Maths Unit Test: Permutations & Combinations(June 28) - JEE MCQ

The number of six-letter words (with or without meaning), formed using all the letters of the word 'VOWELS', so that all the consonants never come together, is ______. (in integers)

If the digits are not allowed to repeat in any number formed by using the digits 0, 2, 4, 6, 8, then the number of all numbers greater than 10,000 is equal to _______. (in integers)

If a, b and c are the greatest values of ¹⁹C_p, ²⁰C_q and ²¹C_r respectively, then

In an examination, there are 5 multiple choice questions with 3 choices, out of which exactly one is correct. There are 3 marks for each correct answer, -2 marks for each wrong answer and 0 marks if the question is not attempted. Then the number of ways a student appearing in the examination gets 5 marks is _____. (in integer)

Let b₁b₂b₃b₄ be a 4-element permutation with b_i ∈ {1, 2, 3, ..., 100} for 1 ≤ i ≤ 4 and b_i ≠ b_j for i ≠ j, such that either b₁, b₂, b₃ are consecutive integers or b₂, b₃, b₄ are consecutive integers.

Then the number of such permutations b₁b₂b₃b₄ is equal to _________. (in integers)

Total number of 6-digit numbers in which only and all the five digits 1, 3, 5, 7 and 9 appear, is

The total number of three-digit numbers, with one digit repeated exactly two times, is ______. (in integers)

Let denote ⁿC_k and .
If A_k =  and A₄ - A₃ = 190 p, then p is equal to __________. (in integers)

The number of ways, 16 identical cubes, of which 11 are blue and rest are red, can be placed in a row so that between any two red cubes there should be at least 2 blue cubes, is _______. (in integers)

The number of 5-digit natural numbers, such that the product of their digits is 36, is _____ . (in integers)

An urn contains 5 red marbles, 4 black marbles and 3 white marbles. Then the number of ways in which 4 marbles can be drawn so that at the most three of them are red is _________. (in integers)

Let n > 2 be an integer. Suppose that there are n Metro stations in a city located along a circular path. Each pair of stations is connected by a straight track only. Further, each pair of nearest stations is connected by blue line, whereas all remaining pairs of stations are connected by red line. If the number of red lines is 99 times the number of blue lines, then the value of n is: