Permutation and combination mock test PYQ 2024 jee mains

Mock Quiz: StudyBeacon

Test your skills with these carefully curated questions. Select an option to reveal the correct answer and solution.

Q1. If n is the number of ways five different employees can sit into four indistinguishable offices where any office may have any number of persons including zero, then n is equal to:

Q2. In an examination of Mathematics paper, there are 20 questions of equal marks and the question paper is divided into three sections: A, B, and C. A student is required to attempt a total of 15 questions taking at least 4 questions from each section. If section A has 8 questions, section B has 6 questions, and section C has 6 questions, then the total number of ways a student can select 15 questions is:

Q3. There are 5 points P_1, P_2, P_3, P_4, P_5 on the side AB, excluding A and B, of a triangle ABC. Similarly, there are 6 points P_6, P_7, \ldots, P_{11} on the side BC and 7 points P_{12}, P_{13},\ldots,P_{18} on the side CA of the triangle. The number of triangles that can be formed using the points P_1, P_2,\ldots,P_{18} as vertices, is:

Q4. 60 words can be made using all the letters of the word BHBJO, with or without meaning. If these words are written as in a dictionary, then the 50th word is:

Q5. The number of 3-digit numbers, formed using the digits 2, 3, 4, 5, and 7, when the repetition of digits is not allowed, and which are not divisible by 3, is equal to ________.

Q6. Number of ways of arranging 8 identical books into 4 identical shelves where any number of shelves may remain empty is equal to:

Q7. The total number of words (with or without meaning) that can be formed out of the letters of the word 'DISTRIBUTION' taken four at a time, is equal to:

Q8. The lines L_1, L_2,\ldots,L_{20} are distinct lines. For n = 1, 2, 3, \ldots, 10, all the lines L_{2n-1} are parallel to each other and all the lines L_{2n} pass through a given point P. The maximum number of points of intersection of pairs of lines from the set \{ L_1, L_2,\ldots,L_{20} \} is equal to ______.

Q9. There are 4 men and 5 women in Group A, and 5 men and 4 women in Group B. If 4 persons are selected from each group, then the number of ways of selecting 4 men and 4 women is ______.

Q10. The number of triangles whose vertices are at the vertices of a regular octagon but none of whose sides is a side of the octagon is:

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