Permutations & Combinations · JEE Main previous year questions

The number of ways, 5 boys and 4 girls can sit in a row so that either all the boys sit together or no two boys sit together, is ________.

From all the English alphabets, five letters are chosen and are arranged in alphabetical order. The total number of ways, in which the middle letter is ' M ', is :

1. A.6084
2. B.5148
3. C.14950
4. D.4356

Let $a_1,a_2,a_3,\dots$ be a G.P. of increasing positive terms. If $a_1{a}_5=28$ and $a_2+a_4=29$, then $a_6$ is equal to:

1. A.812
2. B.784
3. C.628
4. D.526

The number of integers, between 100 and 1000 having the sum of their digits equal to 14 , is __________.

The number of 3-digit numbers, formed using the digits 2, 3, 4, 5 and 7, when the repetition of digits is not allowed, and which are not divisible by 3 , is equal to ________.

The number of ways five alphabets can be chosen from the alphabets of the word MATHEMATICS, where the chosen alphabets are not necessarily distinct, is equal to:

1. A.179
2. B.177
3. C.175
4. D.181

If all the words with or without meaning made using all the letters of the word "NAGPUR" are arranged as in a dictionary, then the word at $315^{\text{th}}$ position in this arrangement is :

1. A.NRAPUG
2. B.NRAGUP
3. C.NRAPGU
4. D.NRAGPU

60 words can be made using all the letters of the word BHBJO, with or without meaning. If these words are written as in a dictionary, then the $50^{\text{th}}$ word is:

1. A.OBBJH
2. B.HBBJO
3. C.OBBHJ
4. D.JBBOH

There are 5 points ${\mathrm{P}}_1,{\mathrm{P}}_2,{\mathrm{P}}_3,{\mathrm{P}}_4,{\mathrm{P}}_5$ on the side $AB$, excluding $A$ and $B$, of a triangle $ABC$. Similarly there are 6 points ${\mathrm{P}}_6,{\mathrm{P}}_7,\dots ,{\mathrm{P}}_{11}$ on the side $\mathrm{BC}$ and 7 points ${\mathrm{P}}_{12},{\mathrm{P}}_{13},\dots ,{\mathrm{P}}_{18}$ on the side $\mathrm{CA}$ of the triangle. The number of triangles, that can be formed using the points ${\mathrm{P}}_1,{\mathrm{P}}_2,\dots ,{\mathrm{P}}_{18}$ as vertices, is:

1. A.751
2. B.776
3. C.796
4. D.771

There are 4 men and 5 women in Group A, and 5 men and 4 women in Group B. If 4 persons are selected from each group, then the number of ways of selecting 4 men and 4 women is ________.

If $\mathrm{n}$ is the number of ways five different employees can sit into four indistinguishable offices where any office may have any number of persons including zero, then $\mathrm{n}$ is equal to :

1. A.47
2. B.53
3. C.51
4. D.43

The total number of words (with or without meaning) that can be formed out of the letters of the word 'DISTRIBUTION' taken four at a time, is equal to __________.

The number of ways in which 21 identical apples can be distributed among three children such that each child gets at least 2 apples, is

1. A.130
2. B.136
3. C.142
4. D.406

All the letters of the word "GTWENTY" are written in all possible ways with or without meaning and these words are written as in a dictionary. The serial number of the word "GTWENTY" is _________.

Number of ways of arranging 8 identical books into 4 identical shelves where any number of shelves may remain empty is equal to

1. A.18
2. B.16
3. C.12
4. D.15

The number of seven digit positive integers formed using the digits 1, 2, 3 and 4 only and sum of the digits equal to 12 is __________.

Let $a_1,a_2,a_3,\dots$ be a G.P. of increasing positive numbers. Let the sum of its $6^{\text{th}}$ and $8^{\text{th}}$ terms be $2$ and the product of its $3^{\text{rd}}$ and $5^{\text{th}}$ terms be $\frac{1}{9}$. Then $6(a_2+a_4)(a_4+a_6)$ is equal to

1. A.$2\sqrt{2}$
2. B.$2$
3. C.$3\sqrt{3}$
4. D.$3$

All words, with or without meaning, are made using all the letters of the word MONDAY. These words are written as in a dictionary with serial numbers. The serial number of the word MONDAY is :

1. A.324
2. B.328
3. C.326
4. D.327

Total numbers of 3-digit numbers that are divisible by 6 and can be formed by using the digits 1, 2, 3, 4, 5 with repetition, is ___________.

The number of five digit numbers, greater than 40000 and divisible by 5 , which can be formed using the digits $0,1,3,5,7$ and $9$ without repetition, is equal to :

1. A.$132$
2. B.$72$
3. C.$120$
4. D.$96$

Let the digits a, b, c be in A. P. Nine-digit numbers are to be formed using each of these three digits thrice such that three consecutive digits are in A.P. at least once. How many such numbers can be formed?

A fair $n(n>1)$ faces die is rolled repeatedly until a number less than $n$ appears. If the mean of the number of tosses required is $\frac{n}{9}$, then $n$ is equal to _________.

In an examination, 5 students have been allotted their seats as per their roll numbers. The number of ways, in which none of the students sits on the allotted seat, is _________.

If the letters of the word MATHS are permuted and all possible words so formed are arranged as in a dictionary with serial numbers, then the serial number of the word THAMS is :

1. A.103
2. B.104
3. C.102
4. D.101

The number of permutations, of the digits 1, 2, 3, ..., 7 without repetition, which neither contain the string 153 nor the string 2467, is ___________.