Question for UPPSC Assistant Professor (Mathematics) 2026 - Quiz / Questions / MCQ

Objective Questions

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

Subjects : General Studies, Mathematics

Question Bank UPPSC Assistant Professor (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 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

What is Net National Product

A
the money value of final goods and services produced annually in the economy
B
the money value of annual service generation in the economy
C
the money value of tangible goods produced annually in the economy
D
The money value of tangible goods available in the economy

Question 7Single Answer

National income is the

A
net national product at market price
B
net national product at factor cost
C
net domestic product at market price
D
net domestic product at factor cost

Question 8Single Answer

Chelliah Committee of 1992 deals with the overhauling of our

A
financial system
B
tax system
C
patents and copyrights
D
Public sector undertakings

Question 9Single Answer

During which Five Year Plan was the annual growth rate of National Income the lowest

A
2^nd plan
B
3^rd plan
C
5^th plan
D
6^th plan

Question 10Single Answer

Which of the following taxes is a progressive tax

A
sales tax
B
custom tax
C
excise tax
D
income tax

Question 11Single 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 12Single Answer

A direct current I flows along the length of an infinitely long straight thin walled pipe, then the magnetic field is

A
uniform throughout the pipe not zero
B
zero only along the axis of the pipe
C
zero at any point inside the pipe
D
maximum at the centre and minimum at the edge

Question 13Single 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 14Single Answer

In the electrolysis of acidulated water, it is desired to obtain 1.12 cc of hydrogen per second under STP condition. The current to be passed is

A
1.93 A
B
9.65 A
C
19.3 A
D
0.965 A

Question 15Single 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 16Single Answer

Which of the following is not a green - house gas ?

A
Water vapour
B
Carbon monoxide
C
Methane
D
Oxygen

Question 17Single 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 18Single 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 19Single 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 20Single 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 21Single 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 22Single Answer

Uttar Pradesh is located in which part of India?

A
Western India
B
Southern India
C
Northern India
D
Eastern India

Question 23Single Answer

What is the capital of Uttar Pradesh?

A
Kanpur
B
Lucknow
C
Prayagraj
D
Varanasi

Question 24Single Answer

Uttar Pradesh was formed in which year (as United Provinces renamed later)?

A
1950
B
1947
C
1937
D
1960

Question 25Single Answer

Uttar Pradesh is the most populous state of India?

A
Not applicable
B
False
C
Partially true
D
True

Question 26Single Answer

Uttar Pradesh shares its boundary with how many Indian states?

Question 27Single Answer

What new authority was granted to Mukhiyas in Uttar Pradesh in May 2026?

A
Approve schemes up to ₹5 lakh
B
Approve schemes up to ₹20 lakh
C
Approve schemes up to ₹15 lakh
D
Approve schemes up to ₹10 lakh

Question 28Single Answer

Which expressway was inaugurated as a major infrastructure project in Uttar Pradesh in May 2026?

A
Bundelkhand Expressway
B
Purvanchal Expressway
C
Ganga Expressway
D
Agra-Lucknow Expressway

Question 29Single Answer

The Indian Navy recently received its second indigenous Diving Support Vessel (DSV). What is its name?

A
Nistar
B
Nipun
C
INS Vikrant
D
INS Arihant

Question 30Single Answer

The Public Examinations (Prevention of Unfair Means) Amendment Bill, 2026, was passed by the Rajya Sabha on which date?

A
27 July 2026
B
29 July 2026
C
31 July 2026
D
30 July 2026

Mathematics

Question 31Single 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 32Single Answer

A
B
C
D
None of these

Question 33Single 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 34Single 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 35Single 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 36Single Answer

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

A
15
B
14
C
16
D
17

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

If A = (–3, 5) and B = [–7, 9], then

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

Question 46Single Answer

In a college

part girls and

part boys attended a social camp. How many parts in the collegs students attended the camp ?

A
B
C
D
E
None of the above

Question 47Single Answer

The sum of two number is 16 and their difference is 2. What is the product to both numbers ?

A
35
B
56
C
56
D
72

Question 48Single Answer

What are the positive factors of 160 .

A
6
B
8
C
5
D
12

Question 49Single Answer

What is the value of (51 + 52 + 53 ........100) ?

A
1325
B
5050
C
3775
D
3325

Question 50Single Answer

What is the sum of all natural numbers that come in the between 1 to 100, which a multiple of 7 ?

A
735
B
745
C
675
D
705

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Mathematics

Question 51Single Answer

What is the unit digit of 279 + 167 × 342 ?

Question 52Single Answer

Which of the given values is completely divisible by 15 ?

A
2365
B
1375
C
4365
D
2275

Question 53Single Answer

For which value of M, the divisor 34M fully divisible by 12 ?

Question 54Single Answer

If 432p1 is completely divisiable 34M fully divisiable by 12 ?

Question 55Single Answer

Which is the smallest number to be added to 100, so that the resulting number is completely divisible by 6 ?

Question 56Single Answer

The Euclidean space ( mathbb{R}ⁿ ) is a vector space with a norm defined as ?

A
( ||x|| = sum_{i=1}^{n} |x_i| )
B
( ||x|| = sqrt{ sum_{i=1}^{n} x_i²} )
C
( ||x|| = max |x_i| )
D
( ||x|| = min |x_i| )

Question 57Single Answer

A function ( f:

mathbb{R}ⁿ

mathbb{R} ) is continuous at a point ( a ) if ?

A
( lim_{x to a} f(x) = f(a) )
B
( f(a) = 0 )
C
( f ) is differentiable at ( a )
D
( f ) is bounded near ( a )

Question 58Single Answer

The derivative of ( f:

mathbb{R}ⁿ

mathbb{R} ) at a point ( a ) is ?

A
A scalar
B
A vector in ( mathbb{R}ⁿ )
C
A matrix of partial derivatives
D
Always zero

Question 59Single Answer

The Chain Rule in several variables allows you to compute ?

A
The gradient of a sum
B
Derivative of a composition of functions
C
Limit of a function
D
Integral of a function

Question 60Single Answer

If ( f ) has continuous second-order partial derivatives, then ?

A
Mixed partial derivatives are equal
B
Partial derivatives are zero
C
( f ) is linear
D
( f ) is discontinuous

Question 61Single Answer

Taylor's theorem in multiple variables expresses a function as ?

A
A linear function
B
A polynomial plus remainder
C
Only a constant term
D
A series of integrals

Question 62Single Answer

The Inverse Function Theorem guarantees ?

A
Existence of an inverse function locally
B
Differentiability everywhere
C
Integrability of the function
D
Uniqueness of solutions globally

Question 63Single Answer

The Implicit Function Theorem allows ?

A
To solve for one variable in terms of others
B
To integrate functions
C
To compute limits
D
To prove continuity

Question 64Single Answer

Lebesgue outer measure is ?

A
Always zero
`
B
A way to assign "size" to sets
C
Only defined for intervals
D
Equal to length for non-measurable sets

Question 65Single Answer

A set ( E

subset

mathbb{R} ) is measurable if ?

A
( m^*(A) = m^*(A cap E) + m^*(A cap E^c) ) for all ( A subset mathbb{R} )
B
Its length is finite
C
It is open
D
It is closed

Question 66Single Answer

A function ( f:

mathbb{R}

mathbb{R} ) is Lebesgue measurable if ?

A
Its preimage of any interval is measurable
B
It is continuous
C
It is differentiable
D
It is bounded

Question 67Single Answer

Borel measurability refers to ?

A
Measurable sets generated by open sets
B
Only intervals
C
Only closed sets
D
Non-measurable sets

Question 68Single Answer

A non-negative measurable function can be integrated using ?

A
Riemann integral only
B
Lebesgue integral
C
Derivative
D
Maximum function

Question 69Single Answer

The integral of a series of non-negative functions satisfies ?

A
( int sum f_n= sum int f_n )
B
Only finite sums
C
Inequality in reverse
D
Does not exist

Question 70Single Answer

A function of bounded variation is one whose total variation is ?

A
Infinite
B
Finite
C
Zero
D
Undefined

Question 71Single Answer

A group G is called simple if?

A
It has no subgroups
B
All subgroups are cyclic
C
It has no normal subgroups other than {e} and G
D
It is abelian

Question 72Single Answer

The composition series of a finite group is?

A
Any chain of subgroups
B
A chain of subgroups where each is normal in the next and factor groups are simple
C
A chain of subgroups where all are abelian
D
A chain of subgroups where all are cyclic

Question 73Single Answer

Jordan-Hölder theorem states that?

A
Every group is abelian
B
All subgroups of a group are normal
C
Composition factors of a finite group are unique up to isomorphism and order
D
Every simple group is cyclic

Question 74Single Answer

A group G is called solvable if?

A
It is abelian
B
Its derived series terminates at the identity subgroup
C
It has a prime order
D
It has a cyclic subgroup

Question 75Single Answer

A group G is nilpotent if?

A
It is cyclic
B
It has order a prime number
C
It has a central series terminating in G
D
It is simple

Question 76Single Answer

Cauchy's theorem for finite groups states that?

A
If a prime p divides |G|, then G has an element of order p
B
Every group has a normal subgroup
C
Every group is cyclic
D
Every subgroup is normal

Question 77Single Answer

Class equation of a finite group G is given by?

A
|G| = sum of orders of all elements
B
|G| = |Z(G)| + sum of indices of centralizers of representatives of non-central conjugacy classes
C
|G| = number of subgroups
D
|G| = product of orders of elements

Question 78Single Answer

The direct product of groups G and H is?

A
A group with elements (g,h) and operation component-wise
B
Always abelian
C
Always simple
D
Intersection of G and H

Question 79Single Answer

Sylow theorems are used to?

A
Find normal subgroups of prime order
B
Solve polynomial equations
C
Determine if group is abelian
D
Determine existence and number of p-subgroups in finite groups

Question 80Single Answer

Structure theorem for finite abelian groups states that?

A
Every finite abelian group is cyclic
B
Every finite abelian group is a direct product of cyclic groups of prime power order
C
Every finite abelian group is simple
D
Every finite abelian group has order a prime

Question 81Single Answer

An integral domain is?

A
A ring with zero divisors
B
A ring where every ideal is prime
C
A commutative ring with identity and no zero divisors
D
A non-commutative ring

Question 82Single Answer

A maximal ideal M of a ring R is?

A
Not contained in any other proper ideal
B
Contained in every ideal
C
Always prime
D
Not prime

Question 83Single Answer

A quotient ring R/I is a field if?

A
I is prime
B
I is maximal
C
R is commutative
D
R has no zero divisors

Question 84Single Answer

A Euclidean ring allows?

A
Infinite units
B
Only factorization
C
Only maximal ideals
D
Division algorithm with a norm function

Question 85Single Answer

Polynomial ring R[x] is?

A
Always Noetherian
B
Always a field
C
Always Euclidean
D
A ring of polynomials over R with usual addition and multiplication

Question 86Single Answer

Which of the following sets is finite?

A
Set of prime numbers less than 50
B
Set of integers
C
Set of natural numbers
D
Set of rational numbers

Question 87Single Answer

A set is countable if it is?

A
Finite only
B
Empty only
C
Uncountable only
D
Finite or countably infinite

Question 88Single Answer

The set of integers is?

A
Finite
B
Countably infinite
C
Uncountable
D
Empty

Question 89Single Answer

The set of rational numbers is?

A
Finite
B
Countably infinite
C
Uncountable
D
Neither countable nor uncountable

Question 90Single Answer

The set of real numbers is?

A
Finite
B
Uncountable
C
Countably infinite
D
Empty

Question 91Single Answer

Which interval is uncountable?

A
{1,2,3}
B
Natural numbers
C
Integers
D
[0,1]

Question 92Single Answer

If A ⊆ B and B ⊆ A, then?

A
A ∩ B = ∅
B
A ∪ B = ∅
C
A ≠ B
D
A = B

Question 93Single Answer

The union A ∪ B contains elements that belong to?

A
A only
B
A or B or both Correct
C
Both A and B only
D
B only

Question 94Single Answer

The intersection A ∩ B consists of elements belonging to?

A
Both A and B
B
B but not A
C
A but not B
D
Neither A nor B

Question 95Single Answer

The difference A − B consists of elements that are?

A
In A but not in B
B
In B but not in A
C
In both A and B
D
Outside A and B

Question 96Single Answer

The complement of the universal set U is?

A
U
B
U × U
C
{0}
D
∅

Question 97Single Answer

The complement of the empty set is?

A
Universal set
B
{0}
C
∅
D
Singleton set

Question 98Single Answer

According to De Morgan's law, (A ∪ B)ᶜ equals?

A
Aᶜ ∪ Bᶜ
B
A ∩ B
C
Aᶜ ∩ Bᶜ
D
A ∪ B

Question 99Single Answer

According to De Morgan's law, (A ∩ B)ᶜ equals?

A
Aᶜ ∪ Bᶜ
B
Aᶜ ∩ Bᶜ
C
A ∩ B
D
A − B

Question 100Single Answer

If A ∩ B = ∅, then A and B are called?

A
Equivalent sets
B
Infinite sets
C
Universal sets
D
Disjoint sets

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

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