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Permutations and Combinations

434 Questions Start JEE Mains Test
All Exams JEE Mains JEE Advanced TS-EAMCET AP-EAPCET BITSAT
2005 Q401 JEE Advanced MCQ
14 Mar 2026
A rectangle with sides of lenght (2m - 1) and (2n - 1) units is divided into squares of unit lenght by drawing parallel lines as shown in the diagram, then the number of rectangles possible with odd side lengths is IIT-JEE 2005 Screening Mathematics - Permutations and Combinations Question 40 English
A.
${(m + n - 1)^2}$
B.
${4^{m + n - 1}}$
C.
${m^2}\,{n^2}$
D.
$m(m + 1)\,n\,(m + 1)$
2005 Q402 JEE Advanced MCQ
14 Mar 2026
If the LCM of p, q is ${r^2}\,{r^4}\,{s^2}$, where r, s, t are prime numbers and p, q are the positive integers then number of ordered pair (p, q) is
A.
252
B.
254
C.
225
D.
224
2005 Q403 JEE Advanced Numerical
14 Mar 2026
If total number of runs scored in n matches is $\left( {{{n + 1} \over 4}} \right)\,\,({2^{n + 1}} - n - 2)\,$ where $n > 1$, and the runs scored in the ${k^{th}}$ match are given by k. $\,{2^{n + 1 - k}}$, where $1 \le k \le n$. Find n.
2004 Q404 JEE Mains MCQ
14 Mar 2026
How many ways are there to arrange the letters in the word GARDEN with vowels in alphabetical order
A.
480
B.
240
C.
360
D.
120
2004 Q405 JEE Mains MCQ
14 Mar 2026
The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is
A.
${}^8{C_3}$
B.
21
C.
${3^8}$
D.
5
2004 Q406 JEE Advanced Numerical
14 Mar 2026
Prove by permulation or otherwise ${{({n^2})!} \over {{{(n!)}^n}}}$ is an integer $(n \in {1^ + })$.
2003 Q407 JEE Mains MCQ
14 Mar 2026
The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by
A.
$7!\, \times 5!\,\,$
B.
$6!\, \times 5!$
C.
$30!$
D.
$5!\, \times 4!$
2003 Q408 JEE Mains MCQ
14 Mar 2026
A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is
A.
346
B.
140
C.
196
D.
280
2003 Q409 JEE Mains MCQ
14 Mar 2026
If ${}^n{C_r}$ denotes the number of combination of n things taken r at a time, then the expression $\,{}^n{C_{r + 1}} + {}^n{C_{r - 1}} + 2\, \times \,{}^n{C_r}$ equals
A.
$\,{}^{n + 1}{C_{r + 1}}$
B.
${}^{n + 2}{C_r}$
C.
${}^{n + 2}{C_{r + 1}}$
D.
$\,{}^{n + 1}{C_r}$
2002 Q410 JEE Mains MCQ
14 Mar 2026
Five digit number divisible by 3 is formed using 0, 1, 2, 3, 4 and 5 without repetition. Total number of such numbers are :
A.
312
B.
3125
C.
120
D.
216
2002 Q411 JEE Mains MCQ
14 Mar 2026
Total number of four digit odd numbers that can be formed using 0, 1, 2, 3, 5, 7 (using repetition allowed) are :
A.
216
B.
375
C.
400
D.
720
2002 Q412 JEE Mains MCQ
14 Mar 2026
The sum of integers from 1 to 100 that are divisible by 2 or 5 is :
A.
3000
B.
3050
C.
3600
D.
3250
2002 Q413 JEE Mains MCQ
14 Mar 2026
Number greater than 1000 but less than 4000 is formed using the digits 0, 1, 2, 3, 4 (repetition allowed). Their number is :
A.
125
B.
105
C.
374
D.
625
2002 Q414 JEE Advanced MCQ
14 Mar 2026
The number of arrangements of the letters of the word BANANA in which the two N's do not appear adjacently is
A.
40
B.
60
C.
80
D.
100
2001 Q415 JEE Advanced MCQ
14 Mar 2026
Let ${T_n}$ denote the number of triangles which can be formed using the vertices of a regular polygon of n sides. If ${T_{n + 1}} - {T_n} = 21$, then n equals
A.
5
B.
7
C.
6
D.
4
2000 Q416 JEE Advanced MCQ
14 Mar 2026
How many different nine digit numbers can be formed from the number 223355888 by rearranging its digits so that the odd digits occupy even positions?
A.
16
B.
36
C.
60
D.
180
1998 Q417 JEE Advanced MCQ
14 Mar 2026
An n-digit number is a positive number with exactly digits. Nine hundred distinct n-digit numbers are to be formed using only the three digits 2, 5 and 7. The smallest value of n for which this is possible is
A.
6
B.
7
C.
8
D.
9
1994 Q418 JEE Advanced Numerical
14 Mar 2026
A committee of 12 is to be formed from 9 women and 8 men. In how many ways this can be done if at least five women have to included in a committee? In how many of these committees? In how may of these committees
(a) The women are in majority?
(b) The men are in majority?
1991 Q419 JEE Advanced Numerical
14 Mar 2026
Eighteen guests have to be seated, half on each side of a long table. Four particular guests desire to sit on one particular side and three others on the other side. Determine the number of ways in which the sitting arrangements can be made.
1989 Q420 JEE Advanced MCQ
14 Mar 2026
A five-digit numbers divisible by 3 is to be formed using the numerals 0, 1, 2, 3, 4 and 5, without repetition. The total number of ways this can be done is
A.
216
B.
240
C.
600
D.
3125
1988 Q421 JEE Advanced Numerical
14 Mar 2026
Total number of ways in which six ' + ' and four ' - ' signs can be arranged in a line such that no two ' - ' signs occur together is.....................................
1988 Q422 JEE Advanced Numerical
14 Mar 2026
There are four balls of different colours and four boxes of colours, same as those of the balls. The number of ways in which the balls, one each in a box, could be placed such that a ball does not go to a box of its own colour is.......................
1986 Q423 JEE Advanced Numerical
14 Mar 2026
A box contains two white balls, three black balls and four red balls. In how many ways can three balls be drawn from the box if at least one black ball is to be included in the draw?
1985 Q424 JEE Advanced Numerical
14 Mar 2026
7 relatives of a man comprises 4 ladies and 3 gentlemen ; his wife has also 7 relatives ; 3 of them are ladies and 4 gentlemen. In how many ways can they invite a dinner party of 3 ladies and 3 gentlemen so that there are 3 of man's relatives and 3 of the wife's relatives?
1985 Q425 JEE Advanced MCQ
14 Mar 2026
The product of any r consecutive natural numbers is always divisible by r!
A.
TRUE
B.
FALSE
1984 Q426 JEE Advanced Numerical
14 Mar 2026
The side AB, BC and CA of a triangle ABC have 3, 4 and 5 interior points respectively on them. The number of triangles that can be constructed using these interior points as vertices is .......................
1983 Q427 JEE Advanced Numerical
14 Mar 2026
m men and n women are to be seated in a row so that no two women sit together. If $m > n$, then show that the number of ways in which they can be seated is $\,{{m!(m + 1)!} \over {(m - n + 1)!}}$
1982 Q428 JEE Advanced MCQ
14 Mar 2026
Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First the women choose the chairs from amongst the chairs marked 1 to 4; and then the men select the chairs from amongst the remaining. The number of possible arrangements is
A.
${}^6{C_3} \times {}^4{C_2}$
B.
${}^4{P_2} \times {}^4{P_3}$
C.
${}^4{C_2} \times {}^4{P_3}$
D.
none of these
1982 Q429 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 Q430 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 Q431 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 Q432 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 Q433 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 Q434 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