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UGEE REAP Mock Test- 4 - JEE MCQ


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30 Questions MCQ Test - UGEE REAP Mock Test- 4

UGEE REAP Mock Test- 4 for JEE 2024 is part of JEE 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 2024 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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A can do a work in 10 days and B can do the same work in 20 days. They work together for 5 days and then A goes away. In how many, more days will B finish the work?

Detailed Solution for UGEE REAP Mock Test- 4 - Question 1
In 5 days the can complete

Remaining is 1/4 part

UGEE REAP Mock Test- 4 - Question 2
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In a fort there was sufficient food for 200 soldiers for 31 day. After 27 days 120 soldiers left the fort. For how many extra days will the rest of the food last for the remaining soldiers?

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

Man x Day = Man. Day

200 x 31 = 6200

After 27 days

200 x 27 = 5400 Man. Day is finished Remaining = 800

Man Day = 800

80 Day = 800

Day = 10

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UGEE REAP Mock Test- 4 - Question 3
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Find the principal if the interest compounded at the rate of 10% per annum for two years is Rs. 420.

Detailed Solution for UGEE REAP Mock Test- 4 - Question 3
P = ?, Cl = Rs. 420, R = 10%, T = 2 years.

UGEE REAP Mock Test- 4 - Question 4
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A sum of money doubles itself in 5 years. In how many years will it become fourfold (if interest is compounded)?
Detailed Solution for UGEE REAP Mock Test- 4 - Question 4

⇒ 4 = [21/5]T

⇒ 22 = 2T/5

⇒ T/5 = 2

∴ T = 10 yrs.

UGEE REAP Mock Test- 4 - Question 5
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Divided Rs. 6000 into two parts so that simple interest on the first part for 2 years at 6% p.a. may be equal to the simple interest on the second part for 3 years at 8% p.a.
Detailed Solution for UGEE REAP Mock Test- 4 - Question 5
Let one part be Rs. x then

12x = 144000 - 24x

36x = 144000

x = 4000

UGEE REAP Mock Test- 4 - Question 6
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Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph, Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
Detailed Solution for UGEE REAP Mock Test- 4 - Question 6

Suppose they meet x hours after 7 a.m.

Distance covered by A in x hours = 20x km

Distance covered by B in (x - 1) hours

= 25 (x - 1)km

∴ 20x + 25 (x - 1) = 110

or 45x = 135 or x = 3.

So, they meet at 10 a.m.

UGEE REAP Mock Test- 4 - Question 7
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Two trains are running in opposite directions towards each other with speeds of 54 kmph and 48 kmph respectively. If the length of the train is 250 m and they cross each other in 18 seconds, the length of the other train is
Detailed Solution for UGEE REAP Mock Test- 4 - Question 7
Relative speed = (54 + 48) kmp

Let the length of the other train be x metres

= 1530 or x = 260 m

∴ The length of the other train is 260 m.

UGEE REAP Mock Test- 4 - Question 8
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A train travelling at 48 kmph completely crosses- another train having half its length and traveling in opposite direction at 42 kmph, in 12 seconds. It also passes a railway platform in 45 seconds. The length of the platform is
Detailed Solution for UGEE REAP Mock Test- 4 - Question 8
Let the length of the first train be x metres.

Then, the length of the second train is (x/2) metres.

Relative speed = (48 + 42) kmp

or x = 200.

∴ Length of first train = 200m.

Let the length of platform be y metres.

Speed of the first train

= 1800 ⇒ y = 400 m

UGEE REAP Mock Test- 4 - Question 9
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A train of length 150 m takes 10 seconds to pass over another train 100 m long coming from the opposite direction, if the speed of the first train be 30 Kmph. the speed of the second train is
Detailed Solution for UGEE REAP Mock Test- 4 - Question 9
Let the speed of the second train be x kmph.

Relative speed = (30 + x) kmph

⇒ x = 60

UGEE REAP Mock Test- 4 - Question 10
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If Po and Ps are the vapour pressures of the solvent and solution respectively and n1​ and n2 are mole fractions of solvent and solute respectively, then
Detailed Solution for UGEE REAP Mock Test- 4 - Question 10

If Po​ and Ps​ are the vapour pressures of the solvent and solution respectively, n1​ and n2​ are the mole fractions of the solvent and solute respectively, then Ps​=Po​n1​. 

 

According to Raoult's law, the vapour pressure of a solvent above a solution is equal to the vapour pressure of the pure solvent at the same temperature scaled by the mole fraction of the solvent present.

UGEE REAP Mock Test- 4 - Question 11
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The velocity of the nitrogen molecule in room temperature air is:
Detailed Solution for UGEE REAP Mock Test- 4 - Question 11

Nitrogen molecule is 28 neuclons×1.67×10-27 kg/neucleon = 4.68 д 10-26 kg. So the average speed of a gas molecule is about 500 m/sec.

UGEE REAP Mock Test- 4 - 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. One of my friends stayed back one day at the show and kept looking at the puppets for a long time. He asked the manager of the show to move the puppets in certain ways. The manager as a kind person and with my friend insisting, he agreed to do what my friend asked for. But he did not the friend if there were magnets in the puppets. But the next day, the friend told us that he was sure that there were magnets inside the puppets' faces. What did he ask the manager to do and what could he have Seen? He must see the effect after asking for moving the puppets
Detailed Solution for UGEE REAP Mock Test- 4 - Question 12

Backwards towards each other.

By this His Friend can get to know the Poles if Magnets were there which Confirms Presence of Magnets in it.

UGEE REAP Mock Test- 4 - Question 13
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If 22x-1 = 1/8x-3 , the value of x is:
Detailed Solution for UGEE REAP Mock Test- 4 - Question 13

If 22x-1 = 1/8x-3 , ⇒ 22x-1 = 1/(23)(x-3)

⇒ 22x-1 = 1/23x-9 ⇒ 22x-1 = 29-3x

∴ 2x - 1 = 9 - 3x or 5x = 10 or x = 2

UGEE REAP Mock Test- 4 - Question 14
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then x is equal to:
Detailed Solution for UGEE REAP Mock Test- 4 - Question 14
On squaring both sides, we get

5 + ∛x = 9 or ∛x = 4.

Cunning both sides, we get

x = (4 x 4 x 4) = 64.

UGEE REAP Mock Test- 4 - Question 15
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If ax = by = cz and b2 = ac, then y equals:
Detailed Solution for UGEE REAP Mock Test- 4 - Question 15

Let ax = by = cz = k.

Then a = k1/x , b = k1/y and c = k1/z.

b2 = ac ⇒ k2/y = k1/x k1/2


y  =  2xz
         x+z

UGEE REAP Mock Test- 4 - Question 16
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If x = ya , y = zb and z = xc , then the value of abc is:
Detailed Solution for UGEE REAP Mock Test- 4 - Question 16

x = ya = (zb)a = zab = (xc)ab = xabc ∴ abc = 1.

UGEE REAP Mock Test- 4 - Question 17
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How many natural numbers between 300 to 500 are multiples of 7?
Detailed Solution for UGEE REAP Mock Test- 4 - Question 17
Between 300 and 500 the first term divisible by 7 is 301 and last term divisible by 7 is 497

So, here a = 301, d = 7

L = a + (n - 1) d

497 = 301 + (n-1) x 7

⇒ 7n = 203

⇒ n = 29

UGEE REAP Mock Test- 4 - Question 18
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The 4th and 10th term of an GP are 1/3 and 243 respectively. Find the 2nd term.
Detailed Solution for UGEE REAP Mock Test- 4 - Question 18

It is given that

ar3 = 1/3 ……(i)

ar9 = 243 ……(ii)

From (i) and (ii) we get

r6 = 729

r = 3

From (i) and (ill) we get

Second term will be 1/27

UGEE REAP Mock Test- 4 - Question 19
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The 7th and 21st terms of an AP are 6 and -22 respectively. Find the 26th term.
Detailed Solution for UGEE REAP Mock Test- 4 - Question 19
It is given that a + 6d = 6 and a + 20d = -22

⇒ 14d = -28, d = -2,

⇒ a = 18

26th term will be -32

UGEE REAP Mock Test- 4 - Question 20
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Find the number of terms of the series 1/81, 1/27, 1/9........ . - 729.
Detailed Solution for UGEE REAP Mock Test- 4 - Question 20
It. is given that

GP is 1/81 , -1/27 , 7/9, …..-729

Here arn-1 = 729

(-3)n-1 = 310, n = 11

UGEE REAP Mock Test- 4 - Question 21
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There are 5 letters and 5 directed envelopes. Find 'the number of ways in which the tetters can be pul into the envelopes so that all are not put in directed envelopes?
Detailed Solution for UGEE REAP Mock Test- 4 - Question 21

  • Here, the first letter can be put in any one of the 5 envelopes in 5 ways. Second letter can be put in any one of the 4 remaining envelopes In 4 ways. Continuing in this way, we get the total number of ways in which 5 letters can be put into 5 envelopes

    = 5 x 4 x 3 x 2 x 1 = 120.

  • Since out of the 120 ways, there is only one way for putting each letter in the correct envelope.

    Hence, the number of ways of putting letters all are not in directed envelopes = 120 - 1 = 119 ways.

UGEE REAP Mock Test- 4 - Question 22
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How many words, with or without meaning, can be formed using all letters of the word EQUATION, using each letter exactly once?
Detailed Solution for UGEE REAP Mock Test- 4 - Question 22
The word EQUATION has exactly 8 letters which are all different.

∴ Number of words that can be formed = number of permutations of 8 letters taken all at a time.

= P(8, 8) = 8!

= 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

= 40320

UGEE REAP Mock Test- 4 - Question 23
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It is required to seat 5 men and 4 women in a row so that the women occupy the even places. How many such arrangements are possible?
Detailed Solution for UGEE REAP Mock Test- 4 - Question 23
Total number of candidates = 5 + 2 = 9

In the row of 9 positions, the even places are 2nd, 6th and 8th. Now, number of even places = 4.

Number of women to occupy the even places = 4.

∴ Even places can be filled = P(4, 4) ways

Number of men = 5

∴ The remaining 5 places can be tilted by 5 men = P(5, 5) ways

∴ By the fundamental principle of counting.

∴ The required number of seating arrangements = P(4, 4) x P(5, 5) = 4! x 5!

= 24 x 120 = 2880.

UGEE REAP Mock Test- 4 - Question 24
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Four books, one each in chemistry, Physics, Biology and Mathematics are to be arranged in a shelf. In how many ways can this be done?
Detailed Solution for UGEE REAP Mock Test- 4 - Question 24
4 different books can be arranged among themselves, in a shelf, in P (4,4)

= 4 x 3 x 2 x 1 = 24 ways.

UGEE REAP Mock Test- 4 - Question 25
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The Probability of raining on day 1 is 0.2 and on day 2 is 0.3. What is the probat of raining on both the days?
Detailed Solution for UGEE REAP Mock Test- 4 - Question 25
0.2 x 0.3 = 0.06
UGEE REAP Mock Test- 4 - Question 26
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A bag contains 5 red balls and 8 blue bans. It also contains 4 green and 7 black balls. If a ball is drawn at random, then find the probability that it is not green.
Detailed Solution for UGEE REAP Mock Test- 4 - Question 26
The probability that the ball drawn is ol green colour = 4/24 = ⅙

Probability that the ball drawn is not of green colour

UGEE REAP Mock Test- 4 - Question 27
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From a pack of 52 playing cards, two cards are drawn together at random. Calculate the probability of both the cards being Kings.
Detailed Solution for UGEE REAP Mock Test- 4 - Question 27
Two cards can be drawn from a pack of 52 playing cards in 52C2 ways.

The event that two kings appear in a single draw can appear in 4C2 ways, i.e. 6 ways.

∴ The probability that the two cards drawn from a pack of 52 cards are kings = 6/1326 = 1/221

UGEE REAP Mock Test- 4 - Question 28
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Rahul's mother is the only daughter of Monika’s father, how is Monika's husband related to Rahul
UGEE REAP Mock Test- 4 - Question 29
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A is B’s sister, C is B’s mother, D is C’s father, E is D's mother. Then, how is A related to D
UGEE REAP Mock Test- 4 - Question 30
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Given that (i) A is brother of B (ii) C is father of A (iii) D is brother of E (iv) E is daughter of B, then uncle of D is
Detailed Solution for UGEE REAP Mock Test- 4 - Question 30
Uncle of D is A
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