Class 11

Math

JEE Main Questions

Permutations and Combinations

The number of different ways in which five "alike dashes" and "eight alike" dots can be arranged using only seven of these "dashes" and "dots" is a. $350$ b. $120$ c. $1287$ d. none of these

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The number of ways of choosing a committee of two women and three men from five women and six men, if Mr. A refuses to serve on the committee if Mr. B is a member and Mr. B can only serve if Miss C is the member of the committee is a. $60$ b. $84$ c. $124$ d. none of these

In how many ways can two distinct subsets of the set $A$ of $k(k≥2)$ elements be selected so that they haves exactly two common elements?

The English alphabet has 5 vowels and 21 consonants. How many words with two different vowels and 2 different consonants can be formed from the alphabet?

A number of 18 guests have to be seated, half on each side of a long table. Four particular guests desire to sit on one particular side and three others on the other side. Determine the number of ways in which the sitting arrangements can be made.

$A$ is a set containing $n$ different elements. A subset $P$ of $A$ is chosen. The set $A$ is reconstructed by replacing the elements of $P$. A subset $Q$ of $A$ is again chosen. The number of ways of choosing $P$ and $Q$ so that $P∩Q$ contains exactly two elements is a. $._{n}C_{3}×2_{n}$ b. $._{n}C_{2}×3_{n−2}$ c. $3_{n−1}$ d. none of these

Prove by combinatorial argument that $._{n+1}C_{r}=_{n}C_{r}+_{n}C_{r−1}˙$

The streets of a city are arranged like the like the lines of a chess board. There are $m$ streets running from north to south and $n$ streets from east to west. Find the number of ways in which a man can travel from north-west to south-east corner, covering shortest possible distance.

A train time table must be compiled for various days of the week, so that two trains twice a day depart for three days, one train daily for two days, and three trains once a day for two days. How many diferent time table can be compiled?