Arjuna JEE 2025 Mathematics Permutations and Combinations PDF

JEE Arjuna JEE 2025 Mathematics...

JEE Arjuna JEE 2025 Mathematics DPP: 10 Permutations and Combinations Q1 The number of ordered triplets of positive Q6 The total number of integral solutions for integers which are solutions are solutions of the (x, y, z) such that xyz = 24 is equation x + y + z = 100, is (A) 36 (B) 90 (A) 6005 (B) 4851 (C) 120 (D) None of these (C) 5081 (D) None of these Q7 There are m points on a straight line AB and n Q2 The number of non-negative integral solutions of points on another line AC, none of them being the equation x + y + z + 5t = 15 is the point A. Triangles are formed these points as (A) 196 vertices when (i) A is excluded (ii) A is included. (B) 224 Then the ratio of the number of triangles in the (C) 312 two cases is m+n−2 (D) 364 (A) m+n (B) m+n−2 Q3 The number of the positive integral solutions 2 (C) m+n−2 (x, y, z) of the equation xyz = 24 is t , then the m+n+2 number of all possible factors of t is (D) None of these (A) 4 (B) 6 Q8 In how many ways 5 different balls can be (C) 8 (D) 9 arranged into 3 different boxes so that no box Q4 Number of ways in which 32 identical blankets remains empty? can be distributed among 4 persons so that each (A) 360 (B) 480 of them gets number of blankets which are (C) 720 (D) 900 divisible by 2 but not by 4, is Q9 In how many ways 5 different balls can be (A) 82 (B) 83 distributed into 3 boxes, so that no box remains (C) 84 (D) 85 empty. The required number of ways is? Q5 The number of non-negative integral solutions of (A) 120 (B) 125 x1 + x2 + x3 + x4 ≤ n (where n is a positive (C) 135 (D) 150 integer) is: Q10 The number of positive integers ≤ 100 which (A) n+3 C3 are not divisible by 2,3 or 5 is (B) n+4 C4 (A) 25 (B) 26 (C) n+5 C5 (C) 29 (D) 30 (D) n+4 Cn Q11 Android App | iOS App | PW Website  JEE Five letters are put in 5 addressed envelops randomly, the number of ways in which no letters goes to the correct envelop is: (A) 41 (B) 43 (C) 44 (D) 46 (A) A → R; B → R; C → Q; D → P Q12 The number of ways of putting at least 3 out of 6 (B) A → R; B → Q; C → R; D → S letters in wrong envelops is (C) A → Q; B → R; C → S; D → P (A) 265 (B) 40 (D) A → Q; B → S; C → S; D → R (C) 704 (D) 50 Q13 A person writes letters to six friends and addresses the corresponding envelopes. Let x be the number of ways so that atleast two of the letters are in wrong envelopes and y be the number of ways so that all the letters are in wrong envelopes. Then, x − y is equal to: (A) 719 (B) 265 (C) 454 (D) None of these Q14 Six cards and six envelopes are numbered 1, 2, 3, 4, 5, 6 and cards are to be placed in envelopes so that each envelope contains exactly one card and no card is placed in the envelope bearing the same number and moreover the card numbered 1 is always placed in envelope numbered 2. Then the number of ways it can be done is (A) 264 (B) 265 (C) 53 (D) 67 Q15 Sum of all the five digits natural numbers formed using all the digits {0, 1, 2, 3, 4} without repetition (A) 2599980 (B) 2666640 (C) 1999980 (D) None of these Q16 Suppose a set A consists of 10 distinct elements x1 , x2 , x3 … …. , x10 The number of subsets of A which contain Android App | iOS App | PW Website  JEE Answer Key Q1 (B) Q9 (D) Q2 (B) Q10 (B) Q3 (C) Q11 (C) Q4 (C) Q12 (C) Q5 (B, D) Q13 (C) Q6 (C) Q14 (C) Q7 (A) Q15 (A) Q8 (C) Q16 (A) Android App | iOS App | PW Website