Environmental Science u0026 Engineering Quiz Quiz

Challenge yourself with this 15-question quiz on GATE 2025 Environmental Science and Engineering General Aptitude. Test your skills in analogies, logic, mathematics, environmental concepts, and problem-solving with realistic scenarios tailored for GATE aspirants.

1. Analogy Completion

   Courage is to Bravery as Yearning is to which of the following?

   1. Glaring
   2. Yelling
   3. Longing
   4. Yawning

2. Sentence Completion

   Select the most appropriate option to complete the sentence: 'We tennis in the lawn when it suddenly started to rain.'

   1. have been playing
   2. could be playing
   3. had been playing
   4. would have been playing

3. Counting in a Matrix

   A 4 x 4 image has pixel intensities as follows: 0 1 0 2; 4 7 3 3; 5 5 4 4; 6 7 3 2. How many pixels have a value less than or equal to 4?

   1. 3
   2. 11
   3. 8
   4. 9

4. Logical Reasoning: Shapes

   Given that numbers are associated with a rectangle, triangle, and ellipse as 1, 2, and 3, and diagram positions P, Q, R must be filled, which combination is most appropriate?

   1. P=6; Q=5; R=3
   2. P=3; Q=6; R=6
   3. P=5; Q3: R=6
   4. P=5; Q=6; R=3

5. Geometry of Rectangles

   A rectangle has length L and width W, where L u003E W. If the width W is increased by 10%, what always holds true?

   1. Perimeter increases by 10%.
   2. Area increases by 10%.
   3. The rectangle becomes a square.
   4. Length of the diagonals increases by 10%.

6. Matching Columns (Reasoning)

   Match the statements in Column-I with the most appropriate responses in Column-II: P. This house is in a mess. Q. I am not happy with the marks given to me. R. Politics is a subject I avoid talking about. S. I don't know what this word means.

   1. P–3; Q–4; R–1; S–2
   2. P–1; Q–2; R–4; S–3
   3. P–2; Q–3; R–1; S–4
   4. P–4; Q–1; R–2; S–3

7. Age and Monotonic Functions

   Two brothers have identical weight-age functions which increase monotonically till age 50 and then decrease. If their ages are a₁ u003C a₂, what is true on the day they have the same weight?

   1. Either a₁ = 50 or a₂ = 50
   2. a₁ u003C a u003C 50
   3. a₁ u003C 50 u003C a₂
   4. 50 u003C a u003C a₂

8. Regular Dodecagon Construction

   A regular dodecagon (12-sided polygon) is inscribed in a circle of radius r cm. All 12 triangles formed are used to assemble squares of side r cm, each triangle used once. How many squares can be formed and how many triangles are needed for each?

   1. 3:3
   2. 4:3
   3. 3:4
   4. 3:2

9. Algebraic Equation Solving

   If a real variable x satisfies 3×2² = 27×9, what is the value of 2ˣ² / (2ˣ)²?

   1. 2⁻¹
   2. 2¹⁵
   3. 2⁰
   4. 2³

10. Statistics: Shifts and Earnings

    If Dr. Gita is paid ₹1000×(X–0.2) per shift, and over 100 shifts the patient distribution per shift is: 5 (20 times), 6 (40 times), 7 (30 times), 8 (10 times), what is her average earning per shift?

    1. 6,100
    2. 6,300
    3. 6,000
    4. 6,500

11. Laplace Transform

    Assuming s u003E |a|, what is the Laplace transform of f(x) = cosh(ax)?

    1. s / (s² – a²)
    2. a / (s² + a²)
    3. a / (s² – a²)
    4. s / (s² + a²)

12. Differential Equations Solutions

    For the ODE d²y/dx² + 4y = 0, which of the following is the general solution?

    1. y = C₁e²ˣ cos 2x + C₂e⁻²ˣ sin 2x
    2. y = C₁e²ˣ + C₂e⁻²ˣ
    3. y = C₁ cos 2x + C₂ sin 2x
    4. y = C₁ cosh 2x + C₂ sinh 2x

13. Series Convergence (Reasoning)

    Consider the two series P: Σ_{n=1}^∞ 1/n and Q: Σ_{n=1}^∞ 1/n². Which statement is correct about their convergence?

    1. Both P and Q converge.
    2. P converges and Q diverges.
    3. P diverges and Q converges.
    4. Both P and Q diverge.

14. Environmental Concept: Water Pollution

    Which one of the following is a primary indicator of the organic pollution level in water bodies?

    1. Biochemical Oxygen Demand (BOD)
    2. Total Dissolved Solids (TDS)
    3. Ozone Concentration
    4. Nitrogen Oxide (NOx)

15. Logical Deduction: Sets

    If set A contains all multiples of 3 less than 20, and set B contains all prime numbers less than 20, how many elements are in the intersection of sets A and B?

    1. 3
    2. 1
    3. 0
    4. 2