CPP-I FIITJEE PROBABILITY

Name:____________________ Batch: Date:

Enrollment No.:_________ Faculty ID: MSV Dept. of Mathematics
SINGLE CHOICE
LEVEL-I

Let P(B) = , P ( A  B  C ) = ,P ( A  B  C ) =
3 1 1
1. then P(B  C) =
4 3 3
1 3
(A) (B)
12 4
5
(C) (D)none of these
12
2. Three persons A1, A2 and A3 are to speak at a function along with 5 other
persons. If the person speak in random order, the probability that A 1 speaks
before A2 and A2 speaks before A3 is’
(A) 1/6 (B) 3/5
(C) 3/8 (D) none of these

3. A can hit a target 3 times in 5 shots, B can hit 2 times in 5 shots and C can hit
3 times in 4 shots. They fire simultaneously. If only one of them hits the target
then the probability that it was A, is
1 63
(A) (B)
3 100
9 2
(C) (D)
31 17
4.
3
4
( 1
3
) ( 1
)
Let P(B) = , P A  B  C = ,P A  B  C = then P(B  C) =
3
1 3
(A) (B)
12 4
5
(C) (D)none of these
12
1 1
5. Let A and B be events of an random experiment and P( A) = , P ( A  B ) = then
4 2
 B 
value of P  c  is
A 
2 1
(A) (B)
3 3
5 1
(C) (D)
6 2
6. Five horses are in a race, Mr.Arun selects two of the horses at random & bets
on them. The probability that Mr. Arun selected the winning horse is
3 1
(A) (B)
5 5
2 4
(C) (D)
5 5

7. In a bag there are 15 red and 5 white balls. Two balls are chosen at random
and one is found to be red. The probability that the second one is also red is
 CPP-I FIITJEE Probability
(A) 7/12 (B) 13/19

(C) 14/19 (D) none of these

8. Let A and B be two independent events such that

1 1
p ( A) = and p ( B ) = . then 3P ( A / A  B ) is  then  is
______
3 4
(A) 2 (B) 3
(C) 4 (D) 5

9. Four boys and eight girls sit at random in a row. The probability that each
boy sits between two girls is
7! 8! 7
C3
(A) (B)
3! 12! 12!
7
C3  8!
(C) (D) none of these
12!

10. Different words are formed using the letters of word FIITJEE, then the
probability that the word contains all consonants together is
1 1
(A) (B)
6 7
1
(C) (D) none of these
4

LEVEL-II

1. an integer is selected at random from between 1 and 200, then probability that
integer is divisible by 2, 3, 6 or 8 is
133 133
(A) (B)
200 198
33 2
(C) (D)
50 3

3x + 1 1− x
2. Events A, B, C are mutually exclusive events such that P ( A ) = , P (B ) =
3 4
1 − 2x
and P ( C ) = . The set of possible values of x are in the interval
2
 1 1
(A) [0, 1] (B)  , 
3 2
1 2  1 13 
(C)  ,  (D)  , 
 3 3  3 3 
 CPP-I FIITJEE Probability
3. A positive integer ‘n’ not exceeding 100, is chosen in such a way that if n  50,
then the probability of choosing n is ‘p’; and if n > 50, then the probability of
choosing n is ‘3p’. The probability that a perfect square is chosen is
(A) 0.08 (B) 0.065

(C) 0.05 (D) 0.09

4. Two boxes containing 20 balls each ball is either black or white. The total
number of black balls is different from the total numbers of white balls. One ball
is drawn at random from each box. The probability that both balls are white is
0.21, then the probability that both the balls drawn are black is
(A) 0.23 (B) 0.24

(C) 0.25 (D) 0.26

5. A bag contains n identical red balls, 2 n identical black balls and 3n identical
whit balls. If probability of drawing n balls of same colour is greater than or equal
1
to , then minimum number of red balls in the bag is equal to
6
_______________

(A) 3 (B) 2

(C) 5 (D) 1

6. Let S be the array of integral points (x,y,z) with x=0,1,2,3 ; y=0,1,2 and
z=0,1,2,3,4. if two points are chosen from S, then the probability that their mid
point is in S is

4 2
(A) (B)
59 59
52
(C) (D) none of these
177

7. 64 players play in a knock out tournament assuming all the players are of

equal strength the parabola that P1 losses to P2 and P2 becomes the eventual

champion is
1 1
(A) (B)
612 672
1 1
(C) (D)
512 63.26
 CPP-I FIITJEE Probability

8. Team A plays with 5 other teams exactly once. Assuming that for each match
the probabilities of a win, draw and loss are equal then
34
(A) the probability that A wins and losses equal number of matches is
81
17
(B) the probability that A wins and losses equal number of matches is
81
17
(C) the probability that A wins more number of matches than it losses is
81
16
(D) the probability that A losses more number of matches than it wins is
81

9. Three distinct vertices are randomly chosen among the vertices of a cube.
The probability that they are the vertices of an equilateral triangle is equal to

2 3
(A) (B)
7 7
4
(C) (D) none of these
7

10. A fair die is tossed three times. Given that the sum of the first two tosses
equals the third. The probability that atleast one ‘2’ has turned up, is equal to

1 91
(A) (B)
6 216
1 8
(C) (D)
2 15

11. Three vertices of the polygon are chosen at random. The probability that these
vertices from an isosceles triangle is

1 3
(A) (B)
3 7

3
(C) (D) none of these
28

12. If the probability of choosing an integer k out of ‘2m’ integers 1,2,3,…..,2m is

inversely proportional to k 4 (1  k  2m ) , then the probability that chosen number
is odd, is
(A) >1 (B) >1/2

(C) =1/2 (D) <1/3

 CPP-I FIITJEE Probability

13. 40 teams play a tournament. Each team plays every other team just once. Each
game result in a win for one team. If each team has a 50% chance of winning
each game, the probability that at the end of the tournament every team has
won a different number of games is

1 40!
(A) (B)
780 2780
40!
(C) 780 (D) none of these
3

14. One mapping is selected at random from all mapping of the set S = 1,2,3,....n
3
into itself. If the probability that the mapping is one-one is , then the value of
32
n is
(A) 2 (B) 3

(C) 4 (D) none of these

15. Six different balls are put in three different boxes, no box being empty. The
probability of putting balls in the boxes in equal numbers is,

(A) 3/10 (B) 1/6

(C) 1/5 (D) none of these

16. ‘n’ is given a value from the set {1, 2, 3, ..... , 12} at random. The probability of
the value of (1 + i)n being real, is
(A) 3/10 (B) 1/6

(C) 1/4 (D) none of these

17. An urn contains 2 white and 2 black balls. A ball is drawn at random. If it is
white it is not replaced, otherwise it is replaced along with another ball of the
same colour. The process is repeated. The probability that the third ball drawn
is black is

11 23
(A) (B)
45 30
22
(C) (D) none of these
25
 CPP-I FIITJEE Probability

18. A car is parked by an owner amongst 25 cars in a row, not at two extremes. On
his return, he finds that exactly 15 places are still occupied. The probability that
both the neighbouring places are vacant, is
15 91
(A) (B)
92 276
151
(C) (D) none of these
253

19. If two distinct numbers m and n are chosen at random from the set
1,2,3,........100 , then the probability that 2m + 2n + 1 is divisible by 3 is
1 49
(A) (B)
2 198
29
(C) (D) none of these
198

20. Box A contains black balls and box B contains white balls take a certain number
of balls from A and place them in B, then take same number of balls from B and
place them in A. The probability that number of white balls in A is equal to
number of black balls in B is equal to
(A) 1/2 (B) 1/3
(C) 1 (D) none of these

21. Set A has 4 elements and set B has 3 elements, the elements of set A are
mapped randomly with elements of set B such that function f : A → B exists. The
probability that the function is into is
(A) 4/9 (B) 5/9
(C) 3/4 (D) none of these

22. Two events A and B are such that P(A) = 0.3,P(B) = 0.4 and P(A  B) = 0.5 then the
 
B
value of P  is
(
 A B ) 

1 1
(A) (B)
6 5
1 1
(C) (D)
3 4

23. Out of six pairs of distinct gloves, 8 gloves are randomly selected find the
probability that there exists exactly two pair in it.
16 17
(A) (B)
33 35
1
(C) (D) none of these
2
 CPP-I FIITJEE Probability
24. The probability of four cricketers A, B , C, D scoring more than 50 runs in a
1 1 1 1
match are , , and respectively . It is known that exactly two of the players
2 3 4 10
scored more than 50 runs in a particular match. The probability that these
players were A and B is
(A) 27/65 (B) 5/6
(C) 1/6 (D) None of these

25. Let A = { 2,3, 4, ….30} . A number is chosen from set A and found to be a prime
number the probability that it is more than 15 is
(A) 4/5 (B) 2/5
(C) 1/5 (D) 3/5

MULTI- CORRECT
1. The contents of 3 urns 1st, 2nd , 3rd respectively are as follows:
1 white, 2 black, 3 red balls;
2 white, 1 black, 1 red balls;
4 white, 5 black, 3 red balls
one urn is selected at random and two balls drawn and these happen to be
white and red. Then the probability that they come from

36 55
(A) 1st urn is (B) 2nd urn is
118 118
33 30
(C) 3rd urn is (D) 3rd urn is
118 118

For two events A and B, P (B ) = P   = and P   = , then

B 1 A 4
2.
 
A 3  
B 7
(A) A and B are mutually exclusive (B) A and B are independent
B 2 A 3
(C) P   = (D) P   =
A 3  B  57

3. The contents of 3 urns 1st, 2nd , 3rd respectively are as follows:

1 white, 2 black, 3 red balls;
2 white, 1 black, 1 red balls;
4 white, 5 black, 3 red balls
one urn is selected at random and two balls drawn and these happen to be
white and red. Then the probability that they come from
36 55
(A) 1st urn is (B) 2nd urn is
118 118
33 30
(C) 3rd urn is (D) 3rd urn is
118 118
 CPP-I FIITJEE Probability

4. Suppose m boys and m girls take their seats randomly around a circle. The
( )
−1
2m −1
probability of their sitting is Cm when

(A) no two boys sit together (B) no two girls sit together

(C) boys and girls sit alternatively (D) all the boys sit together

5. If A and B are any two events then the true relation is/are
(A) P(A  B) is not less than P(A) + P(B) –1

(B) P(A  B) is not greater than P(A) + P(B)

(C) P(A  B) = P(A) + P(B) – P(A  B)

(D) P(A  B) = P(A) + P(B) + P(A  B)

6. 5 players of equal strength play one game each with each other.
P(A)=probability that atleast one player wins all matches he (they) play.
P(B)=probability that atleast one player losses all his (their) matches

5 7
(A) P ( A ) = (B) P (B ) =
16 16
5 15
(C) P ( A  B ) = (D) P ( A  B ) =
32 32

7. There is a set of n biased coin. The probability of getting head in the toss and
1
kth coin is for k=1,2,3,…….,n and the result of the toss for each coin is
2k + 1
independent. If each coin is tossed once then

n
(A) probability of getting odd number of heads is
2n + 1

n +1
(B) probability of getting even number of heads of all tails is
2n + 1

4 ( n!)
(C) probability of getting all tails is
( 2n + 1) !

n +1
(D) probability of getting even number of heads is
2n + 1
 CPP-I FIITJEE Probability

Comprehension-I

A fair die is tossed repeatedly until a six is obtained. Let X denote the number
of tosses required.

1. The probability that X = 3 equals :

25 25
(A) (B)
216 36
5 125
(C) (D)
36 216

2. The probability that X  3 equals :

(A) 25 (B) 25
216 36

(C) 5 (D) 125

36 216

3. The conditional probability that X 6 given X 3 equals :

25 25
(A) (B)
216 36
5 125
(C) (D)
36 216

Comprehension-II
A JEE aspirant estimates that she will be successful with an 80% chance if she
studies 10 hours per day, with 60% chance if she studies 7 hours per day and
with a 40% chance if she studies 4 hours per day. She further believes that she
will study 10 hours, 7 hours and 4 hours per day with probabilities 0.1, 02 and
0.7, respectively.

1. The chance she will be successful is

(A) 0.28 (B) 0.38
(C) 0.48 (D) 0.58

2. Given that she is successful, the chance that she studied for 4 hours is
6 7
(A) (B)
12 12
8 9
(C) (D)
12 12

3. Given that she does not achieve success, the chance she studied for 4 hour is
18 19
(A) (B)
26 26
20 21
(C) (D)
26 26
 CPP-I FIITJEE Probability
Comprehension-III

A is set containing 10 elements. A subset P of A is chosen at random and the set A is

reconstructed by replacing the elements of P. Another subset Q of A is now chosen
at random. Then, the probability that if

1. P  Q = A, is :
10 10
 1 2
(A) 2 (B) 3
   
10 10
3 2
(C) 4 (D) 5
   

2. P and Q have no common elements, is :

10 10
2 3
(A) 3 (B) 4
   
10 10
4 5
(C) 5 (D) 6
   

3. P  Q contains exactly 3 elements, is :

5  38 15  39
(A) (B)
217 217

3  58 7  38
(C) (D)
217 217
Comprehension-IV

There are n urns each containing n + 1 balls such that the ith urn contains i
white and (n+1-i)red balls . Let ui be the event of selecting ith urn , i =
1,2,3……., n and w denotes the event of getting a white ball.

1. If P (ui ) = c, where c is a constant then P (un / w ) is equal to

2 1
(A) (B)
n +1 n +1

n 1
(C) (D)
n +1 2
2. If n is even and E denotes the event of choosing even numbered urn
 1
 P ( ui ) = n  , then the value of P ( w / E ) is
 
n+2 n+2
(A) (B)
2n + 1 2 ( n + 1)
n 1
(C) (D)
n +1 n +1
 CPP-I FIITJEE Probability
Comprehension-V

A box contains n coins. Let P(Ei) be the probability that exactly i out of n coins
are biased. If P(Ei) is directly proportional to i (i + 1) ; 1  i  n.

1. Proportionality constant k is equal to

3 1
(A) (B)
(
n n +1 2
) (n 2
)
+ 1 (n + 2 )
3 1
(C) (D)
n ( n + 1)( n + 2 ) (n + 1)(n + 2 )(n + 3 )

2. If P be the probability that a coin selected at random is biased then lim Pis
n→
1 3
(A) (B)
4 4
3 7
(C) (D)
5 8

3. If a coin selected at random is found to be biased then the probability that it is

the only biased coin in the box is

1 1
(A) (B)
(n + 1)(n + 2 )(n + 3 )(n + 4 ) n ( n + 1)( n + 2 )( 3n + 1)

24 24
(C) (D)
n ( n + 1)( n + 2 )( 2n + 1) n ( n + 1)( n + 2 )( 3n + 1)

Comprehension-VI

In a tournament there are twelve players S1.S2 ,........S12 and divided into six pairs at
random. From each game a winner is decided on the basis of game played between
two players of the pair. Asume all players are of equal strength . Then answer the
following questions

1. Probability that S2 is among the losers is

5 10
(A) (B)
22 11

1 6
(C) (D)
2 11

2. Probability that exactly one of S3 and S4 is among the losers is

 CPP-I FIITJEE Probability
5 10
(A) (B)
22 11

1 6
(C) (D)
2 11

3. Probability that both S2 and S4 are among the winners is

5 10
(A) (B)
22 11

1 6
(C) (D)
2 11

Comprehension-VII

If the squares of a 8  8 chess board are painted either red or black at random

1. The probability that the chess board contains equal number of red and black
squares is
64
C32 64
(A) 64
(B)
2 32 264
232 − 1
(C) (D) none of these
264

2. The probability that all the squares in any column are of same colour and
alternating colour in any row is
1 1
(A) 64
(B)
2 263
1
(C) (D) none of these
2
Comprehension-VIII

A chess match between two grandmasters X and Y is won by whoever first wins
a total of two games. X’s chances of winning, drawing of losing any particular
game are a,b,c respectively. The games are independent and a+b+c=1

1. The probability that X wins the match after (n+1) games (n  1) is

(A) na2bn−1 (B) a2 (nbn−1 + n (n − 1) bn−2c )
(C) na2bc n−1 (D) none of these

2. The probability that Y wins the match after the 4 th game is

(A) 3bc 2 (b + 2a ) 3bc 2 (b + ) (B) bc 2 ( 3b + a )
 CPP-I FIITJEE Probability
(C) 2ac 2 (b + c ) (D) abc ( 2a + 3b )

Comprehension-IX
In the equation A + B + C + D + E = FG, where FG is the two digit number whose
value is 10F + G and letters A,B,C,D,E,F and G each represents different digits.
If FG is a large as possible and a five digit number is made using letters
A,B,C,D,E,F,G (repetition not allowed) then

1. Probability that number made is divisible by 5

2 3
(A) (B)
7 7
4
(C) (D) none of these
7

2. Probability that number made is divisible by 3

1 2
(A) (B)
7 7
3 4
(C) (D)
7 7

3. Probability that number made is divisible by 4

1 2
(A) (B)
7 7
3 4
(C) (D)
7 7
Comprehension-X

An unbiased dice with faces numbered 1, 2, 3, 4, 5, 6 is thrown five times and

list of five numbers showing up is noted then
1. The probability that among the numbers 1, 2, 3, 4, 5 and 6 only four numbers
appear in the list is
883 3600
(A) (B)
7776 7776
483 883
(C) (D)
1296 1396

2. The probability that the five numbers appearing on the list are decreasing
order. is
1 1
(A) (B)
1296 7776
1 1
(C) (D)
216 6

3. The probability that the sum of five numbers on the list is 25 is

256 358
(A) (B)
7776 7776
 CPP-I FIITJEE Probability
126 728
(C) (D)
7776 7776

Comprehension-XI

There are n black balls and balls and 2 red balls in a bag. One by one balls are
from the bag X wins as soon as 2 balls are drawn and Y wins as soon as 2 red
balls are drawn. The game continuous until one of 2 wins. Let X(n) and Y(n)
denotes the probability that X and Y wins respectively

1. Then the value of Y(n) is

1 6
(A) (B)
( n + 1)( n + 2 ) ( n + 1)( n + 2 )

1 1
(C) (D)
n ( n + 1)( n + 2 ) n ( n + 1)( n + 2 )

2. Then value of lim ( y ( 1) + Y ( 2 ) + Y ( 3 ) + ....Y ( n ) ) is

x →

(A) 1/3 (B) ½

(C) 2 (D) 3

3. The value of lim ( X ( 2 ) + ( 3 ) + ( 4 ) + ....X ( n ) ) is

x →
(A) 1/3 (B) 1/10

(C) 1/5 (D) 1/20

Comprehension-XII
If H1 is one of 6 horses entered for a race; and is to be ridden by one of two
persons A and B. It is 2 to 1 that A rides H 1, in which case all the horses are
equally likely to win. If B rides H1 his changes of wining is treble, where E →
the event that horse H1 wins
E1 → the event that person A rides H 1
E2 → the event that person B rides H 1
If A1 = E1  E and E2  E, then

1. The value of P(E/E1) is

(A) 1/3 (B) 1/6

(C) 1/2 (D) None of these

2. The value of P(A2) is

(A) 1/3 (B) 1/6
 CPP-I FIITJEE Probability
(C) 1/2 (D) None of these

3. The odds against wining of A is

(A) 1 : 15 (B) 1 : 13
(C) 2 : 15 (D) 13 : 15

MATCH THE COLUMN

1. Match the following

Column A Column B
(A) Six different balls are put in three different boxes, (P) 20
no box being empty. The probability of putting 27
balls in boxes in equal numbers is
(B) Six letters are posted in 3 letter boxes. The (Q) 1
probability that no letter box remains empty is 6
(C) Two persons A and B throw two dice each. If A (R) 2
throws a sum of 9 then the probability of B 7
throwing a sum greater then A is
(D) If A and B are independent and P ( A ) = 0.3 and (S) 1

( )
P A  B = 0.8 then P (B ) = 4

2.
Column I Column II
(A) 6 different balls are put in 3 different boxes, no (p) 20/27
box being empty. The probability of putting balls
in boxes in equal numbers is
(B) Six letters are posted in 3 letter boxes. The (q) 1/6
probability that no letter box remains empty is
(C) Two persons A and B throw two dice each. If A (r) 2/7
throws a sum of 9 then the probability of throwing
a sum greater than A is

(D) If A and B are independent and P(A) = 0.3 and (s) 1/4
P ( A  B ) = 0.8 than P(B) =

1 1 1
3. Let A and B are two events such that P ( A ) = ,P ( B ) = and P ( A  B ) =
3 4 2
Column – I Column – II
 CPP-I FIITJEE Probability
(A) P ( Bc / A c ) (P) 1
4
(B) P ( B / A c ) (Q) 3
4
(C) P ( A c / Bc ) (R) 1
3
(D) P(B/A) (S) 2
3

4. India and Australia play a series of ‘n’ one day matches and probability that
1
India wins a match against Australia is
2
Column – I Column – II
(A) If ‘n’ is not fixed and series ends when any (P) 4
one of the team completes its 4th win then 27
probability that India wins the series is
(B) If n = 7; then probability that India wins atleast (Q) 47
three consecutive matches is 27
(C) For n = 7. probability that India wins series (R) 1
through consecutive wins is 2
(D) For n = 7, probability that doesn’t win two (S) 17
consecutive matches is 26

5. A is a set containing ‘n’ elements. A subset ‘P’ of ‘A’ is chosen at random. The
set ‘A’ is reconstructed by replacing the elements of the subset ‘P’. A subset ‘Q’
of ‘A’ is chosen at random the probability that

COLUMN – I COLUMN – II
P Q =  3n −1
A P n.
4n
n
3
B P Q is a singleton set Q  
4
2nc
C P Q contains 2 elements R n
4n

P = Q , when x
denotes number of 3n − 2 ( n )( n − 1)
D S
elements in set X 2.4n

6. Match the following

 CPP-I FIITJEE Probability

ColumnA
ColumnB
(A) A painted cube is cut into 27 equal cubes. A cube (P)
is selected at random. Then probability that the 1
selected cube has two sides painted is 12
(B) Six gents and six ladies sit in a row. If first two are (Q) 5
ladies 42
probability that the 3 rd one is also a lady is.

(C) Four identical dice are rolled-probability that all the (R) 2
numbers on them are primes is. 5
(D) A necklace made up of 3 identical Red beads and (S) 4
9 identical white beads. Probability that equal 9
number of white beads between Red beads is

INTEGER-TYPE

1. 7 person are stopped on the road at random and asked about their birthdays. If
the probability that 3 of them are born on Wednesday, 2 on Thursday and the
6K
remaining 2 on Sunday is , then K is equal to
76
2. A letter is known to have come from either MAHARASTRA Or MADRAS. On
the postmark only consecutive letters RA can be read clearly. If P be the
probability that the letter came from MAHARASTRA then the value of (19P – 3)
is

3. A bag contains 5 balls and of these it is equally likely that 0,1,2,3,4,5 are
1
white. A ball drawn is the only white ball is equal to . Find value of k
3k
4. The probability of a bomb hitting a bridge is ½ and two direct hits are needed
to destroy it. Then the least number of bombs required, so that the probability
of the bridge being destroyed is greater than 0.9, _______________.

5. In a hurdle race, a runner has probability P1(0<P1<1) of jumping over a specific

hurdle. Given that in 5 trials, the runner succeeded 3 times, then the probability
that the runner had succeeded in the first trial is P 2 where [5P2 + 2] = (where [.]
denotes the greatest integer function)

6. A locker can be opened by dialing a fixed three-digit code (between 000 and
999). A stranger, who does not know the code, tries to open the locker by dialing
three digits at random. If p is the probability that the stranger succeeds at the
kth trial, then the value of 1000p is equal to ___________.
(Assume that the stranger does not repeat unsuccessful combinations)
 CPP-I FIITJEE Probability

7. On a particular day, six persons pick six different books, one each, from different
counters at a public library. At the closing time, they arbitrarily put their books
to the vacant counters. The probability that exactly two books are at their
p
previous places is (p and q have no common factor other than one), then p
q
equal to

8. If the papers of 4 students can be checked by any one of the 7 teachers. If the
probability that all the 4 papers are checked by exactly 2 teachers is A, then the
value of 49A must be_________.

9. A can hit a target 8 times in 10 shots. B can hit 6 times in 8 shots and C twice
in 3 shots. Each of them fired once, and exactly two of them missed the target.
If probability that A hits the target is p/q then q – p is, (p,q  N and p and q are
co-prime).

10. An urn contains five balls. Two balls are drawn and are found to be white. If
probability that all the balls are white is P, then the value of 6P−1 is equal to
CPP-I FIITJEE Probability
ANSWERS

SINGLE CHOICE
LEVEL-I

1. A 2. A 3. C 4. A 5. B
6. C 7. A 8. A 9. A 10. B

LEVEL-II

1. D 2. B 3. A 4. D
5. C 6. C 7. B 8. B
9. D 10. D 11. B 12. B
13. B 14. C 15. B 16. C
17. B 18. A 19. B 20. C
21. B 22. D 23. A 24. A
25. B
MULTI- CORRECT

1. B,D 2. B,C,D 3. B,D 4. A,B,C

5. A,B,C 6. A,C,D 7. A,B,C

Comprehension-I

1. A 2. B 3. B

Comprehension-Ii

1. C 2. B 3. D
Comprehension-Iii
1. C 2. B 3. A

Comprehension-Iv
1. A 2. B

Comprehension-v

1. C 2. B 3. D

Comprehension-vi

1. C 2. D 3. A

Comprehension-vii

1. A 2. B
CPP-I FIITJEE Probability
Comprehension-viii
1. B 2. A
Comprehension-ix
1. D 2. B 3. B

Comprehension-x

1. B 2. A 3. C

Comprehension-xI
1. B 2. D 3. B

Comprehension-xII
1. C 2. B 3. D

MATCH THE COLUMN

1. A→Q B→P C→Q D→R

2. A→q, B→p, C→q, D→r

3. A → R; B → S; C → P; D→Q

4. A → R; B → Q; C → P; D→S

5 A-Q B-P C-S D- R

6. A→S B→R C→Q D→P

INTEGER-TYPE

1. 5 2. 7 3. 5 4. 8
5. 5 6. 1 7. 3 8: 6
9. 5 10. 2