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UGEE REAP Mock Test- 3 - JEE MCQ


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30 Questions MCQ Test - UGEE REAP Mock Test- 3

UGEE REAP Mock Test- 3 for JEE 2024 is part of JEE preparation. The UGEE REAP Mock Test- 3 questions and answers have been prepared according to the JEE exam syllabus.The UGEE REAP Mock Test- 3 MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for UGEE REAP Mock Test- 3 below.
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UGEE REAP Mock Test- 3 - Question 1
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Apurva can do a piece of work in 12 days. Apurva and Amit completed the work together and were paid Rs. 54 and Rs. 81 respectively. How many days must they have taken to complete the work together?

Detailed Solution for UGEE REAP Mock Test- 3 - Question 1
Payment ratio = 54:81

days work = 1/12 : 1/x

54 : 81 = 1/12 : 1/x

together they will take = (12 x 8)/(12 + 8) = 4.8 days

UGEE REAP Mock Test- 3 - Question 2
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If 12 men and 16 boys can do a piece of work in 5 days and 13 men and 24 boys can do it in 4 days, compare the daily work done by a man with that done by a boy?

Detailed Solution for UGEE REAP Mock Test- 3 - Question 2

12 M + 16 B = 1/5 …..(i)

13 M + 24 B = 1/4 ……(ii)

Also, 36 M + 48 B = 3/5

26 M + 48 B = 2/4

10 M = 1/10, M = 1/100

from eq (1) B = 1/200 , M : B = 2 : 1

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UGEE REAP Mock Test- 3 - Question 3
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15 men could finish a piece of work in 210 days. But at the end of 100 days, 15 additional men are employed. In how many more days will the work be complete?

Detailed Solution for UGEE REAP Mock Test- 3 - Question 3
Man x Day = Man . Day

15 x 210 = 3150, so after 100 days

15 x 100 = 1500 will be completed

remaining work = 1650 Man . Day

Man . Day = 1650

30. Day - 1650

Day = 55

UGEE REAP Mock Test- 3 - Question 4
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If the difference between the simple interest and compound interest on some principal amount at 20% per annum for 3 years in Rs. 48, then the principal amount must be
Detailed Solution for UGEE REAP Mock Test- 3 - Question 4

Here P = ?, R = 20%, T = 3 year Difference Rs. 48

ci = A-P
ci = 

On solving P = 375.

UGEE REAP Mock Test- 3 - Question 5
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Raju lent Rs. 400 to Ajay for 2 years, and Rs, 100 to Manoj for 4 years and received together from both Rs. 60 as interest. Find the rate of interest, simple interest being calculated.
Detailed Solution for UGEE REAP Mock Test- 3 - Question 5

UGEE REAP Mock Test- 3 - Question 6
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It a certain sum of money becomes double at simple interest in 12 years, what would be the rate of interest per annum?
Detailed Solution for UGEE REAP Mock Test- 3 - Question 6

p=2x
so si=p-initial
si=2x-x
si=x

UGEE REAP Mock Test- 3 - Question 7
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A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long coming from opposite direction in 6 seconds. The speed of the second train is
Detailed Solution for UGEE REAP Mock Test- 3 - Question 7
Let the speed of the second train be x kmph Relative speed = (x + 50) kmph

Distance covered = (108+ 112) = 220 m.

or x = 82 kmph

UGEE REAP Mock Test- 3 - Question 8
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A train B speeding with 120 kmph crosses another train C, running in the same direction in 2 minutes. If the lengths of the trains B and C be 100 m and 200m respectively, what is the speed of the train C?
Detailed Solution for UGEE REAP Mock Test- 3 - Question 8
Let the speed of train C be x kmph.

Speed of B relative to C = (120 - x)

Distance covered = (100 4 200)m = 300 m.

⇒ 5400 = 120(600-5x) ⇒ x = 111.

UGEE REAP Mock Test- 3 - Question 9
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A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is
Detailed Solution for UGEE REAP Mock Test- 3 - Question 9
Given

Speed of the first person = 2 km/h

Speed of the second person = 4 km/h

Train taken to overtake the first person = 9 sec

Train taken to overtake the second person = 10 sec

Formula Used:

Speed = Distance/Time

km/h × 5/18 = m/sec

Concept used:

When two bodies move in the same direction, then

Relative speed = Difference of their speeds

Calculation:

Let the length and the speed of a train be L and V respectively.

Speed of the first person = 2 × 5/18 = 5/9 m/sec

Speed of the second person = 4 × 5/18 = 10/9 m/sec

Relative speed of the train and the first person = (V – 5/9) m/sec

⇒ V – 5/9 = L/9

⇒ V = L/9 + 5/9 ----(1)

Relative speed of the train and the first person = (V – 10/9) m/sec

⇒ V – 10/9 = L/10

⇒ V = L/10 + 10/9 ----(2)

Equating equation (1) and equation (2),

⇒ L/9 + 5/9 = L/10 + 10/9

⇒ L/9 – L/10 = 10/9 – 5/9

⇒ (10 × L – 9 × L)/(10 × 9) = (10 – 5)/9

⇒ (10L – 9L)/90 = 5/9

⇒ L = 5/9 × 90

⇒ L = 50 m

∴ The length of the train is 50 m.

UGEE REAP Mock Test- 3 - Question 10
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A square closed loop of area A, lying in the horizontal plane is moving horizontally with velocity v in a uniform vertical magnetic field B. Which one of the following statements is FALSE?
Detailed Solution for UGEE REAP Mock Test- 3 - Question 10

A. True, EMF will be induced by Motional EMF

B. True, Conservation of Work & Energy. Coz,,Work-done by Magnetic Field is zero.

C. False, always work done by Magnetic Field is Zero cozy direction of Force and Displacement are Perpendicular so, Dot Product is Zero always.

D. True, E = [V x B. dl] where, V = Velocity and E = EMF

E. True, E = (V x B), dl where B = Magnetic Field and E = EMF

UGEE REAP Mock Test- 3 - Question 11
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Two liquids A and B are mixed in such a proportion that they form an ideal solution who's total vapor pressure is exactly three times that of the partial pressure of A. If PAº and PBº are the vapor pressures of pure A and B respectively, then the total vapor pressure of the solution is given by Options:
Detailed Solution for UGEE REAP Mock Test- 3 - Question 11

You must Know: Total Pressure PT = PA + PB Where PA is Partial Pressure

And PA = P°AXA where P°A = Vapor Pressure and XA = Mole Fraction of A

Similarly, for PB = P°BXB

We Know XA + XB = 1 ------- -— Sum of Mole Fractions

Given: PT = 3 PA = PA + PB

= 3 P°AXA --------- 3

So, 2PA = PB

2P°AXA = P°BXB --------- 1

XA + XB = 1 --------- 2

From 1 & 2 we get XA = P°B/ (2P°A + P°B)

Put XA in 3 We Get Ans as

PT = 3 P°A P°B / (2 P°A a+ P°B)

UGEE REAP Mock Test- 3 - Question 12
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When I was a child, there used to be a fair in my town during the Diwali and Eid festivities. Among the many things I saw was a strange puppet show. There were three puppets, one of a man, another of a woman and the third one of a rakshasa (demon). Whenever the rakshasa was brought close to the woman, she would turn her face away. But when the man was brought close to her, she would turn back and face the man.

I and my friends looked at this show and argued for hours what caused the woman to turn her face. Choose one or more of the options below about my childhood experience above:

Q. The strange behaviour of the woman puppet was:
Detailed Solution for UGEE REAP Mock Test- 3 - Question 12

Magnetic Attraction & Repulsion Properties must be used.

UGEE REAP Mock Test- 3 - Question 13
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If log102 = 0.3010, the value of log105 is
Detailed Solution for UGEE REAP Mock Test- 3 - Question 13
log10 5 = log10 (10/2) = log10 10 - log10 2.

= 1-log10 2 = (1 - 0.3010) = 0.6990

UGEE REAP Mock Test- 3 - Question 14
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The value of (log927 + log832) is
Detailed Solution for UGEE REAP Mock Test- 3 - Question 14
log927 + log832

UGEE REAP Mock Test- 3 - Question 15
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If log5(x2 + x) - log5(x+ 1) = 2, then the value of x
Detailed Solution for UGEE REAP Mock Test- 3 - Question 15
log5(x2 + x) - log5(x+ 1) = 2

or log5x = 2 or x = 52 = 25.

UGEE REAP Mock Test- 3 - Question 16
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Sum the series to infinity
Detailed Solution for UGEE REAP Mock Test- 3 - Question 16

UGEE REAP Mock Test- 3 - Question 17
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Find the 9th term of the H.P. 6, 4, 3 ............
Detailed Solution for UGEE REAP Mock Test- 3 - Question 17
The given sequence is 6,4,3,...... which is H.P

The sequence of reciprocals of its terms is 1/6 , 1/4 , 1/3 , ... . which is an A.P

∴ 9th term of H.P is 6/5

UGEE REAP Mock Test- 3 - Question 18
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If x > 1, y > 1 , z >1 are in G.P., then are in
Detailed Solution for UGEE REAP Mock Test- 3 - Question 18
∵ x, y, z are in G.P.

∵ y2 = xz

Taking log on both sides

2 log y = log x + log z

⇒ 2 + 2 log y = (1 + log x) + (1 log z)

⇒ 2 (1 + log y) = (1 + log x) + (1 + log z)

⇒ 1 + log x, 1 + log y, 1 + log z, are in A.P.

UGEE REAP Mock Test- 3 - Question 19
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How many straight lines can be formed from 8 non-collinear points on the X-Y plane?
Detailed Solution for UGEE REAP Mock Test- 3 - Question 19
To draw a line we have to choose two points So, BC2 as 28 ways
UGEE REAP Mock Test- 3 - Question 20
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In how many ways can the letters of the word PATNA be rearranged?
Detailed Solution for UGEE REAP Mock Test- 3 - Question 20
This can be in 5!/2! ways

5!/2! = 60

UGEE REAP Mock Test- 3 - Question 21
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In the word-"PATNA", how many words would be there which would start with the letter P?
Detailed Solution for UGEE REAP Mock Test- 3 - Question 21

In PATNA, if P is fixed so we have only four letter ATNA In which there are two A's.

So, 4!/2! = 12

UGEE REAP Mock Test- 3 - Question 22
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A captain and a vice-captain are to be chosen out of a team having 11 players. How many ways are there to achieve this?
Detailed Solution for UGEE REAP Mock Test- 3 - Question 22
11C2 x 2i Ways which is equal to 110.
UGEE REAP Mock Test- 3 - Question 23
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If the probability that A will live 15 years is 7/8 and that B will live 15 years is 9/10 , then what is the probability that both will live after 15 years?
Detailed Solution for UGEE REAP Mock Test- 3 - Question 23

UGEE REAP Mock Test- 3 - Question 24
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If events A and B are independent and P(A) = 0.15, P (A ∪ B) = 0.45 then P(B) =
Detailed Solution for UGEE REAP Mock Test- 3 - Question 24
P(A ∩ B) - P(A) x P(B) = 0.15 x P(B)

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

0.45 = 0.15 + P(B) - (0.15) x P(B)

= 0.15 + P(B)(1-0.15)

= 0.15 + 0.85P(B)

∴ 0.85P(B) = 0.45 - 0.15 = 0.30

∴ P(B) = 0.30/0.85 = 30/85 = 6/17

UGEE REAP Mock Test- 3 - Question 25
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Four different objects 1. 2,3, 4 are distributed at random in four places marked 1, 2, 3, 4. What is the probability that none of the objects occupy the place corresponding to its number?
Detailed Solution for UGEE REAP Mock Test- 3 - Question 25

Probability of Objects Not Occupying Corresponding Place

- Total Number of Ways to Distribute Objects: There are 4 objects and 4 places, so there are 4! = 24 ways to distribute the objects.
- Number of Ways None of the Objects Occupy Corresponding Place: For none of the objects to occupy the place corresponding to its number, each object must be placed in one of the other 3 places.
- For the first object, there are 3 places it can go.
- For the second object, there are 2 places left.
- For the third object, there is 1 place left.
- The fourth object automatically goes in the last place.
- Therefore, the number of ways none of the objects occupy corresponding places is 3 * 2 * 1 = 6 ways.
- Probability: Probability = (Number of favorable outcomes) / (Total number of outcomes) = 6 / 24 = 3 / 12 = 1 / 4 = 0.375
- Therefore, the probability that none of the objects occupy the place corresponding to its number is 3/8.

UGEE REAP Mock Test- 3 - Question 26
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Direction : Read the following information carefully and answer the question below it.

All the six members of a family P, Q, R, S, T and U are travelling together Q is the son of R but R is not the mother of Q. P and R are a married couple. T is the brother of R. S is the daughter of P. U is the brother of Q.

Q. How may male members are there in the family?
Detailed Solution for UGEE REAP Mock Test- 3 - Question 26
→ Q is son of R

→ R is not the mother, then R is father of Q

→ P and R are married couple R -

→ T is the brother of R T .. R

→ S is daughter of P

→ U is the brother of Q Q . . U

Complete Solution

UGEE REAP Mock Test- 3 - Question 27
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Direction : Read the following information carefully and answer the question below it.

All the six members of a family P, Q, R, S, T and U are travelling together Q is the son of R but R is not the mother of Q. P and R are a married couple. T is the brother of R. S is the daughter of P. U is the brother of Q.

Q. Who is the mother of Q?

Detailed Solution for UGEE REAP Mock Test- 3 - Question 27
→ Q is son of R

→ R is not the mother, then R is father of Q

→ P and R are married couple R -

→ T is the brother of R T .. R

→ S is daughter of P

→ U is the brother of Q Q . . U

Complete Solution

UGEE REAP Mock Test- 3 - Question 28
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Direction : Read the following information carefully and answer the question below it.

All the six members of a family P, Q, R, S, T and U are travelling together Q is the son of R but R is not the mother of Q. P and R are a married couple. T is the brother of R. S is the daughter of P. U is the brother of Q.

Q. How many children does P have?

Detailed Solution for UGEE REAP Mock Test- 3 - Question 28
→ Q is son of R

→ R is not the mother, then R is father of Q

→ P and R are married couple R -

→ T is the brother of R T .. R

→ S is daughter of P

→ U is the brother of Q Q . . U

Complete Solution

UGEE REAP Mock Test- 3 - Question 29
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Direction : Read the following information carefully and answer the question below it.

All the six members of a family P, Q, R, S, T and U are travelling together Q is the son of R but R is not the mother of Q. P and R are a married couple. T is the brother of R. S is the daughter of P. U is the brother of Q.

Q. Who is the wife of T?

Detailed Solution for UGEE REAP Mock Test- 3 - Question 29
→ Q is son of R

→ R is not the mother, then R is father of Q

→ P and R are married couple R -

→ T is the brother of R T .. R

→ S is daughter of P

→ U is the brother of Q Q . . U

Complete Solution

UGEE REAP Mock Test- 3 - Question 30
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Direction : Read the following information carefully and answer the question below it.

All the six members of a family P, Q, R, S, T and U are travelling together Q is the son of R but R is not the mother of Q. P and R are a married couple. T is the brother of R. S is the daughter of P. U is the brother of Q.

Q. Which of the following is a pair of females?

Detailed Solution for UGEE REAP Mock Test- 3 - Question 30
→ Q is son of R

→ R is not the mother, then R is father of Q

→ P and R are married couple R -

→ T is the brother of R T .. R

→ S is daughter of P

→ U is the brother of Q Q . . U

Complete Solution

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