Class 11

Math

Algebra

Permutations and Combinations

If $6!1 +7!1 =8!x $, find $x$.

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Let $n$ be a four-digit integer in which all the digits are different. If $x$ is number of odd integers and $y$ is number of even integers, then a. $x<y$ b. $x>y$ c. $x+y=4500$ d. $∣x−y∣=54$

A variable name in certain computer language must be either an alphabet or an alphabet followed by a decimal digit. The total number of different variable names that can exist in that language is equal to a. $280$ b. $390$ c. $286$ d. $296$

Number of points of intersection of $n$ straight lines if $n$ satisfies $_{n}+5P_{n+1}=211(n−1) ×_{n+3}P_{n}$ is a. $15$ b. $28$ c. $21$ d. 10

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.

There are 20 books on Algebra and Calculus in one library. For the greatest number of selections each of which consists of 5 books on each topic. If the possible number of Algebra books are N, then the value N/2 is __________.

How many chords can be drawn through 21 points on a circle?

Statement 1: number of ways in which 10 identical toys can be distributed among three students if each receives at least two toys is $_{6}C_{2}˙$ Statement 2: Number of positive integral solutions of $x+y+z+w=7is_{6}C_{3}˙$

Let $P_{n}$ denotes the number of ways in which three people can be selected out of 'n' people sitting in a row, if no two of them are consecutive. If $P_{n+1}−P_{n}=15$ then the value of 'n\displaystyle{i}{s}_{_}__{.}