Question for UP PGT Mathematics 2026 - Quiz / Questions / MCQ

Objective Questions

Latest UP PGT Mathematics Exam Question (Objective Questions), MCQ in English

Subjects : General Studies, Mathematics

Question Bank UP PGT Mathematics Exam - English

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General Studies

Question 1Single Answer

What is the total size of the Uttar Pradesh Budget for 2026–27?

A
₹7,92,696.35 crore
B
₹8,12,696.35 crore
C
₹9,12,696.35 crore
D
₹10,12,696.35 crore

Question 2Single Answer

The Uttar Pradesh Budget 2026–27 is approximately what percentage higher than the Budget Estimates for 2025–26?

A
8.5%
B
12.9%
C
10.2%
D
15.4%

Question 3Single Answer

What amount was allocated for capital expenditure in the UP Budget 2026–27?

A
₹2,48,225.80 crore
B
₹1,48,225.80 crore
C
₹3,48,225.80 crore
D
₹4,48,225.80 crore

Question 4Single Answer

New schemes worth approximately how much were included in the Uttar Pradesh Budget 2026–27?

A
₹23,565.33 crore
B
₹33,565.33 crore
C
₹43,565.33 crore
D
₹53,565.33 crore

Question 5Single Answer

What is the approximate length of the Ganga Expressway inaugurated in Uttar Pradesh in April 2026?

A
394 km
B
494 km
C
694 km
D
594 km

Question 6Single Answer

The Ganga Expressway was inaugurated in which Uttar Pradesh district in April 2026?

A
Agra
B
Jhansi
C
Gorakhpur
D
Hardoi

Question 7Single Answer

Which city became the site of the simultaneous inauguration of Namo Bharat Rapid Rail and Metro services in February 2026?

A
Agra
B
Prayagraj
C
Meerut
D
Varanasi

Question 8Single Answer

The Namo Bharat Rapid Rail and Meerut Metro were inaugurated together in which year?

A
2026
B
2025
C
2024
D
2027

Question 9Single Answer

Which highway project approved in March 2026 connects Barabanki with Bahraich?

A
NH-27
B
NH-927
C
NH-19
D
NH-34

Question 10Single Answer

What is the approximate length of the approved Barabanki–Bahraich access-controlled highway project?

A
51.515 km
B
101.515 km
C
75.515 km
D
151.515 km

Question 11Single Answer

The Barabanki–Bahraich highway project approved in 2026 is to be implemented under which model?

A
EPC only
B
Build-Lease-Transfer
C
Hybrid Annuity Mode
D
State PPP only

Question 12Single Answer

What was the approved cost of the Barabanki–Bahraich NH-927 project?

A
₹4,969.04 crore
B
₹5,969.04 crore
C
₹6,969.04 crore
D
₹7,969.04 crore

Question 13Single Answer

Which Uttar Pradesh city is to receive a 6-lane Greenfield Elevated Corridor connecting NH-19 and its Ring Road?

A
Varanasi
B
Kanpur
C
Meerut
D
Lucknow

Question 14Single Answer

The NH-19–Varanasi Ring Road corridor approved in July 2026 has a total capital cost of approximately?

A
₹10,447.64 crore
B
₹12,447.64 crore
C
₹16,447.64 crore
D
₹14,447.64 crore

Question 15Single Answer

Which riverbank is associated with the elevated NH-31–Varanasi Ring Road corridor approved in July 2026?

A
Yamuna
B
Gomti
C
Varuna
D
Ghaghara

Question 16Single Answer

The Varuna River Bank elevated corridor in Varanasi is approximately how long?

A
23.218 km
B
33.218 km
C
43.218 km
D
53.218 km

Question 17Single Answer

Which road project approved in July 2026 forms part of the Bhopal–Kanpur Economic Corridor?

A
Lucknow–Ayodhya Highway
B
Kanpur–Agra Highway
C
Kanpur–Kabrai Highway
D
Prayagraj–Varanasi Highway

Question 18Single Answer

What is the approximate length of the Kanpur–Kabrai access-controlled highway project?

A
87.7 km
B
117.7 km
C
97.7 km
D
137.7 km

Question 19Single Answer

The Kanpur–Kabrai highway project was approved under which implementation mode?

A
BOT Toll
B
HAM only
C
EPC only
D
DBFOT Annuity

Question 20Single Answer

The greenfield connectivity project to Jewar International Airport approved with revised cost in March 2026 is approximately how long?

A
21.42 km
B
31.42 km
C
41.42 km
D
51.42 km

Question 21Single Answer

Jewar International Airport is officially known as?

A
Uttar Pradesh International Airport
B
Yamuna International Airport
C
Noida International Airport
D
Gautam Buddha International Airport

Question 22Single Answer

Noida International Airport is located in which district?

A
Ghaziabad
B
Bulandshahr
C
Hapur
D
Gautam Buddha Nagar

Question 23Single Answer

Which expressway connects Lucknow and Ghazipur?

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

Question 24Single Answer

Bundelkhand Expressway primarily improves connectivity in which region of Uttar Pradesh?

A
Rohilkhand
B
Bundelkhand
C
Awadh
D
Braj

Question 25Single Answer

Which Uttar Pradesh city hosted the Maha Kumbh in 2025?

A
Prayagraj
B
Mathura
C
Ayodhya
D
Varanasi

Question 26Single Answer

The Triveni Sangam at Prayagraj is the confluence of Ganga, Yamuna and which traditionally believed river?

A
Narmada
B
Saraswati
C
Godavari
D
Kaveri

Question 27Single Answer

The Uttar Pradesh Defence Industrial Corridor has how many major nodes?

A
Four
B
Six
C
Five
D
Eight

Question 28Single Answer

Which of the following is a node of the Uttar Pradesh Defence Industrial Corridor?

A
Gorakhpur
B
Bareilly
C
Aligarh
D
Moradabad

Question 29Single Answer

Which city is NOT one of the six major nodes of the Uttar Pradesh Defence Industrial Corridor?

A
Jhansi
B
Chitrakoot
C
Kanpur
D
Saharanpur

Question 30Single Answer

One District One Product, widely associated with Uttar Pradesh, is abbreviated as?

A
OSDP
B
ODPD
C
OPOP
D
ODOP

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

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 47Single Answer

Combine terms: 12a + 26b - 4b – 16a .

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

Question 48Single Answer

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

A
25.30
B
25.5
C
25.00
D
12.25

Question 49Single Answer

60 Times of 8 Equals to

A
480
B
300
C
250
D
400

Question 50Single 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

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Mathematics

Question 51Single 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 52Single 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 53Single Answer

Question 54Single 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 55Single Answer

What is the Next Prime Number after 7 ?

A
13
B
12
C
14
D
11

Question 56Single Answer

If A and B are two given sets, then A

B)^C is equal to

Question 57Single Answer

121 Divided by 11 is

A
11
B
10
C
19
D
18

Question 58Single 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 59Single Answer

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

Question 60Single 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 61Single 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 62Single 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 63Single Answer

What are the positive factors of 160 .

A
6
B
8
C
5
D
12

Question 64Single Answer

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

A
1325
B
5050
C
3775
D
3325

Question 65Single 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

Question 66Single Answer

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

Question 67Single Answer

Which of the given values is completely divisible by 15 ?

A
2365
B
1375
C
4365
D
2275

Question 68Single Answer

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

Question 69Single Answer

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

Question 70Single Answer

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

Question 71Single Answer

When a number is divided by 80, the remainded is 20. When the same number is divided by 16, what will be the remainder ?

Question 72Single Answer

Which of the fractions is the largest among

and

A
B
C
D
All are equal

Question 73Single Answer

What is the two digits largest prime number ?

A
91
B
93
C
97
D
99

Question 74Single Answer

What is the sum of first 15 odd natural numbers ?

A
255
B
225
C
235
D
215

Question 75Single Answer

What will be the sum of all natural numbers from 75 to 97 ?

A
1598
B
1978
C
1798
D
1958

Question 76Single Answer

If the quotient

of is positive, which of the following would be true ?

A
a > 0
B
b > 0
C
ab > 0
D
a + b > 0

Question 77Single Answer

If the last two digits of a three-digit number is multiple of 6, then the original integer will always be divisible by ?

A
6
B
3
C
2
D
12

Question 78Single Answer

Find three consecutive numbers, in which sum of the two times of the first, three of second and four time of the third number os 191 ?

A
19, 20, 21
B
21, 22, 23
C
20, 21, 22
D
22, 23, 24

Question 79Single Answer

An office has 108 table and 132 chairs. If

tables and

of the chairs are broken, then how many people can work in the office, if required 1 table and 1 chair ?

A
86
B
90
C
90
D
99

Question 80Single Answer

If the sum of two numbers is a and the product is b, then what will be the sum of their reciprocal ?

Question 81Single Answer

The sum of all prime numbers not greater than 17 is ?

A
59
B
58
C
41
D
42

Question 82Single Answer

What is the decimal fraction of 2.349 ?

Question 83Single Answer

Which of the following number is divisible by 9 ?

A
45699
B
12381
C
45696
D
12348

Question 84Single Answer

The largest 4 - digit number is X, which is divisible by 18, 15 and 12 . Then the value of X will be ?

A
9989
B
9980
C
9999
D
9900

Question 85Single Answer

The sum of two numbers is 20 and the product is 91 . What should be the sum of their reciprocal ?

Question 86Single Answer

Find the smallest 6 digit number which is multiple of 18 ?

A
100000
B
999900
C
100008
D
100006

Question 87Single Answer

The sum of a fraction and its reciprocal

is the fractions is ?

Question 88Single Answer

The sum of digits of a twodigit number is 9 . By subtracting 27 from number, the digits of the number are interchanged, so what is that number ?

A
72
B
63
C
45
D
None of these

Question 89Single Answer

The product of two positive numbers is 2500. If one of these numbers is four times more than the other, then what will be the sum of these two numbers ?

A
25
B
125
C
225
D
None of these

Question 90Single Answer

A studednt were asked to divide a number by 3, but instead of dividing it, multiplied that number by 3, so that he got 29.7 as the result, what would be the correct result ?

A
3.3
B
3.9
C
9.9
D
None of these

Question 91Single Answer

The sum of two times of a number and three times its reciprocal is

What is that number ?

Question 92Single Answer

A number is greater than three times of its reciprocal by

What is that number ?

A
10
B
11
C
9
D
8

Question 93Single Answer

Which of the following numbers is completely divisible by 99 ?

A
57717
B
57625
C
55162
D
56982

Question 94Single Answer

One dividing a number by 38, we get 90 as the quotient and 19 as the remainder . What is that number ?

A
3401
B
3382
C
3458
D
3439

Question 95Single Answer

If the number 583_437 is completely divisible by 9, what will be the minimum integer in the blank space ?

Question 96Single Answer

How many such numbers are there between 1 and 200, which are divisible by 3 but not by 7 ?

A
38
B
45
C
57
D
66

Question 97Single Answer

When 2143 is divided by 38, what will be the quotient value ?

A
56
B
55
C
57
D
54

Question 98Single Answer

What is the sum of all indivisible numbers between 58 and 68 ?

A
179
B
178
C
187
D
183

Question 99Single Answer

The sum of the bouble of a fraction and its reciprocal is

What is the fraction ?

Question 100Single Answer

What is the value of

Question 101Single Answer

A mechnic builds a wall in 70 hours. Taking breaks after 7 hours . How much of the wall is still to be built ?

A
0.9
B
0.8
C
0.5
D
0.75

Question 102Single Answer

If the sum of two numbers is 75 and their difference is 25, what will be the product of both the numbers ?

A
1350
B
1250
C
125
D
100

Question 103Single Answer

The sum of marks of A and B in a test is 120, B and C is 130 and C and A are 140 . How many marks are obtained by C ?

A
65
B
75
C
70
D
60

Question 104Single Answer

A number x is divisible by 7 . When this number is divided by 8, 12 and 16, the remainder is 3 in each case . The minimum value of x is ?

A
148
B
149
C
150
D
147

Question 105Single Answer

The greatst and smallest prime numbers are less than 100, what will be the difference between then ?

A
96
B
97
C
94
D
95

Question 106Single Answer

How to write following in ascending order ?

Question 107Single Answer

The simple fraction of is ?

Question 108Single Answer

The two positive integers are such that the sum of the first number and the double of the second number is 8 and their difference is 2, What are the numbers ?

A
7 and 5
B
6 and 4
C
4 and 2
D
3 and 5

Question 109Single Answer

Which of the following statements are not correct ?

A
Every natural number is an integer
B
Every natural number is a real number
C
Every real number is a rational number
D
Every integer is a rational number

Question 110Single Answer

After his death, Ram left

part of his property in the name of his widowed wife and

part of the remaining property in the name of his daughter and gave the remaining property to the son . If the songets Rs. 6,400 then what was Ram's original property ?

A
Rs. 16,000
B
Rs. 32,000
C
Rs. 24,000
D
Rs. 1,600

Question 111Single Answer

The product of all prime number between 80 and 90 is ?

A
83
B
89
C
7387
D
598347

Question 112Single Answer

5349 is added to 3957. 7062 is subtracted from the amount received . The resulting number will not be divisible by ?

A
4
B
3
C
7
D
11

Question 113Single Answer

Divide 50 in to two parts such that their sum of reciprocal is

A
35, 15
B
20, 30
C
24, 36
D
28, 22

Question 114Single Answer

When n is divided by 6, the remainder become 4 . Accordingly, when 2n is divided by 6, what will be the remainder ?

Question 115Single Answer

'a', dibides 228 and 18 is as remainder. 'a', has the largest twodigit value ?

A
70
B
21
C
35
D
30

Question 116Single Answer

The two numbers 11284 and 7655, when divided by a threedigit number, leave equal remainder Accordingly, what is the sum of the digits of the number (SSC CHSL 2013)

A
8
B
9
C
10
D
11

Question 117Single Answer

In a division question, the divisor is 3 times the quotient and 6 times remainder . According, if the remainder is 2, then what is the divident ?

A
50
B
48
C
36
D
28

Question 118Single Answer

If a number is greater than 31 as is smaller than 75 . So, that the number is ?

A
106
B
44
C
74
D
53

Question 119Single Answer

what will be the be the value of

A
10x
B
100x
C
D

Question 120Single Answer

The temperature has increased from to at a unifrorm rate from 9 : 00 and to 2 : 00 am. Accordingly, exactly what was the temperature at 12 pm ?

A
27^oC
B
30^oC
C
32^oC
D
28.5^oC

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