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

Objective Questions

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

Subjects : General Studies, Mathematics

Question Bank UPPSC Polytechnic Lecturer (Mathematics) Exam Paper 2 - 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

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 11Single Answer

How many districts are there in Uttar Pradesh

A
60
B
57
C
75
D
87

Question 12Single Answer

What are the official languages of Uttar Pradesh ?

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

Question 13Single Answer

How many members of Lok Sabha from Uttar Pradesh ?

A
56
B
78
C
80
D
51

Question 14Single Answer

How many members of Rajya Sabha from Uttar Pradesh ?

A
45
B
51
C
31
D
77

Question 15Single Answer

What is the state flower of Uttar Pradesh ?

A
Lily
B
Rose
C
Palash
D
Sunflower

Question 16Single Answer

What is state sport of Uttar Pradesh ?

A
Field Hockey
B
Cricket
C
Football
D
Swimming

Question 17Single Answer

How many total cities / towns in Uttar Pradesh ?

A
567
B
450
C
689
D
510

Question 18Single Answer

What is state dance of Uttar Pradesh ?

A
Kathak
B
Rauf
C
Kathakali
D
Bharat Natyam

Question 19Single Answer

What is state tree of Uttar Pradesh ?

A
Neem
B
Peepal
C
Ashok
D
Mango

Question 20Single Answer

When was the Constituent Assembly of India formed?

A
1946
B
1947
C
1948
D
1950

Question 21Single Answer

What is the main focus of RBI’s Mission SAKSHAM launched in 2026?

A
Digital lending regulation
B
Capacity building and training for Urban Co-operative Banks (UCBs)
C
Cryptocurrency framework
D
Merger of Regional Rural Banks

Question 22Single Answer

On which date did SEBI operationalise PaRRVA (Past Risk and Return Verification Agency) in 2026?

A
May 1
B
April 15
C
April 29
D
May 4

Question 23Single Answer

What is E-PRAAPTI, launched by EPFO?

A
An online grievance redressal system
B
A new pension scheme
C
A portal for tracing and reactivating inoperative PF accounts using Aadhaar
D
A UPI-based payment gateway

Question 24Single Answer

From when is RBI shifting to the Expected Credit Loss (ECL) framework for asset classification?

A
April 1, 2026
B
April 1, 2027
C
January 1, 2027
D
Immediate effect in May 2026

Question 25Single Answer

Which entities partnered for biometric (OTP-free) card payments in 2026?

A
Amazon & SBI
B
Flipkart, Axis Bank & PayU
C
Myntra & HDFC
D
Reliance Retail & ICICI

Mathematics

Question 26Single 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 27Single 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 28Single 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 29Single 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 30Single 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 31Single 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 32Single 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 33Single 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 34Single 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 35Single 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 36Single 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 37Single 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 38Single 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 39Single Answer

A Euclidean ring allows?

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

Question 40Single 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 41Single Answer

Gaussian integers form?

A
A field
B
A Euclidean domain
C
A non-commutative ring
D
Always finite

Question 42Single Answer

Unique factorization theorem in rings states that?

A
Every element is prime
B
Every element is invertible
C
Every ideal is principal
D
Every non-zero non-unit element can be written as a product of irreducible elements uniquely up to units and order

Question 43Single Answer

A module M over a ring R is?

A
A group
B
A field
C
A vector space only
D
An abelian group with compatible scalar multiplication by R

Question 44Single Answer

A submodule N of a module M is?

A
Any subset of M
B
Always simple
C
Only a cyclic subset
D
A subset closed under addition and scalar multiplication by R

Question 45Single Answer

The quotient module M/N is?

A
The set of cosets of N in M with module operations
B
Always simple
C
Equal to M
D
A submodule of M

Question 46Single Answer

A module is cyclic if?

A
It is finite
B
It has one generator
C
It is simple
D
It is free

Question 47Single Answer

A module is simple if?

A
It has no submodules other than {0} and itself
B
It is cyclic
C
It is free
D
It is finite

Question 48Single Answer

A module M is semi-simple if?

A
Every submodule has a complement
B
It has no submodules
C
It is cyclic
D
It is finite

Question 49Single Answer

Schur's lemma states that?

A
Every homomorphism is injective
B
Every module is simple
C
Every module is cyclic
D
Every simple module homomorphism is zero or an isomorphism

Question 50Single Answer

A free module over a ring R is?

A
Always finite
B
Always simple
C
Generated by a basis, linearly independent set of elements
D
Always cyclic

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Mathematics

Question 51Single Answer

An extension field E of F is?

A
Always normal
B
Always finite
C
Always algebraic
D
A field containing F as a subfield

Question 52Single Answer

A field extension E/F is separable if?

A
It is normal
B
It is finite
C
It is algebraically closed
D
Every element of E is a root of a separable polynomial over F

Question 53Single Answer

A field extension E/F is normal if?

A
It is perfect
B
Every element is algebraic
C
It is finite
D
Every irreducible polynomial over F that has a root in E splits completely in E

Question 54Single Answer

A field F is perfect if?

A
Every algebraic extension is separable
B
Both a and b Correct
C
Every polynomial splits completely
D
F is finite or of characteristic zero

Question 55Single Answer

An automorphism of a field extension E/F is?

A
Any polynomial map
B
Any linear map
C
A bijective map fixing F and preserving field operations
D
Any additive map

Question 56Single Answer

A Galois extension is?

A
Always simple
B
Any finite extension
C
Any algebraic extension
D
A normal and separable extension

Question 57Single Answer

Fundamental theorem of Galois theory relates?

A
Ideals and submodules
B
Subgroups of Galois group and intermediate fields
C
Polynomials and modules
D
Only automorphisms

Question 58Single Answer

A linear transformation T is similar to S if?

A
T and S commute
B
T and S have same trace
C
T and S are nilpotent
D
There exists an invertible matrix P such that (T = P^{-1} S P)

Question 59Single Answer

A Galois extension is?

A
A normal and separable extension
B
Any finite extension
C
Any algebraic extension
D
Always simple

Question 60Single Answer

Fundamental theorem of Galois theory relates?

A
Subgroups of Galois group and intermediate fields
B
Ideals and submodules
C
Polynomials and modules
D
Only automorphisms

Question 61Single Answer

The primary decomposition theorem states?

A
Every operator is diagonalizable
B
Any linear operator on a finite-dimensional vector space can be decomposed into T-invariant subspaces corresponding to distinct eigenvalues
C
Every operator is nilpotent
D
Every operator is invertible

Question 62Single Answer

Jordan form of a linear operator is?

A
A block diagonal matrix of Jordan blocks
B
Always diagonal
C
Always nilpotent
D
Always zero

Question 63Single Answer

Two matrices are similar if?

A
They have the same Jordan form
B
They have the same determinant
C
They have same trace
D
They are equal

Question 64Single Answer

A linear operator is diagonalizable if?

A
Its minimal polynomial has distinct roots
B
Both a and b Correct
C
Its characteristic polynomial splits
D
Its Jordan form has only 1×1 blocks

Question 65Single Answer

Eigenvalues of a nilpotent transformation are?

A
Any scalar
B
Non-zero
C
One
D
Zero

Question 66Single Answer

A simple ring is?

A
Has zero divisors
B
Has maximal ideals
C
Has no non-trivial two-sided ideals
D
Is always commutative

Question 67Single Answer

A division ring is?

A
Has zero divisors
B
Commutative
C
Every non-zero element is invertible
D
Simple ring

Question 68Single Answer

Every finite division ring is?

A
Simple module
B
Non-commutative
C
Nilpotent
D
A field

Question 69Single Answer

If p divides order of finite group G, then number of p-Sylow subgroups is?

A
Always prime
B
Congruent to 1 mod p and divides |G|
C
Always 1
D
Always p

Question 70Single Answer

Every subgroup of index 2 in a group G is?

A
Nilpotent
B
Cyclic
C
Simple
D
Normal

Question 71Single Answer

A field extension E/F is finite if?

A
E is perfect
B
Every element is algebraic
C
Every element is transcendental
D
Dimension [E:F] is finite

Question 72Single Answer

If F is field and f(x) is irreducible in F[x], then F[x]/(f(x)) is?

A
Always Euclidean
B
A ring with zero divisors
C
A field
D
Always integral domain

Question 73Single Answer

Minimal polynomial of a linear operator T is?

A
Always x^n
B
Characteristic polynomial
C
Monic polynomial of smallest degree annihilating T
D
Determinant

Question 74Single Answer

The characteristic polynomial of T is?

A
Nilpotent
B
Minimal polynomial
C
Jordan form
D
det(xI - T)

Question 75Single Answer

Rank-Nullity theorem states?

A
dim(V) = rank(T) + nullity(T)
B
T is diagonalizable
C
T is nilpotent
D
Rank = nullity

Question 76Single Answer

Cyclic module is?

A
Simple
B
Generated by a single element
C
Free
D
Nilpotent

Question 77Single Answer

Primary decomposition theorem is applied to?

A
Find eigenvalues
B
Decompose vector space into T-invariant subspaces corresponding to minimal polynomial factors
C
Diagonalize T
D
Solve system of equations

Question 78Single Answer

Jordan canonical form consists of?

A
Identity matrix
B
Diagonal matrix only
C
Nilpotent matrix
D
Jordan blocks along the diagonal

Question 79Single Answer

Algebraic closure of a field F is?

A
F itself
B
A field containing F in which every polynomial has a root
C
A finite field
D
Only perfect field

Question 80Single Answer

The Galois group of a field extension E/F is?

A
The group of all automorphisms of E fixing F
B
All linear maps from E to F
C
All subfields of E
D
All submodules of E

Question 81Single Answer

An irreducible polynomial over a field F is?

A
Always linear
B
Cannot be factored into polynomials of lower degree over F
C
Always quadratic
D
Has repeated roots

Question 82Single Answer

The splitting field of a polynomial f(x) over F is?

A
Field containing F and zero
B
Smallest field extension of F in which f(x) splits completely
C
Always finite
D
Field of rational numbers

Question 83Single Answer

Factor group G/N is defined if?

A
G is abelian
B
N is cyclic
C
N is normal in G
D
G is simple

Question 84Single Answer

The derived series of a group G is used to check?

A
Nilpotency
B
Simplicity
C
Solvability
D
Order of G

Question 85Single Answer

Central series of a group G is used to check?

A
Solvability
B
Nilpotency
C
Abelian property
D
Cyclic property

Question 86Single Answer

The order of a p-Sylow subgroup is?

A
Any divisor of |G|
B
p
C
p^n where p^n divides |G| and p^(n+1) does not
D
Prime number not dividing |G|

Question 87Single Answer

If a finite abelian group has order n, it is isomorphic to?

A
Cyclic only
B
Direct product of cyclic groups of order dividing n
C
Simple
D
Nilpotent only

Question 88Single Answer

A ring R with no zero divisors is called?

A
Nilpotent ring
B
Field
C
Division ring
D
Integral domain

Question 89Single Answer

A field is always?

A
Simple module
B
Non-commutative
C
Nilpotent
D
Commutative division ring

Question 90Single Answer

If R is a ring, then R[x] is?

A
Ring of polynomials over R
B
Field
C
Module
D
Simple ring

Question 91Single Answer

A linear operator T is triangularizable if?

A
T is invertible
B
T is nilpotent
C
T is diagonalizable
D
There exists a basis such that T has upper triangular matrix

Question 92Single Answer

Eigenvalues of similar matrices are?

A
Zero
B
Different
C
Same
D
Non-zero

Question 93Single Answer

Characteristic polynomial of T is?

A
Minimal polynomial
B
det(xI - T)
C
Rank of T
D
Determinant of T

Question 94Single Answer

Algebraic closure of a field F is unique up to?

A
Multiplication
B
Identity
C
Addition
D
Isomorphism

Question 95Single Answer

A Galois extension has degree equal to?

A
Characteristic of field
B
Number of elements in field
C
Order of its Galois group
D
Zero

Question 96Single Answer

The splitting field of x^n - 1 over Q is?

A
Cyclotomic field
B
Algebraic closure
C
Finite field
D
Rational numbers

Question 97Single Answer

A module M over R is free if?

A
It has a basis generating M
B
It is simple
C
It has no submodules
D
It is cyclic

Question 98Single Answer

A field of characteristic p > 0 is perfect if?

A
It is finite
B
Every element is a p-th power
C
It is algebraically closed
D
It is infinite

Question 99Single Answer

The intersection of all maximal ideals in a ring R is?

A
Zero
B
Jacobson radical
C
Prime ideal
D
Integral domain

Question 100Single Answer

A polynomial f(x) over F is separable if?

A
It has distinct roots in its splitting field
B
It is linear
C
It is irreducible
D
It is quadratic

Question 101Single Answer

The order of an element in a finite group divides?

A
Its subgroup order
B
Prime number
C
Any number
D
Order of the group

Question 102Single Answer

A subgroup of order p^n in a finite group is called?

A
p-Sylow subgroup
B
Normal subgroup
C
Simple subgroup
D
Nilpotent subgroup

Question 103Single Answer

Every subgroup of the center is?

A
Simple
B
Cyclic
C
Normal
D
Nilpotent

Question 104Single Answer

Direct product of two groups G and H is abelian if?

A
At least one is abelian
B
Both G and H are abelian
C
Both are simple
D
Both are cyclic

Question 105Single Answer

Quotient of a ring R by ideal I is a field if?

A
I is prime
B
I is maximal
C
I = 0
D
R is commutative

Question 106Single Answer

Minimal polynomial divides?

A
Only x^n
B
Any polynomial
C
Characteristic polynomial
D
None

Question 107Single Answer

Linear operator T is diagonalizable if?

A
Minimal polynomial has distinct roots
B
Jordan form has only 1×1 blocks
C
Both a and b
D
None Correct

Question 108Single Answer

Every finite subgroup of multiplicative group of a field is?

A
Simple
B
Abelian
C
Nilpotent
D
Cyclic

Question 109Single Answer

Order of a nilpotent matrix equals?

A
Dimension
B
Index of nilpotency
C
Trace
D
Determinant

Question 110Single Answer

Kernel of a linear map is?

A
Image
B
Set of vectors mapped to zero
C
Eigenvectors
D
Eigenvalues

Question 111Single Answer

Image of a linear map is?

A
Set of vectors that are outputs
B
Kernel
C
Zero
D
Identity

Question 112Single Answer

A direct product of rings R × S is?

A
Ring with component-wise operations
B
Field always
C
Integral domain
D
Nilpotent ring

Question 113Single Answer

Every field is?

A
Integral domain
B
Nilpotent
C
Module
D
Simple ring

Question 114Single Answer

Every maximal ideal in a ring R is?

A
Nilpotent
B
Prime if R commutative
C
Zero
D
Free

Question 115Single Answer

In a commutative ring R, R/I is domain if?

A
R is field
B
I is maximal
C
I = 0
D
I is prime

Question 116Single Answer

Order of a p-Sylow subgroup divides?

A
Order of G
B
p only
C
Any number
D
1

Question 117Single Answer

Composition factors of a group are?

A
Ideals
B
Subgroups
C
Simple groups in composition series
D
Modules

Question 118Single Answer

If minimal polynomial splits completely into linear factors, T is?

A
Zero
B
Nilpotent
C
Invertible
D
Triangularizable

Question 119Single Answer

Subgroups of G of index 2 are always?

A
Nilpotent
B
Cyclic
C
Simple
D
Normal

Question 120Single Answer

Minimal polynomial divides

A
Zero polynomial
B
Any polynomial
C
Identity
D
Characteristic polynomial

Question 121Single Answer

Eigenvalues of nilpotent operator

A
-1
B
1
C
0
D
Any scalar

Question 122Single Answer

Kernel of module homomorphism is

A
Submodule
B
Free
C
Zero
D
Field

Question 123Single Answer

A simple module has endomorphism ring

A
Field always
B
Division ring
C
Ring with zero divisors
D
Nilpotent

Question 124Single Answer

Jordan canonical form of T is unique up to

A
Nilpotent part
B
Eigenvalues
C
Order of Jordan blocks
D
Trace

Question 125Single Answer

If a linear operator T has distinct eigenvalues, then T is?

A
Nilpotent
B
Diagonalizable
C
Invertible only
D
Singular

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