Practice Question on permutation and combination 16-30 (For IIT JEE , NDA , BITS ) Set 2

Permutation and Combination

---

Question no. 16

What is the number of three digit odd numbers formed by using the digits 1,2,3,4,5,6 if repetition of digits is allowed ?

looks_one 60

looks_two 108

looks_3 120

looks_4 216

Option looks_two 108

Solution :
Number of digits at one's place = 1 , 3 , 5 [Total number is 3]
Number of digits at ten's place = 6 [1,2,3,4,5,6]
Number of digits at hundred place =6 [ 1, 2 , 3 , 4 , 5 , 6 ]
Total number of ways = 3 * 6 * 6 = 108

Question no. 17

What is the number of ways of arranging the letters of the word "BANANA" so that no two N's appear together?

looks_one 60

looks_two 40

looks_3 80

looks_4 100

Option looks_two 40

Solution :
Total no. of ways = 6!/(3!2!) = 60
Two N's come together = 4!*5 / 3! = 20
No. of ways no two N's appear together = 60 - 20 = 40

Question no. 18

How many times does the digit 3 appear while writing the integers from 1 to 1000?

looks_one 269

looks_two 308

looks_3 300

looks_4 None of these

Option looks_4 None of these

Solution :
3 occur at exactly 3 times (333) = 1
3 occur at exactly 2 times = ³C₂ * 9 = 27
3 occur at exactly 1 time = ³C₁ * 9 * 9 = 243
Total no. of ways = 1 + 27 + 243 = 271

Question no. 19

If C(n ,12) = C(n ,8) , then whats is the value of C( 22, n) ?

looks_one 131

looks_two 231

looks_3 256

looks_4 292

Option looks_two 231

Solution :

Question no. 20

What is the number of words formed from the letters of the word 'JOKE' so that the vowels and consonants alternate ?

looks_one 4

looks_two 8

looks_3 12

looks_4 None of these

Option looks_two 8

Solution :
arrangement of vowel and consonant at alternate = V C V C , C V C V
For V C V C arrangement
No. of ways = 2 * 2 * 1 * 1 = 4
For C V C V arrangement
No. of ways = 2 * 2*1 *1 = 4
total no. of ways = 8

Question no. 21

What is the value of r , if P(5,r) = P(6,r-1) ?

looks_one 9

looks_two 4

looks_3 5

looks_4 2

Option looks_two 4

Solution :

Question no. 22

What is the smallest natural number n such that n! is divisible by 990?

looks_one 9

looks_two 11

looks_3 33

looks_4 99

Option looks_two 11

Solution :
990 is the factor of n!
990 has factor 11 * 10 * 9
So, n! must contain 11 , 10 , 9
only 11 is smallest number which contain all the number

Question no. 23

If P(32,6)= kC(32,6), then what is the value of k?

looks_one 6

looks_two 32

looks_3 120

looks_4 720

Option looks_4 720

Solution :

Question no. 24

From 7 men and 4 women a committee of 6 is to be formed such that the committee contains at least two women . what is the number of ways to do this?

looks_one 210

looks_two 371

looks_3 462

looks_4 5544

Option looks_two 371

Solution :
At least 2 women
No. of ways = ⁷C₄ * ⁴C₂ + ⁷C₃ * ⁴C₃ + ⁷C₂ * ⁴C₄
35* 6 + 35*4 + 21 = 210 + 140 + 21 = 371

Question no. 25

How many words , with or without meaning by using all the letters of the word 'MACHINE' so that the vowels occurs only the odd positions?

looks_one 1440

looks_two 720

looks_3 640

looks_4 576

Option looks_4 576

Solution :
No. of vowels = 3 and No. of letter = 7
4 places and 3 vowels = ⁴P₃ = 4 !
remaining letters can be arranges in ways = 4 !
Total no. of ways = 4! * 4 ! = 576

Question no. 26

In how many ways can 3 books on Hindi and 3 books on English be arranged in a row on a shelf , so that not all the Hindi books are together?

looks_one 144

looks_two 360

looks_3 576

looks_4 720

Option looks_3 576

Solution :
Total no. of ways book can be arranged = 6! = 720
No. of ways all the hindi books are together = 3! * 4! = 144
No. of ways not all the Hindi books are together = 720-144 = 576

Question no. 27

If 7 points out of 12 are in the same straight line, then what is the number of triangles formed?

looks_one 84

looks_two 175

looks_3 185

looks_4 201

Option looks_3 185

Solution :
No. of triangles = ⁿC₃ -^pC₃ where n is total no. of points and p is the collinear points
No. of triangles = ¹²C₃ -⁷C₃
No. of triangles =

Question no. 28

A group consists of 5 men and 5 women. If the number of 27 different five person committees containing k men and 5-k women is 100 , what is the value of k ?

looks_one 2 only

looks_two 3 only

looks_3 2 or 3

looks_4 4

Option looks_3 2 or 3

Solution :

Question no. 29

What is the number of five- digit numbers formed with 0,1,2,3,4 without any repetition of digits?

looks_one 24

looks_two 48

looks_3 96

looks_4 120

Option looks_3 96

Solution :
No. of 5th place digit = 4
No. of 4th place digit = 4
No. of 3rd place digit = 3
no. of 2nd place digit = 2
No. of first place digit = 1
Total no. of ways = 4 * 4 * 3 * 2 * 1 = 96

Question no. 30

The number of ways in which 5 beads of different colours form a necklace is

looks_one 12

looks_two 24

looks_3 120

looks_4 60

Option looks_3 120

Solution :
No. of ways = 5* 4 * 3 * 2 * 1 = 120

Previous Next