Which tense is used in the sentence, "She will have finished her work by evening"?
A
Future perfect
B
Present perfect
C
Past perfect
D
Future continuous
Question 3Single Answer
What is the correct form of the verb in the sentence, "If I ___ rich, I would travel the world"?
A
Am
B
Was
C
Were
D
Will be
Question 4Single Answer
What is the role of a conjunction in a sentence?
A
Connects clauses or sentences
B
Modifies a verb
C
Describes a noun
D
Replaces a noun
Question 5Single Answer
Which sentence uses the correct subject-verb agreement?
A
The team are playing well.
B
The teams is playing well.
C
The team is playing well.
D
The teams has played well.
Question 6Single Answer
What is the correct punctuation for the sentence, "I love reading books however I dont have much time"?
A
I love reading books, however, I don’t have much time.
B
I love reading books, however I don’t have much time.
C
I love reading books however, I don’t have much time.
D
I love reading books; however, I don’t have much time.
Question 7Single Answer
Which part of speech is the word "quickly" in the sentence, "She runs quickly"?
A
Adjective
B
Adverb
C
Noun
D
Verb
Question 8Single Answer
What is the passive voice form of the sentence, "The chef cooked a delicious meal"?
A
A delicious meal was cooked by the chef.
B
A delicious meal is cooked by the chef.
C
The chef was cooking a delicious meal.
D
A delicious meal has been cooked by the chef.
Question 9Single Answer
What is the correct sequence to form a coherent sentence from these words: "always," "she," "carefully," "drives"?
A
She carefully drives always.
B
She drives always carefully.
C
Always she drives carefully.
D
She always carefully drives.
Question 10Single Answer
Which modal verb indicates obligation in the sentence, "You ___ submit your assignment by tomorrow"?
A
Can
B
May
C
Might
D
Must
Question 11Single Answer
What is the main idea of a passage describing the impact of deforestation on wildlife?
A
The beauty of forests
B
The benefits of logging
C
The loss of animal habitats
D
The history of deforestation
Question 12Single Answer
Which sentence contains a dangling modifier?
A
He painted the house with great care.
B
She read the book quietly in the library.
C
The dog barked loudly at the stranger.
D
Running to catch the bus, the bag fell.
Question 13Single Answer
What is the correct use of the apostrophe in the sentence, "The childrens books are on the shelf"?
A
The children’s books’ are on the shelf.
B
The childrens’ books are on the shelf.
C
The children books are on the shelf.
D
The children’s books are on the shelf.
Question 14Single Answer
What is the tone of a literary text that uses vivid imagery to describe a serene lake?
A
Melancholic
B
Peaceful
C
Satirical
D
Suspenseful
Question 15Single Answer
Which clause is dependent in the sentence, "Although it was raining, we went hiking"?
A
Although it was raining
B
We went hiking
C
It was raining
D
We went
Question 16Single Answer
What is the purpose of a non-literary text like a user manual?
A
To inform
B
To persuade
C
To entertain
D
To narrate
Question 17Single Answer
Which sentence uses parallel structure correctly?
A
She likes to swim, jogging, and to read books.
B
She likes to swim, to jog, and reading books.
C
She likes swimming, jogging, and reading books.
D
She likes swimming, to jog, and read books.
Question 18Single Answer
What is the synonym for "benevolent" as used in a literary text?
A
Kind
B
Cruel
C
Indifferent
D
Cautious
Question 19Single Answer
Which sentence is in the subjunctive mood?
A
I will be a bird
B
I am a bird
C
I wish I were a bird
D
I was a bird
Question 20Single Answer
What is the main purpose of a newspaper editorial?
A
To report facts
B
To advertise products
C
To entertain readers
D
To express opinions
Question 21Single Answer
Which sentence uses the correct form of the verb "lie"?
A
She lays on the bed all day.
B
She lain on the bed all day.
C
She laid on the bed all day.
D
She lies on the bed all day.
Question 22Single Answer
What is the implied meaning of the phrase "the calm before the storm" in a literary text?
A
A literal weather change
B
A peaceful moment before chaos
C
A time of celebration
D
A period of exhaustion
Question 23Single Answer
Which sentence contains a misplaced modifier?
A
The dog ran into the house covered in mud
B
The dog, covered in mud, ran into the house.
C
Covered in mud, the dog ran into the house.
D
The dog ran into the house, covered in mud
Question 24Single Answer
What is the purpose of a rhetorical question in a non-literary text?
A
To provide factual information
B
To describe a scene
C
To narrate a story
D
To provoke thought or emphasize a point
Question 25Single Answer
Which sentence uses the correct form of "its" vs. "it’s"?
A
The dog wagged it’s tail happily.
B
Its a sunny day outside.
C
The dog wagged its tail happily.
D
It’s tail was wagging happily.
Question 26Single Answer
What is the central theme of a poem describing the struggles of a farmer?
A
Perseverance and hardship
B
Nature’s beauty
C
Urban life
D
Technological advancement
Question 27Single Answer
Which sentence uses the active voice?
A
The cake was eaten by the children.
B
The cake has been eaten by the children.
C
The children ate the cake.
D
The cake is being eaten by the children.
Question 28Single Answer
What is the antonym of "ephemeral" as used in a literary text?
A
Temporary
B
Permanent
C
Fragile
D
Fleeting
Question 29Single Answer
Which punctuation mark is used to separate items in a list?
A
Colon
B
Comma
C
Semicolon
D
Hyphen
Question 30Single Answer
What is the main idea of a non-literary text discussing the benefits of recycling?
A
The environmental advantages of recycling
B
The history of waste management
C
The cost of recycling programs
D
The challenges of recycling
General Studies
Question 31Single Answer
Yojna a weekly journal
A
Ministry of Finance
B
Ministry of Information and Broadcastin
C
Ministry of Rural Development
D
Planning Commission
Question 32Single Answer
In ruby laser, the stimulated emission is due to transition from
A
metastable state to any lower state
B
any higher state of lower state
C
metastable state to ground state
D
any higher state to ground state
Question 33Single Answer
10-6 M NaOH is diluted 100 times. The pH of the diluted base is
A
between 7 and 8
B
between 5 and 6
C
between 6 and 7
D
between 10 and 11
Question 34Single Answer
The respiratory quotient during cellular respiration would depend on
A
the nature of enzymes involved
B
the nature of the substrate
C
the amount of carbon dioxide released
D
the amount of oxygen utilised
Question 35Single Answer
How many such pairs of letters are there in the word ‘CLEANLINESS’ each of the which has as many letters between them in the word as they have in the English alphabet, in the same sequence?
A
Two
B
Three
C
Five
D
Four
E
None of these
Question 36Single Answer
Team A has scored more goals than Team B
Team C has scored fewer goals than Team B
Team A has scored fewer goals than Team C .
If the first two statements are true, the third statement is
A
True
B
False
C
Uncertain
D
None
Question 37Single Answer
If it is possible to make only one meaningful word with the second, the third, the sixth and the eight letters of the word FRAGMENT using each only once, which of the following will be the third letter of that word ? If no such word can be formed, give ‘X’ as the answer and if more than one such word can be formed, give ‘Y’ as the answer.
A
A
B
E
C
T
D
X
E
Y
Question 38Single Answer
How many such letters are there in the word ORIENTAL each of which is as far away from the beginning of the word as when they are arranged alphabetically?
A
None
B
One
C
Two
D
Three
E
More than three
Question 39Single Answer
How many such pairs of letters in the word CREDIT each of which has as many letters between them in the word as in the English alphabet?
A
None
B
One
C
Two
D
Three
E
More than three
Question 40Single Answer
Passage :
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z .
Which letter in this alphabet is the eighth letter to the right of the letter and which is tenth letter to the left of the last but one letter of the alphabet ?
A
X
B
W
C
I
D
H
Question 41Single Answer
Passage :
Direction : The following question is based on the five words given below:
AND FOR THE BIG SUM (The new words formed after performing the mentioned operations may or may not necessarily the meaningful English words.)
If the third alphabet of each of the words is changed to the next alphabet in the English alphabetical series, which of the following will form a meaningful English word?
A
SUM
B
BIG
C
Both BIG and THE
D
FOR
E
Both FOR and BIG
Question 42Single Answer
Passage :
Direction : The following question is based on the five words given below:
AND FOR THE BIG SUM (The new words formed after performing the mentioned operations may or may not necessarily the meaningful English words.)
If the given words are arranged in the order as they would appear in a dictionary from left to right, which of the following will be second from the right ?
A
AND
B
FOR
C
THE
D
BIG
E
SUM
Question 43Single Answer
Passage :
Direction: The following question is based on the five words given below:
AND FOR THE BIG SUM (The new words formed after performing the mentioned operations may or may not necessarily the meaningful English words.)
If second alphabet in each of the words is changed to next alphabet in the English alphabetical order, how many words having two vowels (same or different vowels) will be formed ?
A
None
B
One
C
Two
D
Three
E
Four
Question 44Single Answer
Passage :
Direction : The following question is based on the five words given below:
AND FOR THE BIG SUM (The new words formed after performing the mentioned operations may or may not necessarily the meaningful English words.)
How many letters are there in the English alphabetical series between the second letter of the word which is second from the right and the second letter of the word which is second from the left of the given words?
A
Two
B
Five
C
Six
D
Nine
E
Three
Question 45Single Answer
The cash difference between the selling prices of an article at a profit of 4% and 6% is Rs. 3. The ratio of the two selling prices is:__________ ?
A
51:52
B
52:53
C
51:53
D
52:55
Question 46Single Answer
Which of the following numbers is irrational ?
A
√49
B
0.125
C
√2
D
22/7
Question 47Single Answer
356 x 936 – 356 x 836 = ?
A
35600
B
34500
C
9630
D
93600
Question 48Single Answer
Arrange in descending order: 5/8, 7/10, 3/4
A
3/4 > 7/10 > 5/8
B
7/10 > 3/4 > 5/8
C
3/4 > 5/8 > 7/10
D
5/8 > 7/10 > 3/4
Question 49Single Answer
What is (3^{4} times 9^{2}) ?
A
36
B
38
C
310
D
96
Question 50Single Answer
Passage :
information given below and answer the question that follow.
The result of an exam is given below. Out of 1000 students who appeared
(i) 658 failed in Physics
(ii) 166 failed in Physics and Chemistry
(iii) 372 failed in Chemistry, 434 failed in Physics and Maths
(iv) 590 failed in Maths, 126 failed in Maths & Chemistry
Find the number of people who failed in (assuming that none is passed in all subjects.
We have the following equations:
a+ b + c + d + e + f + g = 1000
a + b + d + e = 658, b + d = 166
b + d + c + f = 372
d + e = 434 as in the figure.
d + e + f + g = 590, d + f = 126. Find the values
Chemistry but not in Physics.
A
318
B
198
C
213
D
206
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General Studies
Question 51Single Answer
Passage :
Direction: information given below and answer the question that follow.
The result of an exam is given below. Out of 1000 students who appeared
(i) 658 failed in Physics
(ii) 166 failed in Physics and Chemistry
(iii) 372 failed in Chemistry, 434 failed in Physics and Maths
(iv) 590 failed in Maths, 126 failed in Maths & Chemistry
Find the number of people who failed in (assuming that none is passed in all subjects.
We have the following equations:
a+ b + c + d + e + f + g = 1000
a + b + d + e = 658, b + d = 166
b + d + c + f = 372
d + e = 434 as in the figure.
d + e + f + g = 590, d + f = 126. Find the values
Physics or Maths but not in Chemistry.
A
558
B
718
C
628
D
None of these
Question 52Single Answer
Passage :
For the next four question that follow:
In a city, three daily newspapers A, B, C are published, 42% read A; 51% read B; 68% read C; 30% read A and B; 28% read B and C; 36% read A and C; 8% do not read any of the three newspapers.
Let x% people read all the three newspapers.
Since 8% people do not read any newspapers.
(x – 24) + (x – 7) + (x + 4) + (30 – x) + (36 – x) + (28 – x) + x = 92
→ x + 98 – 31 = 92
→ x = 92 – 67 = 25
What is the percentage of persons who read all the three papers ?
A
20%
B
25%
C
30%
D
40%
Question 53Single Answer
Passage :
For the next four : question that follow :
In a city, three daily newspapers A, B, C are published, 42% read A; 51% read B; 68% read C; 30% read A and B; 28% read B and C; 36% read A and C; 8% do not read any of the three newspapers.
Let x% people read all the three newspapers.
Since 8% people do not read any newspapers.
(x – 24) + (x – 7) + (x + 4) + (30 – x) + (36 – x) + (28 – x) + x = 92
→ x + 98 – 31 = 92
→ x = 92 – 67 = 25
What is the percentage of persons who read only two papers?
A
19%
B
31%
C
44%
D
None of these
Question 54Single Answer
Passage :
For the next four : question that follow :
In a city, three daily newspapers A, B, C are published, 42% read A; 51% read B; 68% read C; 30% read A and B; 28% read B and C; 36% read A and C; 8% do not read any of the three newspapers.
Let x% people read all the three newspapers.
Since 8% people do not read any newspapers.
(x – 24) + (x – 7) + (x + 4) + (30 – x) + (36 – x) + (28 – x) + x = 92
→ x + 98 – 31 = 92
→ x = 92 – 67 = 25
What is the percentage of persons who read only one paper ?
A
38%
B
48%
C
51%
D
None of these
Question 55Single Answer
Who was the real founder of Turk rule in Bihar ?
A
Ibn Bakhtiyar Khilji
B
Ibrahim
C
Dariya Khan Noohani
D
Malik Husamuddin
E
None of the above / More than one of the above
Question 56Single Answer
Who was the first Indian Governor of Bihar ?
A
Dr. Shri krishna Singh
B
Brij Kishor Prasad
C
B.P. Mandal
D
Satyendra Prasanna Sinha
E
None of the above/More than one of the above
Question 57Single Answer
Sattriya dance form is famous in which of these states ?
A
Assam
B
Himachal Pradesh
C
Punjab
D
Tamil Nadu
Question 58Single Answer
Which of the following statements is true ?
Statement I: Indian techniques such as Rasa and Bhawa in classical dances have their origins in Bharatmuni's Natyashastra.
Statement II: Bharatanatyam has its origin in Odisha.
A
Only Statement II is true
B
Both Statement I and Statement II are true
C
Neither Statement I nor Statement II is true
D
Only Statement I is true
Question 59Single Answer
"Who said, 'India was a parrot unto itself'?
A
Malik Muhammad Joyce
B
Raskhan
C
Rich Khusrow
D
Rich Hasan
Question 60Single Answer
What was the real name of Amir Khusro?
A
Muhammad Hasan
B
Muhammad Hussain
C
Muhammad Khusrow
D
Muhammad Mine
Question 61Single Answer
Which is the national game of Bhutan ?
A
badminton
B
basketball
C
football
D
archery
Question 62Single Answer
What is the national game of the United States of America ?
A
water polo
B
Rugby
C
Polo
D
baseball
Question 63Single Answer
When was the Constituent Assembly of India formed?
A
1946
B
1947
C
1948
D
1950
Question 64Single Answer
Who was the Chairman of the Drafting Committee of the Indian Constitution?
A
Dr. Rajendra Prasad
B
Dr. B.R. Ambedkar
C
Jawaharlal Nehru
D
Sardar Vallabhbhai Patel
Question 65Single Answer
Who is known as the "Father of the Indian Renaissance" ?
A
Raja Ram Mohan Roy
B
Swami Vivekananda
C
Rabindranath Tagore
D
Mahatma Gandhi
Question 66Single Answer
Which classical dance form is associated with Tamil Nadu ?
A
Kathak
B
Kuchipudi
C
Bharatanatyam
D
Odissi
Question 67Single Answer
What is the study of ethics primarily concerned with ?
A
Economic behavior
B
Human values and moral principles
C
Physical health
D
Political systems
Question 68Single Answer
Which is the longest river in India?
A
Yamuna
B
Ganges
C
Brahmaputra
D
Godavari
Question 69Single Answer
What new authority was granted to Mukhiyas in Bihar in June 2025?
A
Approve schemes up to Rs.10 lakh
B
Approve schemes up to Rs.5 lakh
C
Approve schemes up to Rs.15 lakh
D
Approve schemes up to Rs.20 lakh
Question 70Single Answer
Which initiative was announced to increase the monthly allowance of Panchayati Raj representatives in June 2025?
A
Pragati Yatra
B
Panchayat Empowerment Scheme
C
Rural Governance Reform
D
Bihar Development Mission
Concerned Subject (Mathematics)
Question 71Single Answer
The elements of the set {x : x is an integer, x2 : 4} can be represent as .....Z..... . Here, Z refers to
A
{–2, 2}
B
{–1, 0, 1}
C
{–2, –1, 0, 1, 2}
D
{0, 1, 2}
Question 72Single Answer
A
B
C
D
None of these
Question 73Single Answer
If Y = {x : x is a positive factor of the number 2p – 1(2p – 1), where 2p – 1 is a prime number}, then Y can be represent in roster form as
A
{2}
B
{1, 2}
C
{1, 2, 22, ....., 2p – 1}
D
{1, 2, 22, 23,.... 2p – 1, (2p – 1)}
Question 74Single Answer
The set {x : x is a positive integer less than 6 and 3x – 1 is an even number} in roster form is
A
{1, 2, 3, 4, 5}
B
{1, 2, 3, 4, 5, 6}
C
{2, 4, 6}
D
{1, 3, 5}
Question 75Single Answer
If A B and A B, then
A
A is called a proper subset of B
B
A is called a super set of B
C
A is not a subset of B
D
B is a subset of A
Question 76Single Answer
The number of non-empty subsets of the set{1, 2, 3, 4} is
A
15
B
14
C
16
D
17
Question 77Single Answer
The number of elements of the power set of a set containing m elements is
A
2m – 1
B
m
C
m2
D
2m
Question 78Single Answer
If A = {x : x = n2, n = 1, 2, 3}, then number of proper subsets is
A
3
B
8
C
7
D
None of these
Question 79Single Answer
If A = {x : x = 4n + 1, 2 £ n £ 5},then number of subsets of A is
A
16
B
15
C
4
D
None of these
Question 80Single Answer
Let A and B be two non-empty subsets of a set X such that A is not a subset of B, then
A
A is always a subset of the complement of B
B
B is always a subset of A
C
A and B are always disjoint
D
A and the complement of B are always non-disjoint
Question 81Single Answer
Which of the following is/are empty set?
A = {x : x2 + x + 1 = 0 and x Î Z} B = {x : x is a prime number and 19 < x < 23}
A
A
B
B
C
Both A and B
D
None of the above
Question 82Single Answer
The set {x : x4 = 1 and x R} is .....X.... set. Here, X refers to
A
empty
B
finite
C
infinite
D
singleton
Question 83Single Answer
The universal set for the sets
A = {x : x2 – 5x + 6 = 0} and
B = {x : x2 – 3x + 2 = 0} having least number of elements is
A
{1, 2}
B
{1, 3}
C
{1, 2, 3}
D
{0, 1, 2, 3}
Question 84Single Answer
If A = {1, 2, 3}, B = {x € R : x2 – 2x + 1 = 0},
C = {1, 2, 2, 3} and
D = {x € R : x3 – 6x2 + 11x – 6 = 0}, then the equal sets are
A
A and B
B
A and C
C
A, B and C
D
A, C and D
Question 85Single Answer
If A = (–3, 5) and B = [–7, 9], then
A
A = B
B
A B
C
B A
D
None of these
Question 86Single Answer
Two finite sets have m and n elements, respectively. The total number of subsets of first set is 56 more than the total number of subsets of the second set. The value of m and n respectively are
A
7, 6
B
5, 1
C
6, 3
D
8, 7
Question 87Single Answer
Combine terms: 12a + 26b - 4b – 16a .
A
4a + 22b
B
-28a + 30b
C
-4a + 22b
D
28a + 30b
Question 88Single Answer
The average of first 50 natural numbers is ………… .
A
25.30
B
25.5
C
25.00
D
12.25
Question 89Single Answer
60 Times of 8 Equals to
A
480
B
300
C
250
D
400
Question 90Single Answer
Consider the sets
A = {x : x is a real number and x2 + 1 = 0}
B = {x : x is a real number and x2 – 16 = 0}
C = {x : x is a real number and x2 = x + 2}
Which of the following is are null set ?
A
A
B
A and B
C
A and C
D
A, B and C
Question 91Single Answer
If X = {4n – 3n – 1: n Î N} and Y = {9(n – 1): n Î N}; where N is the set of natural numbers, then X È Y is equal to
A
N
B
Y – X
C
X
D
Y
Question 92Single Answer
Which of the following is / are correct?
I. {2, 3, 4} {1, 2, 3, 4, 5}
II. {a, b, c} {b, c, d}
III. {x : x is an equilateral triangle in a plane} Ì {x : x is a triangle in the same plane}
IV. {x : x is an even natural number} {x : x is an integer}
A
I and III are correct
B
II and III are correct
C
Only IV is correct
D
All above are correct
Question 93Single Answer
A
B
C
D
Question 94Single Answer
Consider the following statements :
1. The set of all irrational numbers between √2 and √5 is an infinite set .
2. The set of all odd integers less than 100 is a finite set .
Which of the statements given above is/are correct ?
A
1 only
B
2 only
C
Both 1 and 2
D
Neither 1 nor 2
Question 95Single Answer
What is the Next Prime Number after 7 ?
A
13
B
12
C
14
D
11
Question 96Single Answer
If A and B are two given sets, then A (A B)C is equal to
A
A
B
B
C
D
Question 97Single Answer
121 Divided by 11 is
A
11
B
10
C
19
D
18
Question 98Single Answer
Let X be the universal set for sets A and B, if n(A) = 200, n(B) = 300 and n = 100, then n is equal to 300 provided n(X) is equal to
A
600
B
700
C
800
D
900
Question 99Single Answer
A
{3, 4, 10}
B
{2, 8, 10}
C
{4, 5, 6}
D
{3, 5, 14}
Question 100Single Answer
Let A = {x : x is a prime factor of 240} B = {x : x is the sum of any two prime factors of 240}, then
A
B
C
D
Question 101Single Answer
If A = {x : x is a multiple of 4 and x N} and B = {x : x is a multiple of 6 and x N}, then A B consists of all multiples of
A
16
B
12
C
8
D
4
Question 102Single Answer
A
A = B
B
B = C
C
A = C
D
None of these
Question 103Single Answer
A
equal
B
disjoint
C
either equal or disjoint
D
none of the above
Question 104Single Answer
A
{–i, i}
B
{–1, 1}
C
{–1, 1, i, –i}
D
None of these
Question 105Single Answer
If A = {x : f(x)= 0} and
B = {x : g(x) = 0}, then A B will be
A
[f(x)]2 + [g(x)]2 = 0
B
C
D
None of the above
Question 106Single Answer
In a group of 400 people, 250 can speak Hindi and 200 can speak English. Then, people who can speak both Hindi and English are
A
60
B
80
C
50
D
45
Question 107Single Answer
20 teachers of a school either teach Mathematics or Physics. 12 of them teach Mathematics while 4 teach both the subjects. The number of teacher teaching Physics only, is
A
12
B
8
C
16
D
20
Question 108Single Answer
In a class of 100 students, 70 have taken Science, 60 have taken Mathematics, 40 have taken both Science and Mathematics. The number of students who have not taken Science or Mathematics or both Science and Mathematics, is equal to
A
90
B
10
C
30
D
20
Question 109Single Answer
A market research group conducted a survey of 1000 consumers and reported that 720 consumers like product A and 450 consumers like the product B, then least number that must have like both products, is
A
730
B
170
C
180
D
1270
Question 110Single Answer
If there are three athletic teams in a school, 21 are in the basketball team, 26 in hockey team and 29 in the football team. 14 play hockey and basketball, 15 play hockey and football, 12 play football and basketball and 8 play all the games. The total number of members is
A
42
B
43
C
45
D
None of these
Question 111Single Answer
A college awarded 38 medals in football, 15 in basketball and 20 in cricket. If these medals went to a total of 58 men and only three men got medals in all the three sports, then number of men who received meal in exactly two of the three sports is
A
18
B
15
C
9
D
24
Question 112Single Answer
In the class of 175 students, the following data shows the number of students opting one or more subjects. Mathematics 100; Physics 70; Chemistry 40; Mathematics and Physics 30; Mathematics and Chemistry 28; Physics and Chemistry 23; Mathematics, Physics and Chemistry 18. Then, number of students opted Mathematics alone is
A
35
B
48
C
60
D
20
Question 113Single Answer
In a town of 10000 families it was found that 40% family buy newspaper A, 20% family buy newspaper B and 10% family buy newspaper C, 5% families buy and B, 3% families buy B and C and 4% families buy A and C. If 2% families buy all the three newspapers. Then, number of families which by A only is
A
3100
B
3300
C
2900
D
1400
Question 114Single Answer
In a city, 20% of the population travles by car, 50% travles by bus and 10% travles by both car and bus. Then, person travelling by car or bus, is
A
80%
B
40%
C
60%
D
70%
Question 115Single Answer
Universal set,
U = {x | x5 – 6x4 + 11x3 – 6 x 2 = 0}
A = {x | x2 – 5x + 6 = 0}
B = {x | x2 – 3x + 2 = 0}
What is the value of (A B)?
A
{1, 3}
B
{1, 2, 3}
C
{0, 1, 3}
D
{0, 1, 2, 3}
Question 116Single Answer
A
B
C
D
Question 117Single Answer
If P(A) denotes the power set of A and A is the void set, then what is the number of elements in P{P{P{P(A)}}}?
A
Zero
B
1
C
4
D
16
Question 118Single Answer
If A = {1, 2, 3, 4, 5}, b = {x : x2 – 5x + 6 = 0} and C = {x : x2 = 4 or x = 1}, then
A
B
C
Both (a) and (b)
D
None of the above
Question 119Single Answer
In a group of 50 people, 35 speak Hindi, 25 speak both English and Hindi and all the people speak atleast one of two languages. The number of people who speak 'English', 'English but not Hindi' are respectively
A
40, 15
B
15, 40
C
35, 15
D
25, 15
Question 120Single Answer
If P = {1, 2}, then P × P × P = {(1, 1, 1), (1, 1, 2), (1, 2, 1), (2, 1, 2), (2, 2, 1), (2, 2, 2)}. The ordered triplet missing in P × P × P are
A
(1, 2), (2, 1)
B
(1, 2, 1), (2, 1, 1)
C
(1, 2, 2), (2, 1, 2)
D
(1, 2, 2), (2, 1, 1)
Question 121Single Answer
If A = {1, 2, 3, 4} and B = {5, 7, 9} then
A
A × B = B × A
B
n(A × B) =n(B × A)
C
Both (a) and (b)
D
None of the above
Question 122Single Answer
Let A and B are two sets having 3 elements in common. If n(A) = 5 and n(B) = 4, then n[(A × B) (B × A)] is equal to
A
20
B
25
C
16
D
9
Question 123Single Answer
If n(A) = 3, n(B) = 4 then, n(A × A × B) is equal to
A
36
B
12
C
108
D
None of these
Question 124Single Answer
If A = {1, 2, 3}, B = {3, 8}, then (A B) × (A B) is equal to
A
{(8, 3), (8, 2), (8, 1), (8, 8)}
B
{(1, 2), (2, 2), (3, 3), (8, 8)}
C
{(3, 1), (3, 2), (3, 3), (3, 8)}
D
{(1, 3), (2, 3), (3, 3), (8, 3)}
Question 125Single Answer
The Cartesian product A × A has 9 elements among which are found (–1, 0) and (0, 1). Then, the remaining elements of A × A are