Permutation as arrangement; combination as selection — NEET & JEE Questions

Question 1 · difficulty L2 · understanding

A person has three different bags and four different books. The number of ways, in which he can put these books in the bags so that no bag is empty, is :

• A. 18
• B. 36
• C. 39
• D. 72

Question 2 · difficulty L2 · understanding

The number of 4-letter words, with or without meaning, each consisting of two vowels and two consonants that can be formed from the letters of the word INCONSEQUENTIAL, without repeating any letter, is:

• A. 2670
• B. 2840
• C. 2920
• D. 3600

Question 3 · difficulty L2 · understanding

The number of ways, of forming a queue of 4 boys and 3 girls such that all the girls are not together, is:

• A. 5040
• B. 3050
• C. 3410
• D. 4320

Question 4 · difficulty L2 · understanding

The number of ways, in which 16 oranges can be distributed to four children such that each child gets at least one orange, is

• A. 384
• B. 403
• C. 429
• D. 455

Question 5 · difficulty L2 · understanding

From a group of 7 batsmen and 6 bowlers, 10 players are to be chosen for a team, which should include atleast 4 batsmen and atleast 4 bowlers. One batsmen and one bowler who are captain and vice-captain respectively of the team should be included. Then the total number of ways such a selection can be made, is

• A. 145
• B. 165
• C. 155
• D. 135

Question 6 · difficulty L2 · understanding

The number of 3 digit numbers, that are divisible by either 3 or 4 but not divisible by 48, is :

• A. 400
• B. 472
• C. 507
• D. 432

Question 7 · difficulty L2 · understanding

The number of numbers, strictly between 5000 and 10000 can be formed using the digits 1, 3, 5, 7, 9 without repetition, is :

• A. 120
• B. 6
• C. 72
• D. 12

Question 8 · difficulty L2 · understanding

The number of 4-letter words, with or without meaning, each consisting of 2 vowels and 2 consonants, which can be formed from the letters of the word UNIVERSE without repetition is __________.

Question 9 · difficulty L2 · understanding

Number of integral solutions to the equation $$x+y+z=21$$, where $$x \ge 1,y\ge3,z\ge4$$, is equal to ____________.

Question 10 · difficulty L2 · understanding

The number of words, with or without meaning, that can be formed using all the letters of the word ASSASSINATION so that the vowels occur together, is ___________.