Permutation and Combination Questions

 

These Permutation and Combination questoins with solutions for CAT examination will help you to practice well for the actual CAT examination.

1) Find the value of ‘n’ if 12 x nP6 =nP4.

a) 8

b) 11

c) 9

d) 7

2) Find the value of x such that: 7Cx-1 + 7Cx = 8Cx+2

a) 2

b) 3

c) 4

d) 5

3) Find the maximum value of 16Cx for any natural number x.

a) 6

b) 4

c) 7

d) 8

4) If nCr = 5 and nPr = 120, then determine the value of n, r.

a) 5, 3

b) 4, 2

c) 7, 4

d) 5, 4

5) Determine the number of ways in which 5 prizes can be distributed among 4 students.

a) 45

b) 54

c) 20

d) 5!/4

6) How many different three-digit numbers can be formed with the digits 1, 2, 3, 4, 5 and 6.

So that none of the digits are repeated?

a) 120

b) 130

c) 150

d) 100

Directions for questions 7-8

7)How many 4 digit numbers greater than 5000 can be formed by using the digits 2, 3, 5, 6, 7 and 8 such that

None of the digits are repeated?

a) 216

b) 240

c) 360

d) 120

8) Digits can get repeated?

a) 765

b) 432

c) 312

d) 864

9) In how many ways can the letters of the word “CONVENIENCE” be arranged?

a) 11!

b) 11!/[(2!)(3!) ]

c)11!/[(2!)(3!)(3!)]

d) 11!/3!

10) In how many ways can the letters of the word “CONVENIENCE” be arranged so that they begin with 2Ns and end with 2Es?

a) 7!

b) 11!/[(2!)(3!)(3!) ]

c)7!/3!

d) 7!/2!

11) A triangle ABC has 2 points marked on the side BC, 5 points marked on the side CA and 3 points marked on side AB.

None of these marked points is coincident with the vertices of the triangle ABC.

All possible triangles are constructed taking any three of thesepoints and the points A, B, C as the vertices.

How many new triangles have atleast one vertex common with the triangle ABC?

a) 256

b) 237

c) 207

d) 127

12) If all the 5 letter words that can be formed using the letters of the word RASAM are arranged as in a dictionary, what will the rank of RASAM be?

a) 40

b) 35

c) 41

d) 42

13) Find the number of natural numbers which lie between 108 and 109 which have products of their digits as 6?

a) 55

b)105

c)81

d) 92

14) In a board meeting, 8 delegates from number 1 to 8 are sitting around a circular table.

Number 4 and 5 always sit together and number 1 always sits next to number 4. If number 8 always sits exactly opposite number 3, how many can the seating be done?

a) 6!

b) 6C2 x 3

c) 4×3!

d) 4! x 2

15) A bag has 3 red balls, 2 yellow balls and 3 black balls. They are drawn one by one and placed in a row.

Find the number of ways they can be arranged.

a) 280

b) 410

c) 560

d) 712

16) A basket has 5 oranges and 4 apples. In how many ways can you make a selection if you have to take at least 1 orange and 1 apple?

a) 20

b) 22

c) 345

d) 465

17) In a college a committee of 7 people has to be selected from a group of 8 fourth year and 6 third year students. In how many ways can this committee be selected if in the committee, majority of fourth year students is required?

a) 2320

b) 1960

c) 1530

d) 2416

Directions for questions 18-19

There are 5 boys and 4 girls. How many ways they can be arranged such that

18) No two girls are together

a) 3600

b) 4200

c) 2400

d) none of these

19) All girls are together

a) 5!x4!

b) 6!x4!

c) 4!x3!

d) 9!

20) How many different 7 digit numbers can be formed by using only 4,5,6 such that each of the numbers has the digit 4 appearing twice?

a) 562

b) 672

c) 982

d) 1234

21) A grid is set up as shown using 5 horizontal and 6 vertical lines. What are the number of ways one can go from point P to point Q walking along the grids but not moving upwards or left or retracing a grid?

Skills Questions

a) 21
b) 35
c) 56
d) None of these

22) 16 points are plotted on 3 parallel lines. What is the maximum number of triangles that can be drawn with these points?

a) 416

b) 340

c) 520

d) none of these

23) An eight digit number divisible by 9 is to be formed by using 8 digits out of the digits 0,1,2,3,4,5,6,7,8,9 without replacement.

The number of ways in which can be done is

a) 9!

b) 2(7!)

c) 4(7!)

d) (36)(7!)

24) How many 4-digit numbers that are divisible by 4 can be formed from the digits 1,2,3, 4 and 6?

a) 36

b) 72

c) 24

d) None of these.

25) There are 7 couples in a dance party. How many dance pairs can be there such that exactly 2 pairs are the original couples?

a) 765

b) 924

c) 1222

d) 904

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