UGEE REAP Mock Test- 1


50 Questions MCQ Test IIITH UGEE Mock Test Series | UGEE REAP Mock Test- 1


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Attempt UGEE REAP Mock Test- 1 | 50 questions in 120 minutes | Mock test for JEE preparation | Free important questions MCQ to study IIITH UGEE Mock Test Series for JEE Exam | Download free PDF with solutions
QUESTION: 1

4 men and 3 women finish a job in 6 days. And 5 men and 7 women can do the same job in 4 days. How long will 1 man and 1 woman take to do the work?

Solution: Let man completes m part in a day and woman completes w part in a day, then

4m + 3w = ⅙ also …(i)

5m + 7w = ¼ …(ii)

After simplifying, we get

20m + 15w = ⅚

20m + 28w = 1

So 13w = ⅙

W = 1/78 …(iii)

From (i) and (iii), we get

m = 5/156

m + w = 5/156 + 1/78 = 7/156

So it requires 156/7 days = 22(2/7)

QUESTION: 2

A can do a piece of work in 20 days. He works at it for 5 days and then B finishes it in 10 more days, in how many days will A and B together finish the work?

Solution:

A’s one day work = 1/20

5 day ’A’ can complete (1/20) x 5 = ¼ part

remaining work = ¾ part

∴ B finishes ¾ part in 10 days.

∴ B finishes 1 part in 10/(¾) = 40/3 days.

together they Can finish it in

QUESTION: 3

Subhash can copy 50 pages in 10 hours; Subhash and Prakash together can copy 300 pages in 40 hours, in how much time can Prakash copy 30 pages?

Solution:

Subhash can copy 50 pages in 10 hours.
That means in 40 hours he can copy 50×4=200 pages.

Subhash and prakash together can copy 300pages in 40 hours.

That means prakash alone can copy 300-200=100 pages in 40 hours.

So to copy 30 pages prakash will take 40/100 ×30 = 12 hours.

QUESTION: 4

Priya can do 1/2 of the work in 8 days, while Preeti can do 1/3 of the work in 6 days. How long will it take for both of them to finish the work?

Solution:

Priya’s days work = (½)/8 = 1/16

Preeti’s days work

⇒ (⅓)/6 = 1/18 days

Together they can finish in.

QUESTION: 5

Rs. 1200 is lent out at 5% per annum simple interest for 3 years. Find the amount after 3 years.

Solution:

Here P = Rs. 1200

R = 5%, T = 3 years

Amount = P + SI = 1200 + 180 = 1380

QUESTION: 6

Rnd the difference between the simple and the compound interest at 5% per annum for 2 years on a principal of Rs. 2000.

Solution:

Here P = Rs. 2000, R = 5%, T = 2 years

= 205 - 200 = Rs. 5

Alternative:

Difference between Cl and Sl for two years

QUESTION: 7

What is the simple interest for five years on a sum of Rs. 700 if the rate of interest for the first 3 years is 8% per annum and for another 2 years is 7% per annum?

Solution:

QUESTION: 8

A train 700 m long is running at 72 kmph. If it crosses a tunnel in 1 minute, the length of the tunnel is

Solution:

Speed (72 x (5/18))m/sec = 20 m/sec

Time = 60 sec.

⇒ x = 500

QUESTION: 9

If a train 110 m long passes a telegraph pole in 3 seconds, then the time taken by it to cross a railway platform 165 m long is

Solution: Speed = (110/3)m/sec

Time is taken to cross railway platform

= [(110 + 165) x (3/110)] sec

= (275 x (3/110))sec = 7.5 sec

QUESTION: 10

Two trains 200 m and 150 m long are running on parallel rails at the rate of 40 kmph and 45 kmph, respectively. In how much time will they cross each other, if they are running in the same direction?

Solution: Relative speed = (45-40)kmph = 5 kmph.

= (5 x (5/18))m/sec = (25/18) m/sec

Total distance covered = Sum of the length of trains = 350 m

∴ Time taken = (350 x (18/25))sec = 252 sec.

QUESTION: 11

It is postulated that huge deposits of NaCI (rock salt) and CaCO3 (chalk and marble) are sites of erstwhile oceans, where the salts had been concentrated through weathering by rain and wind and leaching by rivers. Select the correct explanatory statement in this context.

Solution: The solubility of CaCO3 in water is pH dependent and is enhanced by acidic atmospheric gases. Hence, CaCO3 may be leached into water during weathering.
QUESTION: 12

If log 2 = 0.30103 and log 3 = 0.4771, find the number of digits in (648)5.

Solution:

You must know and Remember that No. of Significant Digit before decimal = [ (Characteristic)base 10 + 1]. To find (Characteristic)base10,

Log (648)5 = 5(log 648) = 5(log 23.34) = 5(3.log2 + 4 log 3) = 5(3(0.301) + 4(0.4771))

(Characteristic)base10,= 14

So, Answer is 14 + 1 = 15

QUESTION: 13

A man can cover a distance in 1hr 24min by covering 2/3 of the distance at 4 km/h and the rest at 5km/h. The total distance is

Solution: You must Know Km/hr (5/18) = m/sec

Say Total Distance be d

(2d/3)/4 + (d/3)/5 = 1+24/60

So, get d = 6 Km

QUESTION: 14

Two chairs (A and B) are in an empty room overnight. Chair A is made of steel, while chair B is made of wood. In the night and in the morning, the room’s temperature is 290 K. In the morning, a person chooses between Chair A and Chair B as the seat by feeling (touching) the chair and choosing one which feels warmer. The person chooses__ (BLANK-1) _ as it feels warmer because _ (BLANK-2)___has__ (BLANK-3)______ (BLANK-4)____ than ___(BLANK-5)___.

 

Find the correct Answer for Blank 1

Solution:
QUESTION: 15

If log 2 ~ 0.3010 and log 3 = 0.4771 then the value of log 4.5 is:

Solution: log 4.5 = log(9/2) = log9 - log2

= log(32) - log 2 = 2log3 - log2

= (2 x 0.4771) = 0.6532.

QUESTION: 16

The value of  is:

Solution:

Given Expression

QUESTION: 17

If log x + log y = log(x+y), then:

Solution:

logx+logy = log(x+y)

⇒ log(x+y) = log(xy)

∴ x + y = xy or x = y (x - 1)

 

QUESTION: 18

If a be the first term of a G.P., l the nth term and P the product of first n terms then P =

Solution:

If r is the common ratio of G.P, then

L = a rn-1 …(i)

The first n terms of the G.P. are

a, ar, ar2, ar3........arn-1

P = a x ar x ar2 x ... x arn-1

= an x r 1+2+3…+(n-1)

QUESTION: 19

Determine k so that ⅔, k, and ⅝ k are three consecutive terms of an A.P.

Solution:

 are in A.P

QUESTION: 20

If 7 times the 7th term of an A.P. is equal to 11 times its, 11th term, then the 18th term of the A.P. is

Solution: Let a be the first term and d, the common difference of an AP.

∴ a7 = a + 6d

A11 = a+10d ∴ 7a7 = 11a11

7 (a + 6d) = 11 (a + 10d)

⇒ 7a + 42d = 11a + 110d

⇒ 4a + 68d = 0

⇒ a + I7d = 0

⇒a18 = 0

QUESTION: 21

How many numbers of 3 digits can be formed with the digits 1, 2, 3, 4, 5 (repetition of digits not allowed)?

Solution: Three digits can be formed in 5P3 ways, that is (5!/(5-3)!) = 60
QUESTION: 22

Flow many numbers between 2000 and 3000 can be formed with the digits 0, 1, 2, 3, 4, 5, 6, 7 (repetition of digits not allowed)?

Solution:

Number between 2000 and 3000 are four digit numbers in which 2 is the first digit So, 2 must be taken in box d1

Now rest box can be filled in 7P3 ways.

QUESTION: 23

In how many ways can a person send Invitation cards to 6 of his friends if he has four servants to distribute the cards?

Solution: Person has six invitation cards 1 card can be given to any of 4 servants so six cards can be distributed in 4 x 4 x 4 x 4 x 4 x 4 = 46 ways
QUESTION: 24

In how many ways can 7 Indians, 5 Pakistanis and 6 Dutch be seated in a row so that all persons of the same nationality sit together?

Solution: We have

→ 7 Indians

→ 5 Pakistanis and

→ 6 Dutch

7 Indians can sit in 7! ways

5 Pakistanis can sit in 5! ways

6 Dutch can sit in 6! ways

Also they can sit together in 3! different ways 7! x 5! x 6! x 3!

QUESTION: 25

The probability that a student is not a swimmer Is 1/5. Then the probability that out of the five students, exactly four are swimmers, is

Solution:
QUESTION: 26

If the probability of rain on any given day in Pune city is 50%. Then what is the possibility that it rains on exactly 3 days in a 5-day period?

Solution: Probability that it rains on any day = ½ and it doesn't rain = 1 - (½) = ½

Prob. that it rains on exactly 3 days in a 6-day period.

= 5C3 x (½)3 x (½)2

5C3 for choosing which three days among given five days. (½)3 for that it rains on three days and (½)2 for it doesn’t rain on the remaining 2 days.

QUESTION: 27

A number is chosen at random among the first 120 natural numbers. The probability of the number chosen being a multiple of 5 or 15 is

Solution:
QUESTION: 28

Introducing Asha to guests, Bhasker said, “Her father is the only son or my father". How is Asha related to Bhasker?

Solution:

Hence, Asha is Bhasker's daughter.

QUESTION: 29

Pointing to a man on the stage. Rita said. "He is the brother of the daughter of the wife of my husband”. How is the man on the stage related to Rita?

Solution:

Hence person on stage is Rita’s son.

QUESTION: 30

A woman introduces a man as the son of the brother of her mother. How is a man related to a woman?

Solution:

Hence man is a woman's Cousin.

QUESTION: 31

Daya has a brother Amit. Daya is the son of Chandra, Bimai is Chandra's father. In terms of relationship, what is Amit to Bimai?

Solution:
QUESTION: 32

Direction : Read the following information carefully and answer the question below it.

In a certain code, ‘II be pee’ means' roses are blue’: 'silk hee' means ‘red flowers' and ‘pee mil hee’ means 'flowers are vegetables’.

Q. How is ‘red’ written in that code?

Solution: In the second and third statements, the common code word is 'hee' and the common word is 'flowers’. So, ‘hee’ stands for 'flowers'. Thus, in the second statement, 'silk- stands for 'red'.
QUESTION: 33

Direction : Read the following information carefully and answer the question below it.

In a certain code, ‘II be pee’ means' roses are blue’: 'silk hee' means ‘red flowers' and ‘pee mil hee’ means 'flowers are vegetables’.

Q. How is ‘roses’ written in that code?

Solution: Since from the given information, we can only find the code for ‘are' in the first statement, it cannot be determined which of the remaining two codes for ‘roses’.
QUESTION: 34

Direction : Read the following information carefully and answer the question below it.

In a certain code, ‘II be pee’ means' roses are blue’: 'silk hee' means ‘red flowers' and ‘pee mil hee’ means 'flowers are vegetables’.

Q. How is ‘vegetables are red flowers’ written in code?

Solution:

Clearly, the required code will consist of the same codes as in the third statements with the code for ‘red’ i.e. silk added to it.

QUESTION: 35

Direction : A cube is divided into 343 identical cubelets. Each cut is made parallel to some surface of the cube. But before doing that the cube is colored with green color on one set of adjacent faces, red on the second and blue on the third set.

Q. How many cubelets are there which are colored with exactly are color?

Solution: From each face 5 x 5 = 25 cubelets are painted is one color. Such total = 25 x 6 = 150 cubelets. Further because each face Is having one similar color adjacent face and 3 other different coloured faces hence 5 x 3 = 15 extra cubelets will come from three edges, where adjacent faces of similar color are meeting hence total = 150 + 15 = 165 cube will be then colored in exactly one color?
QUESTION: 36

Direction : A cube is divided into 343 identical cubelets. Each cut is made parallel to some surface of the cube. But before doing that the cube is colored with green color on one set of adjacent faces, red on the second and blue on the third set.

Q. How many cubelets are thin which are colored exactly three colors?

Solution: Only two cube lets one is visible in figure and 2nd one exactly diagonally opposite corner of it will be colored with 3 three colors.
QUESTION: 37

Direction : Questions are based on the following information.

Three adjacent faces of one cube is painted In pink, one adjacent pair of faces is painted in black and the remaining faces are painted in violet. The cube is the cut into 216 identical cubelets.

Q. How many of cubelets will have all three colors on them?

Solution:

Cube is cut in 6 x 6 x 6 = 216 cubelets

The pattern of painting is as follows.

Let us analyze the color combination.

The small pieces with three colors wilt from corners. Only2-such diagonal opposite y cubelets are possible.

QUESTION: 38

Direction: Questions are based on the following information.

Three adjacent faces of one cube is painted In pink, one adjacent pair of faces is painted in black and the remaining faces are painted in violet. The cube is the cut into 216 identical cubelets.

Q. How many of the cubelets have exactly one color on them?

Solution:

Cube is cut in 6 x 6 x 6 = 216 cubelets

The pattern of the painting is an follows.

Let us analysis the color combination.

The cubelets with exactly one color are

(a) One exactly at corner (PPP)= 1

(b) At the three edges each of PP category = 3(6 - 2) = 12

(c) At the one edge of BB category = 1(6 - 2) = 4

(d) At the middle of each of the six faces = 6 x (6 - 2) = 96

So total cubelets with exactly one colour are 1 + 12 + 4 + 98 = 113

QUESTION: 39

Kuldeep starts from his house towards the West. After walking a distance of 30 m, he again turned towards the right and walked 20 m. He then turned left and moved a distance of 10 m turned to his left, walked 40 m, turned to the left, and walked 5 m. Finally he turns to his left. In which direction is he walking now?

Solution: The movement of Kuldeep are as shown in Fig. from A to G.

Clearly, Kuideep is finally walking in the direction FG i.e, North

QUESTION: 40

I am facing South. I turn left and walk 20 m. Then I turn right again and walk 10 m. Then I turn left and walk 10 m and then turning right walk 20 m. Then I turn right again and walk 60 m. In which direction am I from the starting point?

Solution:

The movements of the person are from A to F, as shown Fig. Clearly, the final position is F which is to the North-east for the starting point A

QUESTION: 41

The door of Adilya’s house faces the East. From the back side of his house, he walks straight 50 m, then turns to the right and walks 50 m again. Finally, he turns towards the left and stops after walking 25 m. Now, Aditya is In which direction from the starting point?

Solution: Since Aditya’s house faces towards the ,,East and he walks from the backside of his house, it means that he starts walking towards West. Thus, the movements of Aditya are as shown in Fig. (A to B, B, to C, C to D).

Clearly, Aditya’s final position is D which is to the North-west of the starting point A.

QUESTION: 42

Direction : In the following figure, the circle stands for employed, the square stands for hard working, the triangle stands for rural and the rectangle stands for intelligent. Study the figure carefully and answer the questions that follow.

Q. Non-rural, employed, hard working and intelligent people are indicated by region

Solution:

The required set of people is represented by the region which lies outside the triangle and is common to the circle, square and rectangle i.e. 9.

QUESTION: 43

Direction : In the following figure, the circle stands for employed, the square stands for hard working, the triangle stands for rural and the rectangle stands for intelligent. Study the figure carefully and answer the questions that follow.

Q. Non-rural, employed people who are neither intelligent nor hard working are represented by region

Solution: The required set of people is represented by the region which Sies outside the triangle, inside the circle but outside the rectangle and the square i.e. 7.
QUESTION: 44

Direction : In the following figure, the circle stands for employed, the square stands for hard working, the triangle stands for rural and the rectangle stands for intelligent. Study the figure carefully and answer the questions that follow.

Q. Intelligent, employed and hard working non rural people are indicated by region
Solution: The required set of people is represented by the region which is common to the rectangle, circle and square but lies outside the triangle i.e. 9.
QUESTION: 45

Direction : In the following figure, the circle stands for employed, the square stands for hard working, the triangle stands for rural and the rectangle stands for intelligent. Study the figure carefully and answer the questions that follow.

Q. Hard working non-rural people who are neither employed nor intelligent are shown in region

Solution: The required set of people of denoted by the region which lies inside the square but outside the triangle, circle and rectangle i.e. 12.
QUESTION: 46

Direction : In the following figure, the circle stands for employed, the square stands for hard working, the triangle stands for rural and the rectangle stands for intelligent. Study the figure carefully and answer the questions that follow.

Q. Employed, hard working and intelligent rural people are Indicated by region
Solution: The required set of people Is denoted by the region common to the circle, square, rectangle and triangle i.e. 1.
QUESTION: 47

Direction :

A, B, C and D are four friends living together in a flat and they have an agreement that whatever edible comes they will share equally am ong themselves. One day A’ s uncle came to him and gave him a box of laddoos. Since no one was around, A divided the laddoos in four equal parts and ate his share after which he put the rest in the box. As he was closing the box, 8 walked in and took the box. He again divided remaining laddoos in four equal parts. A and B ate one part each and kept the remaining laddoos in the box. Suddenly C appeared and snatched the box. He again divided the laddoos in four equal parts, the three of them ate one part each and kept the remaining laddoos in the box. Later when D came, he again divided the laddoos in four equal parts and all four ate their respectively share. In total D ate 3 laddoes.

Q. How many laddoos, in total did A eat?

Solution:

We will start solving this problem from the last line. D ate 3 laddoos.

Before D ate the laddoos there should be 3 x 4 = 12 laddoos.

Before C ate the laddoos, there should be 12 x 3 + 12 « 48 laddoos.

Before B ate the laddoos, there should be 24 x 2 + 48 Sljfeddoos. Before A ate ladoos, these should be (96 x 4)/3 = 128 laddoos.

In the Beginning 128 laddoos

Now we can answer all the questions very easily.

QUESTION: 48

Direction :

A, B, C, and D are four friends living together in a flat and they have an agreement that whatever edible comes, they will share equally am ong themselves. One day A’ s uncle came to him and gave a box of laddoos. Since no one was around, A divided the laddoos in four equal parts and ate his share after which he put the rest in the box. As he was closing the box, 8 walked in and took the box. He again divided remaining laddoos in four equal parts. A and B ate one part each and kept the remaining laddoos in the box. Suddenly C appeared and snatched the box. He again divided the laddoos in four equal parts, the three of them ate one part each and kept the remaining laddoos in the box. Later when D came, he again divided the laddoos in four equal parts and all four ate their respectively share. In total D ate 3 laddoes.

Q. How many ladoos were given to A by his Unde?

Solution:

We will start solving this problem from the last line. D ate 3 laddoos.

Before D ate the laddoos there should be 3 x 4 = 12 laddoos.

Before C ate the laddoos there should be 12 x 3 + 12 « 48 laddoos.

Before B ate the laddoos, there should b e 24 x 2 + 48 Sljfeddoos. Before A ate ladoos, these should be (96 x 4)/3 = 128 laddoos

At the Beginning 128 laddoos

Now we can answer all the question very easily.

QUESTION: 49

Direction :

A, B, C and D are four friends living together in a flat and they have an agreement that whatever edible comes they will share equally am ong themselves. One day A’ s uncle came to him and gave a box of laddoos. Since no one was around, A divided the laddoos in four equal parts and ate his share after which he put the rest in the box. As he was closing the box, 8 walked in and took the box. He again divided remaining laddoos in four equal parts. A and B ate one part each and kept the remaining laddoos in the box. Suddenly C appeared and snatched the box. He again divided the laddoos in four equal parts, the three of them ate one part each and kept the remaining laddoos in the box. Later when D came, he again divided the laddoos in four equal parts and all four ate their respectively share. In total D ate 3 laddoes.

Q. How many laddoos, did A eat the first time?

Solution:

We will start solving this problem from the last line. D ate 3 laddoos.

Before D ate the laddoos there should be 3 x 4 = 12 laddoos.

Before C ate the laddoos there should be 12 x 3 + 12 « 48 laddoos.

Before B ate the laddoos, there should b e 24 x 2 + 48 Sljfeddoos. Before A ate ladoos, these should be (96 x 4)/3 = 128 laddoos

At the Beginning 128 laddoos

Now we can answer all the questions very easily.

QUESTION: 50

Direction: Each of the following questions is followed by two Statements.

Q. Is b positive?

i. a + b is positive.

ii. a ~ b is positive.

Solution: From Statement I, b can be either negative or positive. Also, from Statement II, b can be either negative or positive, so Statements 3 and II cannot be combined.

Hence, we cannot find out the answer.

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