Question for SSB Head Constable 2026 - Quiz / Questions / MCQ

Objective Questions

Latest SSB Head Constable Exam Question (Objective Questions), MCQ in English

Subjects : General Knowledge, Numerical Aptitude, General English, General Reasoning, Mathematics

Question Bank SSB Head Constable Communication (Mathematics) Exam - English

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General Knowledge

Question 1Single Answer

Yojna a weekly journal

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

Question 2Single 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 3Single 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 4Single 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 5Single 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 6Single 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 7Single 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 8Single 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 9Single Answer

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

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

Question 10Single Answer

What was the real name of Amir Khusro?

A
Muhammad Hasan
B
Muhammad Hussain
C
Muhammad Khusrow
D
Muhammad Mine

Question 11Single Answer

When was the Constituent Assembly of India formed?

A
1946
B
1947
C
1948
D
1950

Question 12Single 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 13Single 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 14Single Answer

Who is known as the "Missile Man of India"?

A
Dr. Homi J. Bhabha
B
Dr. Vikram Sarabhai
C
Dr. APJ Abdul Kalam
D
Dr. Satish Dhawan

Question 15Single Answer

In a centrally planned economy, what is the primary mechanism for resource allocation?

A
Market prices
B
Government directives
C
Consumer preferences
D
Private enterprise

Question 16Single Answer

What was launched by MoSPI on Statistics Day (July 1, 2026)?

A
New GDP series
B
Four SDG progress reports
C
Unemployment White Paper
D
Census 2026 preliminary data

Question 17Single Answer

In which state was a new natural gas reserve discovered, as highlighted in July 2026 current affairs compilations?

A
Gujarat
B
Maharashtra
C
Rajasthan
D
Andhra Pradesh

Question 18Single Answer

What is the primary purpose of the JANANI Digital Platform?

A
E-commerce for SHGs
B
Agricultural loan distribution
C
Digital education for rural areas
D
Maternal and Child Health tracking

Question 19Single Answer

What notable achievement did India record in the UN SDG Index around mid-2026?

A
Dropped out of top 50
B
Lowest rank in Asia
C
No change in ranking
D
Highest-ever rank

Question 20Single Answer

When and where did the FIFA World Cup 2026 begin?

A
July 1, 2026, in Europe
B
June 11, 2026, in North America
C
May 2026, in South America
D
August 2026, in Asia

Numerical Aptitude

Question 21Single 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 22Single Answer

Which of the following numbers is irrational ?

A
√49
B
0.125
C
√2
D
22/7

Question 23Single Answer

356 x 936 – 356 x 836 = ?

A
35600
B
34500
C
9630
D
93600

Question 24Single 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 25Single Answer

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

A
3⁶
B
3⁸
C
3¹⁰
D
9⁶

Question 26Single Answer

If 3⁴X^-2 = 729, then find the value of X.

Question 27Single Answer

Convert 0.6 into fraction ?

A
3/5
B
2/3
C
4/5

Question 28Single Answer

The no. plate of a bus had peculiarity. The bus number was a perfect square. It was also a perfect square when the plate numbers were reversed. The bus company had only five hundred buses numbered from 1 to 500. What was the number ?

A
169
B
36
C
196
D
Can not say

Question 29Single Answer

If a and b are positive integers, such that ab = 125, then (a-b)^a+b-4= ?

A
16
B
25
C
28
D
30

Question 30Single Answer

If x^*y = x² + y² – xy, then value of 9^*11 is

A
93
B
103
C
60.5
D
121

General English

Question 31Single Answer

Passage :

Direction : Question below has two blanks, each blank indicting that some thing has been omitted. Choose the word for each blank which best fits the meaning of the sentence as a whole.

The Finance Department has ……………a centralized online databank system for all statutory government bodies to …………an eye on their assets and liabilities.

A
presented , stay
B
introduced , keep
C
announce , make
D
created , let
E
proclaimed , hold

Question 32Single Answer

Passage :

Direction : The five items in this section consists of a word or group of words followed by four words as (a), (b), (c) and (d). Select the word which is nearly opposite to the meaning of the original word or group of words and mark your response as (a), (b), (c) and (d), as the case may be, in your Answer Sheet.

Assets

A
liabilities
B
responsibilities
C
estates
D
profits

Question 33Single Answer

Passage :

Direction : In the question, out of the four alternatives, choose the word which is opposite in meaning to the given word and click the button corresponding to it

Affidavit

A
Affirmation
B
Slander
C
Oath
D
Testimony

Question 34Single Answer

Passage :

Direction: In the following question, out of the four alternatives, choose the word which is opposite in meaning to the given word and click the button corresponding to it

Hollow

A
Alveolate
B
Cleft
C
Cavernous
D
Solid

Question 35Single Answer

Passage :

Directions: In the following question, out of the four alternatives, choose the word which is opposite in meaning to the given word and click the button corresponding to it

Cosset

A
Ignoreb
B
Close
C
Caress
D
Fondle

Question 36Single Answer

Passage :

Directions: In the following question, out of the four alternatives, choose the word which is opposite in meaning to the given word and click the button corresponding to it

Ogle

A
Leer
B
Gaze
C
Ignore
D
Gawk

Question 37Single Answer

Passage :

Directions:In the following question, out of the four alternatives, choose the word which is opposite in meaning to the given word and click the button corresponding to it

Intrinsic

A
Elemental
B
Innate
C
Connate
D
Acquired

Question 38Single Answer

Passage :

Direction : In the following question, out of the four alternatives, choose the word which is opposite in meaning to the given word and click the button corresponding to it

Coalesce

A
Separate
B
Adhere
C
Cleave
D
Amalgamate

Question 39Single Answer

Passage :

Directions: In the following question, out of the four alternatives, choose the word which is opposite in meaning to the given word and click the button corresponding to it

Loiter

A
lag
B
Hasten
C
Amble
D
Loii

Question 40Single Answer

Passage :

Direction : Question below has two blanks, blank indicating that something has been omitted. Choose the set of words for blank which best fits the meaning of the sentence as a whole.

The protests were......... at ......... awareness among the elite and the educated.

A
held, generating
B
aimed, creating
C
targeted, awakening
D
focused, building
E
concentrated, producing

General Reasoning

Question 41Single 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 ?

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 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 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 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 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.)

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 45Single Answer

Passage :

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 46Single 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 in each of the given words, each of the consonant is changed to previous letter and each vowel is changed to next letter in the English alphabetical series, in how many words thus formed will no vowels appear?

A
None
B
One
C
Two
D
Three
E
More than three

Question 47Single Answer

Passage :

Direction : Following question is based on five words given below:
BRU LEGINKCATOWN
(The new words formed after performing the mentioned operations may or may not necessarily be meaningful English words)

If the third alphabet in each of the words is changed to the 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 48Single Answer

Passage :

If the position of the first and the second alphabets of each of the words are interchanged, which of the following will form a meaningful English word?

A
Both CAT and OWN
B
Both BRU and INK
C
Only CAT
D
Only INK
E
Only LEG

Question 49Single Answer

Passage :

Direction: Following question is based on five words given below:
BRU LEGINKCATOWN
(The new words formed after performing the mentioned operations may or may not necessarily be 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 exactly in the middle of the five words?

A
OWN
B
LEG
C
BRU
D
CAT
E
INK

Question 50Single Answer

Passage :

Direction: Following question is based on five words given below:
BRU LEGINKCATOWN
(The new words formed after performing the mentioned operations may or may not necessarily be meaningful English words)

If in each of the given words, each of the consonants is changed to previous letter and each vowel is changed to next letter in the English alphabetical series, in how many words thus formed will the same alphabet appear twice?

A
None
B
One
C
Two
D
Three
E
More than three

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Mathematics

Question 51Single 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 52Single Answer

A
B
C
D
None of these

Question 53Single 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 54Single 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 55Single 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 56Single Answer

The number of non-empty subsets of the set{1, 2, 3, 4} is

A
15
B
14
C
16
D
17

Question 57Single 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 58Single 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 59Single 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 60Single 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 61Single 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 62Single 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 63Single 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 64Single 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 65Single Answer

If A = (–3, 5) and B = [–7, 9], then

A
A = B
B
A B
C
B A
D
None of these

Question 66Single 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 67Single Answer

Combine terms: 12a + 26b - 4b – 16a .

A
4a + 22b
B
-28a + 30b
C
-4a + 22b
D
28a + 30b

Question 68Single Answer

The average of first 50 natural numbers is ………… .

A
25.30
B
25.5
C
25.00
D
12.25

Question 69Single Answer

60 Times of 8 Equals to

A
480
B
300
C
250
D
400

Question 70Single 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 71Single 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 72Single 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 73Single Answer

Question 74Single 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 75Single Answer

What is the Next Prime Number after 7 ?

A
13
B
12
C
14
D
11

Question 76Single Answer

If A and B are two given sets, then A

B)^C is equal to

Question 77Single Answer

121 Divided by 11 is

A
11
B
10
C
19
D
18

Question 78Single 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 79Single Answer

A
{3, 4, 10}
B
{2, 8, 10}
C
{4, 5, 6}
D
{3, 5, 14}

Question 80Single 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 81Single 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 82Single Answer

A
A = B
B
B = C
C
A = C
D
None of these

Question 83Single Answer

A
equal
B
disjoint
C
either equal or disjoint
D
none of the above

Question 84Single Answer

A
{–i, i}
B
{–1, 1}
C
{–1, 1, i, –i}
D
None of these

Question 85Single 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 86Single 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 87Single 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 88Single 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 89Single 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 90Single 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 91Single 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 92Single 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 93Single 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 94Single 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 95Single 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 96Single Answer

Question 97Single 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 98Single 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 99Single 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 100Single 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 101Single 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 102Single 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 103Single 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 104Single 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 105Single 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 106Single 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 107Single 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 108Single 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 109Single 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 110Single 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 111Single Answer

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

Question 112Single 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 113Single Answer

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

Question 114Single Answer

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

Question 115Single 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 116Single 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 117Single 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 118Single Answer

Which of the following functions is inverse of itself?

A
B
C
D
None of the above

Question 119Single 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 120Single 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 121Single 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 122Single 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 123Single Answer

The number of all one-one functions from set

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

Question 124Single Answer

Question 125Single Answer

Question 126Single Answer

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

A
149
B
166
C
50
D
151

Question 127Single Answer

A
-1
B
-2
C
D
None of these

Question 128Single 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 129Single 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 130Single 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

Question 131Single Answer

Let f : R→ R be a function defined by

A
one-one onto
B
one-one but not onto
C
onto but not one-one
D
None of the above

Question 132Single Answer

The mapping f: N→ N given by f(n) = 1 n², n € N where, N is the set of natural numbers is

A
one-one and onto
B
onto but not one-one
C
one-one but not onto
D
neither one-one nor onto

Question 133Single Answer

A
B
C
[ 0 , 1 ]
D
None of the above

Question 134Single Answer

A relation R in a set A is called _______, if (a₁, a₂) ∈ R implies (a₂, a₁) ∈ R, for all a₁, a₂ ∈ A .

A
symmetric
B
transitive
C
equivalence
D
non-symmetric

Question 135Single Answer

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

Question 136Single Answer

Domain of f(x) = sin–1[2 – 4x2] ([.] denotes the greatest integer function) is

A
[–1, 1]
B
(–2, 2)
C
D
None of the above

Question 137Single Answer

Question 138Single Answer

If f(x) = [x²] – [x]², where [.] denotes the greatest integer function and x € [0, 2] then the set of values of f(x) is

A
{–1, 0}
B
{–1, 0, 1}
C
{0}
D
{0, 1, 2}

Question 139Single Answer

A
B
C
D
None of these

Question 140Single Answer

If f: A → B and g: B → C be two functions, then the composition of functions f and g is given by

A
gof(x) = g(f(x))
B
gof(x) = g(x)f(x)
C
fog(x) = g(f(x))
D
None of the above

Question 141Single Answer

If the function gof is defined an onto, then

A
neither f nor g is onto
B
f and g both are necessarily onto
C
f must be onto
D
None of the above

Question 142Single Answer

If f(x) = 2x + 7 and g (x) = x2 + 7, x

R, then which value of x will satisfy fog (x) = 25?

A
–1, 1
B
–2, 2
C
D
None of these

Question 143Single Answer

A
3
B
1
C
D
None of these

Question 144Single Answer

Question 145Single Answer

Question 146Single Answer

A
Zero
B
1
C
-1
D

Question 147Single Answer

a + ib > c + id can be explained only when

A
b = 0, c = 0
B
b = 0, d = 0
C
a = 0, c = 0
D
a = 0, d = 0

Question 148Single Answer

If 3x² + 4x + 2 = 0, then equation has

A
real roots
B
imaginary roots
C
one real and one imaginary root
D
distinct real roots

Question 149Single Answer

Question 150Single Answer

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