How many different sums greater than zero can be formed from a rupees 500 note, a rupees 100
note, a rupees
50 note, a rupees 20 note, a rupees 10 note and a 5 rupee note?
Select one:
a. 63
b. 96
c. 127
d. 255
e. None of the above
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6 types of notes
Each can be used in 2 ways: Selected or Not Selected
Number of ways, Different Sums (including 0) can be created = 2x2x2x2x2x2
The correct answer is: 63.
Question 2
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How many numbers of 3 digits can be formed with the digits 1, 2, 3, 4, 5 with repetition?
Select one:
a. 125
b. 127
c. 191
d. 652
e. None of the above
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Each place can be filled in 5 ways
Count = 5x5x5 =125
The correct answer is: 125.
Question 3
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How many different sums greater than or equal to zero can be formed from two rupees 500 notes, three rupees
100 notes, a rupees 50 note, one rupees 20 note, two rupees 10 notes and a 5 rupee note?
Select one:
a. 96
b. 127
c. 215
d. 239
e. None of the above
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Rupees 500 notes : 3 ways (0-2)
Rupees 100 notes : 4 ways (0-3)
Rupees 50 notes : 2 ways (0-1)
Rupees 20 notes : 2 ways (0-1)
Rupees 10 notes : 3 ways (0-2)
Rupees 5 notes : 2 ways (0-1)
Count = 3x4x2x2x3x2 = 288
The correct answer is: None of the above.
Question 4
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In how many ways 4 different balls can be put in 3 different boxes such that no box is empty?
(A box can contain as many balls, and every ball has to be put in a box).
Select one:
a. 36
b. 63
c. 96
d. 72
e. None of the above
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C(3,1) = Choose Box which has 2 balls
* C(4,2) = Pair of Balls
* 2!
C(3,1)* C(4,2)* 2! = 3 * 6 * 2 = 36
The correct answer is: 36.
Question 5
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In how many ways 6 different balls can be put in 6 different boxes such that exactly one box is empty?
(A box can contain as many balls and every ball has to be put in a box).
Select one:
a. 96
b. 720
c. 9000
d. 10800
e. None of the above
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C(6,1) = Choose Box which has 0 balls
C(5,1) = Choose Box which has 2 balls
* C(6,2) = Pair of Balls
* 4!
C(6,1)* C(5,1)* C(6,2)* 4! = 6 * 5 * 15 * 24
The correct answer is: 10800.
Question 6
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In how many ways can we paint a flag with six horizontal stripes, with 4 available colours, such that no adjacent
strips have the same colour?
Select one:
a. 96
b. 720
c. 900
d. 972
e. None of the above
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4 *3 *3 *3 *3 *3
Stripe 1 Stripe 2 Stripe 3 Stripe 4 Stripe 5 Stripe 6
The correct answer is: 972.
Question 7
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From a group of six players, in how many ways can we make 3 doubles teams to play tennis in a round robin
format amongst themselves?
Select one:
a. 15
b. 72
c. 90
d. 96
e. None of the above
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C(6,2) * C(4,2) * C(2,2) / 3!
Team 1 Team 2 Team 3
The correct answer is: 15.
Question 8
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From a group of six players, in how many ways can we make 2 doubles teams to play a tennis match while the
remaining two would be referees?
Select one:
a. 45
b. 90
c. 96
d. 720
e. None of the above
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C(6,2) * C(4,2) * C(2,2) / 2!
Referee Team 1 Team 2
The correct answer is: 45.
Question 9
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How many 4-digit numbers can be formed by using exactly 3 different digits?
Select one:
a. 75
b. 720
c. 1080
d. 3888
e. None of the above
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Case 1 : number does not contain 0
C(9,1) * C(4,2) * C(8,2) * 2!
Repeat Digit Placed 2 single digits Places
Case 2 : number contains single 0
C(9,1) * C(4,2) * C(8,1) * 2!
Repeat Digit Placed non 0 digit Places
(0 may be as first digit)
Hence, we need to REMOVE / SUBTRACT cases, where 0 is first digit
C(9,1) * C(3,2) * C(8,1) * 1!
Repeat Digit Placed non 0 digit Places
Case 3 : number contains double 0
C(3,2) * C(9,2) * 2!
0 Placed 2 single digits Placed
The correct answer is: 3888.
Question 10
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Find the sum of all five digit number that can be formed using the digits 1, 2, 3, 4 and 5
(repetition of digits not allowed)?
Select one:
a. 345600
b. 691200
c. 1460800
d. 3999960
e. None of the above
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(11111)(1+2+3+4+5) 4!
The correct answer is: 3999960.
Question 11
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Find the total number of 4 letter words which have a vowel only as the first and the last letter.
Select one:
a. 8400
b. 11025
c. 13000
d. 19400
e. None of the above
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C(5,2) * 2! * C(21,2) * 2! Without Repitition
2 Vowels Last/1st 2 consonants in places
OR,
5 * 25 * 25 *5 With Repitition
The correct answer is: 11025.
Question 12
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The number of ways in which three distinct numbers in an AP can be selected from 1, 2....... 24 is
Select one:
a. 132
b. 144
c. 276
d. 572
e. None of the above
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A, B, C are in AP
Case 1: A = 1 => B can be anything from 2 to 12 => 11 Values
Case 2: A = 2 => B can be anything from 3 to 13 => 11 Values
Case 3: A = 3 => B can be anything from 4 to 13 => 10 Values
Case 4: A = 4 => B can be anything from 5 to 14 => 10 Values
Case 5: A = 5 => B can be anything from 6 to 14 => 9 Values
Case 6: A = 6 => B can be anything from 7 to 15 => 9 Values
Case 7: A = 7 => B can be anything from 8 to 15 => 8 Values
Case 8: A = 8 => B can be anything from 9 to 16 => 8 Values
-
-
-
-
-
-
Case 21: A = 21 => B can be anything from 22 to 22 => 1 Value
Case 22: A = 22 => B can be anything from 23 to 23 => 1 Value
The correct answer is: 132.
Question 13
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There are 50 red balls, 50 yellow balls and 50 blue balls of the same size in the bag. What is the minimum
number of balls that must be taken out to confirm that the sum of the number of balls of two colours is larger than
the number of balls of the third colour?
Select one:
a. 100
b. 101
c. 102
d. 103
e. None of the above
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The correct answer is: 101.
Question 14
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The number of ways you can invite 3 of your friends on 5 consecutive days, exactly one friend a day, such that
no friend is invited on more than two days is
Select one:
a. 10
b. 30
c. 60
d. 90
e. None of the above
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If friends are A, B, C
The invitation is AABBC permuted for days and friends
C(3,2) * 5! / 2!2!
The correct answer is: 90.
Question 15
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A number of four digits is formed with the help of the digits 1, 2, 3, 4, 5, 6 and 7 in all possible ways. Find how
many of these are even?
Select one:
a. 168
b. 360
c. 420
d. 840
e. None of the above
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Count (4 Digit Numbers) = Perm(7,4)
3/7 of them are Even
4/7 of them are Odd
The correct answer is: None of the above.
Question 16
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A number of four digits is formed with the help of the digits 1, 2, 3, 4, 5, 6 and 7 in all possible ways. Find how
many of these are exactly divisible by 4?
Select one:
a. 200
b. 250
c. 360
d. 480
e. None of the above
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_ _ _ _
Case 1 2/6 4 2 cases
Case 2 4 - 0 cases
Case 3 1/3/5/7 2/6 8 cases
_ _ _ _
In all 5 4 ways
Total Count = 5 * 4 *(2+0+8) = 200
The correct answer is: None of the above.
Question 17
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A train is going from Cambridge to London stops at nine intermediate station. Six persons enter the train during
the journey with six different tickets. How many different sets of ticket they have had?
Select one:
a. 42C8
b. 42C6
c. 45C6
d. 45C9
e. None of the above
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Total Number of Stations = 11
Total Number of Tickets possible = C(11, 2) = 55
Six different tickets = C(55,6)
The correct answer is: 45C6.
Question 18
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How many numbers lying between 3000 and 4000 are made with the digits 3, 4, 5, 6, 7 and 8 are divisible by 5?
Repetitions are not allowed.
Select one:
a. 4!
b. 5!
c. 6
d. 12
e. None of the above
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_ _ _ _
3 _ _ 5
In all 1 *4 *3 *1 ways
The correct answer is: 12.
Question 19
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How many of the natural numbers from 1 to 1000 have none of their digits repeated?
Select one:
a. 585
b. 589
c. 738
d. 739
e. None of the above
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Case 1 : 1 Digit : 9 Numbers
Case 2 : 2 Digit : 9 * 9 Numbers
Case 3 : 3 Digit : 9 * 9 * 8 Numbers
Case 4 : 4 Digit : 0 Number
The correct answer is: 738.
Question 20
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CAT paper consists of 12 questions divided into parts A and B. Part A contains 7 questions and part B, 5
questions. A candidate is required to attempt 8 questions selecting at least three from each part. In how many
maximum ways can the candidate select the questions?
Select one:
a. 5
b. 100
c. 375
d. 420
e. None of the above
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Case 1: 3 Questions from Part A + 5 Questions from Part B
C(7,3) * C(5,5)
35 * 1
Case 2: 4 Questions from Part A + 4 Questions from Part B
C(7,4) * C(5,4)
35 * 5
Case 3: 5 Questions from Part A + 3 Questions from Part B
C(7,5) * C(5,3)
21 * 10
Count = 35 + 175 +210
The correct answer is: 420.
Question 21
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The letters of the word 'RANDOM' are written in all possible orders and these words are written out in a
dictionary, then the rank of the word 'RANDOM' will be
Select one:
a. 370
b. 502
c. 614
d. 704
e. None of the above
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Starting A = 1* 5!
Starting D = 1* 5!
Starting M = 1* 5!
Starting N = 1* 5!
Starting O = 1* 5!
Starting RAD = 1* 3!
Starting RAM = 1* 3
Starting RAND => RAND MO and RAND OM
Or,
Total - Cases which will come later
The correct answer is: 614.
Question 22
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In how many ways can 24 persons be seated round a table, if there are 13 seats?
Select one:
a. 24!/(13!x11!)
b. 24!/(13 x 11!)
c. 24!/13!
d. 24!/11!
e. None of the above
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Who = C(24,13) = 24! / 11! 13!
How (Circular) = 12!
The correct answer is: 24!/11!.
Question 23
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How many necklace of 12 beads each can be made from 18 beads of different colours ?
Select one:
a. 117! x 13!/13
b. 12! x 18!/2
c. 119 x 13!/2
d. 18! x 11!/2
e. None of the above
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Beads = C(18,12)
How (Circular) = 11!
Necklace can be worn from either side => /2!
Count = (18! / 12! 6!) * 11! / 2!
The correct answer is: None of the above.
Question 24
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In how many ways can a pack of 52 cards be divided equally among 4 players in order?
Select one:
a. 52!/(13! x 12 x 11)
b. 52!/((13!)4)
c. 52!/13!
d. 52!/(4!(13!)4)
e. None of the above
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Player 1 Player 2 Player 3 Player 4
C(52,13) C(39,13) C(26,13) C(13,13)
52! / 13! 39! * 39! / 13! 26! *26! / 13! 13! *1
The correct answer is: None of the above.
Question 25
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In how many ways can a pack of 52 cards be divided equally among 4 sets, three of them having 17 cards each
fourth have just 1 card ?
Select one:
a. 52!/((17!)3 3!)
b. 52!/(17! x 3! )
c. 52!/(17!)3
d. 52!/4! (17!)3
e. None of the above
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Player 1 Player 2 Player 3 Player 4
C(52,17) C(35,17) C(18,17) C(1,1)
Choose player holding 1 Card = C(4,1)
No order among players holding 17 cards each => /3!
The correct answer is: 52!/(17!)3.
Question 26
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Four boys picked up 30 mangoes. In how many ways can they divide them if all mangoes be identical?
Select one:
a. 1764
b. 2460
c. 5456
d. 32736
e. None of the above
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(n+r-1)C(r-1)
Where n = 30 r=4
Answer = C(33,3) = 5456
The correct answer is: 5456.
Question 27
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Find the number of positive solutions of equations X + Y + Z + W = 20 under the conditions when zero values are
excluded?
Select one:
a. 969
b. 1320
c. 4800
d. 6400
e. None of the above
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Assign 1 to each.
X' + Y' + Z' + W' = 16
(n+r-1)C(r-1)
Where n = 16 r=4
Answer = C(19,3) = 969
The correct answer is: 969.
Question 28
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In how many ways can Rs. 5 be paid if only 25 paisa coin and 10 paisa coin are available?
Select one:
a. 11
b. 19
c. 23
d. 28
e. None of the above
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25 A + 10 B = 500 where A and B are number of 25 and 10 paisa coins
=> 5 A + 2 B = 100
=> A changes in steps of 2 and B changes in steps of 5 from Initial Solution (20,0)
The correct answer is: 11.
Question 29
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In how many ways can 12 balls be divided into groups of 5, 4 and 3 balls respectively?
Select one:
a. 13860
b. 14400
c. 15400
d. 27720
e. None of the above
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Groups of 5, 4 and 3 balls
C(12,5) * C(7,4) * C(3,3) = 792 * 35 * 1 = 27720
The correct answer is: 27720.
Question 30
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How many integral solutions are there to x + y + z + t = 29, when x > 1, y > 1, z > 3 and t > 0?
Select one:
a. 2400
b. 2600
c. 2700
d. 3600
e. None of the above
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x + y + z + t = 29, when x > 1, y > 1, z > 3 and t > 0
=> x' + y' + z' + t' = (29 - 2 - 2 - 4 - 0) (Assigning Min values 2,2,4,0 to x,y,z,t intially)
(n+r-1)C(r-1)
Where n = 21 r=4
Answer = C(22,3) = 1540
The correct answer is: None of the above.
