Statistics Quiz Quiz

Test your proficiency in GATE 2025 General Aptitude (Statistics) with this medium-difficulty quiz covering topics such as language skills, logical reasoning, arithmetic, and analytical problem-solving. Ideal for candidates preparing for the Statistics section of competitive exams.

1. Sentence Completion: Skiing Trip

   Even though I had planned to go skiing with my friends, I had to _____ at the last moment because of an injury.

   1. back on
   2. back up
   3. back out
   4. back of

2. Subject-Verb Agreement

   The President, along with the Council of Ministers, _____ to visit India next week.

   1. will wish
   2. wishes
   3. is wishing
   4. wish

3. Energy Consumption Calculation

   A 40-watt desk light is left on for 10 hours each night for 180 days. If the electricity company charges ₹7 per kWh, what is the total cost of energy consumed? If the light is on for 2 more hours per night for 180 days, what is the percentage increase in cost?

   1. 604.8; 12%
   2. ₹504; 20%
   3. 720; 15%
   4. ₹604.8; 10%

4. Logical Deduction: Labeled Blocks

   Given a figure with blocks labeled (i), (ii), (iii), and (iv), which one of the following options correctly represents the entries in these blocks respectively: (i), (ii), (iii), (iv)?

   1. Q, M, 12, and 8
   2. I, J, 10, and 8
   3. K, L, 10 and 14
   4. L, K, 12 and 8

5. Pie Chart: Distribution of Balls

   A bag contains Violet (V), Yellow (Y), Red (R), and Green (G) balls. The following relations are given: (i) Yellow + 2 × Violet = 50, (ii) Violet + Green = 50, (iii) Yellow + Red = 50, (iv) Violet + 2 × Red = 50. Which pie chart correctly shows the proportion of each color?

   1. G 40%, V 10%, R 20%, Y 30%
   2. G 30%, V 40%, Y 20%, R 10%
   3. G 10%, R 40%, V 20%, Y 30%
   4. G 20%, V 30%, Y 10%, R 40%

6. Reading Comprehension: Funeral Passage

   Based on the passage describing a solitary man who worked at all hours and helped others, which statement is true?

   1. Strangers helped create a grand reputation for the solitary man described in the passage.
   2. The solitary man worked in a court where he fell ill.
   3. The solitary man described in the passage found joy in scattering fruits.
   4. The solitary man described in the passage is dead.

7. Clock Arrangement Problem

   If O* = O Q S Z P R T and X* = X Z P W Y O Q for the given clock arrangement, which of the following best represents P*?

   1. PTVQSUW
   2. PUWRTVX
   3. PSUPRTV
   4. PRTOQSU

8. Digit Arrangement Constraints

   Consider a five-digit number PQRST formed by the digits 1 through 5 with all distinct digits and the conditions: Pu003CQ, Su003EPu003ET, Ru003CT. What is the value of P?

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

9. Profit Percentage in Mixture

   A business person mixes potatoes of variety P (cost: ₹300 per 5 kg) and variety Q (cost: ₹800 per 4 kg) and sells the mixture at ₹192 per kg, gaining 8% profit. What is the ratio P:Q by weight?

   1. 3:4
   2. 1:1
   3. 5:4
   4. 3:2

10. Shortest Distance from Point to Line

    Three villages P, Q, and R are such that PQ = 13 km, QR = 14 km, and RP = 15 km. What is the minimum possible length (in km) of a straight road connecting P to the road QR?

    1. 11.0
    2. 12.5
    3. 12.0
    4. 10.5

11. Definite Integral and Function Properties

    Let f: [0, ∞) → [0, ∞) be a differentiable function with f(x) u003E 0 for all x u003E 0, and f(0) = 0. If f satisfies the property (f(x))² = ∫₀ˣ((f(t))² + f(t)) dt for x u003E 0, which of the following is correct?

    1. 3 u003C f(2) ≤ 4
    2. 2 u003C f(2) ≤ 3
    3. 0 u003C f(2) ≤ 1
    4. 1 u003C f(2) ≤ 2

12. Countability of Sets

    Among the following statements about countability and uncountability of sets, which one is correct?

    1. The set of integers with only even digits is uncountable.
    2. The set of rational numbers is uncountable.
    3. The set of natural numbers is countable.
    4. The set of real numbers between 0 and 1 is countable.

13. Analytical Reasoning: Pairing Logic

    If six people are to be seated in a row and two specific people must not sit together, how many arrangements are possible?

    1. 600
    2. 480
    3. 720
    4. 840

14. Algebra: Roots of Quadratic

    If the quadratic equation x² - 5x + 6 = 0 has roots p and q, what is the value of (p+q) - (pq)?

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

15. Probability: Coins

    If two fair coins are tossed, what is the probability that at least one head shows up?

    1. 1/4
    2. 1/2
    3. 2/3
    4. 3/4