UP PET Maths Questions in English

Important Maths (Elementary Arithmetic) Questions Answers with Solution for UPSSSC UP PET Exam 2024 – 2025. Practice set of Mathematics Objective MCQs for preparation of Uttar Pradesh Preliminary Entrance Test.

Elementary Arithmetic for UP PET: (05 Marks)

Whole numbers, fractions and decimals

Questions 1: A number 2X16 is divided by the smallest number divisible by 4 and 9. The resulting number is the square of 9. Find the value of X.

A) 5
B) 3
C) 7
D) 9

Answer
Ans : D) 9
4,9 The smallest number divisible by =36
Square of 9 = 81
36×81=2916
x=9

Question 2: Find the difference between the digits of the largest number which can exactly divide 144 and 216?

A) 3
B) 5
C) 2
D) 4

Answer
Ans : 5
The HCF of 144 and 216 is 72.
Now, find the difference between the digits of HCF (72):
The digits in 72 are 7 and 2
Difference of these digits: 7−2=57 – 2 = 57−2=5

Question 3: What is the smallest positive number which when subtracted from 12 and 21 gives their third ratio as 36?

A) 5
B) 4
C) 3
D) 2

Answer
Ans : 3
12-x : 21-x :: 21-x : 36
x2+441-42x =12×36 -36x
x2-6x+9 =0
x=3

Question 4: If a number is as much greater than 31 as it is less than 75, then what will that number be?

A)160
B) 44
C) 74
D) 53

Answer
Ans: 53
31+x=75-x,
2x=44,
x=22
Number = 31+22=53

Question 5: What is the smallest number that must be added to 2055 so that the sum is exactly divisible by 27?

A) 28
B) 24
C) 27
D) 31

Answer
Ans : 24
When 2055 is divided by 27, the remainder is 3.
Now we need to subtract this remainder from 27 to make it exactly divisible:
27−3=24

Average : UP PET Maths Questions

Question 1: A car travels the first 140 km in 3 hours and the next 180 km in 5 hours. What is its average speed (in km/h) during the entire journey

A) 50
B) 45
C) 30
D) 40

Answer
Ans : 40
140+180 = 320 Km
Time = 3+5 =8Hrs
Average speed=320/8=40 km/h

Question 2: The average weight of eight people is 40 kg. If one person is removed, the average weight becomes 38 kg. What is the weight of the removed person?

A. 33.25 kg
B. 78 kg
C. 38 kg
D. 54 kg

Answer
Ans : 54 kg
total weight of 8 persons = 40×8=320 kg
total weight of seven persons = 38×7=266 kg
weight of the person removed = 320-266= 54 kg

Question 3: Find the average of 512, 620, 428, and 580?

A. 560
B. 480
C. 535
D. 495

Answer
Ans : 535
Sum of 512, 620, 428, and 580 =2140
Average =2140/4=535

Question 4 : The average of 3, 5, 10, and x is 5. The average of 8, 12, 15, x and y is 9. The values ​​of x and y are _______________________________ respectively.

A. 3 and 9
B. 2 and 3
C. 3 and 8
D. 2 and 8

Answer
Ans : 2 and 8
3+5+10+x =5×4 =20, x=20-18=2,
8+12+15+2+y=9×5, y=45-37=8

Question 5: The average of 11 results is 50. If the average of the first six results is 51 and the average of the last six is ​​59, then find the sixth result.

A. 66
B. 86
C. 110
D. 107

Answer
Ans : 110
Grand total=50×11=550
total of first six results=51×6=306
Total of last six results=59×6=354
The sixth result is counted twice, once in the first six results and once in the last six results.
306+354=550-The sixth result,
The sixth result, = 660-550=110

Simple Arithmetic Equations

Question 1: If \frac58 of 184\times 15 \div 5 + K = 513 \div 9 + 435, then find the value of K.

A.136
B.192
C.239
D.147

Answer
Ans : 147
115×3+k=57+435
K=592-345=147

प्रश्न 2 :Simplify the following?
30 % of [ { (820% of 40) – 28 } ] % of 600

A. 200
B. 540
C. 500
D. 250

Answer
Ans : 540
30 % of [ { (40×820/100) – 28 } ] % of 600,
30 % of [ { 328 – 28 } ] % of 600,
30 % of [ 300 ] % of 600,
30 % of 600 x300/100,
30 % of 1800,
1800×30/100=540

प्रश्न 3 : Simplify the following expression:
25 - (4 \div 2) + 11.5 + 9.5

A. 47
B. 45
C. 44
D. 46

Answer
Ans : 44
25 – 2 + 11.5 + 9.5,
23+21=44

Question 4 : Find the value of 3\times 7 + 5 - 6 \div 3 - 9 + 45 \div 5 \times 4 - 45.

A. 36
B. 9
c. 6
D. 7

Answer
Ans : 6
21+5-3-9+36-45
62-56=6

Question 5 : What is the value of 12 % of 4 % of 7 % of 2\times{10}^6?

A.121
B.583
C.672
D.386

Answer
Ans : 672
\frac {2\times{10}^6}{100} \times 7 \times \frac {4}{100} \times \frac{12}{100},
=2x7X4X12=672

Percentage : UP PET Maths Questions

Question 1: The marked price of an item is Rs 1600 but Rohan gets a discount of 20 percent. He sells the item for Rs 1600. What is Rohan’s profit percentage?

A. 25 percentage
B.22 percentage
C.20 percentage
D.18 percentage

Answer
Ans : 25percentage
20 percentage of 1600 = 1600×20/100=320
CP =1600-320 = 1280
profit = 320
profit percentage =320/1280X100 =25%

Question 2: Out of a stock of grain, \frac18 part is rotten. What percent of the grain in that stock is not rotten?

A. 87.5%
B. 75%
C. 77.5%
D. 90%

Answer
Ans : 87.5 %
1-\frac18 =\frac78
In percentage =\frac78 \times100 % = 87.5 %

Question 3: A city had a population of 82,000 at the beginning of 2019. Its population is increasing at the rate of 2% annually. What is its population (rounded off to the nearest integer) at the beginning of 2022?

A. 88000
B. 86789
C. 87019
D. 85000

Answer
Ans : 87019
2019 – 82,000
2020- 82,000 + 1640=83640 (Add 2%)
2021- 83640+1672.8 = 85312.8
2022- 85312.8+1706.256= 87019.056
Population = 87019

Question 4: The price of a painting increased from Rs 140000 to Rs 182000. What is the percentage increase in the price of the painting?

A. 50 Percent
B. 10 Percent
C. 30 Percent
D. 40 Percent

Answer
Ans : 30 Percent
Increase = 182000 – 140000 = 42000
Percentage Increase = 42000/140000X100 = 30%

Question 5: If the price of tea is increased by 20%, then by what percentage should the consumption of tea be reduced so that the expenditure on tea does not increase?

A. 16{\frac23} %
B 33{\frac13} %
C. 25 %
D. 20 %

Answer
Ans : 16{\frac23} %
Let Tea price = 100
New Price + 120 (20% increase)
Increase in spending= Rs 20
What is the percentage reduction in consumption?
\frac{20}{120} \times 100 = 16{\frac23} %

Square and square root : UP PET Maths Questions

Question 1 : If x, y are rational numbers and \frac{5 + \sqrt{11}}{3-2\sqrt{11}} = x + y \sqrt{11}. The values ​​of x and y are

A. x =\frac{-14}{17}, y = \frac{-13}{26}
B. x =\frac{4}{13}, y = \frac{11}{17}
C. x =\frac{-27}{25}, y = \frac{-11}{37}
D. x =\frac{-37}{35}, y = \frac{-13}{35}

Answer
Ans : x =\frac{-37}{35}, y = \frac{-13}{35}
Example – \dfrac{5 +\sqrt{11}}{3-2\sqrt{11}} = x + y\sqrt{11}
\dfrac{5 +\sqrt{11}}{3-2\sqrt{11}}\times{\frac{3+ 2\sqrt {11}}{3+2\sqrt{11}} = x + y\sqrt{11}
\dfrac{15 +3\sqrt{11} + 10\sqrt{11} + 22 }{9-44}} = x+ y\sqrt
\dfrac{37+ 13\sqrt{11}}{-35} = x +y\sqrt{11}
\dfrac - {37}{35} -\frac{13}{35} \sqrt{11} = x + y\sqrt{11}
there fore, x = - \frac{37}{35} and y = -\frac{13}{35}
Hence, the correct option is (d)

Question 2: If \sqrt7 = 2.646, then what is the value of \frac{1}{\sqrt28} up to three decimal places?

A. 0.183
B. 0.185
C. 0.187
D. 0.189

Answer
Ans 0.189
\frac{1}{\sqrt{28}} = {\frac{1}{\sqrt{4\times7}}} ={\frac{1}{2\sqrt7}} ={\frac{1}{2(2.646)}} = {\frac{1}{5.292}}=0.189
Hence, the correct option is (d)

Question 3: If 27^{2x-1} = (243)^3, then what is the value of x?

A. 3
B. 6
C. 7
D. 9

Answer
Ans : 3
Example – 27{2x-1} = (243)^3
(3^{3})^{2x-1} = (3^{5})^{3}
3^{6x-3} = 3^{15}
6x – 3 = 15
6x = 18
x = 3
Hence, the correct option is (a)

Question 4: Which number is the largest among the numbers \sqrt[2]{8},\sqrt[4]{13},\sqrt[5]{16}, \sqrt[10]{41}?

A.\sqrt[4]{13}
B.\sqrt[5]{16}
C.\sqrt[10]{41}
D.\sqrt[2]{8}

Answer
Ans: \sqrt[2]{8}
\sqrt[2]{8} = 8^{1/2} = (8^{10})^{1/20}
\sqrt[4]{13} = 13^{1/4} = (13^{5})^{1/20}
\sqrt[5]{16} = 16^{1/5} = (16^{4})^{1/20}
\sqrt[10]{41} = 41^{1/10} = (41^{2})^{1/20}
Clearly, \sqrt[2]{8}is the largest number.
Hence, the correct option is (d)

Question 5: 553 + 173 – 723 + is equal to 201960?

A. -1
B. 0
C. 1
D. 17

Answer
Ans: 0,
We have, the given expression is
= 55^3 + 17^3 + (-72)^3 - 3(55)(17)(-72)
Since, 55 + 17 – 72 = 0
Therefore, the given expression =0
Hence, the correct option is (b)|

Question 6 : What is the simplified value of (0.2)^3\times 200\div 2000?

A.\dfrac{1}{100}
B. \dfrac{1}{50}
C. \dfrac{1}{10}
D. 1

Answer
Ans 6 : \dfrac{1}{50}
(0.2)^3\times 200\div 2000 of (0.2)^2
=\dfrac{0.008\times 200}{2000\times 0.04} = \dfrac{0.08\times 20}{2000\times0.04}
= \dfrac{2}{100} = \dfrac{1}{50}
Hence, the correct option is (b) |

Question 7 : What is the value of \dfrac{(75.8)^2 -(35.8)^2}{40}?

A. 121.6
B. 40
C. 160
D. 111.6

Answer
Ans : 111.6
\dfrac{(75.8)^2 - (35.8)^2}{40} = \dfrac{(75.8 - 35.8)(75.8 + 35.8)}{(75.8 - 35.8)}
= 75.8 + 35.8 = 111.6
Hence, the correct option is (d)

Question 8 : Simplification:
\dfrac{0.08\times 0.08\times 0.08 + 0.02\times\0.02\times0.02}{0.08\times0.08 - 0.0016 + 0.02 \times 0.02}

A. 0.001
B. 0.1
C. 0.0016
D. 0.016

Answer
Ans : b
Let x = 0.08 और y = 0.02
Therefore, the given expression
=\dfrac{{x}^3 + {y}^3}{{x}^2 - xy +{y}^2}
= x + y = 0.08 + 0.02 = 0.1
Hence, the correct option is (b)

Question 8: What is 0.75 \times 7.5 - 2 \times 7.5 \times 0.25 + 0.25 \times 2.5 equal to?

A. 250
B. 2500
C. 2.5
D. 25

Answer
Ans : 2.5
Let x = 0.75 और y = 0.25
So it was given
= 10\times(0.75)^2 - 10\times 2\times0.75\times0.25 + 10\times (0.25)^2
= 10(x^2 - 2xy + y^2) = 10 (x - y )^2
=10(0.75 - 0.25 )^2 = 10 (0.5)^2 = 2.5
Hence, the correct option is (C)

Question 9: [ 3 - 4 (3 - 4) ^{-1}]^{-1} is equal to?

A. 7
B. -7
C.\frac17
D.\frac-17

Answer
Ans : \frac17
=\{3-\frac{4}{3-4}\}^{-1}
={\{3 + 4}\}^{-1} = \frac17
Hence, the correct option is (C)

Thanks for attempt Maths Questions practice set in English for UPSSSC UP PET exams.

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