PET Practice Set 19

UPSSSC PET (Preliminary Eligibility Test) · 2026 · with answers and explanations

questions
30
Total marks
30
Duration
120 minutes
Negative marking
−0.25

Subjects: Aptitude (Reasoning) · Mathematics

Question 1

Aptitude (Reasoning) · 1 marks · −0.25

The mirror image of the word "bEd" (lowercase b, uppercase E, lowercase d) when a vertical mirror is placed on the right will look closest to which of the following?

  1. A.bEd
  2. B.dEb
  3. C.beD
  4. D.dEB

Correct answer: A

Explanation: When a vertical mirror is placed to the right, lateral inversion occurs. The letter 'b' becomes 'd' and 'd' becomes 'b', while 'E' stays the same (symmetric). The reversed order d-E-b with inversion gives b-E-d, which looks exactly like the original word. This is why "AMBULANCE" is written backwards on the front of the vehicle — so it reads correctly in a mirror.

Question 2

Aptitude (Reasoning) · 1 marks · −0.25

In a group of 200 students, 140 like tea, 120 like coffee, and 80 like both tea and coffee. How many students like only tea?

  1. A.60
  2. B.70
  3. C.80
  4. D.90

Correct answer: A

Explanation: Students who like only tea = Total tea lovers - Both = 140 - 80 = 60.

Question 3

Aptitude (Reasoning) · 1 marks · −0.25

In a group of 200 students, 140 like tea, 120 like coffee, and 80 like both. How many students like neither tea nor coffee?

  1. A.30
  2. B.20
  3. C.10
  4. D.40

Correct answer: B

Explanation: Total who like at least one = 140 + 120 - 80 = 180. Neither = 200 - 180 = 20.

Question 4

Aptitude (Reasoning) · 1 marks · −0.25

Which Venn diagram best represents the relationship among Dogs, Cats, and Pets?

  1. A.Three mutually overlapping circles
  2. B.Two separate small circles inside a large circle
  3. C.Three separate non-overlapping circles
  4. D.Two overlapping circles inside a large circle

Correct answer: B

Explanation: Dogs and cats are entirely different from each other (no overlap), but both are types of pets. So dogs and cats are two separate sets both contained within the larger set of pets.

Question 5

Aptitude (Reasoning) · 1 marks · −0.25

Which Venn diagram best represents the relationship among Mountains, Forests, and Earth?

  1. A.Three separate circles
  2. B.Two separate circles inside a big circle
  3. C.Two overlapping circles inside a big circle
  4. D.Three mutually overlapping circles

Correct answer: C

Explanation: Mountains and forests are both parts of the Earth (both inside the big circle). Some mountains have forests and some forests are on mountains (the two overlap), but they are not identical.

Question 6

Aptitude (Reasoning) · 1 marks · −0.25

In a survey of 100 people, 60 read newspaper A, 50 read newspaper B, and 20 read both. How many read at least one newspaper?

  1. A.90
  2. B.80
  3. C.110
  4. D.70

Correct answer: A

Explanation: Using inclusion-exclusion: at least one = A + B - Both = 60 + 50 - 20 = 90.

Question 7

Aptitude (Reasoning) · 1 marks · −0.25

Which Venn diagram best represents: Singers, Artists, Musicians?

  1. A.Three non-overlapping circles
  2. B.Three mutually overlapping circles
  3. C.One circle inside another inside a third
  4. D.Two circles inside one big circle

Correct answer: B

Explanation: All singers are artists, some musicians are singers, and some artists are musicians. All three groups partially overlap with each other, so three mutually overlapping circles is the best representation.

Question 8

Aptitude (Reasoning) · 1 marks · −0.25

Statements: All cats are dogs. All dogs are animals. Conclusions: I. All cats are animals. II. Some animals are dogs.

  1. A.Only I follows
  2. B.Only II follows
  3. C.Both I and II follow
  4. D.Neither follows

Correct answer: C

Explanation: From the chain "All cats are dogs" + "All dogs are animals," it follows that all cats are animals (I). Since all dogs are animals, some animals must be dogs (II). Both follow.

Question 9

Aptitude (Reasoning) · 1 marks · −0.25

Statements: Some pens are books. No book is a pencil. Conclusions: I. Some pens are not pencils. II. All books are pens.

  1. A.Only I follows
  2. B.Only II follows
  3. C.Both follow
  4. D.Neither follows

Correct answer: A

Explanation: Some pens are books, and no book is a pencil, so those pens that are books cannot be pencils — hence I follows. II does not follow because the first statement says only "some" pens are books, not all books are pens.

Question 10

Aptitude (Reasoning) · 1 marks · −0.25

Statements: All chairs are tables. Some tables are wooden. Conclusions: I. Some chairs are wooden. II. All tables are wooden.

  1. A.Only I follows
  2. B.Only II follows
  3. C.Both follow
  4. D.Neither follows

Correct answer: D

Explanation: We know all chairs are tables and some tables are wooden, but we cannot determine which tables are wooden — they might not include any chairs. So I does not follow. II clearly does not follow since only "some" tables are wooden.

Question 11

Aptitude (Reasoning) · 1 marks · −0.25

Statements: All birds are animals. Some animals are reptiles. Conclusions: I. Some reptiles are birds. II. Some animals are birds.

  1. A.Only I follows
  2. B.Only II follows
  3. C.Both follow
  4. D.Neither follows

Correct answer: B

Explanation: Since all birds are animals, some animals are definitely birds (II follows). However, the reptile-animal overlap may not include any birds, so I does not follow.

Question 12

Aptitude (Reasoning) · 1 marks · −0.25

Statements: No apple is an orange. All oranges are fruits. Conclusions: I. No apple is a fruit. II. Some fruits are not apples.

  1. A.Only I follows
  2. B.Only II follows
  3. C.Both follow
  4. D.Neither follows

Correct answer: B

Explanation: All oranges are fruits and no apple is an orange, so the oranges that are fruits are not apples — hence some fruits are not apples (II follows). But apples could still be fruits through some other route, so I does not follow.

Question 13

Aptitude (Reasoning) · 1 marks · −0.25

Statements: Some boys are intelligent. All intelligent people are hardworking. Conclusions: I. Some boys are hardworking. II. All hardworking people are intelligent.

  1. A.Only I follows
  2. B.Only II follows
  3. C.Both follow
  4. D.Neither follows

Correct answer: A

Explanation: Some boys are intelligent, and all intelligent are hardworking, so those boys who are intelligent must be hardworking (I follows). II reverses the universal statement — hardworking does not imply intelligent.

Question 14

Aptitude (Reasoning) · 1 marks · −0.25

Statement: "The government has increased the import duty on electronic goods." Conclusion I: The prices of electronic goods will increase. Conclusion II: People will stop buying electronic goods.

  1. A.Only I follows
  2. B.Only II follows
  3. C.Both follow
  4. D.Neither follows

Correct answer: A

Explanation: Increased import duty logically leads to higher prices (I follows). However, people will not necessarily stop buying — they may buy less, but "stop" is too extreme (II does not follow).

Question 15

Aptitude (Reasoning) · 1 marks · −0.25

Statement: "Police increased morning vigilance in the residential areas." Conclusion I: Petty crime incidents reduced significantly. Conclusion II: Residents feel safer walking in the morning.

  1. A.Only I follows
  2. B.Only II follows
  3. C.Both follow
  4. D.Neither follows

Correct answer: C

Explanation: Increased police vigilance directly leads to reduced crime (I follows) and makes residents feel safer (II follows). Both are logical consequences.

Question 16

Aptitude (Reasoning) · 1 marks · −0.25

Statement: "All students who scored above 90% in the board exams are eligible for the merit scholarship." Conclusion I: Some students will receive the merit scholarship. Conclusion II: Students who scored below 90% are not eligible for the scholarship.

  1. A.Only I follows
  2. B.Only II follows
  3. C.Both follow
  4. D.Neither follows

Correct answer: C

Explanation: If the threshold is 90%, then those above it are eligible (and presumably some exist, so I follows), while those below are not eligible (II follows directly from the statement).

Question 17

Aptitude (Reasoning) · 1 marks · −0.25

Statement: "Due to heavy rains, many trains have been cancelled." Conclusion I: People may face difficulty in travelling. Conclusion II: It has been raining continuously for several days.

  1. A.Only I follows
  2. B.Only II follows
  3. C.Both follow
  4. D.Neither follows

Correct answer: A

Explanation: Cancelled trains cause travel difficulty (I follows). However, "heavy rains" does not necessarily mean "continuous for several days" — it could be one severe storm (II does not follow).

Question 18

Aptitude (Reasoning) · 1 marks · −0.25

Statements: Only students can participate in the race. Some participants in the race are girls. All girl participants are invited for coaching. Which conclusion follows?

  1. A.All participants in the race are invited for coaching.
  2. B.All students are invited for coaching.
  3. C.All participants in the race are students.
  4. D.None of the above is correct.

Correct answer: C

Explanation: Statement 1 says "only students can participate," which directly means all participants are students (C follows). Not all participants are girls (only some), so A doesn't follow. Not all students participate, so B doesn't follow.

Question 19

Aptitude (Reasoning) · 1 marks · −0.25

RAKHI is coded as 36-2-22-16-18 and SHALU is coded as 38-16-2-24-42. How will MANJU be coded?

  1. A.13-2-28-10-24
  2. B.13-2-14-10-24
  3. C.26-1-14-20-42
  4. D.26-2-28-20-42

Correct answer: D

Explanation: Each letter's position is multiplied by 2. M=13×2=26, A=1×2=2, N=14×2=28, J=10×2=20, U=21×2=42. Code: 26-2-28-20-42.

Question 20

Aptitude (Reasoning) · 1 marks · −0.25

SHORTLY is coded as OHSYLTR. How will WALKING be coded?

  1. A.LAWNIKG
  2. B.KLAWGNI
  3. C.AWKLNIG
  4. D.LAWGNIK

Correct answer: D

Explanation: First 3 letters are reversed, then the last 4 letters are reversed. WALKING → WAL reversed = LAW; KING reversed = GNIK. Combined: LAWGNIK.

Question 21

Aptitude (Reasoning) · 1 marks · −0.25

Find the missing number: 2, 3, 5, 7, 11, 13, ?

  1. A.15
  2. B.17
  3. C.19
  4. D.16

Correct answer: B

Explanation: These are consecutive prime numbers. The next prime after 13 is 17.

Question 22

Aptitude (Reasoning) · 1 marks · −0.25

Find the next term: 1, 1, 2, 3, 5, 8, ?

  1. A.11
  2. B.12
  3. C.13
  4. D.14

Correct answer: C

Explanation: This is the Fibonacci series where each term = sum of the two preceding terms. 5 + 8 = 13.

Question 23

Mathematics · 1 marks · −0.25

Three numbers are in the ratio 1:2:3 and their HCF is 12. The numbers are:

  1. A.12, 24, 36
  2. B.11, 22, 33
  3. C.12, 24, 32
  4. D.5, 10, 15

Correct answer: A

Explanation: Let the numbers be x, 2x, 3x. Since 1, 2, 3 are coprime, HCF = x = 12. So the numbers are 12, 24, 36.

Question 24

Mathematics · 1 marks · −0.25

What is the least number which when divided by 8, 12, 16, and 20 leaves a remainder of 5 in each case?

  1. A.240
  2. B.245
  3. C.265
  4. D.235

Correct answer: B

Explanation: LCM(8, 12, 16, 20) = 240. Required number = 240 + 5 = 245.

Question 25

Mathematics · 1 marks · −0.25

7^(6n) − 6^(6n), where n > 0, is divisible by:

  1. A.13
  2. B.127
  3. C.559
  4. D.All of these

Correct answer: D

Explanation: Factor as (7^3 − 6^3)(7^3 + 6^3) = (343 − 216)(343 + 216) = 127 × 559. Since 559 = 13 × 43, the expression is divisible by 13, 127, and 559.

Question 26

Mathematics · 1 marks · −0.25

The least number of soldiers that can be drawn up in troops of 12, 15, 18, and 20 and also in the form of a solid square is:

  1. A.900
  2. B.400
  3. C.1600
  4. D.2500

Correct answer: A

Explanation: LCM(12, 15, 18, 20) = 180. For a perfect square, 180 = 2^2 × 3^2 × 5. Multiply by 5 to make 900 = 30^2.

Question 27

Mathematics · 1 marks · −0.25

Find the remainder when 2^256 is divided by 17.

  1. A.1
  2. B.16
  3. C.14
  4. D.None of these

Correct answer: A

Explanation: 2^256 = (2^4)^64 = 16^64. Since 16 ≡ −1 (mod 17), (−1)^64 = 1.

Question 28

Mathematics · 1 marks · −0.25

Find the remainder when 4^96 is divided by 6.

  1. A.0
  2. B.2
  3. C.3
  4. D.4

Correct answer: D

Explanation: 4^1 mod 6 = 4, 4^2 mod 6 = 4, ... The pattern repeats: remainder is always 4 for any positive power of 4.

Question 29

Mathematics · 1 marks · −0.25

A man has Rs. 480 in denominations of one-rupee, five-rupee, and ten-rupee notes, with equal number of notes of each. The total number of notes is:

  1. A.45
  2. B.60
  3. C.75
  4. D.90

Correct answer: D

Explanation: Let the number of each type = x. Then x + 5x + 10x = 480, so 16x = 480, x = 30. Total notes = 3 × 30 = 90.

Question 30

Mathematics · 1 marks · −0.25

If a − b = 3 and a^2 + b^2 = 29, find the value of ab.

  1. A.10
  2. B.12
  3. C.15
  4. D.18

Correct answer: A

Explanation: (a − b)^2 = a^2 − 2ab + b^2 = 9. So 29 − 2ab = 9, giving 2ab = 20, ab = 10.

View all papers — UPSSSC PET (Preliminary Eligibility Test)

Practice this paper with a timer

Attempt it online, get scored instantly, and see which subjects are costing you marks.

Start practising free