jee-main 2021 Q73
Counting Functions with ConstraintsView
Let $x$ denote the total number of one-one functions from a set $A$ with 3 elements to a set $B$ with 5 elements and $y$ denote the total number of one-one functions from the set $A$ to the set $A \times B$. Then: (1) $y = 273 x$ (2) $2 y = 273 x$ (3) $2 y = 91 x$ (4) $y = 91 x$
jee-main 2021 Q81
Forming Numbers with Digit ConstraintsView
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
jee-main 2021 Q83
Forming Numbers with Digit ConstraintsView
The number of seven digit integers with sum of digits equal to 10 and formed by using the digits 1, 2 and 3 only is
jee-main 2022 Q61
Forming Numbers with Digit ConstraintsView
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 (1) 72 (2) 48 (3) 24 (4) 60
jee-main 2022 Q70
Counting Functions with ConstraintsView
The total number of functions, $f : \{1,2,3,4\} \rightarrow \{1,2,3,4,5,6\}$ such that $f(1) + f(2) = f(3)$, is equal to (1) 60 (2) 90 (3) 108 (4) 126
jee-main 2022 Q82
Forming Numbers with Digit ConstraintsView
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 $\_\_\_\_$.
jee-main 2022 Q82
Dictionary Order / Rank of a PermutationView
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 $\_\_\_\_$.
jee-main 2022 Q82
Forming Numbers with Digit ConstraintsView
The number of 5-digit natural numbers, such that the product of their digits is 36, is $\_\_\_\_$.
jee-main 2022 Q85
Distribution of Objects into Bins/GroupsView
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
jee-main 2023 Q62
Forming Numbers with Digit ConstraintsView
The number of ways of selecting two numbers $a$ and $b$, $a \in \{2, 4, 6, \ldots, 100\}$ and $b \in \{1, 3, 5, \ldots, 99\}$ such that 2 is the remainder when $a + b$ is divided by 23 is (1) 186 (2) 54 (3) 108 (4) 268
jee-main 2023 Q63
Forming Numbers with Digit ConstraintsView
The number of integers, greater than 7000 that can be formed, using the digits $3,5,6,7,8$ without repetition is (1) 120 (2) 168 (3) 220 (4) 48
jee-main 2023 Q63
Dictionary Order / Rank of a PermutationView
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 (1) 576 (2) 578 (3) 580 (4) 582
jee-main 2023 Q63
Word Permutations with Repeated LettersView
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 (1) 2835 (2) 5670 (3) 1890 (4) 945
jee-main 2023 Q63
Dictionary Order / Rank of a PermutationView
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) 327 (2) 328 (3) 324 (4) 326
jee-main 2023 Q63
Forming Numbers with Digit ConstraintsView
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 (1) 21 (2) 20 (3) 22 (4) 18
jee-main 2023 Q63
Forming Numbers with Digit ConstraintsView
The number of numbers, strictly between 5000 and 10000 can be formed using the digits $1,3,5,7,9$ without repetition, is (1) 6 (2) 12 (3) 120 (4) 72
jee-main 2023 Q63
Dictionary Order / Rank of a PermutationView
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 : (1) 89 (2) 84 (3) 86 (4) 79
jee-main 2023 Q63
Word Permutations with Repeated LettersView
The number of seven digits odd numbers, that can be formed using all the seven digits $1, 2, 2, 2, 3, 3, 5$ is
jee-main 2023 Q63
Word Permutations with Repeated LettersView
The number of arrangements of the letters of the word "INDEPENDENCE" in which all the vowels always occur together is (1) 16800 (2) 33600 (3) 18000 (4) 14800
jee-main 2023 Q63
Forming Numbers with Digit ConstraintsView
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) 132 (2) 120 (3) 72 (4) 96
jee-main 2023 Q64
Forming Numbers with Digit ConstraintsView
The total number of 4-digit numbers whose greatest common divisor with 54 is 2 , is $\_\_\_\_$
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 (1) 720 (2) $126 ( 5 ! ) ^ { 2 }$ (3) $7 ( 360 ) ^ { 2 }$ (4) $7 ( 720 ) ^ { 2 }$
jee-main 2023 Q67
Factorial and Combinatorial Expression SimplificationView
If ${}^{2n+1}P_{n-1} : {}^{2n-1}P_n = 11 : 21$, then $n^2 + n + 15$ is equal to $\_\_\_\_$.
jee-main 2023 Q67
Forming Numbers with Digit ConstraintsView
The number of 3 digit numbers, that are divisible by either 3 or 4 but not divisible by 48 , is (1) 472 (2) 432 (3) 507 (4) 400
jee-main 2023 Q69
Linear Arrangement with ConstraintsView
The number of 9-digit numbers, that can be formed using all the digits of the number 123456789, such that the even digits occupy only even places, is (1) 2880 (2) 2520 (3) 2160 (4) 2400