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```INFOMATHS
WORK-SHEET-2 (OLD QUESTIONS)
PERMUTATION & COMBINATION / PROBABILITY
19.
PERMUTATIONS & COMBINATIONS
1.
How many words can be formed out of the letters of the word
‘PECULIAR’ beginning with P and ending with R ?
PU CHD-2012
(A) 100
(B) 120
(C) 720
(D) 150
2.
If M = {1, 2, 3, 4, 5, 7, 8, 10, 11, 14, 17, 18}. Then how many
subsets of M contains only odd integers.
Pune-2012
(a) 26
(b) 212
(c) 211
(d) None of these
3.
No. of seven digit integers with sum of digits equal to 10, formed
by digits 1, 2, 3 only are
Pune-2012
(a) 55
(b) 66
(c) 77
(d) 88
4.
How many nos. between 1 and 10,000 which are either even, ends
up with 0 or have the sum of their digits divisible by 9.
Pune-2012
(a) 5356
(b) 5456
(c) 5556
(d) 5656
5.
The number of words that can be formed by using the letters of
the word Mathematics that start as well as end with T is
NIMCET-2012
(a) 80720
(b) 90720 (c) 20860
(d) 37528
6.
The number of different license plates that can be formed in the
format 3 English letters (A …. Z) followed by 4 digits (0, 1 ….. 9)
with repetitions allowed in letters and digits is equal to
NIMCET-2012
(a) 263 × 104
(b) 263 + 104
(c) 36
(d) 263
7.
In which of the following regular polygons, the number of
diagonals is equal to number of sides?
NIMCET-2012
(a) Pentagon
(b) Square
(c) Octagon
(d) Hexagon
8.
100 ! = 1  2  3  …..  100 ends exactly in how many zeroes?
HCU-2011
(a) 24
(b) 10
(c) 11
(d) 21
9.
Let a and b be two positive integers. The number of factors of 5 a7b
are
HCU-2011
(a) 2(a+b) (b) a + b + 2 (c) ab + 1
(d) (a + 1) (b + 1)
10. A polygon has 44 diagonals, the number of its sides is
NIMCET-2011, PU CHD-2011
(a) 9
(b) 10
(c) 11
(d) 12
11. The number of ways of forming different nine digit numbers from
the number 223355888 by rearranging its digit so that the odd
digits occupy even positions is
NIMCET-2011
(a) 16
(b) 36
(c) 60
(d) 180
12. There are n numbered seats around a round table. Total number of
ways in which n1(n1 < n) persons can sit around the round table, is
equal to
BHU-2011
(a)
13.
14.
15.
16.
17.
18.
n
Cn1
(b)
n
Pn1
(c)
n
20.
21.
22.
23.
24.
25.
26.
27.
How many different words can be formed by jumbling the word
MISSISSIPPI in which no two S are adjacent?
KIITEE-2010
(a) 8.6C4.7C4 (b) 6.78C4 (c) 6.8.7C4 (d) 7.6C4.8C4
The number of ways in which 6 men and 5 women can dine at a
roundtable, if no two women are to sit together is given by
KIITEE-2010
(a) 6!  5! (b) 30
(c) 5!  4! (d) 7!  5!
Total number of divisors of 200 are
PGCET-2010
(a) 10
(b) 6
(c) 12
(d) 5
How many different paths in the xy-plane are there from (1, 3) to
(5, 6) if a path proceeds one step at a time by going either one
step to the right (R) or one step upward (U)? (NIMCET – 2009)
(a) 35 (b) 40 (c) 45 (d) None of these
There are 10 points in a plane. Out of these 6 are collinear. The
number of triangles formed by joining these points is
(NIMCET – 2009)
(a) 100
(b) 120
(c) 150
(d) None of these
A man has 7 friends. The number of ways in which he can invite
one or more of his friends to a party is
(KIITEE – 2009)
(a) 132
(b) 116
(c) 127
(d) 130
The number of ways in which the letter of word ARTICLE can be
rearranged so that the odd places are always occupied by
consonants is
(KIITEE – 2009)
(a) 576
(b) 4C3  4! (c) 2(4!)
(d) None of these
Nine hundred distinct n – digit positive numbers are to be formed
using only the digits 2, 5, 7. The smallest value of n for which this
is possible is
(KIITEE – 2009)
(a) 6
(b) 8
(c) 7
(d) 9
Total number of 6 – digit numbers in which all the odd digits and
only odd digits appear is
(KIITEE – 2009)
(a)
28.
29.
30.
31.
32.
Cn1 1 (d) n Pn1 1
The number of subsets of a set containing n distinct object is
BHU-2011
(a) nC1 + nC2 + nC3 + nC4 + …… + nCn
(b) 2n – 1
(c) 2n + 1
(d) nC0 + nC1 + nC2 + ….. + nCn
A five digit number divisible by 3 is to be formed using the
numbers 0, 1, 2, 3, 4 and 5 without repetitions. The total number
of ways this can be done is :
PU CHD-2011
(A) 216
(B) 600
(C) 240
(D) 3125
Total number of ways in which five + and seven – signs can be
arranged in a line such that no two + signs occur together is :
PU CHD-2010
(A) 56
(B) 42
(C) 28
(D) 21
All letters of the word AGAIN are permuted in all possible ways
and the words so formed (with or without meaning) are written in
dictionary order then the 50th word is :
PU CHD-2010
(A) NAAGI (B) NAAIG (C) IAANG (D) INAGA
How many ways are there to arranged the letters in the word
GARDEN with the vowels in alphabetical order? PU CHD-2009
(a) 120
(b) 480
(c) 360
(d) 240
A student is to answer 10 out of 13 questions in an examination
such that he must choose at least 4 from the first five questions.
The number of choices available to him is :
KIITEE-2010
(a) 346
(b) 140
(c) 196
(d) 280
33.
34.
35.
36.
37.
38.
39.
1
5
(6!)
2
(b)
1
(6!)
2
(c) 6!
(d) N.O.T
Find the total number of ways a child can be given at least one
rupee from four 25 paise coins, three 50 paise coins and two onerupee coins
(a) 53
(b) 51
(c) 54
(d) 55
How many 5-digit prime numbers can be formed using the digits
3, 5, 7, 2 and 1 once each?
(a) 1
(b) 5! – 4! (c) 0
(d) 5!
If there are 20 possible lines connecting non-adjacent points of a
polygon, how many sides does it have?
(a) 12
(b) 10
(c) 8
(d) 9
From 5 different green balls, four different blue balls and three
different red balls, how many combinations of balls can be chosen
taking at least one green and one blue ball?
(a) 60
(b) 3720
(c) 4096
(d) None of these
The number of even proper factors of 1008 is
(a) 24
(b) 22
(c) 23
(d) 25
An eight digit number divisible by 9 is to be formed by using 8
digits out of the digits 0, 1, … 9 without replacement. The
number of ways in which this can be done is
NIMCET - 2008
(a) 9!
(b) 2(7!)
(c) 4(7!)
(d) 36(7!)
The number of ordered pairs (m, n), m, n  {1, 2, … 100} such
that 7m + 7n is divisible by 5 is
NIMCET - 2008
(a) 1250
(b) 2000
(c) 2500
(d) 5000
Twenty apples are to be given among three boys so that each gets
atleast four apples. How many ways it can be distributed?
KIITEE - 2008
(a) 22C20
(b) 90
(c) 18C8
(d) None
The number of arrangements of the letters of the word SWAGAT
taking three at a time is
KIITEE - 2008
(a) 72
(b) 120
(c) 14
(d) None
The number of points (x, y, z) in space, whose each co-ordinate is
a negative integer such that x + y + z + 12 = 0 is KIITEE - 2008
(a) 110
(b) 385
(c) 55
(d) None
There are three piles of identical yellow, black and green balls and
each pile contains at least 20 balls. The number of ways of
selecting 20 balls if the number of black balls to be selected is
twice the number of yellow balls is.
KIITEE - 2008
(a) 6
(b) 7
(c) 8
(d) 9
x1, x2, x3  N. The number of solutions of the equations x1. x2. x3
= 24300 is
IP Paper – 2006
INFOMATHS/MCA/MATHS/OLD QUESTIONS
INFOMATHS
40.
41.
42.
43.
(a) 480
(b) 512
(c) 560
(d) 756
In how many different ways can the letters of the word
DISTANCE can be arranged so that all the vowels come together
Karnataka PG-CET paper – 2006
(a) 720
(b) 4320
(c) 4200
(d) 3400
In a chess tournament each of the six players will play every other
player exactly once. How many matches will be played during the
tournament?
Karnataka PG-CET paper – 2006
(a) 12
(b) 15
(c) 30
(d) 36
In an objective type examination, 120 objective type questions are
there : each with 4 options P, Q, R and S. A candidate can choose
either one of these options or can leave the question unanswered.
How many different ways exist for answering this question paper?
NIMCET – 2008
(a) 5120
(b) 4120
(c) 1205
(d) 1204
A four digit number a3a2a1a0 is formed from digits 1 … 9 such that
3.
4.
 a i 1
 2
if ai + 1 is even otherwise i = 0, 1, 2 5.
ai  
a  a 
 i 1  or  i 1 
 2   2 
a is the smallest integer larger than a and a is the largest
44.
45.
46.
integer smaller than a. The smallest value that a3 can have is
(a) 5
(b) 7
(c) 9
(d) 1
Four students have to be chosen – 2 girls as captain and vice –
captain and 2 boys as captain and vice – captain. There are 15
eligible girls and 12 eligible boys. In how many ways can they be
chosen if Sunitha is sure to be captain?
(a) 114
(b) 1020
(c) 360
(d) 1848
From city A to B, there are 3 different roads. From B to C there
are 5 and from C to D there are 2 different roads. Laxman has to
go from A to D attending to some work in B and C on the way and
has to come back in the reversed order. In how many ways can he
complete his journey if he does not take the exact same path while
coming back? HYDERABAD CENTRAL UNIVERSITY - 2009
(a) 250
(b) 870
(c) 90
(d) 100
The number of ways in which 12 blue balls, 12 green balls and
one black ball can be arranged in a row with the black ball in the
middle and arrangements of the colours of balls being
symmetrical about the black ball, is
IP Paper – 2006
(a)
(c)
47.
24!
2  2  !12  !
(b)
2  24 !
6.
(c)
x
k mn
k  m  n
(d)
kx
k mn
7.
8.
9.
A4 B4
the
lines
A1 B1 ,
A2 B2 ,
16
81
1 1
(b) ,
2 4
1
(c) ,1
2
10.
x
k
137
81
1 1 1
, , respectively. If they all
2 3 4
1
2
(b)
1
2n
(c)
1
2n1
(d) None of these
One hundred identical coins each with probability P of showing
up heads re tossed. If 0 < P < 1 and the probability of heads
showing on 50 coins is equal to that of heads on 51 coins; then the
value of P is
NIMCET-2012
(a)
12.
1
(d) 1,
2
try to solve the problem, what is the probability that the problem
will be solved?
NIMCET-2012, MP-2008
(a) 1/2
(b) 1/4
(c) 1/3
(d) 3/4
If a fair coin is tossed n times, then the probability that the head
comes odd number of times is
NIMCET-2012
(a)
11.
A3 B3
(D)
A determinant is chosen at random from the set of all
determinants of matrices of order 2 with elements 0 and 1 only.
The probability that the determinant chosen is non-zero is
NIMCET-2012
(a) 3/16
(b) 3/8
(c) 1/4
(d) None of these
Coefficients of quadratic equation ax2 + bx + c = 0 are chosen by
tossing three fair coins where ‘head’ means one and ‘tail’ means
two. Then the probability that roots of the equation are imaginary
is
NIMCET-2012
(a) 7/8
(b) 5/8
(c) 3/8
(d) 1/8
A problem in Mathematics is given to three students A, B and C
whose chances of solving it are
1
2
(b)
49
101
(c)
50
101
(d)
51
101
Let P be a probability function on S = (l1, l2, l3, l4) such that
1
1
1
P  l2   , P  l3   , P  l4   . Then P(l1) is
3
6
9
PROBABILITY
1.
All the coefficients of the equation ax2 + bx + c = 0 are
determined by throwing a six-sided un-biased dice. The
probability that the equation has real roots is
HCU-2012
(a) 57/216 (b) 27/216 (c) 53/216 (d) 43/216
2.
Suppose 4 vertical lines are drawn on a rectangular sheet of paper.
name
(C)
NIMCET-2012
A student took five papers in an examination, where the full marks
were the same for each paper. The marks obtained by the student
in these papers were in the proportion 6:7:8:9:10. The student
obtained 3/5 of the total full marks. The number of papers in
which the student obtained less than 45 per cent marks is
IP Paper – 2006
(a) 2
(b) 3
(c) 4
(d) None of these
We
137
729
1
, the values of P(A|B) and P (B|A) respectively are
2
1 1
(a) ,
4 2
12!
 6 ! 6 !
(b)
(B)
Let P(E) denote the probability of event E. Given P(A) = 1, P(B)

A contractor hires k people for a job and they complete the job in
x days. A month later he gets a contract for an identical job. At
this time he has with him k + m + n people for the job, the number
of days it will require for them to complete it, is IP Paper – 2006
(a) x + m + n
48.
(A)
12!
(d)
2  6  ! 6  !
12 !12 
What is the probability that the figure thus formed has
disconnected loops?
HCU-2012
(a) 1/3
(b) 2/3
(c) 3/6
(d) 1/6
In a village having 5000 people, 100 people suffer from the
disease Hepatitis B. It is known that the accuracy of the medical
test for Hepatitis B is 90%. Suppose the medical test result comes
out to be positive for Anil who belongs to the village, then what is
the probability that Anil is actually having the disease.
HCU-2012
(a) 0.02
(b) 0.16
(c) 0.18
(d) 0.3
Let A, B and C be the three events such that
P(A) = 0.3, P(B) = 0.4, P(C) = 0.8, P(A B) = 0.08, P(A C) =
0.28, P(A B C) = 0.09.
If P(A B C) 0.75, then P(B C) satisfies :
PU CHD-2012
(A) P(B C) ≤0.23
(B) P(B C) ≤0.48
(C) 0.23 ≤P(B C) ≤0.48
(D) P(B C) ≤0.15
A number is chosen from each of the two sets {1, 2, 3, 4, 5, 6, 7,
8, 9} and {1, 2, 3, 4, 5, 6, 7, 8, 9}. If P denotes the probability that
the sum of the two numbers be 10 and Q the probability that their
sum be 8, then (P + Q) is
PU CHD-2012
BHU-2012
(a) 7/18
13.
and
respectively. Suppose two players A and B join two
14.
disjoint pairs of end points within A1 to A4 and B1 to B4
respectively without seeing how the other is marking.
2
(b) 1/3
(c) 1/6
(d) 1/5
The probability that A, B, C can solve problem is
1 1 1
, ,
3 3 3
respectively they attempt independently, then the probability that
the problem will solved is :
BHU-2012
(a) 1/9
(b) 2/9
(c) 4/9
(d) 2/3
In a single throw with two dice, the chances of throwing eight is :
BHU-2012
INFOMATHS/MCA/MATHS/OLD QUESTIONS
INFOMATHS
15.
16.
17.
18.
19.
20.
21.
(a) 7/36
(b) 1/18
(c) 1/9
(d) 5/36
A single letter is selected at random from the word “probability”.
The probability that it is a vowel, is :
BHU-2012
(a) 3/11
(b) 4/11
(c) 2/11
(d) 0
An unprepared student takes a five question true-false exam and
guesses every answer. What is the probability that the student will
pass the exam if at least four correct answers is the passing grade?
HCU-2011
(a) 3/16
(b) 5/32
(c) 1/32
(d) 1/8
Answer questions 17 and 18 using the following text:
In a country club, 60% of the members play tennis, 40% play
shuttle and 20% play both tennis and shuttle. When a member is
chosen at random,
What is the probability that she plays neither tennis nor shuttle?
HCU-2011
(a) 0.8
(b) 0.2
(c) 0.5
(d) 0.4
If she plays tennis, what is the probability ability that she also
plays shuttle?
HCU-2011
(a) 2/3
(b) 2/5
(c) 1/3
(d) 1/2
If E is the event that an applicant for a home loan in employed C
is the event that she possesses a car and A is the event that the
loan application is approved, what does P(A|E  C) represent in
words?
HCU-2011
(a) Probability that the loan is approved, if she is employed and
possesses a car
(b) Probability that the loan is approved, if she is either employed
or possesses a car
(c) Probability that the loan is approved, if she is neither employed
nor possesses a car.
(d) Probability that the loan is approved and she is employed,
given that she possesses a car
An anti-aircraft gun can take a maximum of four slots at an enemy
plane moving away from it. The probability of hitting the plane at
the first, second, third and fourth slots are 0.4, 0.3, 0.2 and 0.1
respectively. The probability that the gun hits the plane then is
NIMCET-2011
(a) 0. 5
(b) 0.7235 (c) 0.6976 (d) 1.0
A random variable X has the following probability distribution
x
0 1
2
3
4
5
6
7
8
P(X = x) a 3a
5a
Then the value of ‘a’ is
22.
23.
26.
27.
28.
29.
11a
13a
15a
1
8
(B)
2
7
(C)
1
625
(D)
1
2
(b)
49
50
(c)
101
101
(d)
51
101
30.
A dice is tossed 5 times. Getting an odd number is considered a
success. Then the variance of distribution of success is
KIITEE-2010
(a) 8/3
(b) 3/8
(c) 4/5
(d) 5/4
31.
If
A and
B
are
events
such
3
P  A  B  ,
4
that

 

2
1
P  A  B   , P A  , then P A  B is
3
4
32.
33.
34.
KIITEE-2010
(a) 5/12
(b) 3/8
(c) 5/8
(d) 1/4
If A and B are any two mutually exclusive events, then P(A|AB)
is equal to
(PGCET– 2009)
(a) P(AB)
(b) P(A)/(P(A) + P(B))
(c) P(B)/P(AB)
(d) None of these
A man has 5 coins, two of which are double – headed, one is
double – tailed and two are normal. He shuts his eyes, picks a coin
at random, and tosses it. The probability that the lower face of the
(NIMCET – 2009)
(a) 1/5
(b) 2/5
(c) 3/5
(d) 4/5
A and B are independent witnesses in a case. The probability that
A speaks the truth is ‘x’ and that B speaks the truth is ‘y’. If A and
B agree on a certain statement, the probability that the statement is
true is
(NIMCET – 2009)
(a)
(c)
35.
xy
xy  (1  x)(1  y )
(b)
1  x 1  y 
xy  1  x 1  y 
(d)
17a
36.
37.
3N  1
N 1
5N  3
4N  3
(B)
(C)
(D)
N
9N  3
3N
9N  3
38.
Probability of happening of an event A is 0.4 Probability that in 3
independent trials, event A happens atleast once is:PU CHD-2009
(a) 0.064
(b) 0.144
(c) 0.784
(d) 0.4
A die is thrown. Let A be the event that the number obtained is
greater than 3. Let B be the event that the number obtained is less
than 5. Then P(A  B) is :
PU CHD-2009
(a) 3/5
(b) 0
(c) 1
(d) 1/6
India plays two matches each with West Indies and Australia. In
any match the probabilities of India getting points 0, 1 and 2 are
0.45, 0.05 and 0.50 respectively. Assuming that the outcomes are
independent, the probability f India getting at least 7 points is
NIMCET-2010
(a) 0.8750 (b) 0.0875 (c) 0.0625 (d) 0.0250
A coin is tossed three times The probabilities of getting head and
tail alternatively is
NIMCET-2010
(a) 1/11
(b) 2/3
(c) 3/4
(d) 1/4
One hundred identical coins, each with probability P of showing up
a head, are tossed. If 0 < p < 1 and if the probability of heads on
39.
40.
41.
42.
3
1  x 1  y 
xy
and P ( A )

1
.
4
Then
events A and B are
(NIMCET – 2009)
(a) independent but not equally likely
(b) mutually exclusive and independent
(c) equally likely and mutually exclusive
(d) equally likely but not independent.
The probability that a man who is 85 yrs. old will die before
attaining the age of 90 is 1/3. A1, A2, A3 and A4 are four persons
who are 85 yrs. old. The probability that A1 will die before
attaining the age of 90 and will be the first to die is
(NIMCET – 2009)
(a)
16
625
xy
1  x 1  y 
Let A and B be two events such that
1
1
P ( A  B )  , P ( A  B) 
6
4
The numbers X and Y are selected at random (without
replacement) from the set (1, 2, .....3N). The probability that x2 –
y2 is divisible by 3 is :
PU CHD-2010
(A)
25.
9a
(a)
NIMCET-2011
(a) 1/81
(b) 2/82
(c) 5/81
(d) 7/81
Three coins are thrown together. The probability of getting two or
BHU-2011
(a) 1/4
(b) 1/2
(c) 2/3
(d) 3/8
If four positive integers are taken at random and are multiplied
together, then the probability that the last digit is 1, 3, 7 or 9 is :
PU CHD-2010
(A)
24.
7a
exactly 50 coins is equal to that of heads on exactly 51 coins then
the value of p, is
NIMCET-2010
65
81
(b)
13
81
(c)
65
324
(d)
13
108
An anti aircraft gun can take a maximum of four shots at an
enemy plane moving away from it. The probabilities of hitting the
plane at first, second, third and fourth shot are 0.4, 0.3, 0.2 and 0.1
respectively. The probability that the gun hits the plane then is
(MCA : NIMCET – 2009)
(a) 0.6972 (b) 0.6978 (c) 0.6976 (d) 0.6974
Let A = [2, 3, 4, …., 20, 21] number is chosen at random from the
set A and it is found to be a prime number. The probability that it
is more than 10 is
(MCA : KIITEE – 2009)
(a) 9/10
(b) 1/5
(c) 1/10
(d) None of these
Find the probability that a leap year will contain either 53 Tuesday
or 53 Wednesdays.
(a) 1/5
(b) 2/5
(c) 2/3
(d) 3/7
Probability that atleast one of A and B occurs is 0.6. If A and B
occur simultaneously with probability 0.3, then P(A') + P(B') is
(a) 0.9
(b) 1.15
(c) 1.1
(d) 2
The sum of two positive real numbers is 2a. The probability that
product of these two numbers is not less than 3/4 times the
greatest possible product is
(a) 1/2
(b) 1/3
(c) 1/4
(d) 9/16
If two events A and B such that P(A') = 0.3, P(B) = 0.5 and P(A 
B) = 0.3, then P(B/AB') is :
NIMCET - 2008
(a) 1/4
(b) 3/8
(c) 1/8
(d) None
INFOMATHS/MCA/MATHS/OLD QUESTIONS
INFOMATHS
43.
44.
A pair of unbiased dice is rolled together till a sum of either 5 or 7
is obtained. The probability that 5 comes before 7 is.
NIMCET - 2008
(a) 3/5
(b) 2/5
(c) 4/5
(d) None
A letter is taken at random from the letters of the word
‘STATISTICS’ and another letter is taken at random from the
letters of the word ‘ASSISTANT’. The probability that they are
the same letter is.
NIMCET - 2008
(a)
45.
46.
47.
(c)
49.
13
90
(c)
19
90
45  3 
 
2 4
90
2
(b)
1
132
(b)
1
44
(c)
5
132
(a)
54.
56.
57.
58.
63.
64.
2
(d)
7
132
66.
1 1
,
3 4
and
1
. The probability that exactly one
5
5
12
(b)
7
30
(c)
13
30
(d)
3
5
67.
1
6
(b)
2
3
(c)
625
1296
(d)
69.
671
1296
70.
3
10
(b)
7
10
(c)
24
91
(d)
71.
72.
73.
67
91
Probability of four digit numbers, which are divisible by three,
formed out of digits 1, 2, 3, 4, 5 is :
MP COMBINED – 2008
(a) 1/5
(b) 1/4
(c) 1/3
(d) 1/2
Let A and B be two events with P(A) = 1/2, P(B) = 1/3 and P(A 
B) = 1/4 , What is P(A  B)?
KARNATAKA - 2007
(a) 3/7
(b) 4/7
(c) 7/12
(d) 9/122
If three unbiased coins are tossed simultaneously then the
probability of getting exactly two heads is
ICET - 2007
(a) 1/8
(b) 2/8
(c) 3/8
(d) 4/8
A person gets as many rupees as the number he gets when an
unbiassed 6 – faced die is thrown. If two such dice are thrown the
probability of getting Rs. 10 is.
ICET - 2007
(a) 1/12
(b) 5/12
(c) 13/10
(d) 19/10
76.
4
31
256
(d)
37
256
7
12
(b)
11
12
(c)
1
2
(d)
5
6
1
12
(b)
1
15
(c)
2
27
(d)
1
10
(e)
1
20
3
14
(b)
1
2
(c)
3
13
(d)
1
3
16
256
(b)
1
286
(c)
37
256
(d)
28
256
1
 13 
 
2
(b)
 3
 9 
 16  (c)  10 
 
 
(d) N.O.T.
If P(A'  B') is equal to 19/60 then P(AB) is equal to
UPMCAT Paper – 2002
(a)
75.
(c)
Prob. of getting an odd number or a no. less than 4 in throwing a
dice is :
MP– 2004
(a) 1/3
(b) 2/3
(c) 1/2
(d) 3/5
Given A and B are mutually exclusive events. IFP (B) = 0. 15,
P(A  B) = 0.85, P(A) is equal to
UPMCAT Paper – 2002
(a) 0.65
(b) 0.3
(c) 0.70
(d) N.O.T.
In a pack of 52 cards, the probability of drawing at random such
that it is diamond or card king is :
UPMCAT Paper – 2002
(a) 1/26
(b) 4/13
(c) 3/13
(d) 1/4
Given A and B are mutually exclusive events. if:
P (A  B) = 0.8, P(B) = 0.2 then P(A) is equal to UPMCAT–2002
(a) 0.5
(b) 0.6
(c) 0.4
(d) N.O.T.
Two dice are thrown once the probability of getting a sum 9 is
given by :
UPMCAT Paper – 2002
(a) 1/12
(b) 1/18
(c) 1/6
(d) N.O.T.
In a pack of 52 cards. Two cards are drawn at random. The
probability that it being club card is :
UPMCAT Paper – 2002
(a)
74.
29
256
The probability of getting atleast 6 head in 8 trials is: MP– 2004
(a)
68.
(b)
The probabilities that a husband and wife will be alive 20 years
from now are given by 0.8 and 0.9 respectively. What is the
probability that in 20 years at least one, will be alive?
Karnataka PG-CET : Paper – 2006
(a) 0.98
(b) 0.02
(c) 0.72
(d) 0.28
A bag contains 4 white and 3 black balls and a second bag
contains 3 white and 3 black balls. If a ball is drawn from each of
the bags, then the probability that both are of same colour is :
MP Paper – 2004
(a)
MP COMBINED – 2008
39
256
A and B play a game of dice. A throws the die first. The person
who first gets a 6 is the winner. What is the probability that A
wins?
PUNE Paper – 2007
(a) 6/11
(b) 1/2
(c) 5/6
(d) 1/6
A player is going to play a match either in the morning or in the
afternoon or in the evening all possibilities being equally likely.
The probability that he wins the match is 0.6, 0.1 and 0.8
according as if the match is played in the morning, afternoon or in
the evening respectively. Given that he has won the match, the
probability that the match was played in the afternoon is
IP Univ. Paper – 2006
(a)
65.
and the probability that neither of them occurs is 1/6.
If two dice are tossed the probability of getting the sum at least 5
is
PUNE Paper – 2007
(a)
An untrue coin is such that when it is tossed the chances of
appearing head is twice the chances of appearance of tail. The
chance of getting head in one toss of the coin is :
MP COMBINED – 2008
(a) 1/3
(b) 1/2
(c) 2/3
(d) 1
The probability of randomly chosing 3 defectless bulbs from 15
electric bulbs of which 5 bulbs are defective, is :
MP COMBINED – 2008
(a)
55.
1
90  
4
62.
1
3
Then the probability of occurrence of A is.
ICET – 2005
(a) 5/6
(b) 1/2
(c) 1/12
(d) 1/18
8 coins are tossed simultaneously. The probability of getting
ICET – 2005
(a)
Different words are written with the letters of PEACE. The
probability that both E’s come together is :
MP COMBINED – 2008
(a) 1/3
(b) 2/5
(c) 3/5
(d) 4/5
The probability of throwing 6 at least one in four throws of a die
is:
MP COMBINED – 2008
(a)
53.
61.
Probabilities of three students A, B and C to pass an examination
student will pass is:
52.
5
8
(d) None
210
are respectively
51.
(d)
Let E be the set of all integers with 1 in their units place. The
probability that a number n chosen from [2, 3, 4, … 50] is an
element of E is
ICET - 2007
(a) 5/49
(b) 4/49
(c) 3/49
(d) 2/49
A and B independent events. The probability that both A and B
occur is
Two balls are drawn at random from a bag containing 6 white, 4
red and 5 black balls. The probability that both these balls are
black, is :
MP COMBINED – 2008
(a) 1/21
(b) 2/15
(c) 2/21
(d) 2/35
6 boys and 6 girls sit in a row randomly. The probability that all
the girls sit together is :
MP COMBINED – 2008
(a)
50.
(b)
60.
A six faced die is a biased one. It is thrice more likely to show an
odd number than to show an even number. It is thrown twice. The
probability that the sum of the numbers in the two throws is even,
is.
NIMCET - 2008
(a) 4/8
(b) 5/8
(c) 6/8
(d) 7/8
A letter is known to have come from either TATANAGAR or
CALCUTTA. On the envelope, just two consecutive letters, TA,
are visible. The probability that the letter has come from
CALCUTTA is
NIMCET - 2008
(a) 4/11
(b) 1/3
(c) 5/12
(d) None
A card is drawn from a pack. The card is replaced and the pack is
reshuffled. If this is done six times, the probability that 2 hearts, 2
diamonds and 2 club cards are drawn is.
KIITEE – 2008
(a)
48.
1
45
59.
41
60
(b)
37
60
(c)
31
60
(d) N.O.T.
If the events A and B are mutually exclusive then P (A  B) is
given by :
UPMCAT Paper – 2002
(a) P(A) + P(B)
(b) P(A)P(B)
(c) P(A) P(B/A)
(d) N.O.T.
If A and B are two events, the prob. that exactly one of them,
occurs in given by:
UPMCAT Paper – 2002
INFOMATHS/MCA/MATHS/OLD QUESTIONS
   
(c) P  A  B   P  A  B 
(a)
77.
78.
P A B  P A B
(b)

 
P A B  P A B
INFOMATHS

1
11
D
21
A
31
A
41
A
51
B
61
D
71
C
(d) None of these
A bag contains 6 red and 4 green balls. A fair dice is rolled and a
number of balls equal to that appearing on the dice is chosen from
the urn at random. The probability that all the balls selected are
red is.
NIMCET – 2008
(a) 1/3
(b) 3/10
(c) 1/8
(d) none
A number x is chosen at random from (1, 2, …. 10). The
probability that x satisfies the equation (x – 3) (x – 6) (x – 10) = 0
is
ICET - 2007
(a) 2/5
(b) 3/5
(c) 3/10
(d) 7/10
2
12
A
22
B
32
B
42
D
52
D
62
D
72
D
3
13
4
B
14
A
D
23
D
33
C
43
D
53
C
63
A
73
D
24
C
34
A
44
C
54
C
64
B
74
A
PROBABILITY
5
6
C
D
15
16
+
B
25
26
C
35
36
A
C
45
46
B
A
55
56
A
C
65
66
A
B
75
76
A
D
7
B
17
27
B
37
C
47
B
57
C
67
D
77
D
8
A
18
28
D
38
D
48
C
58
A
68
B
78
C
9
D
19
29
D
39
D
49
A
59
B
69
B
10
A
20
C
30
D
40
C
50
C
60
B
70
B
1
C
11
C
21
C
31
B
41
B
2
A
12
B
22
A
32
C
42
A
PERMUTATIONS & COMBINATIONS
3
4
5
6
7
8
9
C
C
B
A
A
A
D
13
14
15
16
17
18
19
D
A
A
B
C
C
D
23
24
25
26
27
28
29
A
C
D
C
A
C
C
33
34
35
36
37
38
39
D
C
C
A
C
B
D
43
44
45
46
47
48
D
D
B
B
D
D
10
C
20
A
30
C
40
B
5
INFOMATHS/MCA/MATHS/OLD QUESTIONS
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