Question for Bihar Higher Secondary School Teacher - Mathematics 2026 - Quiz / Questions / MCQ

Objective Questions

Latest Bihar Higher Secondary School Teacher Mathematics Exam Question (Objective Questions), MCQ in English

Subjects : English and Hindi Language, General Studies, Mathematics

Question Bank Bihar Higher Secondary School Teacher (Mathematics) Exam - English

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English and Hindi Language

Question 1Single Answer

शुद्ध वर्तनी का चयन कीजिए

A
अधम्र
B
अध्रम
C
अधर्म
D
अध्रिम

Question 2Single Answer

शुद्ध वर्तनी का चयन कीजिए

A
स्थायि
B
स्थायी
C
स्थाई
D
स्थाइ

Question 3Single Answer

वर्तनी की दृष्टि से सही शब्द है?

A
महत्व
B
महतव
C
महत्तव
D
महतत्व

Question 4Single Answer

निम्नलिखित में से शुद्ध छांटिए?

A
आयुष्मान
B
आयुश्मान
C
आयुशमान
D
आयुश्यमान

Question 5Single Answer

शुद्ध शब्द नहीं हैं?

A
कवियत्री
B
कौसल्या
C
एश्वर्य
D
श्रृंगार

Question 6Single Answer

शुद्ध वर्तनी है -

A
पूज
B
पुजय
C
पूज्य
D
पुज्य

Question 7Single Answer

शुद्ध वर्तनी है -

A
अनुसरण
B
अनूशरणन
C
अनुशरण
D
अणुशर

Question 8Single Answer

किस क्रमांक में सभी शुद्ध हैं?

A
एक्य,साप्ताहिक
B
आजीविका,आशीर्वाद
C
आर्शिवाद ,अनूकूल
D
निरिक्षण ,कृपालु

Question 9Single Answer

'उज्वल' शब्द का शुद्ध रूप है ?

A
उज्जव
B
उज्ज्ल
C
उज्ज्वल
D
उजवल

Question 10Single Answer

निम्नलिखित प्रश्न में चार वैकल्पिक वर्तनियाॅ दी गई है?

A
जागृत
B
जाग्रति
C
जाग्रित
D
जाग्रत

Question 11Single Answer

निम्नलिखित प्रश्न में चार वैकल्पिक वर्तनियाॅ दी गई है?

A
उन्नति
B
उनति
C
उन्ती
D
उनती

Question 12Single Answer

निम्नलिखित प्रश्न मे चार वैकल्पिक वर्तनियाॅ दी गई है?

A
अनुशहरण
B
अनोसरण
C
अनुसरन
D
अनुसरण

Question 13Single Answer

'पृथ्वीराज रासो' किस काल की रचना है ?

A
आदिकाल
B
रीतिकाल
C
भक्तिकाल
D
आधुनिक काल

Question 14Single Answer

हिन्दी की उत्पत्ति किस भाषा से हुई है?

A
प्राकृत
B
संस्कृत
C
शौरसैनी अपभ्रंश
D
मागधी

Question 15Single Answer

राजभाषा आयोग के प्रथम अध्यक्ष थे ?

A
बी. जी. खरे
B
राजा लक्ष्मण सिंह
C
प्रताप नारायण मिश्र
D
इंशाअल्ला खा

Question 16Single Answer

Read sentence to find out whether there is any grammatical error in it. The sentences are In three separate parts and each one is labelled (a), (b), (c) and (d). In that case, letter (d) will signify a ‘No error’ response.

A
He was in the temper
B
and refused
C
discuss the matter again
D
No error

Question 17Single Answer

A
A flower makes no garland
B
so we must do a thing together
C
in a unit for a good result
D
No error

Question 18Single Answer

A
My friend is a software engineer
B
and his wife is doctor
C
so they don’t have enough time for each other
D
No error

Question 19Single Answer

A
I don’t have much time that
B
I hear you in detail with verbosity
C
tell everything in nutshell
D
No error

Question 20Single Answer

A
The atmosphere is changing
B
so I have severe pain in my body
C
if you have any painkiller, please give it to me
D
No error

Question 21Single Answer

A
No one is without fault
B
because no one is God
C
and only God is fault free
D
No error

Question 22Single Answer

A
Your
B
clock is
C
one hour fast
D
No error

Question 23Single Answer

A
The lose of jobs
B
is regarded by some as an necessary evil
C
in the fight against infliation
D
No error

Question 24Single Answer

A
In science, the credit goes to a man
B
who convinces the world
C
not to the man to whom the idea first occurs
D
No error

Question 25Single Answer

A
It is only after
B
the match is over
C
that people realize how exciting it is
D
No error

Question 26Single Answer

A
Off the two
B
sisters, she
C
is better
D
No error

Question 27Single Answer

A
A interesting book
B
‘A Tale of two cities’
C
was written by Alexander Dumas
D
No error

Question 28Single Answer

A
I shall never
B
forget a good
C
deed you did to me, when I was in crisis
D
No error

Question 29Single Answer

A
Wisdom of Vikramaditya
B
solved many riddles
C
that people brought to him for solution
D
No error

Question 30Single Answer

A
News you broke to his wife
B
made her nervous
C
and she broke down
D
No error

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

Kurukshetra a journal on rural development is published by

A
Ministry of Finance
B
Ministry of Information and Broadcastin
C
Ministry of Rural Development
D
Planning Commission

Question 33Single Answer

Devaluation of a currency means

A
Fixing the value of the currency in conjuction with the movement in the value of a basket of predetermined currencies
B
Reduction in the value of a currency vis-à-vis major internationally traded currencies
C
Fixing the value of currency in multilateral consultaion with the IMF the World Bank and major trading partners
D
Permitting the currency to seek its worth in the international market

Question 34Single Answer

In India rural incomes are generally lower than the urban incomes, which of the following reasons account for this
1. a large number of farmers are illiterate and know little about scientific agriculture
2. prices of primary products are lower than those of manufactured products
3. Investments in agriculture has been low when compared to investment in industry

A
1 and 3
B
2 and 3
C
1 and 2
D
1,2 and 3

Question 35Single Answer

Which of the following programmes aims at the promotion of savings among rural women

A
Rashtriya Mahila Kosh
B
Indira Mahila Yojna
C
Jawahar Rozgar Yojna
D
Mahila Samridhi Yojna

Question 36Single 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 37Single 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 38Single 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 39Single 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 40Single 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 41Single 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.

Question 42Single 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 43Single 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 44Single Answer

The earlist manuscripts were written on

A
palm leaves
B
paper
C
wood
D
stones

Question 45Single Answer

What does BC and AD stands for?

A
Anno Domini and Before Common
B
Before Christ and Anno Domini
C
Anno Domini and Before Christ
D
None of the above

Question 46Single 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 47Single Answer

Which of the following numbers is irrational ?

A
√49
B
0.125
C
√2
D
22/7

Question 48Single Answer

356 x 936 – 356 x 836 = ?

A
35600
B
34500
C
9630
D
93600

Question 49Single 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 50Single Answer

What is (3^{^}{4} times 9^{^}{2}) ?

A
3⁶
B
3⁸
C
3¹⁰
D
9⁶

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General Studies

Question 51Single Answer

The grain size (USDA) of silt in soil ranges between :

A
0.2 mm to 0.5 mm
B
0.5 mm to 0.1 mm
C
0.1 mm to 0.05 mm
D
0.05 mm to 0.002 mm

Question 52Single Answer

What will be BOD, for a wastewater sample when 21 ml of sample is diluted to 300 ml in BOD bottle to determine dissolved oxygen .
[Given: Initial DO, = 10 mg/l; Five days later DO5 = 5 mg/l]

A
~ 5 mg/l
B
~ 25 mg/l
C
~ 71.4 mg/l
D
~75 mg/l

Question 53Single 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 54Single 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 55Single Answer

In which year the Chauri Revolt of Bihar took place ?

A
1842
B
1798
C
1784
D
1832
E
None of the above / More than one of the above

Question 56Single Answer

In which year was Orissa separated from Bihar ?

A
1936
B
1956
C
2000
D
1912
E
None of the above/ More than one of the above

Question 57Single Answer

During which movement 'Azad Dasta' was active in Bihar ?

A
Non-Cooperation Movement
B
Civil Disobedience Movement
C
Quit India Movement
D
Champaran Satyagraha
E
None of the above / More than one of the above

Question 58Single Answer

Who established a branch of Anushilan Samiti in Patna in 1913 AD ?

A
Ramanada Sinha
B
Satish Jha
C
Sachindra Nath Sanyal
D
Bipin Jha
E
None of the above / More than one of the above

Question 59Single Answer

In which year was Bihar divided to create Jharkhand ?

A
2000
B
2001
C
2004
D
2005
E
None of the above More than one of the above

Question 60Single Answer

Who invited Gandhiji to come Champaran ?

A
Raj Kumar Shukla
B
Rajendra Prasad
C
Jayaprakash Narayan
D
Krishna Sahay
E
None of the above / More than one of the above

Question 61Single Answer

Who had formed the Bihar Socialist Party in 1931 AD ?

A
Phulan Chand Tiwari and Rajendra Prasad
B
Phulan Prasad Varma and Jayaprakash Narayan
C
Raj Kumar Shukla and Swami Agnivesh
D
Swami Sahajananda and Swami Yogananda
E
None of the above More than one of the above

Question 62Single Answer

Who formed the 'Bihar Socialist Party' in 1931 ?

A
Phulan Prasad Varma
B
Swami Yoganand
C
Narhari Parikh
D
Dadabhai Naoroji
E
None of the above / More than one of the above

Question 63Single Answer

"Who said, 'India was a parrot unto itself'?

A
Malik Muhammad Joyce
B
Raskhan
C
Rich Khusrow
D
Rich Hasan

Question 64Single Answer

When was the Constituent Assembly of India formed?

A
1946
B
1947
C
1948
D
1950

Question 65Single 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 66Single 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 67Single Answer

Which is the longest river in India?

A
Yamuna
B
Ganges
C
Brahmaputra
D
Godavari

Question 68Single Answer

The Western Ghats are also known as:

A
Sahyadris
B
Vindhyas
C
Satpuras
D
Aravallis

Question 69Single Answer

What astronomical discovery was announced by astronomers in March 2026?

A
New planet in solar system
B
Discovery related to 1,900 light-years away (specific object)
C
Black hole merger
D
Exoplanet with life signs

Question 70Single Answer

On what date in March 2026 did Prime Minister Narendra Modi become India’s longest-serving head of government?

A
15 March
B
20 March
C
22 March
D
25 March

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
2^m – 1
B
m
C
m²
D
2^m

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

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

B)^C is equal to

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

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

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

A
(0, 0), (0, 1), (0, –1), (–1, 1), (–1, 0), (1, 0), (1, –1)
B
(–1, 1), (–1, 0), (0, 0), (0, –1), (0, 1), (1, 0), (1, –1)
C
(0, –1), (1, 0), (1, –1)
D
None of the above

Question 126Single Answer

Let A = {1, 2, 3}. The total number of distinct relations that can be defined over A, is

A
2⁹
B
6
C
8
D
None of these

Question 127Single Answer

Let A = {x, y, z} and B = {1, 2}. Then, the number of relations from A to B is

A
32
B
64
C
128
D
8

Question 128Single Answer

Let A = {x, y, z} and B = {a, b, c, d}. Then, which one of the following is not a relation from A to B?

A
{(x, a), (x, c)}
B
{(y, c), (y, b)}
C
{(z, a), (z, d)}
D
{(z, b), (y, b), (a, d)}

Question 129Single Answer

The relation R defined on the set of natural numbers as {(a, b): a differs from b by 3} is given by

A
{(4, 1), (5, 2), (6, 3),....}
B
{(1, 3), (2, 6), (3, 9),....}
C
{(1, 4), (2, 5), (3, 6),....}
D
None of the above

Question 130Single Answer

If R is a relation on a finite set A having (n – 1) elements, then the number of relations on A is

A
2^n-1
B
C
(n-1)²
D
(n-1)^n-1

Question 131Single Answer

A
{ 0, 1, 2, }
B
{ 0, -1 , -2 }
C
{ -2 , -1 ,0 , 1 , 2 , }
D
None of the above

Question 132Single Answer

Let R = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9),
(3, 12), (3, 6)} be a relation on the set A ={3, 6, 9, 12}
The relation is

A
an equivalence reation
B
reflexive symmetric
C
reflexive and trasitive
D
Only reflexive

Question 133Single Answer

A
reflexive and transitive
B
symmetric only
C
reflexive and symmetric
D
equivalence relation

Question 134Single Answer

A
reflexive and transitive
B
an equivalence relation
C
symmetric but neither reflexive nor transitive
D
neither reflexive nor symmetic but transitive

Question 135Single Answer

The relation ' has the same father as ' over the set of children is

A
Only reflexive
B
Only symmetric
C
Only transitive
D
an equivalence relation

Question 136Single Answer

If N be the set of natural numbers and define the relation R on N by R = {(1, 2)(2, 5), (3, 10)(4, 17)(5, 26)}. Then, the set builder form of R is

A
{(x, x²+ 1) | N and x < 6}
B
{(x, x² – 1) | N and x < 6}
C
{(x, 2x + 1) | N and x < 6}
D
None of the above

Question 137Single Answer

Let R be a relation in the set {1, 2, 3, 4} given by

R = {(1, 1), (1, 2), (2, 2), (4, 4), (1, 3), (3, 3), (3, 2)}.

Choose the correct option

A
R is reflexive
B
R is transitive
C
R is symmetric
D
R is reflexive and transitive but not symmetric

Question 138Single Answer

Which of the following functions is inverse of itself?

A
B
C
D
None of the above

Question 139Single Answer

If f(x) = e^x and g(x) = logex, then which of the following is true?

A
f{g(x)} g{f(x)}
B
f{g(x)} = g{f(x)}
C
f{g(x)} + g{f(x)} = 0
D
f{g(x)} – g{f(x)} = 1

Question 140Single Answer

The value of parameter a, for which the function f : R → R given by f(x) = 1 + ax, a

0 is the inverse of itself, is

A
–2
B
–1
C
1
D
2

Question 141Single Answer

Let f: (2, 3) → (0, 1) be defined by f(x) = x – [x]. Then, f–1(x) equals to

A
x – 2
B
x + 1
C
x – 1
D
x + 2

Question 142Single Answer

The greatest integer function f: R → R, given by f(x) = [x] is

A
one-one
B
onto
C
both one-one and onto
D
neither one-one nor onto

Question 143Single Answer

The number of all one-one functions from set

A = {1, 2, 3} to itself is

Question 144Single Answer

Question 145Single Answer

Question 146Single Answer

The number of 3-digit numbers divisible by 6, is ………….. .

A
149
B
166
C
50
D
151

Question 147Single Answer

A
-1
B
-2
C
D
None of these

Question 148Single Answer

Let N be the set of natural numbers and the relation R be defined such that R = {(x, y): y = 2x, x,

N}. Then,

A
R is a function
B
R is not a function
C
domain range and codomain is N
D
None of the above

Question 149Single Answer

If G represents the name of the function in below graph, then G is a/an

A
identity function
B
constant function
C
modulus function
D
None of the above

Question 150Single Answer

Let X = {–1, 0, 1}, Y = {0, 2} and a function f: X → Y defined by y = 2x4, is

A
one-one onto
B
one-one into
C
many-one onto
D
many-one into

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