Class 11

Math

JEE Main Questions

Permutations and Combinations

Evaluate (i) $8!$ (ii) $4!3!$

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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 $n$ 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. $∣x−y∣=54$

Find r, if $5_{4}P_{r}=6_{5}P_{r−1}$.

Rajdhani Express going from Bombay to Delhi stops at five intermediate stations, 10 passengers enter the train during the journey with 10 different ticket of two class. The number of different sets of tickets they may have is a. $_{15}C_{10}$ b. $_{20}C_{10}$ c. $_{30}C_{10}$ d. none of these

The total number of times, the digit 3 will be written when the integers having less than 4 digits are listed is equal to a. $300$ b. $310$ c. $302$ d. $306$

Statement 1: the number of ways of writing 1400 as a product of two positive integers is 12. Statement 2: 1400 is divisible by exactly three prime factors.

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 __________.

If $8!1 +9!1 =10!x ,$find x