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Objective Questions

Latest HPSC Assistant Professor Mathematics Exam Question (Objective Questions), MCQ in English

Subjects : Mathematics, General Knowledge, Reasoning

Question Bank HPSC Assistant Professor Mathematics Exam (Screening Test) - English

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Mathematics

Question 1Single 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 2Single Answer

A
B
C
D
None of these

Question 3Single 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 4Single 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 5Single 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 6Single Answer

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

A
15
B
14
C
16
D
17

Question 7Single 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 8Single 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 9Single 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 10Single 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 11Single 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 12Single 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 13Single 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 14Single 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 15Single Answer

If A = (–3, 5) and B = [–7, 9], then

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

Question 16Single 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 17Single Answer

Combine terms: 12a + 26b - 4b – 16a .

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

Question 18Single Answer

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

A
25.30
B
25.5
C
25.00
D
12.25

Question 19Single Answer

60 Times of 8 Equals to

A
480
B
300
C
250
D
400

Question 20Single 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 21Single 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 22Single 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 23Single Answer

Question 24Single 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 25Single Answer

What is the Next Prime Number after 7 ?

A
13
B
12
C
14
D
11

Question 26Single Answer

If A and B are two given sets, then A

B)^C is equal to

Question 27Single Answer

121 Divided by 11 is

A
11
B
10
C
19
D
18

Question 28Single 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 29Single Answer

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

Question 30Single 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 31Single 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 32Single Answer

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

Question 33Single Answer

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

Question 34Single Answer

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

Question 35Single 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 36Single 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 37Single 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 38Single 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 39Single 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 40Single 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 41Single 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 42Single 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 43Single 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 44Single 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 45Single 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 46Single Answer

Question 47Single 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 48Single 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 49Single 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 50Single 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)

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Mathematics

Question 51Single 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 52Single 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 53Single 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 54Single 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 55Single 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 56Single 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 57Single 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 58Single 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 59Single 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 60Single 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 61Single Answer

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

Question 62Single 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 63Single Answer

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

Question 64Single Answer

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

Question 65Single 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 66Single 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 67Single 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 68Single Answer

Which of the following functions is inverse of itself?

A
B
C
D
None of the above

Question 69Single 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 70Single 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 71Single 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 72Single 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 73Single Answer

The number of all one-one functions from set

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

Question 74Single Answer

Question 75Single Answer

Question 76Single Answer

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

A
149
B
166
C
50
D
151

Question 77Single Answer

A
-1
B
-2
C
D
None of these

Question 78Single 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 79Single 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 80Single 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 81Single 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 82Single 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 83Single Answer

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

Question 84Single 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 85Single 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 86Single 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 87Single Answer

Question 88Single 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 89Single Answer

A
B
C
D
None of these

Question 90Single 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

Reasoning

Question 91Single 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 92Single 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 93Single 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 94Single 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 95Single 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

General Knowledge

Question 96Single Answer

In ancient times Haryana was known as ........

A
Brahmawata
B
Gujarat
C
Kurukshetra
D
Delhi

Question 97Single Answer

By what name was the state of Haryana known in ancient times ?

A
Brahmavrata Pradesh
B
Brahmashri Pradesh
C
Brahma Ki Uttawedi
D
All of the above

Question 98Single Answer

The ancient and sacred river of Haryana is…………… .

A
Saraswati
B
Drishadvati
C
Ganga
D
Both (a) and (b)

Question 99Single Answer

Which organization developed the "Bharatpol" portal?

A
Intelligence Bureau
B
Central Bureau of Investigation
C
National Investigation Agency
D
Enforcement Directorate

Question 100Single Answer

Who is the President of Singapore who visited India from?

A
Bongbong Marcos
B
Lee Hsien Loong
C
Tharman Shanmugaratnam
D
Sam Altman

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Latest HPSC Assistant Professor Mathematics Exam Question (Objective Questions), MCQ in English

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