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Permutations and Combinations

56 Questions Start JEE Advanced Test
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1982 Q51 JEE Advanced MCQ
14 Mar 2026
Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the numbers of words which have at least one letter repeated are
A.
69760
B.
30240
C.
99748
D.
none of these
1982 Q52 JEE Advanced MCQ
14 Mar 2026
The value of the expression $\,{}^{47}{C_4} + \sum\limits_{j = 1}^5 {^{52 - j}\,{C_3}} $ is equal to
A.
${}^{47}{C_5}$
B.
${}^{52}{C_5}$
C.
${}^{52}{C_4}$
D.
none of these
1982 Q53 JEE Advanced Numerical
14 Mar 2026
In a certain test, ${a_i}$ students gave wrong answers to atleast i questions, where i = 1, 2,..., k. No student gave more than k wrong answers. The total number of wrong answers given is.....................................
1981 Q54 JEE Advanced Numerical
14 Mar 2026
Five balls of different colours are to be placed in there boxes of different size. Each box can hold all five. In how many different ways can be place the balls so that no box remains emply?
1979 Q55 JEE Advanced MCQ
14 Mar 2026
${}^n{C_{r - 1}} = 36,{}^n{C_r} = 84\,\,and\,\,{}^n{C_{r + 1}} = 126$, then r is :
A.
1
B.
2
C.
3
D.
None of these.
1978 Q56 JEE Advanced Numerical
14 Mar 2026
Six X' s have to be placed in the squares of figure below in such a way that each row contains at least one X. In how many different ways can this be done. IIT-JEE 1978 Mathematics - Permutations and Combinations Question 34 English