Question for UPPSC GIC Lecturer (Mathematics) 2026 - Quiz / Questions / MCQ

Objective Questions

Latest UPPSC GIC Lecturer Mathematics Exam Question (Objective Questions), MCQ in English

Subjects : General Studies, Mathematics

Question Bank UPPSC GIC Lecturer Mathematics Prelims Exam - English

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General Studies

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 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 5Single 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 6Single 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 7Single Answer

Passage :

Direction: Study the given information carefully and answer the given question
P, Q, R, S, T, V, X and Y are seated in a straight line facing North. P sits fourth to the left of V. V sits either sixth from the left end of the line or fourth from the right end of the line. S sits second to the right of R. R is not an immediate neighbor of V. T and Q are immediate neighbours of each other but neither T not Q sits at extreme ends of the line. Only one person sits between T and X. X does not sit at the extreme end of the line

According to the passage, what is the main purpose of data protection laws ?

A
To ensure that foreign countries invest in research for drugs to treat diseases like TB
B
To attract Indian scientists back to the country
C
To prevent misuse of research to make profit by competing companies
D
To make clinical trials more acceptable to the public
E
None of these

Question 8Single Answer

‘Gram’ is relatd to ‘Mass’ in the same way as ‘Centimetre’ is related to

A
Area
B
Volume
C
Length
D
Sound
E
Energy

Question 9Single Answer

'Mustard' is related to 'Seed' in the same way as 'Carrot' is related to

A
Fruit
B
Stem
C
Flower
D
Root
E
None of these

Question 10Single Answer

Which of the following pairs of words have the same relationship as Fan : Heat?

A
Water : Drink
B
Light : Night
C
Teach : Student
D
Air : Breathe
E
Food : Hunger

Question 11Single Answer

'Radish' is related to 'Root', in the same way as 'Brinjal' is related to

A
Fruit
B
Stem
C
Flower
D
Root
E
None of these

Question 12Single Answer

'Jackal' is related to 'Carnivorous', in the same way as 'Goat' is related to

A
Omnivorous
B
Carnivorous
C
Herbivorous
D
Multivorous
E
None of these

Question 13Single Answer

Which of the following pairs has similar relationship as Run : Race?

A
Party : Dance
B
Study : Book
C
Lecture : Study
D
Enjoy : Journey
E
None of these

Question 14Single 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 15Single Answer

Which of the following numbers is irrational ?

A
√49
B
0.125
C
√2
D
22/7

Question 16Single Answer

356 x 936 – 356 x 836 = ?

A
35600
B
34500
C
9630
D
93600

Question 17Single 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 18Single Answer

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

A
3⁶
B
3⁸
C
3¹⁰
D
9⁶

Question 19Single Answer

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

Question 20Single Answer

Convert 0.6 into fraction ?

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

Question 21Single 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 22Single Answer

When Uttar Pradesh got it officially as statehood ?

A
24 January, 1950
B
26 January, 1952
C
1 January, 1956
D
18 February, 1957

Question 23Single Answer

How many districts are there in Uttar Pradesh

A
60
B
57
C
75
D
87

Question 24Single Answer

What are the official languages of Uttar Pradesh ?

A
Hindi & Urdu
B
Only Hindi
C
Only Urdu
D
Kumaoni

Question 25Single Answer

How many members of Lok Sabha from Uttar Pradesh ?

A
56
B
78
C
80
D
51

Question 26Single Answer

How many members of Rajya Sabha from Uttar Pradesh ?

A
45
B
51
C
31
D
77

Question 27Single Answer

What is the state flower of Uttar Pradesh ?

A
Lily
B
Rose
C
Palash
D
Sunflower

Question 28Single Answer

What is state sport of Uttar Pradesh ?

A
Field Hockey
B
Cricket
C
Football
D
Swimming

Question 29Single Answer

How many total cities / towns in Uttar Pradesh ?

A
567
B
450
C
689
D
510

Question 30Single Answer

What is state dance of Uttar Pradesh ?

A
Kathak
B
Rauf
C
Kathakali
D
Bharat Natyam

Question 31Single Answer

What is state tree of Uttar Pradesh ?

A
Neem
B
Peepal
C
Ashok
D
Mango

Question 32Single Answer

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

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

Question 33Single Answer

When was the Constituent Assembly of India formed?

A
1946
B
1947
C
1948
D
1950

Question 34Single Answer

Which is the longest river in India?

A
Yamuna
B
Ganges
C
Brahmaputra
D
Godavari

Question 35Single Answer

The Western Ghats are also known as:

A
Sahyadris
B
Vindhyas
C
Satpuras
D
Aravallis

Question 36Single Answer

Which day is observed on October 1, 2025 to promote elderly care and respect?

A
World Heart Day
B
International Day of Older Persons
C
World Habitat Day
D
International Coffee Day

Question 37Single Answer

Which international day is observed on October 1, 2025 to raise awareness about habitat and urban issues?

A
World Habitat Day
B
World Animal Day
C
International Day of Non-Violence
D
World Teachers' Day

Question 38Single Answer

India's first indigenous 5G mmWave module was developed by which organization on October 1, 2025?

A
DRDO
B
C-DOT
C
BEL
D
ISRO

Question 39Single Answer

The "PM Vishwakarma Scheme" was launched on October 1, 2025, targeting which group?

A
Farmers
B
Artisans and craftsmen
C
Students
D
Senior citizens

Question 40Single Answer

Which international day is observed on October 1, 2025, to honor Mahatma Gandhi?

A
Gandhi Jayanti
B
International Day of Non-Violence
C
World Peace Day
D
Human Rights Day

Mathematics

Question 41Single 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 42Single Answer

A
B
C
D
None of these

Question 43Single 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 44Single 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 45Single 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 46Single Answer

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

A
15
B
14
C
16
D
17

Question 47Single 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 48Single 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 49Single 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 50Single 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

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Mathematics

Question 51Single 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 52Single 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 53Single 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 54Single 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 55Single Answer

If A = (–3, 5) and B = [–7, 9], then

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

Question 56Single 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 57Single Answer

Combine terms: 12a + 26b - 4b – 16a .

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

Question 58Single Answer

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

A
25.30
B
25.5
C
25.00
D
12.25

Question 59Single Answer

60 Times of 8 Equals to

A
480
B
300
C
250
D
400

Question 60Single 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 61Single 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 62Single 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 63Single Answer

Question 64Single 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 65Single Answer

What is the Next Prime Number after 7 ?

A
13
B
12
C
14
D
11

Question 66Single Answer

If A and B are two given sets, then A

B)^C is equal to

Question 67Single Answer

121 Divided by 11 is

A
11
B
10
C
19
D
18

Question 68Single 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 69Single Answer

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

Question 70Single 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 71Single 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 72Single Answer

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

Question 73Single Answer

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

Question 74Single Answer

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

Question 75Single 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 76Single 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 77Single 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 78Single 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 79Single 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 80Single 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 81Single 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 82Single 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 83Single 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 84Single 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 85Single 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 86Single Answer

Question 87Single 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 88Single 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 89Single 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 90Single 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 91Single 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 92Single 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 93Single 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 94Single 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 95Single 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 96Single 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 97Single 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 98Single 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 99Single 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 100Single 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 101Single Answer

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

Question 102Single 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 103Single Answer

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

Question 104Single Answer

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

Question 105Single 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 106Single 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 107Single 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 108Single Answer

Which of the following functions is inverse of itself?

A
B
C
D
None of the above

Question 109Single 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 110Single 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 111Single 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 112Single 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 113Single Answer

The number of all one-one functions from set

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

Question 114Single Answer

Question 115Single Answer

Question 116Single Answer

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

A
149
B
166
C
50
D
151

Question 117Single Answer

A
-1
B
-2
C
D
None of these

Question 118Single 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 119Single 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 120Single 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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