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Let \( A=\{1,3,7,9,11\} \) and \( B=\{2,4,5,7,8,10,12\} \). Then the total number of one-one maps \( f:A\to B \), such that \( f(1)+f(3)=14 \), is:

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

The number of elements in the set \( S=\{(x,y,z):x,y,z\in\mathbb{Z},\;x+2y+3z=42,\;x,y,z\ge 0\} \) equals ______.

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

There are \( 4 \) men \( 5 \) 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 __________ .

The number is integers, between \( 100 \) and \( 1000 \) having the sum of their digits equals to \( 14 \), is ________.

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:

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:

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 is:

Let \( \alpha=\dfrac{(4!)!}{(4!)^{3!}} \) and \( \beta=\dfrac{(5!)!}{(5!)^{4!}} \). Then:

If \( n \) is the number of ways five different employees can sit into four indistinguished offices where any office may have any number of persons including zero, then \( n \) is equal to:

Let the set \( S=\{2,4,8,16,\ldots,512\} \) be partitioned into \( 3 \) sets \( A,B,C \) with equal number of elements such that \( A\cup B\cup C=S \) and \( A\cap B=B\cap C=A\cap C=\phi. \). The maximum number of such possible partitions of \( S \) is equal to:

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 students is required to attempt total \( 15 \) questions taking at least \( 4 \) questions from each section. If section \( A \) has \( 8 \) questions, section \( B \) has \( 6 \) questions and section \( C \) \( 6 \) questions, then the total number of ways a student can select \( 15 \) questions is ______.

The lines \( L_1,L_2,\ldots,L_{20} \) are distinct. For \( n = 1, 2, 3, \ldots, 10 \) all the lines \( l_{2n-1} \) are parallel to each other and all the lines \( L_{2n} \) pass through a given \( P \). The maximum number of points of intersection of pairs of lines form the set \( \{L_1,L_2,\ldots,L_{20}\} \) is equal to \( \_\_\_\_\_\_\_\_\_\_ \).

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 __________.

There are \( 5 \) points \( P_{1},P_{2},P_{3},P_{4},P_{5} \) on the side \( AB \), excluding \( A \) and \( B \), of a triangle \( ABC \). Similarly there are \( 6 \) points \( P_{6},P_{7},\ldots,P_{11} \) on the side \( BC \) and \( 7 \) points \( P_{12},P_{13},\ldots,P_{18} \) on the side \( CA \) of the triangle. The number of Triangles, that can be formed using the points \( P_{1},P_{2},\ldots,P_{18} \) as vertices, is:

The number of ways of getting a sum \( 16 \) on throwing a dice four times 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 _______.

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:

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 symmetric relations defined on the set \( \{ 1, 2, 3, 4 \} \) which are not reflexive is _______.

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JEE Main 2024 29th Jan Morning Shift

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 __________.