7/21/2019 Permutation and Combination Questions

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  Permutation & Combination - Questions for Practice Straight Objective Type

Q 1. Number of different words that can be formed using all the letters of the word “DEEPMALA”, if two vowls are together and the other two are also together but separated from the first two is

(A) 960 (B) 1200 (C) 2160 (D) 1440

Q 2.   If all the letters of the words “QUEUE” are arranged in all possible manner as they are in a dictionary, then the rank of the word QUEUE is; (A) 15th  (B) 16th| (C) 17th  (D) 18th

Q3. There are three coplanar parallel lines. If any p points are taken on each the lines, the maximumnumber of triangles with vertices at these points is(A) 3p2 (p – 1) + 1 (B) 3p2 (p – 1) (C) p2 (4p – 3) (D) none of these

Q 4. The number of times the digit 5 will be written while listing the integers from 1 to 1000 is(A) 271 (B) 275 (C) 285 (D) 300

Q 5. Let A = { 1, 2, 3, ...., n}, B = {x, y, z}, then number of mappings from A to B which are not onto is equalto(a) 3n – 2n (b) 3 . 2n (c) 3(2n – 1) (d) none of these

Q 6. There are 4 letters and 4 directed envelopes. the number of ways in which all the letters could be putinto the wrong envelopes is(a) 8 (b) 9 (c) 16 (d) none of these

Q 7. The number of ways in which 6 different red rose and 3 different white roses can form a granted so thatall the white roses come together is(a) 2160 (b) 2155 (c) 2165 (d) 2170

Q 8. There are counters available in x different colours. The counters are all alike except for the colour. Thetotal number of arrangements consisting of y counters, assuming sufficient number of counters of eachcolour. if no arrangement consists of all counters of the same colour is(a) xy – x (b) xy – y (c) yx – x (d) yx – y

Q 9. The number of 5 digit numbers that contain 7 exactly once is

(a) 341 9 (b) 337 9 (c) 47 9 (d) 441 9

Q 10. Team A and B play in a tournament. The first team that wins two games in a row or wins a total of four games is considered to win the tournament. The number of ways in which tournament can occur is(a) 14 (b) 9 (c) 10 (d) 11

Q 11. Total number of positive integral solutions of 15 < x1 + x

2 + x

3   20, is equal to

(a) 1125 (b) 1150 (c) 1245 (d) 685

Q 12. The number of different necklaces formed by using (2n) identical pearls and 3 different jewels whenexactly two jewels are always together is(a) 6n (b) 6n – 3 (c) 6n – 6 (d) none of these

Q 13. There are 10 seats in the first row of a theatre of which 4 are to be occupied. The number of ways of arranging 4 persons so that no two persons sit side by side is

(a) 7

4C (b) 7

34. P (c) 7

3C (d) 420

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7/21/2019 Permutation and Combination Questions

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  Permutation & Combination - Questions for Practice

 Matrix Match Type

  Column - I Column - II

  (A) The number of five - digit numbers having the (p) 77  product of digits 20 is  (B) A man took 5 space plays out of an engine to (q) 30  clean them. The number of ways in which he can

  place atleast two plays in the engine from where  they came out is

  (C) The number of integer between 1 & 1000 inclusive (r) 50  in which atleast two consecutive digits are equal is

  (D) The value of1 i j 9

1

15  

i . j (s) 181

(t) 31

Subjective Answer Type

 Q 1. Clay targets are arranged as shown. In how many ways can they be shot(one at a time) if no targetcan be shot until the target(s) below it have been shot.

Q 2.  A necklace is made up of 3 beads of one sort and 6n of another, bears of each sort being similar.Find the total number of possible arrangements of the beads.

Q 3. In a certain test there are n questions.In this test 2n - i students given wrong answer to atleast ’ i ’

questions (1 i n ). If total number of wrong answers is 2047 then find n.

Q 4. There are 12 intermediate stations on a railway line between 2 stations. In how many ways can a train bemade to stop at 4 of these intermediate stations, no two of these halting stations being cosecutive ?

Q 5. Find the number of ways is which 14 different pens can be(i) distributed among 6 students such that 2 students get 3 pens each and 4 students get 2 pens each.(ii) divided into 6 sets such that 2 sets contain 3 pens and 4 sets contain 2 pens.(iii) What will be the answer to (i) part if all pens are identical ?

Q 6. n different things are arranged around a circle. In how many ways can 3 objects be selected when no two of 

the selected objects are consecutive?