GATE 2024 Biomedical Engineering General Aptitude Challenge Quiz

This quiz tests advanced concepts from the GATE 2024 Biomedical Engineering (BM) General Aptitude section, covering logical reasoning, mathematics, and scientific analysis. Assess your mastery of problem-solving skills, complex numerical puzzles, and sentence completion patterns relevant to biomedical engineering.

1. Analogous Sequence Reasoning

   If '→' denotes increasing order of intensity, then the word sequence [simmer → seethe → smolder] is analogous to [break → raze → ___]. Which option best fits the blank?

   1. obfuscate
   2. fissure
   3. fracture
   4. obliterate

2. House Numbering Puzzle

   On a street, house-numbers on one side are consecutive odd numbers starting from 301, and on the other side, consecutive even numbers starting from 302; both sides have the same number of houses. If the difference in the sum of house-numbers is 27, how many houses are there on each side?

   1. 26
   2. 52
   3. 54
   4. 27

3. Numerical Pattern Completion

   Which is a possible value of X in the sequence 3, 7, 15, X, 63, 127, 255?

   1. 31
   2. 35
   3. 40
   4. 45

4. Clock Hands Intersection

   Between 12:05:00 and 12:55:00, how many times do the second-hand and the minute-hand of a clock cross each other?

   1. 55
   2. 49
   3. 50
   4. 51

5. Verb Agreement in Context

   Select the correct set of words to fill the blanks: From the ancient Athenian arena to the modern stadiums, athletics (i) the potential for a spectacle. The crowd (ii) with bated breath as the artist twists his body... Twelve strides in, he begins to cross-step. Six cross-steps (iii) in an abrupt stop. As his body (iv) like a door turning on a hinge, the javelin is launched.

   1. (i) holds (ii) wait (iii) culminates (iv) pivot
   2. (i) holds (ii) waits (iii) culminate (iv) pivots
   3. (i) hold (ii) wait (iii) culminate (iv) pivots
   4. (i) hold (ii) waits (iii) culminates (iv) pivot

6. Combinatorics: Twin Seating

   Three distinct sets of indistinguishable twins must be seated at a circular table with 8 identical chairs, with each person sitting next to their twin. How many unique seating arrangements are possible?

   1. 12
   2. 10
   3. 14
   4. 28

7. Electricity Capacity Factor Analysis

   Given four power generation technologies (T1–T4) with respective installed capacities and electricity generations over 1000 hours, and knowing the capacity factor = electricity generated / (installed capacity × hours), which technology has the highest capacity factor?

   1. T3
   2. T2
   3. T4
   4. T1

8. Cross Arrangement in Array

   Given a 4×4 array where each cell in the first three columns contains either an 'X' or a number (the number gives the count of crosses in adjacent cells), what is the maximum number of crosses that can be placed in the empty fourth column?

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

9. Trigonometry: Earth-Moon-Sun Ratio

   During a half-moon phase, if the Moon-Earth-Sun angle is measured as 89.85°, what is the ratio (to the nearest integer) of the Earth-Sun distance to the Earth-Moon distance?

   1. 328
   2. 382
   3. 238
   4. 283

10. Complex Analysis: Contour Integral

    Evaluate the contour integral ∫_{|z|=3} [8 / (z(z-2)(z-4))] dz taken counter-clockwise.

    1. +j2π
    2. +j10π
    3. −j2π
    4. −j10π

11. Newton-Raphson Iteration Selection

    To solve the equation x = 2 cos x using Newton-Raphson's method, which iteration formula is correct?

    1. xn+1 = xn − (1 + 2 sin xn) / (xn − 2 cos xn)
    2. xn+1 = xn − (xn − 2 cos xn) / (1 + 2 sin xn)
    3. xn+1 = xn + (xn − 2 cos xn) / (1 + 2 sin xn)
    4. xn+1 = xn + (1 + 2 sin xn) / (xn − 2 cos xn)

12. Analytical Reasoning: Missing Integer

    In the sequence 2, 6, 14, __, 62, 126, what value fills the blank if the pattern is consistently followed?

    1. 28
    2. 30
    3. 34
    4. 32

13. Probability: Dice Combinations

    Two fair dice are rolled together. What is the probability that the sum is a prime number greater than 6?

    1. 5/18
    2. 7/36
    3. 4/9
    4. 17/36

14. Logical Deduction: Binary String

    If a 5-digit binary number starts with '1' and ends with '0', how many such distinct numbers are possible?

    1. 16
    2. 12
    3. 8
    4. 6

15. Geometry: Inscribed Angle

    A triangle is inscribed in a circle of radius r. If one side passes through the center and measures r, what is the measure (in degrees) of the angle subtended by the side at the circumference?

    1. 120
    2. 150
    3. 90
    4. 60