JEE Main Questions
Permutations and Combinations
Evaluate r!(n−r)!n!, when n = 5, r = 2.
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.
Find the number of different 8-letter arrangements that can be made from the letters of the word DAUGHTER so that(i) all vowels occur together (ii) all vowels do not occur together.
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. .nC3×2n b. .nC2×3n−2 c. 3n−1 d. none of these
The total number of six-digit natural numbers that can be made with the digits 1, 2, 3, 4, if all digits are to appear in the same number at least once is a. 1560 b. 840 c. 1080 d. 480
In an examination, a question paper consists of 12 questions divided into two parts i.e., Part I and Part II, containing 5 and 7 questions, respectively. A student is required to attempt 8 questions in all, selecting at least 3 from each part. In how many ways can a student select the questions?
How many 3 -digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated?