a) 216
b) 243
c) 215
d) 729
Explanation:
Since each ring consists of six different letters, the total number of attempts possible with the three rings is = 6 * 6 * 6 = 216. Of these attempts, one of them is a successful attempt.
Maximum number of unsuccessful attempts = 216 - 1 = 215.2. The number of ways in which six boys and six girls can be seated in a row for a photograph so that no two girls sit together is -.
a) (6!)^2
b) 6! * ⁷P₆
c) 2(6!)
d) 6! * 7
Explanation:
We can initially arrange the six boys in 6! ways.
Having done this, now three are seven places and six girls to be arranged. This can be done in ⁷P₆ ways.Hence required number of ways = 6! * ⁷P₆
3. How many four digit numbers can be formed using the digits {1, 3, 4, 5, 7,9}(repetition of digits is not allowed)?
a) 360
b) 60
c) 300
d) 18
Explanation:
The given digits are six.
The number of four digit numbers that can be formed using six digits is ⁶P₄ = 6 * 5 * 4 * 3 = 360.4. How many four digit even numbers can be formed using the digits {2, 3, 5, 1, 7, 9}
a) 100
b) 360
c) 120
d) 240
Explanation:
The given digits are 1, 2, 3, 5, 7, 9
A number is even when its units digit is even.
Source: Quantitative Aptitude Quiz for UPSI: 10 April 2021
Of the given digits, two is the only even digit.Units place is filled with only '2' and the remaining three places can be filled in ⁵P₃ ways.
Number of even numbers = ⁵P₃ = 60.
5. In how many ways can six members be selected from a group of ten members?
a) ⁶C₄
b) ¹⁰C₄
c) ¹⁰C₅
d) ¹⁰P₄
Explanation:
Six members can be selected from ten members in
¹⁰C₆ = ¹⁰C₄ ways.6. A bag contains nine yellow balls, three white balls and four red balls. In how many ways can two balls be drawn from the bag?
a) ⁹C₂
b) ³C₂
c) ¹⁶C₂
d) ¹²C₂
Explanation:
Total number of balls = 9 + 3 + 4
Two balls can be drawn from 16 balls in ¹⁶C₂ ways.7. In how many ways can three consonants and two vowels be selected from the letters of the word "TRIANGLE"?
a) 25
b) 13
c) 40
d) 20
Explanation:
The word contains five consonants. Three vowels, three consonants can be selected from five consonants in ⁵C₃ ways, two vowels can be selected from three vowels in ³C₂ ways.
3 consonants and 2 vowels can be selected in ⁵C₂ . ³C₂ ways i.e., 10 * 3 = 30 ways.8. In a class there are 20 boys and 25 girls. In how many ways can a boy and a girl be selected?
a) 400
b) 500
c) 600
d) 20
Explanation:
We can select one boy from 20 boys in 20 ways.
We select one girl from 25 girls in 25 waysWe select a boy and girl in 20 * 25 ways i.e., = 500 ways.
9. In how many ways can a committee consisting of three men and four women be formed from a group of six men and seven women?
a) ⁶C₄ ⁷C₃
b) ⁶C₃ ⁷C₅
c) ⁶C₃⁷C₄
d) ⁷C₅ ⁶C₄
Explanation:
The group contain six men and seven women
Three men can be selected from six men in ⁶C₃ ways.Four women can be selected from seven women in ⁷C₄ ways.
Total number of ways = (⁷C₄)(⁶C₃).
10. A question paper consists of five problems, each problem having three internal choices. In how many ways can a candidate attempt one or more problems?
a) 63
b) 511
c) 1023
d) 15
Explanation:
Given that, the question paper consists of five problems. For each problem, one or two or three or none of the choices can be attempted.
Hence, the required number of ways = 45 - 1.= 210 - 1 = 1024 - 1 = 1023
