Permutations and Combinations

198 questions · Mathematics · JEE Main

Permutations and Combinations

198 questions · Mathematics · JEE Main

The number of sequences of ten terms, whose terms are either 0 or 1 or 2 , that contain exactly five 1 s and exactly three 2 s , is equal to :2025 · 2 Apr · Shift 1 · Q42 · MCQ
The number of ways, in which the letters A, B, C, D, E can be placed in the 8 boxes of the figure below so that no row remains empty and at most one letter can be placed in a box, is : Includes diagram2025 · 2 Apr · Shift 2 · Q28 · MCQ
All five letter words are made using all the letters A, B, C, D, E and arranged as in an English dictionary with serial numbers. Let the word at serial number $n$ be denoted by $W_{n}$ . Let the probability $P (W_{n})$ …2025 · 3 Apr · Shift 1 · Q46 · Numerical
If the number of seven-digit numbers, such that the sum of their digits is even, is $m \cdot n \cdot 1 0^{n}; m, n \in {1, 2, 3, \dots, 9}$ , then $m + n$ is equal to 2025 · 3 Apr · Shift 1 · Q50 · Numerical
Line $L_{1}$ of slope 2 and line $L_{2}$ of slope $\frac{1}{2}$ intersect at the origin O . In the first quadrant, $P_{1}$ , $P_{2}, \dots, P_{12}$ are 12 points on line $L_{1}$ and $Q_{1}, Q_{2}, \dots, Q_{9}$ are 9 points on line $L_{2}$ . Then…2025 · 3 Apr · Shift 2 · Q27 · MCQ
Let m and $n, (m < n)$ , be two 2-digit numbers. Then the total numbers of pairs $(m, n)$ , such that $gcd (m, n) = 6$ , is .2025 · 4 Apr · Shift 2 · Q50 · Numerical
From a group of 7 batsmen and 6 bowlers, 10 players are to be chosen for a team, which should include atleast 4 batsmen and atleast 4 bowlers. One batsmen and one bowler who are captain and vice-captain respectively of the team should be…2025 · 7 Apr · Shift 1 · Q26 · MCQ
There are 12 points in a plane, no three of which are in the same straight line, except 5 points which are collinear. Then the total number of triangles that can be formed with the vertices at any three of these 12 points is2025 · 8 Apr · Shift 2 · Q41 · MCQ
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 :2025 · 22 Jan · Shift 1 · Q32 · MCQ
In a group of 3 girls and 4 boys, there are two boys $B_{1}$ and $B_{2}$ . The number of ways, in which these girls and boys can stand in a queue such that all the girls stand together, all the boys stand together, but $B_{1}$ and $B_{2}$ are not…2025 · 22 Jan · Shift 2 · Q38 · MCQ
The number of words, which can be formed using all the letters of the word "DAUGHTER", so that all the vowels never come together, is :2025 · 23 Jan · Shift 1 · Q28 · MCQ
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 .2025 · 23 Jan · Shift 2 · Q48 · Numerical
The number of 3 -digit numbers, that are divisible by 2 and 3 , but not divisible by 4 and 9 , is .2025 · 24 Jan · Shift 1 · Q50 · Numerical
Group A consists of 7 boys and 3 girls, while group B consists of 6 boys and 5 girls. The number of ways, 4 boys and 4 girls can be invited for a picnic if 5 of them must be from group $A$ and the remaining 3 from group $B$ , is equal to :2025 · 24 Jan · Shift 2 · Q41 · MCQ
Number of functions $f : {1, 2, \dots, 100} \to {0, 1}$ , that assign 1 to exactly one of the positive integers less than or equal to 98 , is equal to .2025 · 24 Jan · Shift 2 · Q49 · Numerical
Let $^{n} C_{r - 1} = 28,^{n} C_{r} = 56$ and $^{n} C_{r + 1} = 70$ . Let $A (4 cost, 4 sin t), B (2 sin t, - 2 cos t)$ and $C (3 r - n, r^{2} - n - 1)$ be the vertices of a triangle $A B C$ , where $t$ is a parameter. If $(3 x - 1)^{2} + (3 y)^{2} = α$ …2025 · 28 Jan · Shift 1 · Q34 · MCQ
The number of different 5 digit numbers greater than 50000 that can be formed using the digits 0 , $1, 2, 3, 4, 5, 6, 7$ , such that the sum of their first and last digits should not be more than 8 , is2025 · 28 Jan · Shift 1 · Q41 · MCQ
The number of natural numbers, between 212 and 999, such that the sum of their digits is 15, is .2025 · 28 Jan · Shift 2 · Q50 · Numerical
Let $P$ be the set of seven digit numbers with sum of their digits equal to 11. If the numbers in $P$ are formed by using the digits 1, 2 and 3 only, then the number of elements in the set $P$ is :2025 · 29 Jan · Shift 1 · Q27 · MCQ
The number of 6-letter words, with or without meaning, that can be formed using the letters of the word MATHS such that any letter that appears in the word must appear at least twice, is .2025 · 29 Jan · Shift 1 · Q50 · Numerical
If all the words with or without meaning made using all the letters of the word "KANPUR" are arranged as in a dictionary, then the word at 440th position in this arrangement is :2025 · 29 Jan · Shift 2 · Q44 · MCQ
If $n$ 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 $n$ is equal to :2024 · 1 Feb · Shift 1 · Q35 · MCQ
The number of elements in the set $S = {(x, y, z) : x, y, z \in Z, x + 2 y + 3 z = 42, x, y, z ⩾ 0}$ equals .2024 · 1 Feb · Shift 1 · Q52 · Numerical
There are 5 points $P_{1}, P_{2}, P_{3}, P_{4}, P_{5}$ on the side $A B$ , excluding $A$ and $B$ , of a triangle $A B C$ . Similarly there are 6 points $P_{6}, P_{7}, \dots, P_{11}$ on the side $BC$ and 7 points $P_{12}, P_{13}, \dots, P_{18}$ …2024 · 4 Apr · Shift 1 · Q34 · MCQ
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 .2024 · 4 Apr · Shift 2 · Q60 · Numerical
The number of ways of getting a sum 16 on throwing a dice four times is .2024 · 5 Apr · Shift 1 · Q54 · Numerical
Let the set $S = {2, 4, 8, 16, \dots, 512}$ be partitioned into 3 sets $A, B, C$ with equal number of elements such that $A \cup B \cup C = S$ and $A \cap B = B \cap C = A \cap C = ϕ$ …2024 · 5 Apr · Shift 2 · Q43 · MCQ
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 $5 0^{th}$ word is:2024 · 5 Apr · Shift 2 · Q48 · MCQ
The number of triangles whose vertices are at the vertices of a regular octagon but none of whose sides is a side of the octagon is2024 · 6 Apr · Shift 1 · Q47 · MCQ
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 $31 5^{th}$ position in this arrangement is :2024 · 6 Apr · Shift 2 · Q45 · MCQ
Let $0 \leq r \leq n$ . If $^{n + 1} C_{r + 1} :^{n} C_{r} :^{n - 1} C_{r - 1} = 55 : 35 : 21$ , then $2 n + 5 r$ is equal to :2024 · 6 Apr · Shift 2 · Q47 · MCQ
Let $[t]$ be the greatest integer less than or equal to $t$ . Let $A$ be the set of all prime factors of 2310 and $f : A \to Z$ be the function $f (x) = [lo g_{2} (x^{2} + [\frac{x ^{3}}{5}])]$ . The…2024 · 8 Apr · Shift 1 · Q47 · MCQ
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 .2024 · 8 Apr · Shift 1 · Q55 · Numerical
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:2024 · 8 Apr · Shift 2 · Q46 · MCQ
The number of integers, between 100 and 1000 having the sum of their digits equals to 14 , is .2024 · 9 Apr · Shift 2 · Q58 · Numerical
Let $α = \frac{( 4 !)!}{( 4 ! ) ^{3!}}$ and $β = \frac{( 5 !)!}{( 5 ! ) ^{4!}}$ . Then :2024 · 27 Jan · Shift 2 · Q46 · MCQ
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 .2024 · 29 Jan · Shift 1 · Q57 · Numerical
Number of ways of arranging 8 identical books into 4 identical shelves where any number of shelves may remain empty is equal to2024 · 29 Jan · Shift 2 · Q31 · MCQ
In an examination of Mathematics paper, there are 20 questions of equal marks and the question paper is divided into three sections : $A, B$ and $C$ . A student is required to attempt total 15 questions taking at least 4 questions from each…2024 · 30 Jan · Shift 2 · Q51 · Numerical
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 .2024 · 31 Jan · Shift 1 · Q58 · Numerical
The number of ways in which 21 identical apples can be distributed among three children such that each child gets at least 2 apples, is2024 · 31 Jan · Shift 2 · Q31 · MCQ
If for some $m, n;^{6} C_{m} + 2 (^{6} C_{m + 1}) +^{6} C_{m + 2} >^{8} C_{3}$ and $^{n - 1} P_{3} :^{n} P_{4} = 1 : 8$ , then $^{n} P_{m + 1} +^{n + 1} C_{m}$ is equal to2024 · 31 Jan · Shift 2 · Q46 · MCQ
The value of $\frac{1}{1 ! 50 !} + \frac{1}{3 ! 48 !} + \frac{1}{5 ! 46 !} + \dots . + \frac{1}{49 ! 2 !} + \frac{1}{51 ! 1 !}$ is :2023 · 1 Feb · Shift 1 · Q22 · MCQ
The number of 3-digit numbers, that are divisible by either 2 or 3 but not divisible by 7, is .2023 · 1 Feb · Shift 1 · Q39 · Numerical
The number of words, with or without meaning, that can be formed using all the letters of the word ASSASSINATION so that the vowels occur together, is .2023 · 1 Feb · Shift 1 · Q40 · Numerical
Number of integral solutions to the equation $x + y + z = 21$ , where $x \geq 1, y \geq 3, z \geq 4$ , is equal to .2023 · 1 Feb · Shift 2 · Q44 · Numerical
The total number of six digit numbers, formed using the digits 4, 5, 9 only and divisible by 6, is .2023 · 1 Feb · Shift 2 · Q46 · Numerical
The number of ways of giving 20 distinct oranges to 3 children such that each child gets at least one orange is .2023 · 6 Apr · Shift 1 · Q42 · Numerical
All the letters of the word PUBLIC are written in all possible orders and these words are written as in a dictionary with serial numbers. Then the serial number of the word PUBLIC is :2023 · 6 Apr · Shift 2 · Q26 · MCQ
The number of 4-letter words, with or without meaning, each consisting of 2 vowels and 2 consonants, which can be formed from the letters of the word UNIVERSE without repetition is .2023 · 6 Apr · Shift 2 · Q39 · Numerical
The number of arrangements of the letters of the word "INDEPENDENCE" in which all the vowels always occur together is :2023 · 8 Apr · Shift 1 · Q22 · MCQ
The number of ways, in which 5 girls and 7 boys can be seated at a round table so that no two girls sit together, is :2023 · 8 Apr · Shift 1 · Q27 · MCQ
Let the number of elements in sets $A$ and $B$ be five and two respectively. Then the number of subsets of $A \times B$ each having at least 3 and at most 6 elements is :2023 · 8 Apr · Shift 1 · Q34 · MCQ
If the number of words, with or without meaning, which can be made using all the letters of the word MATHEMATICS in which $C$ and $S$ do not come together, is $(6!) k$ , then $k$ is equal to :2023 · 8 Apr · Shift 2 · Q30 · MCQ
The number of permutations, of the digits 1, 2, 3, ..., 7 without repetition, which neither contain the string 153 nor the string 2467, is .2023 · 10 Apr · Shift 1 · Q43 · Numerical
Some couples participated in a mixed doubles badminton tournament. If the number of matches played, so that no couple played in a match, is 840, then the total number of persons, who participated in the tournament, is …2023 · 10 Apr · Shift 1 · Q45 · Numerical
Eight persons are to be transported from city A to city B in three cars of different makes. If each car can accommodate at most three persons, then the number of ways, in which they can be transported, is :2023 · 10 Apr · Shift 2 · Q22 · MCQ
The sum of all the four-digit numbers that can be formed using all the digits 2, 1, 2, 3 is equal to .2023 · 10 Apr · Shift 2 · Q35 · Numerical
The number of triplets $(x, y, z)$ , where $x, y, z$ are distinct non negative integers satisfying $x + y + z = 15$ , is :2023 · 11 Apr · Shift 1 · Q38 · MCQ
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 .2023 · 11 Apr · Shift 1 · Q44 · Numerical
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 :2023 · 11 Apr · Shift 2 · Q27 · MCQ
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 :2023 · 12 Apr · Shift 1 · Q27 · MCQ
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?2023 · 12 Apr · Shift 1 · Q36 · Numerical
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 .2023 · 13 Apr · Shift 1 · Q40 · Numerical
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 :2023 · 13 Apr · Shift 2 · Q23 · MCQ
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 .2023 · 13 Apr · Shift 2 · Q43 · Numerical
The total number of three-digit numbers, divisible by 3, which can be formed using the digits $1, 3, 5, 8$ , if repetition of digits is allowed, is :2023 · 15 Apr · Shift 1 · Q26 · MCQ
A person forgets his 4-digit ATM pin code. But he remembers that in the code all the digits are different, the greatest digit is 7 and the sum of the first two digits is equal to the sum of the last two digits. Then the maximum number of…2023 · 15 Apr · Shift 1 · Q38 · Numerical
A boy needs to select five courses from 12 available courses, out of which 5 courses are language courses. If he can choose at most two language courses, then the number of ways he can choose five courses is 2023 · 24 Jan · Shift 1 · Q41 · Numerical
The number of 9 digit numbers, that can be formed using all the digits of the number 123412341 so that the even digits occupy only even places, is .2023 · 24 Jan · Shift 1 · Q44 · Numerical
The number of integers, greater than 7000 that can be formed, using the digits 3, 5, 6, 7, 8 without repetition is :2023 · 24 Jan · Shift 2 · Q25 · MCQ
The number of square matrices of order 5 with entries from the set {0, 1}, such that the sum of all the elements in each row is 1 and the sum of all the elements in each column is also 1, is :2023 · 24 Jan · Shift 2 · Q32 · MCQ
Let $x$ and $y$ be distinct integers where $1 \leq x \leq 25$ and $1 \leq y \leq 25$ . Then, the number of ways of choosing $x$ and $y$ , such that $x + y$ is divisible by 5, is .2023 · 25 Jan · Shift 1 · Q41 · Numerical
The number of numbers, strictly between 5000 and 10000 can be formed using the digits 1, 3, 5, 7, 9 without repetition, is :2023 · 25 Jan · Shift 2 · Q34 · MCQ
$k = 0 \sum 6^{51 - k} C_{3}$ is equal to :2023 · 25 Jan · Shift 2 · Q37 · MCQ
A triangle is formed by X-axis, Y-axis and the line $3 x + 4 y = 60$ . Then the number of points P(a, b) which lie strictly inside the triangle, where a is an integer and b is a multiple of a, is .2023 · 25 Jan · Shift 2 · Q40 · Numerical
Suppose Anil's mother wants to give 5 whole fruits to Anil from a basket of 7 red apples, 5 white apples and 8 oranges. If in the selected 5 fruits, at least 2 oranges, at least one red apple and at least one white apple must be given,…2023 · 25 Jan · Shift 2 · Q43 · Numerical
If all the six digit numbers $x_{1} x_{2} x_{3} x_{4} x_{5} x_{6}$ with $0 < x_{1} < x_{2} < x_{3} < x_{4} < x_{5} < x_{6}$ are arranged in the increasing order, then the sum of the digits in the $7 2^{th}$ number is …2023 · 29 Jan · Shift 1 · Q45 · Numerical
Five digit numbers are formed using the digits 1, 2, 3, 5, 7 with repetitions and are written in descending order with serial numbers. For example, the number 77777 has serial number 1. Then the serial number of 35337 is …2023 · 29 Jan · Shift 1 · Q47 · Numerical
The letters of the word OUGHT are written in all possible ways and these words are arranged as in a dictionary, in a series. Then the serial number of the word TOUGH is :2023 · 29 Jan · Shift 2 · Q26 · MCQ
The number of 3 digit numbers, that are divisible by either 3 or 4 but not divisible by 48, is :2023 · 29 Jan · Shift 2 · Q28 · MCQ
The total number of 4-digit numbers whose greatest common divisor with 54 is 2, is .2023 · 29 Jan · Shift 2 · Q39 · Numerical
Number of 4-digit numbers (the repetition of digits is allowed) which are made using the digits 1, 2, 3 and 5, and are divisible by 15, is equal to .2023 · 30 Jan · Shift 1 · Q34 · Numerical
The number of ways of selecting two numbers $a$ and $b, a \in {2, 4, 6, \dots ., 100}$ and $b \in {1, 3, 5, \dots .., 99}$ such that 2 is the remainder when $a + b$ is divided by 23 is :2023 · 30 Jan · Shift 2 · Q25 · MCQ
The number of seven digits odd numbers, that can be formed using all the seven digits 1, 2, 2, 2, 3, 3, 5 is .2023 · 30 Jan · Shift 2 · Q37 · Numerical
Let 5 digit numbers be constructed using the digits $0, 2, 3, 4, 7, 9$ with repetition allowed, and are arranged in ascending order with serial numbers. Then the serial number of the number 42923 is .2023 · 31 Jan · Shift 1 · Q41 · Numerical
Number of 4-digit numbers that are less than or equal to 2800 and either divisible by 3 or by 11 , is equal to .2023 · 31 Jan · Shift 1 · Q43 · Numerical
Let $A = [a_{ij}], a_{ij} \in Z \cap [0, 4], 1 \leq i, j \leq 2$ . The number of matrices A such that the sum of all entries is a prime number $p \in (2, 13)$ is .2023 · 31 Jan · Shift 2 · Q40 · Numerical
If $^{2 n + 1} P_{n - 1} :^{2 n - 1} P_{n} = 11 : 21$ , then $n^{2} + n + 15$ is equal to :2023 · 31 Jan · Shift 2 · Q41 · Numerical
In an examination, there are 5 multiple choice questions with 3 choices, out of which exactly one is correct. There are 3 marks for each correct answer, $-$ 2 marks for each wrong answer and 0 mark if the question is not attempted. Then,…2022 · 24 Jun · Shift 1 · Q36 · Numerical
The number of 7-digit numbers which are multiples of 11 and are formed using all the digits 1, 2, 3, 4, 5, 7 and 9 is .2022 · 24 Jun · Shift 2 · Q39 · Numerical
The letters of the word 'MANKIND' are written in all possible orders and arranged in serial order as in an English dictionary. Then the serial number of the word 'MANKIND' is .2022 · 25 Jul · Shift 1 · Q37 · Numerical
The number of 3-digit odd numbers, whose sum of digits is a multiple of 7, is .2022 · 25 Jun · Shift 1 · Q39 · Numerical
Let A be a 3 $\times$ 3 matrix having entries from the set { $-$ 1, 0, 1}. The number of all such matrices A having sum of all the entries equal to 5, is .2022 · 25 Jun · Shift 1 · Q43 · Numerical
The total number of three-digit numbers, with one digit repeated exactly two times, is .2022 · 25 Jun · Shift 2 · Q43 · Numerical
The number of 5-digit natural numbers, such that the product of their digits is 36 , is .2022 · 26 Jul · Shift 1 · Q40 · Numerical
Numbers are to be formed between 1000 and 3000 , which are divisible by 4 , using the digits $1, 2, 3, 4, 5$ and 6 without repetition of digits. Then the total number of such numbers is .2022 · 26 Jul · Shift 2 · Q35 · Numerical
There are ten boys B1, B2, ......., B10 and five girls G1, G2, ........, G5 in a class. Then the number of ways of forming a group consisting of three boys and three girls, if both B1 and B2 together should not be the members of a group,…2022 · 26 Jun · Shift 1 · Q34 · Numerical
The total number of 3-digit numbers, whose greatest common divisor with 36 is 2, is .2022 · 26 Jun · Shift 2 · Q43 · Numerical
The number of ways, 16 identical cubes, of which 11 are blue and rest are red, can be placed in a row so that between any two red cubes there should be at least 2 blue cubes, is .2022 · 27 Jun · Shift 1 · Q38 · Numerical
Let A be a matrix of order 2 $\times$ 2, whose entries are from the set {0, 1, 2, 3, 4, 5}. If the sum of all the entries of A is a prime number p, 2 < p < 8, then the number of such matrices A is .2022 · 27 Jun · Shift 2 · Q39 · Numerical
Let $S$ be the set of all passwords which are six to eight characters long, where each character is either an alphabet from ${A, B, C, D, E}$ or a number from ${1, 2, 3, 4, 5}$ with the repetition of characters allowed. If the number of…2022 · 28 Jul · Shift 1 · Q38 · Numerical
A class contains b boys and g girls. If the number of ways of selecting 3 boys and 2 girls from the class is 168 , then $b + 3 g$ is equal to .2022 · 28 Jul · Shift 2 · Q36 · Numerical
The total number of 5-digit numbers, formed by using the digits 1, 2, 3, 5, 6, 7 without repetition, which are multiple of 6, is :2022 · 28 Jun · Shift 1 · Q26 · MCQ
The number of ways to distribute 30 identical candies among four children C1, C2, C3 and C4 so that C2 receives at least 4 and at most 7 candies, C3 receives at least 2 and at most 6 candies, is equal to :2022 · 28 Jun · Shift 2 · Q24 · MCQ
The number of matrices of order $3 \times 3$ , whose entries are either 0 or 1 and the sum of all the entries is a prime number, is .2022 · 29 Jul · Shift 1 · Q44 · Numerical
The number of natural numbers lying between 1012 and 23421 that can be formed using the digits $2, 3, 4, 5, 6$ (repetition of digits is not allowed) and divisible by 55 is .2022 · 29 Jul · Shift 2 · Q39 · Numerical
Let b1b2b3b4 be a 4-element permutation with bi $\in$ {1, 2, 3, ........, 100} for 1 $\leq$ i $\leq$ 4 and bi $e$ bj for i $e$ j, such that either b1, b2, b3 are consecutive integers or b2, b3, b4 are consecutive integers. Then the number of…2022 · 29 Jun · Shift 1 · Q41 · Numerical
The total number of four digit numbers such that each of first three digits is divisible by the last digit, is equal to .2022 · 29 Jun · Shift 2 · Q41 · Numerical
The number of 6-digit numbers made by using the digits 1, 2, 3, 4, 5, 6, 7, without repetition and which are multiple of 15 is .2022 · 30 Jun · Shift 1 · Q34 · Numerical
Let P1, P2, ......, P15 be 15 points on a circle. The number of distinct triangles formed by points Pi, Pj, Pk such that i +j + k $e$ 15, is :2021 · 1 Sep · Shift 2 · Q34 · MCQ
All the arrangements, with or without meaning, of the word FARMER are written excluding any word that has two R appearing together. The arrangements are listed serially in the alphabetic order as in the English dictionary. Then the serial…2021 · 1 Sep · Shift 2 · Q43 · Numerical
Consider a rectangle ABCD having 5, 7, 6, 9 points in the interior of the line segments AB, CD, BC, DA respectively. Let $α$ be the number of triangles having these points from different sides as vertices and $β$ be the number of…2021 · 16 Mar · Shift 2 · Q28 · MCQ
Team 'A' consists of 7 boys and n girls and Team 'B' has 4 boys and 6 girls. If a total of 52 single matches can be arranged between these two teams when a boy plays against a boy and a girl plays against a girl, then n is equal to :2021 · 17 Mar · Shift 1 · Q35 · MCQ
If the sides AB, BC and CA of a triangle ABC have 3, 5 and 6 interior points respectively, then the total number of triangles that can be constructed using these points as vertices, is equal to :2021 · 17 Mar · Shift 2 · Q21 · MCQ
The sum of all the 4-digit distinct numbers that can be formed with the digits 1, 2, 2 and 3 is :2021 · 18 Mar · Shift 1 · Q38 · MCQ
The number of times the digit 3 will be written when listing the integers from 1 to 1000 is :2021 · 18 Mar · Shift 1 · Q40 · Numerical
The missing value in the following figure is Includes diagram2021 · 18 Mar · Shift 1 · Q42 · Numerical
If $r = 1 \sum 10 r! (r^{3} + 6 r^{2} + 2 r + 5) = α (11!)$ , then the value of $α$ is equal to .2021 · 18 Mar · Shift 2 · Q37 · Numerical
There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsman and 2 are wicketkeepers. The number of ways, a team of 11 players be selected from them so as to include at least 4 bowlers, 5 batsman and 1 wicketkeeper, is…2021 · 20 Jul · Shift 1 · Q43 · Numerical
If the digits are not allowed to repeat in any number formed by using the digits 0, 2, 4, 6, 8, then the number of all numbers greater than 10,000 is equal to .2021 · 22 Jul · Shift 2 · Q39 · Numerical
A scientific committee is to be formed from 6 Indians and 8 foreigners, which includes at least 2 Indians and double the number of foreigners as Indians. Then the number of ways, the committee can be formed, is :2021 · 24 Feb · Shift 1 · Q29 · MCQ
The students S1, S2, ....., S10 are to be divided into 3 groups A, B and C such that each group has at least one student and the group C has at most 3 students. Then the total number of possibilities of forming such groups is …2021 · 24 Feb · Shift 2 · Q40 · Numerical
The total number of positive integral solutions (x, y, z) such that xyz = 24 is :2021 · 25 Feb · Shift 1 · Q28 · MCQ
The total number of numbers, lying between 100 and 1000 that can be formed with the digits 1, 2, 3, 4, 5, if the repetition of digits is not allowed and numbers are divisible by either 3 or 5, is .2021 · 25 Feb · Shift 1 · Q39 · Numerical
There are 5 students in class 10, 6 students in class 11 and 8 students in class 12. If the number of ways, in which 10 students can be selected from them so as to include at least 2 students from each class and at most 5 students from the…2021 · 25 Jul · Shift 1 · Q42 · Numerical
If $^{n} P_{r} =^{n} P_{r + 1}$ and $^{n} C_{r} =^{n} C_{r - 1}$ , then the value of r is equal to :2021 · 25 Jul · Shift 2 · Q39 · MCQ
If $^{1} P_{1} + 2.^{2} P_{2} + 3.^{3} P_{3} + .... + 15.^{15} P_{15} =^{q} P_{r} - s, 0 \leq s \leq 1$ , then $^{q + s} C_{r - s}$ is equal to .2021 · 26 Aug · Shift 1 · Q36 · Numerical
The number of three-digit even numbers, formed by the digits 0, 1, 3, 4, 6, 7 if the repetition of digits is not allowed, is .2021 · 26 Aug · Shift 1 · Q41 · Numerical
The number of seven digit integers with sum of the digits equal to 10 and formed by using the digits 1, 2 and 3 only is :2021 · 26 Feb · Shift 1 · Q27 · MCQ
A natural number has prime factorization given by n = 2x3y5z, where y and z are such that y + z = 5 and y $-$ 1 + z $-$ 1 = $\frac{5}{6}$ , y > z. Then the number of odd divisions of n, including 1, is :2021 · 26 Feb · Shift 2 · Q29 · MCQ
A number is called a palindrome if it reads the same backward as well as forward. For example 285582 is a six digit palindrome. The number of six digit palindromes, which are divisible by 55, is .2021 · 27 Aug · Shift 1 · Q40 · Numerical
Let S = {1, 2, 3, 4, 5, 6, 9}. Then the number of elements in the set T = {A $\subseteq$ S : A $e ϕ$ and the sum of all the elements of A is not a multiple of 3} is .2021 · 27 Aug · Shift 2 · Q38 · Numerical
Let n be a non-negative integer. Then the number of divisors of the form "4n + 1" of the number (10)10 . (11)11 . (13)13 is equal to .2021 · 27 Jul · Shift 2 · Q42 · Numerical
The number of six letter words (with or without meaning), formed using all the letters of the word 'VOWELS', so that all the consonants never come together, is .2021 · 31 Aug · Shift 1 · Q42 · Numerical
If the letters of the word 'MOTHER' be permuted and all the words so formed (with or without meaning) be listed as in a dictionary, then the position of the word 'MOTHER' is .2020 · 2 Sep · Shift 1 · Q27 · Numerical
Let n > 2 be an integer. Suppose that there are n Metro stations in a city located along a circular path. Each pair of stations is connected by a straight track only. Further, each pair of nearest stations is connected by blue line,…2020 · 2 Sep · Shift 2 · Q27 · MCQ
The value of (2.1P0 – 3.2P1 + 4.3P2 .... up to 51th term) + (1! – 2! + 3! – ..... up to 51th term) is equal to :2020 · 3 Sep · Shift 1 · Q26 · MCQ
The total number of 3-digit numbers, whose sum of digits is 10, is .2020 · 3 Sep · Shift 2 · Q30 · Numerical
A test consists of 6 multiple choice questions, each having 4 alternative answers of which only one is correct. The number of ways, in which a candidate answers all six questions such that exactly four of the answers are correct, is …2020 · 4 Sep · Shift 2 · Q22 · Numerical
The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word ’SYLLABUS’ such that two letters are distinct and two letters are alike, is :2020 · 5 Sep · Shift 1 · Q20 · Numerical
Four fair dice are thrown independently 27 times. Then the expected number of times, at least two dice show up a three or a five, is .2020 · 5 Sep · Shift 1 · Q25 · Numerical
There are 3 sections in a question paper and each section contains 5 questions. A candidate has to answer a total of 5 questions, choosing at least one question from each section. Then the number of ways, in which the candidate can choose…2020 · 5 Sep · Shift 2 · Q35 · MCQ
Two families with three members each and one family with four members are to be seated in a row. In how many ways can they be seated so that the same family members are not separated?2020 · 6 Sep · Shift 1 · Q38 · MCQ
The number of words (with or without meaning) that can be formed from all the letters of the word “LETTER” in which vowels never come together is .2020 · 6 Sep · Shift 2 · Q30 · Numerical
Total number of 6-digit numbers in which only and all the five digits 1, 3, 5, 7 and 9 appear, is :2020 · 7 Jan · Shift 1 · Q23 · MCQ
The number of ordered pairs (r, k) for which 6.35Cr = (k2 - 3). 36Cr + 1, where k is an integer, is :2020 · 7 Jan · Shift 2 · Q23 · MCQ
An urn contains 5 red marbles, 4 black marbles and 3 white marbles. Then the number of ways in which 4 marbles can be drawn so that at the most three of them are red is .2020 · 8 Jan · Shift 1 · Q21 · Numerical
If a, b and c are the greatest value of 19Cp, 20Cq and 21Cr respectively, then :2020 · 8 Jan · Shift 1 · Q39 · MCQ
The number of 4 letter words (with or without meaning) that can be formed from the eleven letters of the word 'EXAMINATION' is .2020 · 8 Jan · Shift 2 · Q21 · Numerical
If the number of five digit numbers with distinct digits and 2 at the 10th place is 336 k, then k is equal to :2020 · 9 Jan · Shift 1 · Q28 · MCQ
All possible numbers are formed using the digits 1, 1, 2, 2, 2, 2, 3, 4, 4 taken all at a time. The number of such numbers in which the odd digits occupy even places is :2019 · 8 Apr · Shift 1 · Q42 · MCQ
The number of four-digit numbers strictly greater than 4321 that can be formed using the digits 0,1,2,3,4,5 (repetition of digits is allowed) is :2019 · 8 Apr · Shift 2 · Q42 · MCQ
A committee of 11 members is to be formed from 8 males and 5 females. If m is the number of ways the committee is formed with at least 6 males and n is the number of ways the committee is formed with at least 3 females, then :2019 · 9 Apr · Shift 1 · Q43 · MCQ
Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, if there are two specific boys A and B, who refuse to be the members of the same team, is :2019 · 9 Jan · Shift 1 · Q40 · MCQ
The number of natural numbers less than 7,000 which can be formed by using the digits 0, 1, 3, 7, 9 (repitition of digits allowed) is equal to :2019 · 9 Jan · Shift 2 · Q29 · MCQ
Let S be the set of all triangles in the xy-plane, each having one vertex at the origin and the other two vertices lie on coordinate axes with integral coordinates. If each triangle in S has area 50 sq. units, then the number of elements…2019 · 9 Jan · Shift 2 · Q36 · MCQ
The number of 6 digit numbers that can be formed using the digits 0, 1, 2, 5, 7 and 9 which are divisible by 11 and no digit is repeated is :2019 · 10 Apr · Shift 1 · Q34 · MCQ
Suppose that 20 pillars of the same height have been erected along the boundary of a circular stadium. If the top of each pillar has been connected by beams with the top of all its non-adjacent pillars, then the total number of beams is :2019 · 10 Apr · Shift 2 · Q36 · MCQ
If $r = 0 \sum 25 {^{50} C_{r} .^{50 - r} C_{25 - r}} = K (^{50} C_{25}),$ then K is equal to :2019 · 10 Jan · Shift 2 · Q37 · MCQ
The number of ways of choosing 10 objects out of 31 objects of which 10 are identical and the remaining 21 are distinct, is :2019 · 12 Apr · Shift 1 · Q29 · MCQ
A group of students comprises of 5 boys and n girls. If the number of ways, in which a team of 3 students can randomly be selected from this group such that there is at least one boy and at least one girl in each team, is 1750, then n is…2019 · 12 Apr · Shift 2 · Q38 · MCQ
Consider three boxes, each containing, 10 balls labelled 1, 2, … , 10. Suppose one ball is randomly drawn from each of the boxes. Denote by ni, the label of the ball drawn from the ith box, (i = 1, 2, 3). Then, the number of ways in which…2019 · 12 Jan · Shift 1 · Q32 · MCQ
There are m men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of games played by the men between themselves exceeds the number of games played between the…2019 · 12 Jan · Shift 2 · Q27 · MCQ
n $-$ digit numbers are formed using only three digits 2, 5 and 7. The smallest value of n for which 900 such distinct numbers can be formed, is :2018 · 15 Apr · Shift 1 · Q26 · MCQ
The number of four letter words that can be formed using the letters of the word BARRACK is :2018 · 15 Apr · Shift 2 · Q26 · MCQ
The number of numbers between 2,000 and 5,000 that can be formed with the digits 0, 1, 2, 3, 4 (repetition of digits is not allowed) and are multiple of 3 is :2018 · 16 Apr · Shift 1 · Q33 · MCQ
From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is :2018 · Shift 0 · Q27 · MCQ
If all the words, with or without meaning, are written using the letters of the word QUEEN and are arranged as in English dictionary, then the position of the word QUEEN is :2017 · 8 Apr · Shift 1 · Q26 · MCQ
The number of ways in which 5 boys and 3 girls can be seated on a round table if a particular boy B1 and a particular girl G1 never sit adjacent to each other, is :2017 · 9 Apr · Shift 1 · Q26 · MCQ
A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 are men. Assume X and Y have no common friends. Then the total number of ways in which X and Y together can throw a party…2017 · Shift 0 · Q26 · MCQ
If the four letter words (need not be meaningful ) are to be formed using the letters from the word “MEDITERRANEAN” such that the first letter is R and the fourth letter is E, then the total number of all such words is :2016 · 9 Apr · Shift 1 · Q23 · MCQ
The value of $r = 1 \sum 15 r^{2} (\frac{^{15} C _{r}}{^{15} C _{r - 1}})$ is equal to :2016 · 9 Apr · Shift 1 · Q30 · MCQ
If $\frac{^{n + 2} C _{6}}{^{n - 2} P _{2}}$ = 11, then n satisfies the equation :2016 · 10 Apr · Shift 1 · Q22 · MCQ
The sum $r = 1 \sum 10 (r^{2} + 1) \times (r!)$ is equal to :2016 · 10 Apr · Shift 1 · Q28 · MCQ
If all the words (with or without meaning) having five letters,formed using the letters of the word SMALL and arranged as in a dictionary, then the position of the word SMALL is :2016 · Shift 0 · Q35 · MCQ
The number of integers greater than 6,000 that can be formed, using the digits 3, 5, 6, 7 and 8, without repetition, is:2015 · Shift 0 · Q40 · MCQ
Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of A $\times$ B having 3 or more elements is :2013 · Shift 0 · Q27 · MCQ
Let $T_{n}$ be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If $T_{n + 1} - T_{n}$ = 10, then the value of n is :2013 · Shift 0 · Q40 · MCQ
Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is:2012 · Shift 0 · Q41 · MCQ
Statement - 1: The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is emply is $^{9} C_{3}$ . Statement - 2: The number of ways of choosing any 3 places from 9 different places is $^{9} C_{3}$ .2011 · Shift 0 · Q46 · MCQ
These are 10 points in a plane, out of these 6 are collinear, if N is the number of triangles formed by joining these points. then:2011 · Shift 0 · Q47 · MCQ
There are two urns. Urn A has 3 distinct red balls and urn B has 9 distinct blue balls. From each urn two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is2010 · Shift 0 · Q45 · MCQ
From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. Then the number of such arrangement is :2009 · Shift 0 · Q43 · MCQ
How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent?2008 · Shift 0 · Q49 · MCQ
In a shop there are five types of ice-cream available. A child buys six ice-cream. Statement - 1: The number of different ways the child can buy the six ice-cream is $^{10} C_{5}$ . Statement - 2: The number of different ways the child can…2008 · Shift 0 · Q50 · MCQ
The set S = {1, 2, 3, ........., 12} is to be partitioned into three sets A, B, C of equal size. Thus $A \cup B \cup C = S, A \cap B = B \cap C = A \cap C = ϕ$ . The number of ways to partition S is2007 · Shift 0 · Q58 · MCQ
At an election, a voter may vote for any number of candidates, not greater than the number to be elected. There are 10 candidates and 4 are of be selected, if a voter votes for at least one candidate, then the number of ways in which he…2006 · Shift 0 · Q72 · MCQ
If the letter of the word SACHIN are arranged in all possible ways and these words are written out as in dictionary, then the word SACHIN appears at serial number2005 · Shift 0 · Q98 · MCQ
How many ways are there to arrange the letters in the word GARDEN with vowels in alphabetical order2004 · Shift 0 · Q103 · MCQ
The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is2004 · Shift 0 · Q105 · MCQ
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 is2003 · Shift 0 · Q105 · MCQ
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 by2003 · Shift 0 · Q107 · MCQ
If $^{n} C_{r}$ denotes the number of combination of n things taken r at a time, then the expression $^{n} C_{r + 1} +^{n} C_{r - 1} + 2 \times^{n} C_{r}$ equals2003 · Shift 0 · Q108 · MCQ
Number greater than 1000 but less than 4000 is formed using the digits 0, 1, 2, 3, 4 (repetition allowed). Their number is :2002 · Shift 0 · Q107 · MCQ
The sum of integers from 1 to 100 that are divisible by 2 or 5 is :2002 · Shift 0 · Q108 · MCQ
Five digit number divisible by 3 is formed using 0, 1, 2, 3, 4 and 5 without repetition. Total number of such numbers are :2002 · Shift 0 · Q109 · MCQ
Total number of four digit odd numbers that can be formed using 0, 1, 2, 3, 5, 7 (using repetition allowed) are :2002 · Shift 0 · Q94 · MCQ