5Permutations and Combinations
CHAPTER
& Probability
for
6. Ram and Ramesh appeared in an interview
MCQ TYPE QUESTIONS two vacancies in the same department.
The
that of
probability of Ram's selection is 1/6 and
2016 Ramesh is 1/8. What is the probability that only
1. Shaquille O' Neal is a 60% career free throw one of them will be selected?
shooter, meaning that he successfully makes 60
47
free throws out of 100 attempts on average. What (a) 48 ()
is the probability that he will successfully make 13 35
exactly 6 free throws in 10 attempts? c) 48 d)48
(a) 0.2508 (6) 0.2816 7. Given set A =
2, 3, 4, 5) and Set B =
{11, 12, 13,
(c) 0.2934 d) 0.6000 14, 15), two numbers randomly selected, one
are
from each set. What is probability that the sum
2015 of the two numbers equals 16?
2. Four cards are randomly selected from a pack of (a) 0.20 (b) 0.25
52 cards. If the first two cards are kings, what is (c) 0.30 (d) 0.33
the probability that the third card is a king?
8. The probabilities that a student passes in
(a) 4/52 (6) 2/50 Mathematics, Physics and Chemistry are m, p
(c) 1/52 x (1/52) (d) 1/52 x (1/52) x (1/50) and c respectively. Of these subjects, the student
has 75% chance of passing in at least one, a 50%
3. Five teams have to compete in a league, with
team exactly once, chance of passing in at least two and a 40%o chance
every team playing every other
before going to the next round. How many of passing in exactly two. Following relations are
matches will have to be held complete the league drawn in m, p.c:
27 13
round of matches? I. p+m +C20 II. p +m +c=
6) 10
20
(a) 20
(c) 8 d) 5 IIL.p)x (m) x (c) = 1
10
4. Right triangle PQR is to be constructed in the (a) Only relation I is true.
line
xy-plane so that the right angle is at P and (6) Only relation II is true.
PR is parallel to the-axis. Thex and y coordinates (c)Relations II and III are true.
of P, Q, and R are to be integers that satisfy the
inequalities: 4 Sx S 5 and 6 Sys 16. How many (d) Relations I and III are true.
different triangles could be constructed with these 2014
properties? 9. A five digit number is formed using the digits
a) 110 b) 1,100 1,3,5,7 and 9 without repeating any of them. What
numbers?
(c) 9,900 (d) 10,000 is the sum of all such possible five digit
that (6) 6666600
5. A coin is tossed thrice. Let X be the event (a) 6666660
head occurs in each of the first two tosses. Let Y (d) 6666606
(c) 6666666
be the event that a tail occurs on the third toss. 10. You are given three coins: one has heads on both
Let Z be the event that two tails occurs in three
faces, the second has tails on both faces, and the
tosses. Based on the above information, which third has a head on one face and a tail on the
one of the following statements is TRUE? other. You choose a coin at random and toss it,
(a) X and Y are not independent and it comes up heads. The probability that the
other face is tails is
(6) Y and Z are dependent
(c) Yand Z are independent a) 1/4 (b) 1/3
(c) 1/2 (d) 2/3
d) X and Z independent
CHAPTER
& Probability
for
6. Ram and Ramesh appeared in an interview
MCQ TYPE QUESTIONS two vacancies in the same department.
The
that of
probability of Ram's selection is 1/6 and
2016 Ramesh is 1/8. What is the probability that only
1. Shaquille O' Neal is a 60% career free throw one of them will be selected?
shooter, meaning that he successfully makes 60
47
free throws out of 100 attempts on average. What (a) 48 ()
is the probability that he will successfully make 13 35
exactly 6 free throws in 10 attempts? c) 48 d)48
(a) 0.2508 (6) 0.2816 7. Given set A =
2, 3, 4, 5) and Set B =
{11, 12, 13,
(c) 0.2934 d) 0.6000 14, 15), two numbers randomly selected, one
are
from each set. What is probability that the sum
2015 of the two numbers equals 16?
2. Four cards are randomly selected from a pack of (a) 0.20 (b) 0.25
52 cards. If the first two cards are kings, what is (c) 0.30 (d) 0.33
the probability that the third card is a king?
8. The probabilities that a student passes in
(a) 4/52 (6) 2/50 Mathematics, Physics and Chemistry are m, p
(c) 1/52 x (1/52) (d) 1/52 x (1/52) x (1/50) and c respectively. Of these subjects, the student
has 75% chance of passing in at least one, a 50%
3. Five teams have to compete in a league, with
team exactly once, chance of passing in at least two and a 40%o chance
every team playing every other
before going to the next round. How many of passing in exactly two. Following relations are
matches will have to be held complete the league drawn in m, p.c:
27 13
round of matches? I. p+m +C20 II. p +m +c=
6) 10
20
(a) 20
(c) 8 d) 5 IIL.p)x (m) x (c) = 1
10
4. Right triangle PQR is to be constructed in the (a) Only relation I is true.
line
xy-plane so that the right angle is at P and (6) Only relation II is true.
PR is parallel to the-axis. Thex and y coordinates (c)Relations II and III are true.
of P, Q, and R are to be integers that satisfy the
inequalities: 4 Sx S 5 and 6 Sys 16. How many (d) Relations I and III are true.
different triangles could be constructed with these 2014
properties? 9. A five digit number is formed using the digits
a) 110 b) 1,100 1,3,5,7 and 9 without repeating any of them. What
numbers?
(c) 9,900 (d) 10,000 is the sum of all such possible five digit
that (6) 6666600
5. A coin is tossed thrice. Let X be the event (a) 6666660
head occurs in each of the first two tosses. Let Y (d) 6666606
(c) 6666666
be the event that a tail occurs on the third toss. 10. You are given three coins: one has heads on both
Let Z be the event that two tails occurs in three
faces, the second has tails on both faces, and the
tosses. Based on the above information, which third has a head on one face and a tail on the
one of the following statements is TRUE? other. You choose a coin at random and toss it,
(a) X and Y are not independent and it comes up heads. The probability that the
other face is tails is
(6) Y and Z are dependent
(c) Yand Z are independent a) 1/4 (b) 1/3
(c) 1/2 (d) 2/3
d) X and Z independent
