iiith-ugee-previous-years-questions - Practice Questions - Logical Reasoning - Mathematics - Science

Sep 27, 2026

A compilation of U.G.E.E. style practice questions covering Logical Reasoning, Mathematics, and Science (Physics, Chemistry, Biology). Topics include series completion, coding-decoding, direction sense, logical deduction, analogies, algebraic identities, geometry area change, trigonometry values, coordinate geometry line equations, and calculus derivatives. Science sections address projectile maximum height, pH from ion concentration, eye pupil control, SI unit of power, baking soda formula, energy-momentum relations, sublimation, ribosome function, and conservation laws. Advanced logical reasoning variants include seating arrangement, critical reasoning strengthening, and data interpretation prompts.

LanguageEnglish

CategoryExam

FormatPDF

Pages5

Reading Time13 min

AccessFree to download

Logical Reasoning

Series Completion

Coding-Decoding

Direction Sense

Logical Deduction

Analogy

Mathematics

Algebra

Geometry

Trigonometry

Coordinate Geometry

Calculus

Science (Physics, Chemistry, Biology)

Physics

Chemistry

Biology

Logical Reasoning (Advanced)

Complex Seating Arrangement

Critical Reasoning

Data Interpretation

Part 1 : Logical Reasoning 1. Series Completion: ○ Find the missing term: 2 , 5 , 10 , 17 ,? ○ Answer: 26 (The difference between consecutive terms increases by 2: +3 , +5 ,+7 , +9) 2. Coding-Decoding: ○ If "MASTER" is coded as "NBTUFS", then how will "DEGREE" be coded? ○ Answer: EFHSFF ( Each letter is shifted one position forward in the alphabet) 3. Direction Sense: ○ A person walks 10 meters towards the east, then turns left and walks 5 meters, then turns left again and walks 10 meters. In which direction is he from his starting point? ○ Answer: North 4. Logical Deduction: ○ Statements: All pens are pencils. Some pencils are erasers. ○ Conclusions: ■ I. Some pens are erasers. ■ II. No pen is an eraser. ○ Which conclusion(s) follow? ○ Answer: Neither I nor II (The relationship between pens and erasers is not definitively established. ) 5. Analogy: ○ "Bird: Feather:: Dog: ?" ○ Answer: Fur Part 2: Mathematics 1. Algebra: ○ If x+x1=3 , then find the value of x2+x21 . ○ Answer: 7 (Square the given equation: (x+x1)2=x2+2+x21=9 , then x2+x21=7) 2. Geometry: ○ The length of a rectangle is increased by 20% and the breadth is decreased by 20% . What is the percentage change in its area? ○ Answer: 4% decrease. 3. Trigonometry: ○ If sin(θ)=53 , find cos(θ) when θ is in the first quadrant. ○ Answer: 54 4. Coordinate Geometry: ○ Find the equation of the line passing through the points ( 1 , 2) and (3 , 4) . ○ Answer: y=x+1 5. Calculus: ○ Find the derivative of f(x)=x3−2x2+5x−7 . ○ Answer: f′(x)=3x2−4x+5 Part 3 : Science ( Physics, Chemistry, Biology) 1. Physics: ○ A body is thrown vertically upwards with a velocity of 20 m/s. What is the maximum height it reaches? (Assume g= 10 m/s2) ○ Answer: 20 meters. 2. Chemistry: ○ What is the pH of a solution with a hydrogen ion concentration of 10−3 M? ○ Answer: 3 3. Biology: ○ Which part of the human eye controls the size of the pupil? ○ Answer: Iris 4. Physics: ○ What is the SI unit of power? ○ Answer: Watt 5. Chemistry: ○ What is the chemical formula of baking soda? ○ Answer: NaHCO3 Logical Reasoning: ● 1. Seating Arrangement: ○ Five friends A, B, C, D, and E, are sitting in a row facing north. A sits to the left of B, but not to the immediate left. D sits to the right of E. C sits between B and D. Who is sitting in the middle of the row? ○ Answer: C. ● 2. Figure Series: ○ (Questions involving patterns in sequences of shapes, rotations, and changes in design elements. ) ○ (These are very visual, so I can't write one out, but be sure to practice these from visual reasoning books or online practice tests. ) ● 3. Blood Relations: ○ "Pointing to a photograph, a man said, ' I have no brother or sister, but that man's father is my father's son.' Whose photograph was it? ○ Answer: His son. ● 4. Syllogisms: ○ Statements: Some books are magazines. All magazines are newspapers. ○ Conclusions: ■ I. Some books are newspapers. ■ II. No book is a newspaper. ○ Which conclusion(s) follow? ○ Answer: Only conclusion I can follow. ● 5. Odd One Out: ○ Choose the word that is different from the rest: Apple, Banana, Carrot, Orange. ○ Answer: Carrot. Mathematics: ● 1. Permutations and Combinations: ○ In how many ways can the letters of the word "ARRANGE" be arranged? ○ Answer: 1260 ● 2. Probability: ○ A bag contains 5 red balls and 3 blue balls. Two balls are drawn at random. What is the probability that both balls are red? ○ Answer: 5/14 ● 3. Series and Progressions: ○ Find the sum of the first 20 terms of the arithmetic progression 2 , 5 , 8 , 11 , ... ○ Answer: 590 ● 4. Functions: ○ If f(x) = x^2 + 1 , what is f(f(x))? ○ answer: x^4 + 2x^2 + 2 ● 5. Matrices: ○ If A = [[1 , 2], [3 , 4]], find the determinant of A. ○ Answer: -2 Science ( Physics, Chemistry, Biology) : ● Physics: ○ What is the relationship between kinetic energy and momentum?

FAQs

What kinds of questions are included in the Logical Reasoning section?

It includes series completion, coding-decoding, direction sense, logical deduction with syllogisms, and analogy-style questions with provided answers.

Which mathematics topics are covered in the practice set?

The mathematics portion covers algebra, geometry (percentage change in area), trigonometry, coordinate geometry (line through two points), and calculus (derivatives of polynomials).

What Science subtopics appear in the Physics, Chemistry, and Biology sections?

Physics includes projectile maximum height, SI unit of power, kinetic energy-momentum relationship, and conservation of momentum. Chemistry includes pH from concentration, baking soda formula, sublimation, and allotropes. Biology includes the iris controlling pupil size and ribosomes’ role in protein synthesis.

Sep 27, 2026

Uploaded by Riley West