JEE Main Permutations and Combinations Practice Questions With Solutions

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:

Let $[t]$\left[\right. t \left]\right. be the greatest integer less than or equal to $t$t. Let $A$A be the set of all prime factors of 2310 and $f:A\to \mathbb{Z}$f : A \rightarrow \mathbb{Z} be the function $f(x)=[{\log }_2(x^2+\left[\frac{x^3}{5}\right])]$f \left(\right. x \left.\right) = \left[\right. log_{2} ⁡ \left(\right. x^{2} + \left[\right. \frac{x^{3}}{5} \left]\right. \left.\right) \left]\right.. The number of one-to-one functions from $A$A to the range of $f$f is

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 }}$315^{\text{th}\textrm{ }} position in this arrangement is :

Let $0\le r\le n$0 \leq r \leq n. If ${}^{n+1}{C}_{r+1}:{}^n{C}_r:{}^{n-1}{C}_{r-1}=55:35:21$^{n + 1} C_{r + 1} : ^{n} C_{r} : ^{n - 1} C_{r - 1} = 55 : 35 : 21, then $2n+5r$2 n + 5 r is equal to :

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

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

There are 5 points $P_1,P_2,P_3,P_4,P_5$P_{1} , P_{2} , P_{3} , P_{4} , P_{5} on the side $AB$A B, excluding $A$A and $B$B, of a triangle $ABC$A B C. Similarly there are 6 points ${\mathrm{P}}_6,{\mathrm{P}}_7,\dots ,{\mathrm{P}}_{11}$P_{6} , P_{7} , \ldots , P_{11} on the side $\mathrm{BC}$BC and 7 points ${\mathrm{P}}_{12},{\mathrm{P}}_{13},\dots ,{\mathrm{P}}_{18}$P_{12} , P_{13} , \ldots , P_{18} on the side $\mathrm{CA}$CA of the triangle. The number of triangles, that can be formed using the points ${\mathrm{P}}_1,{\mathrm{P}}_2,\dots ,{\mathrm{P}}_{18}$P_{1} , P_{2} , \ldots , P_{18} as vertices, is:

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