Question for APPSC Degree Lecturer Mathematics 2026 - Quiz / Questions / MCQ

Objective Questions

Latest APPSC Degree Lecturer Mathematics Exam Question (Objective Questions), MCQ in English

Subjects : Mathematics

Question Bank APPSC Degree Lecturer Mathematics Exam - English

Back to Exam

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

DNone 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

AA is called a proper subset of B
BA is called a super set of B
CA is not a subset of B
DB is a subset of A

Question 6Single Answer

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

Question 7Single Answer

The number of elements of the power set of a set containing m elements is

A2^m – 1
Bm
Cm²
D2^m

Question 8Single Answer

If A = {x : x = n², n = 1, 2, 3}, then number of proper subsets is

A3
B8
C7
DNone of these

Question 9Single Answer

If A = {x : x = 4n + 1, 2 £ n £ 5},then number of subsets of A is

A16
B15
C4
DNone 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

AA is always a subset of the complement of B
BB is always a subset of A
CA and B are always disjoint
DA 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}

AA
BB
CBoth A and B
DNone of the above

Question 12Single Answer

The set {x : x⁴ = 1 and x

R} is .....X.... set. Here, X refers to

Aempty
Bfinite
Cinfinite
Dsingleton

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

AA and B
BA and C
CA, B and C
DA, C and D

Question 15Single Answer

If A = (–3, 5) and B = [–7, 9], then

AA = B
BA B
CB A
DNone 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

A7, 6
B5, 1
C6, 3
D8, 7

Question 17Single Answer

Combine terms: 12a + 26b - 4b – 16a .

A4a + 22b
B-28a + 30b
C-4a + 22b
D28a + 30b

Question 18Single Answer

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

A25.30
B25.5
C25.00
D12.25

Question 19Single Answer

60 Times of 8 Equals to

A480
B300
C250
D400

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 ?

AA
BA and B
CA and C
DA, 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

AN
BY – X
CX
DY

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}

AI and III are correct
BII and III are correct
COnly IV is correct
DAll 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 ?

A1 only
B2 only
CBoth 1 and 2
DNeither 1 nor 2

Question 25Single Answer

What is the Next Prime Number after 7 ?

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

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

A600
B700
C800
D900

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

Question 32Single Answer

AA = B
BB = C
CA = C
DNone of these

Question 33Single Answer

Aequal
Bdisjoint
Ceither equal or disjoint
Dnone of the above

Question 34Single Answer

A{–i, i}
B{–1, 1}
C{–1, 1, i, –i}
DNone 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
DNone 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

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

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

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

A730
B170
C180
D1270

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

A42
B43
C45
DNone 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

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

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

A3100
B3300
C2900
D1400

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

A80%
B40%
C60%
D70%

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)}}}?

AZero
B1
C4
D16

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

CBoth (a) and (b)
DNone 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

A40, 15
B15, 40
C35, 15
D25, 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)

Important Questions Package

APPSC Degree Lecturer Mathematics Exam Online Question Bank Package

Buy APPSC Degree Lecturer Mathematics Important Questions, MCQ, question answer in Hindi & English. It will help you to score high marks in APPSC Degree Lecturer Mathematics question bank 2026 in Online, PDF & Print study material.

+ Free Monthly Current Affairs, GK & more PDF Download

Sr.	Package Name	Amount
1.	APPSC Degree Lecturer Mathematics Exam Paper II - English (Old) Description : 1500 Question with Answer	₹131 ~~[₹500]~~
2.	APPSC Degree Lecturer Mathematics Exam - English Description : 1000 Question with Answer.	₹101 ~~[₹500]~~
3.	APPSC Degree Lecturer Mathematics Exam - English Description : 1000 Question & Answer Download in PDF (Send by Email)	₹151 ~~[₹450]~~
4.	APPSC Degree Lecturer Mathematics Exam Question Bank Book - English Description : 1000 Question with Answer (Printed Material)	₹390 ~~[₹600]~~

Mathematics

Question 51Single Answer

If A = {1, 2, 3, 4} and B = {5, 7, 9} then

AA × B = B × A
Bn(A × B) =n(B × A)
CBoth (a) and (b)
DNone 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)

â€‹ (B × A)] is equal to

Question 53Single Answer

If n(A) = 3, n(B) = 4 then, n(A × A × B) is equal to

A36
B12
C108
DNone 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)
DNone of the above

Question 56Single Answer

Let A = {1, 2, 3}. The total number of distinct relations that can be defined over A, is

A2⁹
B6
C8
DNone of these

Question 57Single Answer

Let A = {x, y, z} and B = {1, 2}. Then, the number of relations from A to B is

A32
B64
C128
D8

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),....}
DNone 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

A2^n-1
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 , }
DNone 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

Aan equivalence reation
Breflexive symmetric
Creflexive and trasitive
DOnly reflexive

Question 63Single Answer

Areflexive and transitive
Bsymmetric only
Creflexive and symmetric
Dequivalence relation

Question 64Single Answer

A reflexive and transitive
Ban equivalence relation
Csymmetric but neither reflexive nor transitive
Dneither reflexive nor symmetic but transitive

Question 65Single Answer

The relation ' has the same father as ' over the set of children is

AOnly reflexive
BOnly symmetric
COnly transitive
Dan 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) | â€‹ N and x < 6}
B{(x, x² – 1) | â€‹ N and x < 6}
C{(x, 2x + 1) | â€‹ N and x < 6}
DNone 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

AR is reflexive
BR is transitive
CR is symmetric
DR is reflexive and transitive but not symmetric

Question 68Single Answer

Which of the following functions is inverse of itself?

DNone of the above

Question 69Single Answer

If f(x) = e^x and g(x) = logex, then which of the following is true?

Af{g(x)} â€‹ g{f(x)}
Bf{g(x)} = g{f(x)}
Cf{g(x)} + g{f(x)} = 0
Df{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
C1
D2

Question 71Single Answer

Let f: (2, 3) → (0, 1) be defined by f(x) = x – [x]. Then, f–1(x) equals to

Ax – 2
Bx + 1
Cx – 1
Dx + 2

Question 72Single Answer

The greatest integer function f: R → R, given by f(x) = [x] is

Aone-one
Bonto
Cboth one-one and onto
Dneither 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 ………….. .

A149
B166
C50
D151

Question 77Single Answer

A-1
B-2
DNone 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,

AR is a function
BR is not a function
Cdomain range and codomain is N
DNone 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
Bconstant function
Cmodulus function
DNone 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

Aone-one onto
Bone-one into
Cmany-one onto
Dmany-one into

Question 81Single Answer

Let f : R→ R be a function defined by

A
one-one onto
Bone-one but not onto
Conto but not one-one
DNone 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

Aone-one and onto
Bonto but not one-one
Cone-one but not onto
Dneither one-one nor onto

Question 83Single Answer

C[ 0 , 1 ]
DNone 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 .

Asymmetric
Btransitive
Cequivalence
Dnon-symmetric

Question 85Single Answer

A
f is one-one onto
Bf is one-one into
Cf is many-one onto
Df 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)
DNone 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

DNone 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

Agof(x) = g(f(x))
Bgof(x) = g(x)f(x)
Cfog(x) = g(f(x))
DNone of the above

Question 91Single Answer

If the function gof is defined an onto, then

Aneither f nor g is onto
Bf and g both are necessarily onto
Cf must be onto
DNone of the above

Question 92Single 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
DNone of these

Question 93Single Answer

A3
B1
DNone of these

Question 94Single Answer

Question 95Single Answer

Question 96Single Answer

AZero
B1
C-1

Question 97Single Answer

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

Ab = 0, c = 0
Bb = 0, d = 0
Ca = 0, c = 0
Da = 0, d = 0

Question 98Single Answer

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

Areal roots
Bimaginary roots
Cone real and one imaginary root
Ddistinct real roots

Question 99Single Answer

Question 100Single Answer

Question 101Single Answer

Question 102Single Answer

If square root of –7 + 24i is x + iy, then x is equal to

A±1
B±2
C±3
D±4

Question 103Single Answer

Question 104Single Answer

Question 105Single Answer

Question 106Single Answer

Question 107Single Answer

Ai
C1
DZero

Question 108Single Answer

B
1/2
Cn
DZero

Question 109Single Answer

C-12 - 9i
D-12 + 9i

Question 110Single Answer

The locus of the poins z which satisfy the condition

Aa straight line
Ba circle
Ca parabola
Dnone of these

Question 111Single Answer

Ax = 1
Bx = –1
Cx = ±1
DNo real roots

Question 112Single Answer

If z is a complex number such that Re(z) = Im(z), then

ARe(z²) = 0
BIm(z²) =0
CRe(z²) = Im(z²)
DRe(z²) = –Im(z²)

Question 113Single Answer

If 2a = –1 – i and 2b = –1 + i then
â€‹5a4 + 5b4 + 7a–1b–1 is equal to

A–1
B–2
CZero
D2

Question 114Single Answer

The real value of a for which the expression

is purely real is, when n € N

DNone of these

Question 115Single Answer

Question 116Single Answer

A1
B–1
C2
D–2

Question 117Single Answer

What is the conjugate of

Question 118Single Answer

be the conjugate of the complex number z,then which of the following relations is false?

Question 119Single Answer

If z₁, z₂ and z₃ be the three complex numbers such that |z₁ + 1| < 1, |z₂ + 2| < 2 and |z₃ + 4| < 4, then the maximum value of |z₁| + |z₂| + |z₃| is

A7
B
10
C12
D14

Question 120Single Answer

Question 121Single Answer

AZero

Question 122Single Answer

Question 123Single Answer

Question 124Single Answer

Re(z²) = 1 is represented by

Athe circle x² + y² = 1
Bthe hyperbola x² – y² = 1
Cparabola or a circle
Dall of the above

Question 125Single Answer

If the complex numbers iz, z and z + iz represent the three vertices of a triangle, then the area of the triangle is

Question 126Single Answer

If Z₁, Z_2, Z₃ and z₄are the affixes of four points in the argand plane and z is the affix of a point, such that |z – z₁| = |z – z₂| = |z – z₃| = |z – z₄|, then z₁, z₂, z₃ and z₄ are

Aconcyclic
Bvertices of parallelogram
Cvertices of a rhombus
Din a straight line

Question 127Single Answer

Let z₁ and z₂ be the non-real roots of the equation + 3z^â€‹2 + b = 0. If the origin together with the points represented by z₁ and z₂ form an equilateral triangle, then the value of b is

A1
B2
C3
DNone of these

Question 128Single Answer

If the sum of a certain n number of terms of the AP, 25, 22, 19,....... is 116, then the last term is

A4
B3
C2
D–4

Question 129Single Answer

If a, 4, b are in Arithmetic Progression; a, 2, b are in Geometric Progression; then a, 1, b are in

AA.P
BG.P
CH.P
DNone of these

Question 130Single Answer

What is the value of n sot that

geometric mean between a and b ? where

Cn = 2
D–2

Question 131Single Answer

If logax, logbx, logex be in HP, then a, b, c are in

AAP
BHP
CGP
DNone of these

Question 132Single Answer

If A is the arithmetic mean and G1, G2 be two geometric means between any two numbers, then

is equal to

A2A
BA
C3A
DNone of these

Question 133Single Answer

Question 134Single Answer

Question 135Single Answer

Blog_e2
Dlog_e2 + 1

Question 136Single Answer

Question 137Single Answer

The domain of a sequence can be subset of natural numbers of the type

A{3, 4, 5,.....k}
B{1, 2, 3, 4, 5,......k}
C{0, 1, 2, 3, 4.,....k}
DNone of the above

Question 138Single Answer

Question 139Single Answer

The number which should be added to the numbers 2, 14, 62, so that the resulting numbers may be in GP, is

Question 140Single Answer

The sum of the geometric progression 0.15, 0.015, 0.0015, ..... 20 terms is

DNone of these

Question 141Single Answer

The value of 0.234 is

Question 142Single Answer

If log 2, log (2ⁿ– 1) and log (2ⁿ + 3) are in AP, then n is is equal to

Blog₂5
Clog₃5

Question 143Single Answer

In a cricket tournament 16 school terms participated. A sum of Rs,8000 is to be awarded among themselves as prize money. If the last placed team is awarded `Rs 275 in prize money and the award increases by the same amount for successive finishing places, amount will be first place team received is

ARs 720
BRs 725
CRs 735
DRs 780

Question 144Single Answer

A909
B75
C750
D900

Question 145Single Answer

The sum of integers from 1 to 100 that are divisible by 2 or 5 is

A3000
B3050
C4050
DNone of these

Question 146Single Answer

If a², b², c² are in AP, then which of the following is also in AP?

AsinA, sinB, sinC
BtanA, tanB, tanC
CcotA, cotB, cotC
DNone of the above

Question 147Single Answer

A20
B30
C40
DNone of the above

Question 148Single Answer

If a, b, c are in GP and loga – log 2b, log 2b – log 3c and log 3c – log a are in AP, then a, b, c are the length of the sides of a triangle which is

Aacute angled
Bobtuse angled
Cright angled
Dequilateral

Question 149Single Answer

AAP
BHP
CGP
DNone of these

Question 150Single Answer

If x, 1, z are in AP and x, 2, z are in GP, then x, 4, z will be in

AAP
BGP
CHP
DNone of these

Back to Exam

Latest APPSC Degree Lecturer Mathematics Exam Question (Objective Questions), MCQ in English

Mathematics

APPSC Degree Lecturer Mathematics Exam Online Question Bank Package

Mathematics

Quick View