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UGEE REAP Mock Test- 5 - JEE MCQ


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30 Questions MCQ Test - UGEE REAP Mock Test- 5

UGEE REAP Mock Test- 5 for JEE 2024 is part of JEE preparation. The UGEE REAP Mock Test- 5 questions and answers have been prepared according to the JEE exam syllabus.The UGEE REAP Mock Test- 5 MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for UGEE REAP Mock Test- 5 below.
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UGEE REAP Mock Test- 5 - Question 1
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A cistern is normally filled in 5 hours. However, it takes 6 hours when there is leak in its bottom. If the cistern is full, in what time shall the leak empty it?

Detailed Solution for UGEE REAP Mock Test- 5 - Question 1
In one hour 1/5 part is filled now leak can empty in x hour then

⇒ 1/30 = 1/x , x = 30 hours

UGEE REAP Mock Test- 5 - Question 2
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Pipe A and B running together can fill a cistern in 6 minutes. If B takes 5 minutes more than A to fill the cistern, then the time in which A and B will fill the cistern separately will be respectively?

Detailed Solution for UGEE REAP Mock Test- 5 - Question 2
Let pipe A can fill in x and pipe B in x+5 minutes

x = 10, x + 5 = 15

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UGEE REAP Mock Test- 5 - Question 3
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There are two pipes in a tank. Pipe A is for filling the tank & Pipe B is for emptying the tank. If A can fill the tank in 10 hours and B can empty the tank in 15 hours then find how many hours will it take to completely fill a half empty tank?

Detailed Solution for UGEE REAP Mock Test- 5 - Question 3

So it takes 30 hours to fill the tank and 15 horse to fill half the tank

UGEE REAP Mock Test- 5 - Question 4
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There are three Taps A, B and C in a tank. They can fill the tank in 10 hrs, 20 hrs and 25 hrs respectively. At first, all of them are opened simultaneously. Then after 2 hours tap C is closed and A and B are kept running. After the 4th hour, tap B is also closed. The remaining work is done by Tap A alone. Find the percentage of the work done by Tap A by itself.
Detailed Solution for UGEE REAP Mock Test- 5 - Question 4

So remaining part after 5 hour is

32/10 = 3.2 hours

% of work done by A

UGEE REAP Mock Test- 5 - Question 5
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A sum-of money placed at compound interest doubles itself in 3 years. In how many years will it amount to 8 times itself?
Detailed Solution for UGEE REAP Mock Test- 5 - Question 5
Let sum = x

⇒ 8 = [21/3]T

⇒ 23 = 2T/3

⇒ T/3 = 3

∴ T = 9 yrs.

Alternative:

If a certain sum of money becomes ‘m’ times in ‘y’ years. Then it will become (mn) times in ‘n x y’ years. Hence 23 in 3 x 3 = 9 years,

UGEE REAP Mock Test- 5 - Question 6
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A sum of money becomes 7/4 of itself in 6 years at a certain rate of simple interest. Find the rate of interest.
Detailed Solution for UGEE REAP Mock Test- 5 - Question 6
Let sctm be x

T = 6 Years , R = ?

UGEE REAP Mock Test- 5 - Question 7
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A sum of Rs. 600 amounts to Rs. 720 in 4 years at simple interest. What will it amount to if the rate of interest is increased by 2%?
Detailed Solution for UGEE REAP Mock Test- 5 - Question 7

P = Rs. 600, A = Rs. 720

T = 4 years, R = ?

at 7% Rate

A = 600 + 168 = 768

UGEE REAP Mock Test- 5 - Question 8
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A man sees a train passing over a bridge 1 km long. The length of the train is half that of the bridge, if the train clears the bridge in 2 minutes, the speed of the train is
Detailed Solution for UGEE REAP Mock Test- 5 - Question 8
Distance travel in 2 minute

Distance covered in hour

∴ Speed of the train = 45 km/hr

UGEE REAP Mock Test- 5 - Question 9
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Helium is two times heavier than H2, The average kinetic energy per molecule for helium at 300K is
Detailed Solution for UGEE REAP Mock Test- 5 - Question 9

Kinetic energy per mole or per molecule of a gas depends only on the temperature and not on the nature of the gas.


 

KE=2/3​RT
 

So, average kinetic energy of a helium atom is the same as that of a hydrogen molecule.

UGEE REAP Mock Test- 5 - Question 10
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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. If there were magnets fixed in the heads the puppets inside the head such that one end of the magnet was at the mouth (M) and the other at the back of the head (B), then the arrangement of the north (N) and south (S) poles of the magnets must be like:
Detailed Solution for UGEE REAP Mock Test- 5 - Question 10
Woman Head & demon Head Repels means, they must have Similar Poles coz, Similar Poles Repels Hence option 4 got Rejected, now after Turning, Woman Back & Man Head must Repel means They must be Similar So, Option 1, 3 got Rejected also. Hence, option 2 is Correct.
UGEE REAP Mock Test- 5 - Question 11
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log32 x = 0.8, then x is equal to:

Detailed Solution for UGEE REAP Mock Test- 5 - Question 11
log32 x = 0.8 ⇒ x = (32)0.8

= (25)4/5 = 24 = 16.

UGEE REAP Mock Test- 5 - Question 12
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Detailed Solution for UGEE REAP Mock Test- 5 - Question 12

= logabc a + logabc b + logabc c

= logabc (abc) = 1

UGEE REAP Mock Test- 5 - Question 13
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If log2[log3(log2x)] = 1, then x is equal to:
Detailed Solution for UGEE REAP Mock Test- 5 - Question 13

log2[log3(log2 x)] = 1

⇒ log3(log2 x) = 2

⇒ log2 x = 32 = 9

⇒ x = 29 = 512

UGEE REAP Mock Test- 5 - Question 14
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If log10 2 = 0.3010, then log2 10 is :
Detailed Solution for UGEE REAP Mock Test- 5 - Question 14

UGEE REAP Mock Test- 5 - Question 15
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A ball rolling up an incline covers 36 metres during the first second, 32 metres during the second, 28 meters during the next and so on. How much distance will it travel during the 8th second?
Detailed Solution for UGEE REAP Mock Test- 5 - Question 15
Distance covered during the 1st second = 36 m

Distance covered during the 2nd second = 32 m

Distance covered during the 3rd second = 28 m.

The distance covered form an A.P.

= 36 + 32 + 28 .... in which

a = 38, d = -4

∴ Distance covered in 8th second

= 8th term of the A.P.

= a + 7d = 36 + 7 (-4)

= 38 - 28 = 8 metres.

UGEE REAP Mock Test- 5 - Question 16
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The sum of first three terms of a GP. is to the sum of first six terms is 125:152. Find the common ratio of G.P.
Detailed Solution for UGEE REAP Mock Test- 5 - Question 16

⇒ 125r3 = 27 ⇒ r3 = 27/125

or, r3 = (3/5)3 , ∴ r = 3/5

UGEE REAP Mock Test- 5 - Question 17
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Detailed Solution for UGEE REAP Mock Test- 5 - Question 17
(2 + 31) + (2 + 32) +...+ (2 + 311)

= 2 + 2 + 2 + …..up to 11 terms + (3 + 32 + 33 + …...up tp 11 terms)

UGEE REAP Mock Test- 5 - Question 18
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The common ratio of a G.P. is and the sum to infinity is 80/9. Find the First term.
Detailed Solution for UGEE REAP Mock Test- 5 - Question 18

Hence, the first term is 16.

UGEE REAP Mock Test- 5 - Question 19
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In how many ways can Ram choose a vowel and a consonant from the letter ALLAHABAD?
Detailed Solution for UGEE REAP Mock Test- 5 - Question 19
In Allahabad we have 4 As that is only one vowel and 4 consonants (B, D, H, L)

So any four combinations.

AB, AD, AH, AL are only 4 possibilities so..

UGEE REAP Mock Test- 5 - Question 20
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In how many ways can the letters of the word EQUATION be arranged so that all the vowels come together?
Detailed Solution for UGEE REAP Mock Test- 5 - Question 20
In EQUATION there are five vowels A, E, I, O and U and three consonants N, Q, T so the possible. arrangements, will b e 4! x 5 ! ways.
UGEE REAP Mock Test- 5 - Question 21
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There are 25 points on a plane of which 7 are collinear. Now solve the following:

Q. How many straight lines can be formed?
Detailed Solution for UGEE REAP Mock Test- 5 - Question 21

Total number of straights lines

= 25C2 - 7C2 + 1 = 280

25C2 selecting 2 points from total of 25 points
7C2  selecting 2 points from total of 7 points [ subtracting them because they are collinear 

UGEE REAP Mock Test- 5 - Question 22
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There are 25 points on a plane of which 7 are collinear. Now solve the following:

Q. How many triangles can be formed from these points?
Detailed Solution for UGEE REAP Mock Test- 5 - Question 22
Total triangle formed will be equal to 25C3 - 7C3 = 2265
UGEE REAP Mock Test- 5 - Question 23
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Three coins are tossed. Find the probability of no heads.

Detailed Solution for UGEE REAP Mock Test- 5 - Question 23
Sample space S = |HHH, HHT, HTH, HTT, THT, TTH, THH, TTT)

Number of exhaustive cases = -8

P (no heads) = P (ail tails) = 1/8 (∵ there is only favourable case TTT)

UGEE REAP Mock Test- 5 - Question 24
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What is the chance that a leap year, selected at random, will contain 53 Sunday?
Detailed Solution for UGEE REAP Mock Test- 5 - Question 24
We know that a leap year has 366 days and thus a leap year has 52 weeks and 2 days over.

The two left over (successive days have the following likely cases:

(i) Sunday and Monday

(ii) Monday and Tuesday

(iii) Tuesday and Wednesday

(iv) Wednesday and Thursday

(v) Thursday and Friday

(vi) Friday and Saturday

(vii) Saturday and Sunday

∴ Number of exhaustive cases ‘n’ = 7

Out of these, the favourable cases are...(i) and (vii)

∴ Number of favourable cases ‘m’ = 2

∴ Probability of having 53 Sunday = 2/7

UGEE REAP Mock Test- 5 - Question 25
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In a simultaneous throw of two dice, find P (A or B) if A denotes the event 'a total of 11 and B denotes the event’ ‘an odd number on each die'.
Detailed Solution for UGEE REAP Mock Test- 5 - Question 25
A: Getting total of 11 B: Getting odd number one each die

A = [(6, 5), (5, 6)]

B = [(1, 1), (1, 3), (1, 5), (3, 1), (3, 3), (3, 5), (5, 1), (5, 3), (5, 5)]

P(A) = 2/36, P(B) = 9/36 , P(A∩B) = 0

∴ Required probability

= P(A) + P(B) - P(A∩B)

UGEE REAP Mock Test- 5 - Question 26
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Direction: Read the following in Information carefully and answer the question below it.

A family consists of six members P, Q, R, X, Y and Z. Q is the son of R but R is not mother of Q. P and R are a married couple. Y is the brother of R. X is the daughter is the brother of P. Z is the brother of P.

Who is the brother-in-law of R?
Detailed Solution for UGEE REAP Mock Test- 5 - Question 26

Y..R - P..Z

Q..X

UGEE REAP Mock Test- 5 - Question 27
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Direction: Read the following in Information carefully and answer the question below it.

A family consists of six members P, Q, R, X, Y and Z. Q is the son of R but R is not mother of Q. P and R are a married couple. Y is the brother of R. X is the daughter is the brother of P. Z is the brother of P.

How is Q related to X?
Detailed Solution for UGEE REAP Mock Test- 5 - Question 27

 

Explanation:


  • Q is the son of R, so Q is the child of R.

  • Since P and R are a married couple, X is the daughter of P and R.

  • Since Y is the brother of R, Y is also the brother of X.

  • Therefore, Q and X are siblings, making Q the brother of X.


    •  
UGEE REAP Mock Test- 5 - Question 28
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Direction: Read the following information carefully and answer the question below it

P. Q. R. S. T. U and V are seven positive integers and (P x Q x R x S x T x U x V) is odd.

Maximum how many of these integers can be odd?

Detailed Solution for UGEE REAP Mock Test- 5 - Question 28
All integer should be odd to get odd result.
UGEE REAP Mock Test- 5 - Question 29
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Direction: Read the following information carefully and answer the question below it

P. Q. R. S. T. U and V are seven positive integers and (P x Q x R x S x T x U x V) is odd.

Minimum how many of these integers can be even?

Detailed Solution for UGEE REAP Mock Test- 5 - Question 29
None of the Integer should be even
UGEE REAP Mock Test- 5 - Question 30
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Direction: A cuboid is divided into 192 identical cubelets This is done by making minimum no. ot cuts possible. All cuts are parallel to some of the face. But before doing so. The cube is painted with green color on one set of opposite faces. Blue on other set of opposite faces and red on their pair of annosit faces.

What is the maximum number of cubelets possible which one colored with green colored only?
Detailed Solution for UGEE REAP Mock Test- 5 - Question 30
As we want maximize number of cubelets with green in color only cuboid has to painted with green color on set of opposite faces of 6 x 8. Hence no. of green colored only cubelets will (6 - 2) x (8 - 4) = 4 x 6 = 24, from face. There are two such faces hence maximum total no. of only green painted cubelets will be = 24 x 2 = 48

Hence option (a)

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