Permutations & Combinations PYQs Set 11 (PDF)

Set 11 of 11 · Questions 301-315 of 315

In the print window choose “Save as PDF”. The file prints without a web address or date line.

Mere Teacher · Previous Year Questions JEE Main Mathematics · Permutations & Combinations · Set 11 (Q301-315)
Scan or visit mereteacher.com for free PYQ practice, timed CBT tests, step-by-step solutions and BroBot AI. Answers and solutions are free with a sign-up.
301. $There are two urns. Urn A has 3 distinct red balls and urn B has 9 distinct blue balls. From each urn two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is$ (1) $36$ (2) $66$ (3) $108$ (4) $3$ 302. $The number of all four digit numbers that can be formed with the digits 0, 1, 2, 3, 4, 5 when the repetition of the digits is not allowed, is$ (1) $360$ (2) $600$ (3) $240$ (4) $300$ 303. $A debate club consists of 6 girls and 4 boys. A team of 4 members is to be selected from this club including the selection of a captain (from among these 4 members) for the team. If the team has to include at most one boy. Then the number of ways of selecting the team is$ (1) $380$ (2) $320$ (3) $260$ (4) $95$ 304. $Some identical balls are arranged in rows to form an equilateral triangle. The first row consists of one ball, the second row consists of two balls and so on. If 99 moreidentical balls are added to the total number of balls usedin forming the equilateral triangle, then all these balls can be arranged in a square whose each side contains exactly 2 balls less than the number of balls each side of thetriangle contains. Then the number of balls used to form the equilateral triangle is:$ (1) $157$ (2) $262$ (3) $225$ (4) $190$ 305. $Match the items of List-I to the items of List-II List-I (A) The number of ways of not selecting (n - r) things from n different things (B) (n - r + 1) \cdot^{n} C_{r - 1} (C) The number of ways of selecting at least (n - r) things from n different things (D) (n - r) (^{n - 1} C_{r - 1} +^{n - 1} C_{r}) List-II (I) 1 + n +^{n} C_{2} + \dots +^{n} C_{r} (II) (r + 1) \cdot^{n} C_{r + 1} (III) r \cdot^{n} C_{r} (IV) 2^{n} - 1 - n -^{n} C_{2} - \dots -^{n} C_{r} (V)^{n} C_{n - r} The correct match is (A, B, C, D):$ (1) $V III IV II$ (2) $I II IV III$ (3) $V III I II$ (4) $I V IV III$ 306. $A simple graph contains 24 edges. Degree of each vertex is 3 . The number of vertices is$ (1) $12$ (2) $8$ (3) $16$ (4) $21$ 307. $All possible numbers are formed using the digits 1, 1, 2, 2, 2, 2, 3, 4, 4 taken all at a time. The number of such numbers in which the odd digits occupy even places is:$ (1) $180$ (2) $175$ (3) $160$ (4) $162$ 308. $How many ways are there to arrange the letters in the word "GARDEN" with the vowels in alphabetical order ?$ (1) $120$ (2) $240$ (3) $360$ (4) $480$ 309. $The number of ways in which 6 men and 5 women can dine at a round table, if no two women are to sit together, is given by -$ (1) $6! \times 5!$ (2) $30$ (3) $5! \times 4!$ (4) $7! \times 5!$ 310. $The number of ways of distributing 8 identical balls in 3 distinct boxes, so that none of the boxes is empty, is -$ (1) $5$ (2) $21$ (3) $38$ (4) $8C3$ 311. $At an election, a voter may vote for any number of candidates, not greater than the number to be elected. There are 10 candidates and 4 are to be elected. If a voter votes for at least one candidate, then the number of ways in which he can vote is$ (1) $5040$ (2) $6210$ (3) $385$ (4) $1110$ 312. $^{37} C_{4} + \sum_{r = 1}^{5} (42 - r)_{C_{r}} =$ (1) $^{41} C_{4}$ (2) $^{39} C_{4}$ (3) $^{38} C_{4}$ (4) $^{42} C_{4}$ 313. $If all the six digit numbers x_{1} x_{2} x_{3} x_{4} x_{5} x_{6} with 0 < x_{1} < x_{2} < x_{3} < x_{4} < x_{5} < x_{6} are arranged in the increasing order, then the sum of the digits in the 72^{th} number is _______$ 314. $A number is called a palindrome if it reads the same backward as well as forward. For example 285582 is a six digit palindrome. The number of six digit palindromes, which are divisible by 55, is .$ 315. $If the digits are not allowed to repeat in any number formed by using the digits 0,2,4,6,8,then the number of all numbers greater than 10,000is equal to$