cm + 3) . Find A
3
+ B + C.
13. 12 persons are to be arranged to a round table. If two particular persons among them are not to be
side by side, the total number of arrangements is A.9!. Find A.
14. The number of ways in which an arrangement of 4 letters of the word ‘PROPORTION’ can be made is
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Permutations and Combinations
Numerical Question Bank for JEE Main
15. The number of different words that can be formed out of the letters of the word ‘MORADABAD’ taken
four at a time is
16. There are three girls in a class of 10 students. The number of different ways in which they can be
8
seated in a row such that no two of the three girls are together is A ! PB . Find AB.
n
r
 n   n 
𝑛+𝐴
 + 
 is equal to (𝑟 + 𝐵 ), then find A + B.

r
−
1

  r − 2
17. For 2  r  n,   + 2 
18. The number of positive integral solutions of a b c = 30 is
19. How many different nine-digit numbers can be formed from the digits of the number 223355888 by
rearrangement of the digits so that the odd digits occupy even places
20. A dictionary is printed consisting of 7 lettered words only that can be made with a letter of the word
CRICKET. If the words are printed at the alphabetical order, as in an ordinary dictionary, then the
number of words before the word CRICKET is
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