Class 11

Math

JEE Main Questions

Permutations and Combinations

The total number of five-digit numbers of different digits in which the digit in the middle is the largest is a. $n=4∑9 _{n}P_{4}$ b. $33(3!)$ c. $30(3!)$ d. none of these

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In how many of the distinct permutations of the letters in MISSISSIPPI do the four Is not come together?

The number of distinct natural numbers up to a maximum of four digits and divisible by 5, which can be formed with the digits 0, 1 , 2, 3, 4, 5, 6, 7, 8, 9 each digit not occurring more than once in each number, is a. $1246$ b. $952$ c. $1106$ d. none of these

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. $∣x−y∣=54$

An n-digit number is a positive number with exactly $n$ Nine hundred distinct n-digit numbers are to be formed using only the three digits $2,5,and7.$ The smallest value of $n$ for which this is possible is (a) $6$ (b) $7$ (c) $8$ (d) $9$

If $N$ is the number of ways in which 3 distinct numbers canbe selected from the set ${3_{1},3_{2},3_{3},,3_{10}}$ so that they form a G.P. then the value of $N/5$ is ______.

Find the number of three-digit numbers from 100 to 999 including all numbers which have any one digit that is the average of the other two.

Numbers greater than 1000 but not greater than 4000 which can be formed with the digits 0, 1, 2, 3, 4 (repetition of digits is allowed) are a. $350$ b. $375$ c. $450$ d. $576$

Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination.