Class 11

Math

JEE Main Questions

Permutations and Combinations

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

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How many five-digit numbers can be made having exactly two identical digits?

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. $576$

Let $f(n,k)$ denote the number of ways in which $k$ identical balls can be colored with $n$ colors so that there is at least one ball of each color. Then $f(2n,n)$ must be equal to a. $_{2}nC_{n}$ b. $_{2}n−1C_{n+1}$ c. $_{2}n−1C_{n}$ d. none of these

Number of ways in which 200 people can be divided in 100 couples is a. $2_{100}(100!)(200)! $ b. $1×3×5××199$ c. $(2101 )(2102 )………….(2200 )$ d. $(100)!(200)! $

Determine $n$ if (i) $_{2n}C_{3}:_{n}C_{3}=12:1$ (ii) $_{2n}C_{3}:_{n}C_{3}=11:1$

The number of $n$ digit numbers which consists of the digit 1 and 2 only if each digit is to be used at least nece is equal to 510, then $n$ is equal to ________.

Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First, the women choose the chairs from amongst the chairs marked 1 to 4, and then the men select th chairs from amongst the remaining. The number of possible arrangements is a.$_{6}C_{3}×_{4}C_{2}$ b. $_{4}P_{2}×_{4}P_{3}$ c. $_{4}C_{2}×_{4}P_{3}$ d. none of these