2 Jun 2017

Practice Quantitative Aptitude Questions For NICL AO & Upcoming Exams 2017 (Permutation & Combination and Ratio & Proportion)

Practice Quantitative Aptitude Questions For NICL AO & Upcoming Exams 2017 (Permutation & Combination and Ratio & Proportion):
Dear Readers, Important Practice Aptitude Questions for  Upcoming Exams was given here with Solutions. Aspirants those who are preparing for the Bank Examination and other Competitive Examination can use this.

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

1)a   2)c  3)b   4)d   5)a   6)c  7)d   8)d  9)a  10)a

Explanation:

1). a)
4C4 × 6C1 + 3C3 × 4C2
=  {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 = 14C10 = 14! / (10! × 4!) = 1001

3). b)
EDUCATION è there are 5 vowels and 4 consonants
5 × 4 × 7! [since, remaining 7 places]
= 20 × 7!

4). d)
PREPARATION è _ 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) = 7/11 à 11 (7 + x) = 7 (15 + x)
x = 7

7). d)
Let the numbers be X and Y,
1/2 of X = 65% of Y
x/2 = 65y/100 è x/y = 130/100 = 13/10 è X:Y = 13:10

8). d)
M: W = X: 4.2
The number of adult men in the town is, 9: 7 = X: 42
è X = 4.2 × (9/7)
è X=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