Harry was given homework by his class teacher, he did not like math at all, harry

needs help in finding out the rank of the word CHASM, if the letters of the word
CHASM are rearranged to form 5 letter words such that none of the words repeat and
the results are arranged in ascending order as in a dictionary:
A. 47
B. 56
C. 84
D. 32
ANSWER: D

On the occasion of his birthday, Rahul invited all of his pals to a party at his
father's farm. The seating arrangement called for 5 males and 4 females, with the
females taking the even-numbered seats. How many of these configurations are
possible?
A. 2020
B. 1440
C. 2880
D. 1550
ANSWER: C

Max and his father were on a flight from Australia to Dubai. However, they each
managed to forget how to open their bag's lock. Three dials with six different
letter markings each make up the letter lock. How many unsuccessful efforts to
unlock the latch can be made because Harry's mother will be furious if the bag is
permanently locked?
A. 268
B. 234
C. 215
D. 286
ANSWER: D

Seema is playing a game at a stall in a fair. She needs to throw the ball in the
ring with the number which can be calculated by the following riddle : How many 6-
digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 and 7 so that the
digits should not repeat and the second last digit is even. Seema wants to know
this number so that she can win the game.
A. 760
B. 425
C. 840
D. 720
ANSWER: D

20 people in total participated. Find the number of arrangements that may be made
so that there is always one person between each of the two representatives, Mohan
and Mohit, at a circular table.
A. 2×(18!)
B. (3!)×(18!)
C. 17!
D. 2×(17!)
ANSWER: A

Harsh purchased eight cartons of candy. There are 1 to 8 different chocolates in

each box. How many different ways are there in which he can distribute four of
these boxes—one to each of his four friends—so that the first friend receives more
chocolates than any of the other three, the second friend receives more chocolates
than either the third or the fourth friend, and the third friend receives more
chocolates than the fourth friend?
A. 84
B. 74
C. 65
D. 72
ANSWER: D

Nitin has been assigned a task to calculate how many total numbers of unique 4-
wheel vehicle numbers can be generated using two letters followed by two numbers
given letters need to be unique. The correct answer given by Nitin is:
A. 32000
B. 65000
C. 74000
D. 59000
ANSWER: B

By tasting a cup of tea, Saloni asserts that she can quickly determine whether milk
or tea leaves were added to the water first. 10 cups of tea are made, 5 in one
method and 5 in another, to test these claims. Find several possible ways to
provide the expert with these 10 cups so that it is challenging for her.
A. 352
B. 252
C. 286
D. 238
ANSWER:B

Raj loves Tina and wants to marry her. Raj prepared a bouquet of flowers that
included 14 white roses and 16 red roses in preparation for his proposal to Tina on
her birthday. Raj requests that Tina choose four flowers from all of the blooms.
How many different ways are there for them to be chosen so that at least one red
rose gets chosen and he can eventually express his love for her?
A. 27404
B. 32986
C. 19764
D. 20005
ANSWER: A

Three volleyball games, two soccer games, and four basketball games are all on the
V.K. Sports Academy's schedule. You are able to go to three of the games thanks to
your ticket. You definitely want to go to a basketball game as well as other
events. How many different methods are there to attend two basketball games and one
other event?
A. 75
B. 30
C. 65
D. 25
ANSWER: B

The class teacher of Rajat planned a celebration for the students to celebrate the
new year.Every student in the class sends the other students cards for the New
Year. What is the total number of greeting cards the class has exchanged if there
are 21 students?
A. 380
B. 460
C. 500
D. 420
ANSWER: D

Sixteen basketball players attend college. Out of these 16 players, a team of seven
players will be chosen, along with a captain. How many options are available for
selection?
A. 80080
B. 65540
C. 85000
D. 79650
ANSWER: A

To celebrate the Indian Team's World Cup victory, my buddies and I went to an ice
cream shop.There were 9 flavors available. We each took a cone with two flavors on
it. We each selected a different combination, and we had each taken every possible
combination. How many buddies visited the ice cream parlor?
A. 58
B. 36
C. 42
D. 60
ANSWER: B

In a company with 41 employees, there are one more female employees than male
employees. For a forthcoming project, a team of four people must be assembled. The
team's four members cannot be of the same gender. There shouldn't be an equal
distribution of men and women on the team. How many different ways can a team like
this be formed, allowing the project to be easily completed?
A. 53455
B. 50540
C. 52860
D. 55000
ANSWER: B

How many words can be made using 4 consonants and 3 vowels out of an initial set of
8 consonants and 4 vowels?
A. 102555
B. 2546000
C. 1411200
D. 1322200
ANSWER: C

A box contains 4 white balloons, 3 blue balloons and 4 red balloons. In how many
ways can 3 balloons be drawn from the box, if at least one red balloon is to be
included in the draw?
A. 110
B. 145
C. 90
D. 130
ANSWER: D

In how many ways can you rearrange the word BRINJAL such that the rearranged word
starts with a vowel?
A. 1440
B. 1410
C. 960
D. 1280
ANSWER: A

In the evening, at Town Hall Park, Anish and Shruti were playing chess. Rahul
arrived and issued a challenge to Shruti: How many different ways are there in
which four squares on a chessboard can be arbitrarily selected so that they lie on
a diagonal?
A. 182
B. 364
C. 250
D. 198
ANSWER: B

The most notorious and sought-after criminal, Vijay, is currently in Ireland.

According to his research, the locker code for the bank he intends to loot there is
an odd number between 50 and 450. Additionally, he is aware that the numbers belong
to a set: 0, 1, 2, 3, 4, and 5. How many attempts at the most can he make to open
the locker?
A. 54
B. 108
C. 72
D. 96
ANSWER: C

In the city of Nadar, parallel highways p and q run from north to west and from
east to south, respectively. How many rectangles are created by these highways'
sides?
A. pq4
B. pqP-1q-14
C. P-1q-12
D. None of above
ANSWER: B

12 ants were seen crawling across an entomologist's table. There were exactly 10
men and 2 women among them. He noted that they weren't crawling on the table in a
straight line, but rather in a random order, with never three of them in a row. All
four ants were suddenly in a single line as three of the male ants started to
follow one of the female ants.Then the maximum number of distinct straight lines
that the entomologist can draw passing through any two ants is
A. 61
B. 42
C. 74
D. 66
ANSWER: A

Manish finished his studies and began working in an electrical shop. Four different
black bulbs, three different white bulbs, and five different yellow bulbs are
provided. The number of possible bulb combinations, assuming at least one yellow
and one black bulb, is thus :
A. 3000
B. 2880
C. 4250
D. 3720
ANSWER: D

An ill octopus lived in a region of frigid terrain.So he set up a shoe and a pair
of socks for each of its eight legs.Given that the sock must go on before the shoe
in each leg, how many distinct ways can the octopus put on its socks and shoes?
A. 8!2
B. 8!223
C. 12816!
D. None of the above
ANSWER: C

The transport government has been ordered to mark neon flags on the road by the
Supreme court due to an increase in the number of road accidents at night. Six
flags are marked on a straight road and five flags are marked on another road which
is parallel to the first road. How many straight lines, including the first two,
can be formed with these flags connecting both sides of the road?
A. 32
B. 46
C. 48
D. 25
ANSWER: A

Between Delhi and Coimbatore, there are 24 stations. How many second class tickets
must be printed in order for a passenger to travel between any two stations?
A. 440
B. 380
C. 650
D. 560
ANSWER: C

Only 12 of the hundreds of students who applied to the UPSC in 2022 were chosen to
move on in the selection process.Twelve students will take one of two exam
variations.How many different ways can the students be arranged into two rows of
six each, making sure that no two rows have the same arrangement and that the
students seated one behind the other have the same arrangement?
A. 2×6!×6!
B. 2×12C6×(6!)2
C. 2×12C6×(6!)
D. None of the above
ANSWER: A

After the summer break, the students were seated in the class based on the grades
they received for the various projects.Once, four students received the same grade
and, as a result, the same rank.The principal wants to write down every conceivable
arrangement for their seats on a separate piece of paper so they can choose one by
drawing lots.How many paper chits are needed?
A. 46
B. 22
C. 18
D. 42
ANSWER: D

Our seniors threw a celebration for their classmates, but there weren't enough
drinks for everyone.So it was determined that three persons would share the seven
distinct cocktails.And everyone will be subject to this rule.How many different
ways are there to do this if one or two of them aren't allowed to drink in that
group of three?
A. 381
B. 84
C. 156
D. 93
ANSWER: A

Also, two people getting no drinks can be done in 3 ways.Thus, the answer is 378 +
3 = 381Shravan maintains a healthy lifestyle while juggling his job and exercise.He
owns five pairs of athletic shoes in addition to seven pairs of dress shoes.He has
put everything in a box, and each shoe is pulled one at a time.What is the minimum
number of shoes that must be drawn out in order to guarantee that at least one pair
of black shoes gets removed?
A. 13
B. 23
C. 18
D. 11
ANSWER: C

For the position of Technical Lead in the Product Team, the State Council issued an
application call.Currently, 11 software engineers and 7 civil engineers have been
shortlisted based on the eligibility requirements.How many different ways can they
be arranged in a row so that no civil engineers sit next to one another throughout
the exam?
A. 18!−(12!×7!)
B. 18P4−2!
C. 18!−(11!×7!)
D. [/latex] ^{18}\textrm{P}_{4} \times 11 [/latex]
ANSWER: A

Mukesh completed his class 12 and got himself admitted into a reputed college in
the city. After visiting the college he observed that there are 6 lectures in each
working day of a college. Now he has a query that in how many ways can they
organize 5 subjects such that each subject is allowed at least one lecture?
A. 3250
B. 1905
C. 2680
D. 1800
ANSWER: D

There are 10 extensions on a satellite, and each extension can adopt 5 different
locations (including position of the rest). How many signals can the satellite send
out at once?
A. 510-5
B. 10P5
C. 510-1
D. 10P5-1
ANSWER: C

There are 12 bottles of Limca, 7 bottles of Pepsi, 3 varieties of Sprite, and 2

varieties of Dew in the store. How many different ways are there to choose one or
more bottles?
A. 3111
B. 3227
C. 4104
D. 3685
ANSWER: B

Rajesh was the top student and a nice guy.He now wants to enroll in college and
takes the required exam.Rajesh was made aware that there will be two sections, P
and Q, with a total of 10 questions in each when preparing for the R.K.G. College
entrance exam.How many different ways may he choose 8 questions from part P and 4
questions from part Q in accordance with the stated guidelines?
A. 9450
B. 6020
C. 7330
D. 9110
ANSWER: A

Duke gave his lover seven different types of beads as a token of his love.His
partner had the idea to use the provided beads to create a necklace.She headed to
the local jewelry store.How many different ways are there to string seven beads
together to make a necklace?
A. 360
B. 480
C. 560
D. 120
ANSWER: A
Ants are known to have a very steady, diligent, and cooperative attitude.They are
always there for one another.There are 55 ants in the ant colony.Each ant sends out
a greeting card to every other ant.How many cards did they post as greetings?
A. 1980
B. 2970
C. 880
D. 1620
ANSWER: B

Only two of the six applicants invited for the interview are qualified for the
position of analyst, but they are all qualified for the position of junior analyst.
A decision must be made for one post of analyst and two posts of junior
analysts.Which of the following is the combinations of the shortlisted candidates?
A. 20
B. 18
C. 26
D. 4
ANSWER: A

How many words can be formed by using all letters of the word ‘VISHAL’?
A. 120
B. 720
C. 80
D. 440
ANSWER: B

Sandeep was given a job at the GLB school of management as a librarian.As requested
by the dean, he has been given the assignment to arrange the books on the
shelf.There are two books of five volumes each as well as two books of two volumes
apiece.How many different ways can these books be stacked together so that all of
the volumes of the same book stay together?
A. 4!×5!×2!
B. 4!×14!
C. 4!×5!×5!×2!×2!
D. None of the above
ANSWER: C

There is a direct water supply line from the Ganges river.There are men employed by
the water board authority who fill the bottles from the available taps.Assuming a
tap cannot be used more than once, how many different ways may five guys collect
water from them?
A. 60
B. 180
C. 720
D. 120
ANSWER: D