UGEE REAP Mock Test- 3 - JEE MCQ

The solution is that A is the Manager:

• The Manager is the grandfather of F, the Engineer.
• C, the Salesman, is married to the lady Teacher.
• B is the mother of F and E.
• The Doctor, D, is married to the Manager.

This confirms that A must be the Manager.

Let’s assign positions based on height, using the clues to build the order from tallest (1) to shortest (8).

• Position 4 (H): H is explicitly stated to be “fourth from the top.”
  • Height order so far: [ ?, ?, ?, H, ?, ?, ?, ? ].
• Position 2 (E): E is second to the tallest.
  • Height order: [ ?, E, ?, H, ?, ?, ?, ? ].
• E is taller than B: Since E is in position 2, B must be in position 3 or lower (i.e., positions 3, 5, 6, 7, or 8, as 4 is taken by H).
• F’s Height Constraints:
  • F is shorter than H and B: Since H is in position 4, F must be in positions 5, 6, 7, or 8. B must be taller than F, and since B > F and H > F, B cannot be in positions 5–8 (as that would contradict B > F if F is also there). Thus, B must be in position 3 (since position 1 is still open, but we’ll check).
  • F is taller than A and D: F > A, D, so A and D are in positions below F.
• Tentative B Placement: Let’s place B in position 3, as it’s the only position above H that E (position 2) is taller than:
  • Height order: [ ?, E, B, H, ?, ?, ?, ? ].
• F Placement: F is shorter than H (position 4) and B (position 3), so F is in positions 5, 6, 7, or 8. We’ll determine the exact position later.
• G’s Height: G is shorter than D but taller than A (D > G > A).
• Remaining Friends: A, C, D, F, G remain for positions 1, 5, 6, 7, 8.
• Position 1 (Tallest): The tallest does not play football. Possible candidates for position 1 are A, C, D, F, G (since E, B, H are placed). We’ll determine this later.
• A, D, F, G Relations:
  • F > A, D.
  • D > G > A.
  • Combining: F > D > G > A.
  • Thus, in descending order, the sequence among these four is F, D, G, A, occupying four of the positions 5, 6, 7, 8 (since F is below H).
• Height Order for 5–8: Since F > D > G > A, assign:
  • Position 5: F,
  • Position 6: D,
  • Position 7: G,
  • Position 8: A.
  • Tentative height order: [ ?, E, B, H, F, D, G, A ].
• Position 1: The only remaining friend is C. Thus:
  • Position 1: C.
• Complete Height Order:
  • 1: C
  • 2: E
  • 3: B
  • 4: H
  • 5: F
  • 6: D
  • 7: G
  • 8: A

To find the maximum possible difference between the runs scored by Sourav and Yuvi in any match, consider the following:

• The total runs scored by India in any match is between 250 and 300.
• The graph shows the percentage share of runs scored by each batsman.
• For the maximum difference, we need to calculate the runs when both the total runs and the percentage share of the batsmen are at opposite extremes.
• Assume Sourav has the highest percentage and Yuvi the lowest for one match, and vice versa for another.

In conclusion, the maximum difference cannot be determined precisely without exact percentages, leading to option D: None of these.

It is given that team score lies in between 250 and 300.
We can thus see that the total score is more or less same in all the matches. So percentage share in total runsb scored by the team is enough to answer who scored the
minimum runs.
Yuvi has the lower percentage share.

The task is to find the maximum possible difference in the total runs scored by four Indian batsmen across two matches.

• The total runs scored by India in any match is between 250 and 300.
• Assume the batsmen’s percentage share of total runs is the same in each match.
• Calculate the possible runs for maximum total (300) and minimum total (250) for each batsman.
• The difference in the total runs by the batsmen between these two scenarios gives the maximum possible difference.

Therefore, the answer is 100.

Total work = N × 9 worker-days.
Workers adjusted at the start:

• Day 1: N,
• Day 2: N - 2 (2 withdrawn),
• Day 3: N - 1 (1 added),
• Day 4: N - 3,
• Day 5: N - 2, ... ,
• Day 18: N - 10.

N − 10 = 0 ⇒ N = 10.
Work over 17 days (sum of workers from day 1 to 17) = 10 + 8 + 9 + 7 + 8 + 6 + 7 + 5 + 6 + 4 + 5 + 3 + 4 + 2 + 3 + 1 + 2 = 90, equals 10 × 9.
Job completes by day 17, and on day 18, workers = 0, aligning with "double time" (18 days) approximately.
Answer: N = 10 (B).

To find the number of shells n n n that should be fired at point I to maximize the probability of hitting the target:

1. Define Probabilities:
   • Probability that the target is at point I: 8/9​
   • Probability that the target is at point II: 1/9 
   • Probability that a shell hits the target: 1/2 
2. Total Number of Shells:
   • Total shells: 21
3. Maximize Probability:
   • Calculate the total probability P(total) for each possible number of shells n fired at point I.
   • The total probability is given by:
     
4. Optimal Number of Shells:
   • The answer is found by maximizing P(total). It turns out the maximum is at n = 12.

Therefore, the number of shells to be fired at point I for maximum probability is 12.

The correct order is:

Let x = Number of days it rained in the morning and had clear afternoons.
y = Number of days it rained in the afternoon and had clear mornings.
z = Number of days it rained in the morning or afternoon.
So according to question,
x + y = 7 
x + z = 5 
y + z = 6 
Adding all three equations, x + y + z = 9
So, d = 9 days

In region II or between the plates, the electric field

Since, electric field due to an infinite-plane sheet of charge does not depend on the distance of observation point from the plane sheet of charge. So, for the given distances, the ratio of E will be 1 : 1.

In order to estimate the electric field due to a thin finite plane metal plate, we take a cylindrical cross-sectional area A and length 2r as the gaussian surface.

The 1st to 5th terms are 0, 5, 22, 57, 116. These terms are 1–1, 8–3, 27–5, 64–7, 125–9. So, these are 1³–1, 2³–3, 3³–5, 4³–7, 5³–9. So, nth term of series is n³ – (2 × n – 1). So, 6^th term is 6³ – (2 × 6 – 1) = 216 – 11 = 205

The set S = {(x, y) : |x| + |y| = 2} forms a diamond with vertices at (2, 0), (-2, 0), (0, 2), and (0, -2).

The diameter is the maximum distance between any two points, which is between opposite vertices:

• Distance between (2, 0) and (-2, 0) = 

The man who is now Municipal Commissioner worked as a security guard at the university

αβ = 4
Now,

To determine the probability that the bridge will be destroyed, we need to find the probability that at least one of the three bombers hits the bridge.
The given probabilities of the bombers hitting the bridge are 0.3, 0.4, and 0.7, respectively.
First, calculate the probability that each bomber misses the bridge:

• Probability that the first bomber misses: 1 − 0.3 = 0.7

• Probability that the second bomber misses: 1 − 0.4 = 0.6

• Probability that the third bomber misses: 1 − 0.7 = 0.3

The probability that all three bombers miss the bridge is:
P(all miss) = 0.7 × 0.6 × 0.3 
Calculate this:
P(all miss) = 0.7 × 0.6 × 0.3 = 0.126

Now, the probability that at least one bomber hits the bridge is:
P(at least one hits) = 1 − P(all miss)

Thus:
P(at least one hits) = 1 − 0.126 = 0.874

Therefore, the probability that the bridge will be destroyed is:
0.874

To find the number of shortest paths in an m×n grid, calculate the combinations of moves. You need to make:

• (m-1) down moves
• (n-1) right moves

This totals to (m+n-2) steps. The number of ways to arrange these moves is given by:

C(m+n-2, m-1) = (m+n-2)! / [(m−1)! (n−1)!]

This corresponds to option D.

The given group of elements is 25$391@4.
This group follows condition (ii).
Hence, the code is ECXWONTE.

Step-by-Step Solution:

• The group is "1$24925".
• Break it into individual elements: 1 (first), $, 2, 4, 9, 2, 5 (last).
• Identify the first and last elements:
  • First element = 1 (odd digit).
  • Last element = 5 (odd digit).
• Apply Condition (i): Since both the first (1) and last (5) elements are odd digits, code both as 'A'.
  • Replace 1 with A and 5 with A.
  • New group becomes "A$2492A".
• Code each element using the table:
  • A (replaced 1) → Remains A (per condition i).
  • $ → X
  • 2 → G
  • 4 → B
  • 9 → O
  • 2 → G
  • A (replaced 5) → Remains A (per condition i).
• Resulting code: A X G B O G A
• Combine into a single string: AXGBOGA

Compare with Options:

• a) AXKPMGA
• b) BPKXMGB
• c) BXKPMBA
• d) None of these

The derived code "AXGBOGA" does not match any of the provided options. Let’s re-examine the process to ensure no mistakes:

• The application of condition (i) is correct because 1 and 5 are odd digits.
• The coding of each element (X for $, G for 2, B for 4, O for 9, G for 2) follows the table accurately.
• No other condition applies: (ii) doesn’t apply (not both even), (iii) doesn’t apply (first is odd, last is digit), (iv) doesn’t apply (not both symbols).
   
• Original group: "1$24925"
• First element 1 (odd), last element 5 (odd) → Condition (i) applies, so 1 and 5 become A.
• Middle elements ($2492) are coded as X G B O G.
• This confirms "AXGBOGA".

Given:
The in-radius and circumradius of a right-angle triangle is 3 cm and 12.5 cm.

Concept used:
Inradius of right-angle triangle = (P + B - H)/2
Circumradius of a right angle triangle = H/2
Area of a right angle triangle = (1/2 x P x B)

Where,
P = Perpendicular
B = Base
H = Hypotenuse

Calculation:
According to the question
Inradius of right-angle triangle = (P + B - H)/2
=> (P + B - H)/2 = 3
=> P + B - H = 6 ...(1)

Circumradius of a right angle triangle = H/2
=> H/2 = 12.5
=> H = 25

Putting the value of H in equation (1)
=> P + B - 25 = 6
=> P + B = 31

Now,
=> (P² + B²) = (25)²
=> P² + B² = 625

P + B = 31
=> (P - B)² = (31)²
=> P² + B² - 2PB = 961
=> 2PB = 961 - 625
=> 2PB = 336
=> PB = 168

So, area of triangle = 1/2 x PB
=> (1/2 x 168) = 84 cm²

∴ The area of the triangle is 84 cm²

The correct spelling is 'Manageable.' This word is spelled with an 'e' after 'g,' making it distinct from the other options, which contain misspellings such as:

• Missing letters
• Incorrect letter combinations

∴ The maximum force decreases by K times.

A dielectric is an insulating material that can be polarized by an electric field. This means it does not conduct electricity but can support electrostatic fields.

Among the given options, glass is a known dielectric as it is non-conductive and is used in applications like capacitors. Here’s a breakdown of the materials:

• Copper (A): This is a conductor.
• Antimony (C): Although it is a metalloid, it isn't typically classified as a dielectric.
• Glass (B): This is the correct answer as it is a dielectric material.

Therefore, the correct answer is B.

A polar molecule is one in which the centre of gravity for positive and negative charges are separated.

The correct explanation is that the comb polarizes the paper, which leads to induced charges on the paper's surface, creating an attractive force between the comb and the paper.

The pattern for the code is as follows:

Hence, JAIHIND will be written as ZJEDEWF.

Let the ratio of household consumption to other consumption be x:y.
Therefore,
-20x + 70y = -25(x + y)
⇒ -20x + 70y = -25x - 25y
⇒ 5x = -95y
which is not possible.
Therefore, option (d) is correct.

The given number series is based on the following pattern:
467 - 444 = 23 = 23 × 1
513 - 467 = 46 = 23 × 2
582 - 513 = 69 = 23 × 3
674 - 582 = 92 = 23 × 4
789 - 674 = 115 = 23 × 5
Thus, ? = 789 + 23 × 6 = 789 + 138 = 927
Hence, 927 will replace the question mark.

Here logic is:
The total number of letters in a word × 3
RAT (3 × 3) = 9
GAME (4 × 3) = 12
LIVER (5 × 3) = 15
Thus,
POLYSTER (8 × 3) = 24
Hence, the correct answer is 24.