**Permutation& Combination and Ratio& Proportion**

**1). A committee of 5 members is going to be formed from 3 trainees, 4 professor and 6 research associates. How many ways can they be selected, if there are 4 professor and 1 research associate or 3trainees and 2 professor?**

a) 12

b) 13

c) 24

d) 52

e) None of these

**2). In how many ways, a cricket team of 11 players can be made from 15 players, if a particular player is always chosen?**

a) 1835

b) 1635

c) 1001

d) 1100

e) None of these

**3). How many ways the word ‘EDUCATION’ can be arranged such that, the word start with a vowel and ends with a consonant?**

a) 21×8!

b) 20 × 7!

c) 9×7!

d) 20 ×8!

e) None of these

**4). How many ways the word ‘PREPARATION’ can be arranged, if vowels always come together?**

a) (7! ×5!) / (2! × 4!)

b) (7! ×5!) / (2! × 2!)

c) (6! ×5!) / (2! × 2! ×2!)

d) (7! ×5!) / (2! × 2! ×2!)

e) None of these

**5). Find the number of ways, in which 12 different flowers can be arranged to form a garland?**

a) 11! / 2

b) 10! / 2

c) 12! / 2

d) Cannot be determined

e) None of these

**6). Which number is added to the ratio 7:15 that number became 7:11?**

a) 6

b) 9

c) 7

d) 8

e) 5

**7). One- half of a certain number is equal to 65% of the second number. Find the ratio of first number to second number?**

a) 10:13

b) 8:13

c) 13:8

d) 13:10

e) None of the above

**8). In a town, 80% of the populations are adults of which the men and women are in the ratio of 9:7 respectively. If the number of adult women is 4.2 lakh, what is the total population of the town?**

a) 9.6 lakh

b) 9.8 lakh

c) 11.6 lakh

d) 12 lakh

e) None of these

**9). A certain distance is covered at a certain speed. If half of this distance is covered in double the time than what is the ratio of the two speeds?**

a) 4:1

b) 1:4

c) 1/4:1

d) 2:1

e) 1:2

**10). 35% of a number is two times 75% of another number. What is the ratio between the first and the second number?**

a) 30:7

b) 35:6

c) 23:7

d) 32:9

e) None of these

__Answers:__

__Explanation:__

**1). a)**

^{4}C

_{4}

**×**

^{6}C

_{1}+

^{3}C

_{3}

**×**

^{4}C

_{2}

= {4!/[4!(4 – 4)!]}

**×**{6!/[1!(6 – 1)!]} + {3!/[3!(3 – 3)!]} × {4!/[2!(4 – 2)!]} [0! = 1]= 1× 6 + 1 × 6 = 12

**2). c)**

The particular player is always chosen,

Since, 11-1=10 players are selected out of 14 players.

∴ Required number of ways =

^{14}C_{10}= 14! / (10!**×**4!) = 1001_{ }

**3). b)**

EDUCATIONèthere are 5 vowels and 4 consonants

5

**×**4**×**7! [since, remaining 7 places]= 20

**×**7!

**4). d)**

PREPARATIONè_ P_ R _P _R_T _ N_ (E A A I O)

There are 7 places to the vowels and 3 letters are repeated in the word.

So,

_{}(7!**×**5!) / (2!**×**2! × 2!)

**5). a)**

Required number of arrangements = (1/2)

**×**(12 – 1)!**=**11! / 2

**6). c)**

(7 + x) / (15 + x) = 7/11à11 (7 + x) = 7 (15 + x)

x = 7

x = 7

**7). d)**

Let the numbers be X and Y,

1/2 of X = 65% of Y

x/2 = 65y/100èx/y = 130/100 = 13/10èX:Y = 13:10

**8). d)**

M: W = X: 4.2

The number of adult men in the town is, 9: 7 = X: 42

èX = 4.2 × (9/7)

èX=5.4 lakh

∴ total number of adults = 4.2 + 5.4 = 9.6 lakh

Since, total population of the town is = (9.6×100) / 80 = 12 lakh

**9). a)**

First speed, S= Distance/Time

Second speed, S = (Distance / 2) / (2 × Time) = distance /( 4 × Time)

∴ Required ratio is, 4:1

**10). a)**

Let the numbers be X and Y

X × (35/100) = 2 × y × (75/100)

x/y = 30:7

X : Y = 30:7

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