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UGEE REAP Mock Test- 4 - JEE MCQ


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30 Questions MCQ Test UGEE Mock Test Series 2025 - UGEE REAP Mock Test- 4

UGEE REAP Mock Test- 4 for JEE 2025 is part of UGEE Mock Test Series 2025 preparation. The UGEE REAP Mock Test- 4 questions and answers have been prepared according to the JEE exam syllabus.The UGEE REAP Mock Test- 4 MCQs are made for JEE 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for UGEE REAP Mock Test- 4 below.
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UGEE REAP Mock Test- 4 - Question 1
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In a certain code language, if the word SOLUTIONS is coded as SNOITULOS, then how is the word ANSWER coded in that language?

Detailed Solution for UGEE REAP Mock Test- 4 - Question 1

Word: SOLUTIONS
Logic: The letters in the given word are reversed.
Code: SNOITULOS
Similarly, the code for is ANSWER is REWSNA.

UGEE REAP Mock Test- 4 - Question 2
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A ball of diameter 15 cm is floating so that the top of the ball is 5 cm above the smooth surface (water) of the pond. What is the circumference in centimeters of the circle formed by the contact of the water surface with the ball?

Detailed Solution for UGEE REAP Mock Test- 4 - Question 2

Radius of the circle cm 
Hence, circumference = 10√2π cm.

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UGEE REAP Mock Test- 4 - Question 3
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2 matched with ____ ?

Detailed Solution for UGEE REAP Mock Test- 4 - Question 3

To solve this problem, analyze the Waama sentences for recurring patterns and match them to the English translations based on subjects, verbs, objects, tense/aspect markers, negation, questions, and modifiers. Below are the key patterns:

  • Subjects: Kofi, Ama, Mi (I), Wo (you), A (he/she)

  • Verbs: sɛ (eat), tu (cook), pɛ (cut)

  • Objects: mani (yam), kuku (chicken), da (house)

  • Tense/Aspect Markers: ka- (past), ki- (future), na (present progressive or will)

  • Negation: ma (not)

  • Question Marker: na? (indicates a question)

  • Modifiers: ba (big), tɔ (today), wɛ (yesterday)

  • Word Order: Subject-(Marker)-Verb-Object-(Modifier)-(Question Marker)

  • Ama ka-sɛ kuku wɛ. → M. Ama ate the chicken yesterday.

    • "ka-sɛ" (ate), "kuku" (chicken), "wɛ" (yesterday).

UGEE REAP Mock Test- 4 - Question 4
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3 matched with ___?
Detailed Solution for UGEE REAP Mock Test- 4 - Question 4

  1. Mi na tu da. → K. Mi will dig the house.

    • "na tu" (will cook/dig), "da" (house); "dig" fits contextually.

UGEE REAP Mock Test- 4 - Question 5
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7 matched with _____?
Detailed Solution for UGEE REAP Mock Test- 4 - Question 5

  • Ama ka-tu kuku. → F. Ama cooked the chicken.

    • "ka-tu" (cooked), "kuku" (chicken).

UGEE REAP Mock Test- 4 - Question 6
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A natural number x is chosen at random from the first one hundred natural numbers. What is the probability that

Detailed Solution for UGEE REAP Mock Test- 4 - Question 6

To solve the inequality x + 100/x  > 50 for natural numbers x from 1 to 100:
Consider f(x) = x + 100/x. Solve x2 - 50x + 100 = 0: roots are x =25 ± 5√21, approximately 2.085 and 47.915.
Since the quadratic opens upward, x2 - 50x + 100 > 0 for x < 2.085 or x > 47.915.
Favorable natural numbers: x = 1, 2 (since 1,2 < 2.085) and x = 48, 49, ... , 100 (since 48 > 47.915).
Verify: f(2) = 52 > 50, f(3) ≈ 36.333 < 50, f(47) ≈ 49.128 < 50, f(48) ≈ 50.083 > 50.
Total favorable: 2 + (100 - 48 + 1) = 55.
Probability: 55/100 = 11/20.

UGEE REAP Mock Test- 4 - Question 7
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If m be the greatest value of k for which 100! is divisible by 3k, then the number of ways of distributing k different things among 5 persons so that two of them get 10 things each, two get 12 things each and the fifth one gets four things is
Detailed Solution for UGEE REAP Mock Test- 4 - Question 7

Greatest k such that 3k divides 100!: [100/3] + [100/9] + [100/27] + [100/81] = 48. So, k = 48.
Distribute 48 distinct items among 5 distinct persons (2 get 10, 2 get 12, 1 gets 4):
Assign roles: (5/2) × (3/2) × (1/1) = 30
Distribute items for a fixed assignment: 

UGEE REAP Mock Test- 4 - Question 8
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Cathode rays were discovered by
Detailed Solution for UGEE REAP Mock Test- 4 - Question 8

Cathode rays were discovered by J.J. Thomson during his experiments in the late 19th century. His work led to the identification of these rays as streams of electrons, which was a significant milestone in the history of physics.

While William Crookes contributed to the study of cathode rays through the invention of the Crookes tube, it was Thomson who provided the critical evidence that led to their understanding as negatively charged particles.

UGEE REAP Mock Test- 4 - Question 9
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Let N cells be numbered 1, 2, 3, ..., N. We randomly throw balls into them. The process is continued until any one of the cells receives two balls. What is the probability that more than n throws will be necessary?
Detailed Solution for UGEE REAP Mock Test- 4 - Question 9

The problem asks for the probability that more than n throws are needed for any cell to receive two balls. This is equivalent to the probability that no cell receives two balls in the first n throws.

  • Total possible outcomes: Each throw can go to any of N cells, so there are Nⁿ possible ways to distribute n balls.
  • Favorable outcomes: To ensure no cell gets more than one ball, we need to choose n cells out of N and distribute the balls among these cells, which can be done in P(N, n) ways (permutations of n balls in N cells).
  • Probability: The probability is the number of favorable outcomes divided by the total possible outcomes: Probability = P(N, n) / Nⁿ
UGEE REAP Mock Test- 4 - Question 10
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6, 15, 33, 69, _____, 285
Detailed Solution for UGEE REAP Mock Test- 4 - Question 10

1st to 4th & 6th terms are 6, 15, 33, 69, x, 285. These terms are 3 × 2, 3 × 5, 3 × 11, 3 × 23, x, 3 × 95
It can be observed all terms are 3 × an. Where a1 = 2 & an = 2an-1 + 1. So, x = 3 × [2(23) + 1] = 3 × 47 = 141

UGEE REAP Mock Test- 4 - Question 11
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Michael lives 10 km away from where I live. Ahmed lives 5 km away and Susan lives 7 km away from where I live. Arun is farther away than Ahmed but closer than Susan from where I live. From the information provided here, what is one possible distance (in km) at which I live from Arun’s place?
Detailed Solution for UGEE REAP Mock Test- 4 - Question 11

In the question, it is given that Ahmed is 5 km away and Susan is 7 km away from where I live. Further, it is given that Arun is farther away than Ahmed from where I live and not as far as Susan. That means Arun must be living at a distance more than 5 km but less than 7 km from my house, which is according to given options can be 6.02 km.

UGEE REAP Mock Test- 4 - Question 12
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If regular household expenses as a percentage of salary exceed 50%, then the living style in that year is said to be aristocratic. How many years Mayank has lived aristocratically in all the years given above?
Detailed Solution for UGEE REAP Mock Test- 4 - Question 12

1. Interpret the Bar Chart:

  • Each bar represents the breakdown of Mayank’s salary into regular household expenses, expenses on girlfriend, and savings.

  • The bar is divided into three sections:

    • The bottom section (gray) represents regular household expenses.

    • The middle section (dotted) represents expenses on girlfriend.

    • The top section (striped) represents savings.

2. Analyze Each Year:

  • 2000: Regular household expenses are approximately 40% of the salary.

  • 2001: Regular household expenses are approximately 40% of the salary.

  • 2002: Regular household expenses are approximately 40% of the salary.

  • 2003: Regular household expenses are approximately 40% of the salary.

In all four years, the regular household expenses do not exceed 50% of the salary.

Conclusion:

  • Mayank has not lived aristocratically in any of the years given.
  • Therefore, the number of years Mayank has lived aristocratically is: 0

So the correct answer is: (a) 0

UGEE REAP Mock Test- 4 - Question 13
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If two people are selected at random from the surveyed group without replacement, what is the probability that they are from different age groups and both use the most popular mode of transport for their respective age groups?
Detailed Solution for UGEE REAP Mock Test- 4 - Question 13

  1. Identify the Most Popular Mode for Each Age Group:

    • 18-25: Car (50), Bus (100), Bike (80), Walk (20) → Most popular: Bus (100)

    • 26-35: Car (120), Bus (80), Bike (60), Walk (40) → Most popular: Car (120)

    • 36-45: Car (150), Bus (50), Bike (30), Walk (70) → Most popular: Car (150)

    • 46+: Car (110), Bus (30), Bike (20), Walk (90) → Most popular: Car (110)

  2. Determine Favorable Outcomes:We need pairs of people from different age groups, where each uses their age group’s most popular mode. List all pairs of distinct age groups and calculate the number of favorable unordered pairs:

    • 18-25 (Bus, 100) and 26-35 (Car, 120): 100 × 120 = 12,000

    • 18-25 (Bus, 100) and 36-45 (Car, 150): 100 × 150 = 15,000

    • 18-25 (Bus, 100) and 46+ (Car, 110): 100 × 110 = 11,000

    • 26-35 (Car, 120) and 36-45 (Car, 150): 120 × 150 = 18,000

    • 26-35 (Car, 120) and 46+ (Car, 110): 120 × 110 = 13,200

    • 36-45 (Car, 150) and 46+ (Car, 110): 150 × 110 = 16,500

    Total favorable pairs = 12,000 + 15,000 + 11,000 + 18,000 + 13,200 + 16,500 = 85,700

  3. Calculate Total Possible Outcomes:Total ways to select 2 people from 1100 = C(1100, 2) = (1100 × 1099) / 2 = 1,208,900 / 2 = 604,450

  4. Compute the Probability:Probability = (Number of favorable pairs) / (Total pairs) = 85,700 / 604,450

  5. Simplify the Fraction:

    • Factorize 85,700: 85,700 = 100 × 857 = 2² × 5² × 857 (857 is prime)

    • Factorize 604,450: 604,450 = 50 × 12,089 = 2 × 5² × 12,089 (12,089 = 7 × 11 × 157)

    • GCD = 50 (since 85,700 / 50 = 1,714 and 604,450 / 50 = 12,089 have no common factors)

    • Simplified: 85,700 / 604,450 = 1,714 / 12,089

Thus, the probability is 1,714 / 12,089.

UGEE REAP Mock Test- 4 - Question 14
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Nobody knows how the Indian cricket team is going to cope with the difficult and seamer-friendly wickets in Australia.
Choose the option which is closest in meaning to the underlined phrase in the above sentence.
Detailed Solution for UGEE REAP Mock Test- 4 - Question 14

The phrase ‘cope with’ means to deal or manage with something, especially a problem or difficulty.

Among the given options, ‘put up with’ is closest in meaning as it suggests:

  • Enduring a difficult situation
  • Tolerating challenges
UGEE REAP Mock Test- 4 - Question 15
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Which of the following is CORRECT with respect to grammar and usage?

Mount Everest is _________.
Detailed Solution for UGEE REAP Mock Test- 4 - Question 15

The sentence is stating the highest peak in the world. Since it is a specific thing, we need to use the definite article ‘the’ before it. Also the sentence is using the superlative degree and so we say ‘the highest peak in the world’, making option (a) the correct answer. There cannot be many highest peaks in the world and so options (c) and (d) are incorrect.

UGEE REAP Mock Test- 4 - Question 16
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A pack of playing cards was found to contain only 51 cards. If the first 13 cards, which are examined, are all red, what is the probability that the missing card is black?
Detailed Solution for UGEE REAP Mock Test- 4 - Question 16

To find the probability that the missing card is black given that the first 13 cards examined are all red, use conditional probability.
Let M be the event that the missing card is black, and R be the event that the first 13 cards are red. We need P(M | R).
P(M) = 26/52 = 1/2 (26 black cards in a full deck).
If M occurs (missing card is black), the pack has 26 red and 25 black cards. P(R | M) = C(26, 13) / C(51, 13) (probability of drawing 13 red from 26 red, 51 total).
If not M (missing card is red), the pack has 25 red and 26 black cards. P(R | not M) = C(25, 13) / C(51, 13).
P(R) = P(R | M) * P(M) + P(R | not M) * P(not M) = [C(26, 13) / C(51, 13)] * (1/2) + [C(25, 13) / C(51, 13)] * (1/2).
Thus, P(M | R) = [C(26, 13) * (1/2)] / P(R) = C(26, 13) / [C(26, 13) + C(25, 13)].
Since C(26, 13) / C(25, 13) = 26 / 13 = 2, then P(M | R) = 2 / (2 + 1) = 2/3.

UGEE REAP Mock Test- 4 - Question 17
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Let (1 + x + x²)⁹ = α₀ + α₁x + …., α18x18, then which of the following is true?
Detailed Solution for UGEE REAP Mock Test- 4 - Question 17

Step 1: Total Sum of Coefficients

To find the sum of all coefficients, plug in x = 1:
(1 + 1 + 1)⁹ = 3⁹ = 19683

So the total sum a₀ + a₁ + ... + a₁₈ = 19683

Step 2: Check Option (a)

Option (a) says:
a₀ + a₁ + ... + a₁₈ = a₁ + a₃ + ... + a₁₇
That implies the sum of even-indexed coefficients equals the sum of odd-indexed ones.

But the total sum 19683 is odd, and if even and odd terms were equal, their sum would be even. So,
Option (a) is false.

Step 3: Check Option (b)

Option (c) says the total sum is divisible by 9.
We already have the total sum as 19683, and 19683 ÷ 9 = 2187, which is an integer.
So,
Option (b) is true

Step 4: Check Option (c)

To find the sum of even-indexed coefficients, we use this trick:

  • Plug x = 1: gives total sum = 19683

  • Plug x = –1:
    (1 – 1 + 1)⁹ = (1)⁹ = 1

Now add these two: 19683 + 1 = 19684
Now divide by 2 to get the sum of even-indexed coefficients:
19684 ÷ 2 = 9842

Since 9842 is even,
Option (c) is false

Step 5: Check Option (d)

Option (d) says the total sum is divisible by 3 but not by 9.
But we just proved the sum is divisible by 9, so
Option (d) is false

Final Answer: Option C

UGEE REAP Mock Test- 4 - Question 18
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Directions: In each of the following question a number series is given. After the series, a number is given followed by (a), (b), (c), (d) and (e). You have to complete the series starting with the number given, following the sequence of the original series and answer the questions that follow the series.

What will come in place of (D)?
Detailed Solution for UGEE REAP Mock Test- 4 - Question 18

The given series is based on the following pattern:

Similarly, 

Hence, 284 will come in place of d. 

UGEE REAP Mock Test- 4 - Question 19
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The number that least fits this set: (324, 441, 97, and 64) is _________.
Detailed Solution for UGEE REAP Mock Test- 4 - Question 19

Analyzing given numbers, we get
324 = 182
441 = 212
64 = 82
But 97 is not the square of any numbers, hence, least fits the given set.

UGEE REAP Mock Test- 4 - Question 20
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Social science disciplines were in existence in an amorphous form until the colonial period when they were institutionalized. In varying degrees, they were intended to further the colonial interest. In the time of globalization and the economic rise of postcolonial countries like India, conventional ways of knowledge production have become obsolete.

Which of the following can be logically inferred from the above statements?
(i) Social science disciplines have become obsolete.
(ii) Social science discipline had a pre-colonial origin.
(iii) Social science disciplines always promote colonialism.
(iv) Social science must maintain disciplinary boundaries.
Detailed Solution for UGEE REAP Mock Test- 4 - Question 20

On the basis of the given passage, it can be concluded that statement (ii) 'social science disciplines had a pre-colonial origin' is correct. Therefore, option (a) is only correct.

UGEE REAP Mock Test- 4 - Question 21
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In how many ways can one arrange letters in the word 'INSTITUTION' such that no two same letters come together along with the following conditions:
(A) There is no 'T' which is immediately preceded as well as followed by 'N'.
(B) There is no 'T' which is immediately preceded as well as followed by 'T'.
Detailed Solution for UGEE REAP Mock Test- 4 - Question 21

The word "INSTITUTION" has 11 letters with frequencies I:3, T:3, N:2, S:1, U:1, O:1.
Total arrangements without restrictions are 
The conditions (no two identical letters adjacent, no 'T' in N-T-N or T-T-T sequences) reduce this number significantly.
The provided solution incorrectly assumes 10 letters and does not properly address the conditions, yielding an unjustified 40320.
A detailed combinatorial calculation is needed, but none of the options (32256, 40320, 60480) align with "INSTITUTION" under these constraints. Thus, the correct answer is "D: None of these."

UGEE REAP Mock Test- 4 - Question 22
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In [0, π], the curves f(x) = sin x and g(x) = cos x intersect at x =
Detailed Solution for UGEE REAP Mock Test- 4 - Question 22

For the point of intersection, we have
sin x = cos x

UGEE REAP Mock Test- 4 - Question 23
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Detailed Solution for UGEE REAP Mock Test- 4 - Question 23


UGEE REAP Mock Test- 4 - Question 24
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Detailed Solution for UGEE REAP Mock Test- 4 - Question 24

UGEE REAP Mock Test- 4 - Question 25
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Find what should come in place of the question mark (?) in the following number series:

12, 12, 18, 45, 180, 1170, ?
Detailed Solution for UGEE REAP Mock Test- 4 - Question 25

The given number series is based on the following pattern:
12 × 1 = 12
12 × 1.5 = 18
18 × (1 + 1.5) = 18 × 2.5 = 45
45 × (1.5 + 2.5) = 45 × 4 = 180
180 × (4 + 2.5) = 180 × 6.5 = 1170
∴ ? = 1170 × (4 + 6.5) = 1170 × 10.5 = 12285
Hence, 12285 will replace the question mark.

UGEE REAP Mock Test- 4 - Question 26
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40% of deaths on city roads may be attributed to drunken driving. The number of degrees needed to represent this as a slice of a pie chart is
Detailed Solution for UGEE REAP Mock Test- 4 - Question 26

100% = 360°
⇒ 1% = 3.6°
Now, 
40% = 40 × 3.6 = 4 × 36 = 144°

UGEE REAP Mock Test- 4 - Question 27
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Translate into English → waiku dakaayang man damat yak?
Detailed Solution for UGEE REAP Mock Test- 4 - Question 27

The question asks for the English translation of 'waiku dakaayang man damat yak?' Among the options provided, option A, 'I hear a moon below you,' is the most plausible translation.

The phrase seems to break down into components that align with this meaning:

  • 'waiku' could imply hearing or sound.
  • The rest of the words collectively suggest 'a moon below you.'

Thus, the correct answer is: The given question translates to English as 'I hear a moon below you,' which corresponds to option A.

UGEE REAP Mock Test- 4 - Question 28
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Translate into English → wasni yaihnit yak sunilu palani yamtaman.?
Detailed Solution for UGEE REAP Mock Test- 4 - Question 28

The correct translation of 'You make the dog's raft next to the water' matches exactly with Option D.

UGEE REAP Mock Test- 4 - Question 29
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Two dice are thrown simultaneously. What is the probability that the sum of the numbers is a multiple of 4?
Detailed Solution for UGEE REAP Mock Test- 4 - Question 29

When two dice are thrown, the total number of outcomes is:
6 × 6 = 36

Now, list all outcomes where the sum is a multiple of 4:
Multiples of 4 between 2 and 12: 4, 8, 12

Sum = 4 → Pairs:

(1,3), (2,2), (3,1) → 3 outcomes

Sum = 8 → Pairs:

(2,6), (3,5), (4,4), (5,3), (6,2) → 5 outcomes

Sum = 12 → Pairs:

(6,6) → 1 outcome

Total favorable outcomes = 3 + 5 + 1 = 9
Total possible outcomes = 36

So,
Probability = 9 / 36 = 1 / 4

Final Answer: (c) 1/4

UGEE REAP Mock Test- 4 - Question 30
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To whom is Chhaya married?
Detailed Solution for UGEE REAP Mock Test- 4 - Question 30

From the given information, two conclusions can be obtained:
1. Anand is not married to Bharti or Chhaya, i.e. Anand can be married to either Divya or Alka.

2. Basant and Diganto are not married to Divya or Bharti, i.e. Basant and Diganto are married to Alka or Chhaya.

From these two conclusions, we can see that since Alka would be married to either Basant or Diganto, Anand would surely be married to Divya, which leaves Chetan and Bharti as a pair as well. This gives two final possible sets of pairs of males and females.
1. When Basant is married to Alka

2. When Basant is married to Chhaya

Following these two possibilities, the partners of Basant and Diganto, i.e. Chhaya and Alka cannot be known for sure without any more information.
Therefore, it cannot be determined whom Chhaya is married to.

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