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UGEE REAP Mock Test- 2 - JEE MCQ


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30 Questions MCQ Test - UGEE REAP Mock Test- 2

UGEE REAP Mock Test- 2 for JEE 2024 is part of JEE preparation. The UGEE REAP Mock Test- 2 questions and answers have been prepared according to the JEE exam syllabus.The UGEE REAP Mock Test- 2 MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for UGEE REAP Mock Test- 2 below.
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UGEE REAP Mock Test- 2 - Question 1
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Sashi can do a piece of work in 25 days and Rishi can do it in 20 days. They work for 5 days, then Sashi goes away. In how many more days will Rishi finish the work?

Detailed Solution for UGEE REAP Mock Test- 2 - Question 1

Shashi’s one day work = 1/25

Rishi’s one day work = 1/20

Together they can finish 1/25 + 1/20 = 9/100 part in a day

∴ Work in 5 days (9/100)x5 = 45/100 part

55/100 part is remaining. Rishi can finish it in (55/100)/(1/20) = 11 days.

UGEE REAP Mock Test- 2 - Question 2
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Manoj takes twice as much time as Ajay and thrice as much as Vijay to finish a piece of work. Together they finish the work in 1 day. What is the time taken by Manoj to finish the work?

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

Let Manoj takes 6x days Ajay takes 3x days and vijay 2x days then 1/6x + 1/3x + 1/2x = 1

1/x [⅙ + ⅓ + ½ ] = 1

1/x = 1, So x = 1

Manoj will take 6 days.

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UGEE REAP Mock Test- 2 - Question 3
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Raju works twice as Vijay. Together, they finish the work in 14 days, in how many days can Vijay alone do the same work?

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

Let Raju can do the work in x days then Vijay in 2x days

Together they can complete in

x = 21 days, 2x = 42 days

UGEE REAP Mock Test- 2 - Question 4
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What is the rate of simple interest for the first 4 years if the sum of Rs. 360 becomes Rs. 540 in 9 years and the rate of interest for the last 5 years is 6%?
Detailed Solution for UGEE REAP Mock Test- 2 - Question 4
P = Rs. 360, A = Rs. 540, SI = Rs. 180.

SI = PRT/100

UGEE REAP Mock Test- 2 - Question 5
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A jay borrows Rs. 1500 from two money-lenders. He pays interest at the rate of 12% per annum for one loan and at the rate of 14% per annum for the other. The total interest he pays for the entire year is Rs. 186. How much does he borrow at the rate of 12%?
Detailed Solution for UGEE REAP Mock Test- 2 - Question 5
P = 1500, R1 = 12%, Rε = 14%, T = 1 year SI = 186

Let Rs. x be amount invested at 12% Rate

UGEE REAP Mock Test- 2 - Question 6
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Two equal sums were borrowed at 8% simple interest per annum for 2 years and 3 years respectively. The difference in the interest was Rs. 56. The sum borrowed were
Detailed Solution for UGEE REAP Mock Test- 2 - Question 6

UGEE REAP Mock Test- 2 - Question 7
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Sanjay borrowed Rs. 900 at 4% p.a. and Rs. 1100 at 5% p.a. for the same duration. He had to pay Rs. 364 in all as interest. What is the time period in years?

Detailed Solution for UGEE REAP Mock Test- 2 - Question 7

36T + 55T = 364

T = 4 years

UGEE REAP Mock Test- 2 - Question 8
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A train 150 m long moving at a speed of 25 metres per second overtakes a man moving at 5 metres/sec in opposite direction.The train will pass the man in
Detailed Solution for UGEE REAP Mock Test- 2 - Question 8
Speed of train relative to man

= (25 + 5) m/sec

= 30 m/sec

∴ Time taken to pass the man

= (150/30)sec = 5 sec.

UGEE REAP Mock Test- 2 - Question 9
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Two Train 126 m and 114 m long are running in opposite directions, one at the rate of 30 kmph and another one at 42 kmph. From the moment they meet will cross each other in
Detailed Solution for UGEE REAP Mock Test- 2 - Question 9
Relative speed = (30+42) kmph = 72 kmph

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

Distance covered in crossing each other = (126 + 114) m = 240 m.

Required time = (240/20)sec = 12 sec.

UGEE REAP Mock Test- 2 - Question 10
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A train 110m long passes a man, running at 6 kmph in the direction opposite to that of the train, in 6 seconds. The speed of the train is
Detailed Solution for UGEE REAP Mock Test- 2 - Question 10
Speed of the train relative to man = (110/6) m/sec. =

= 66 kmph.

Let the speed of the train be x kmph.

Then, relative speed = (x + 6) kmph.

x + 6 = 66 or x = 60 kmph.

UGEE REAP Mock Test- 2 - Question 11
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A system consists of N particles, interacting with each other (for example, protein molecules). Which one of the following statements is FALSE?
Detailed Solution for UGEE REAP Mock Test- 2 - Question 11

The number of vibrational degrees of freedom depends on the total degrees of freedom for the system minus the translational and rotational degrees of freedom. For a system of N particles, there are 3N total degrees of freedom. Therefore, the number of vibrational degrees of freedom is 3N - (3 translational + 3 rotational) = 3N - 6, which is not always equal to 3.

UGEE REAP Mock Test- 2 - Question 12
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Three pipes A, B and C can fill a tank in 6 hrs. After working at it together for 2 hrs C is closed and A and B can fill the remaining part in 7 hrs. The total number of hrs taken by C alone to fill the tank is
Detailed Solution for UGEE REAP Mock Test- 2 - Question 12

Say Pipe A can do a piece of work in 1 hr

Say Pipe B can do b piece of work in 1 hr

Say Pipe C can do c piece of work in 1 hr.

So, (a+b+c)6 = 1 ----------1st Condition (a+b+c)2 + (a+b)7 = 1 ------------- 2(1/6) + (a+b)7 = 1

So, a+b = 2/21 ............. Eqn l

So, c = 1/6-2/21 = 1/14

Now C can do 1/14 piece of work Hence, 1 piece of work can be done by C in 14 days.

UGEE REAP Mock Test- 2 - Question 13
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If (√3)5 x 92 = 3α x 3√3, then α equals:
Detailed Solution for UGEE REAP Mock Test- 2 - Question 13
(√3)5 x 92 = 3α x 3√3

UGEE REAP Mock Test- 2 - Question 14
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If x, y, z are real numbers, then the value of: is
Detailed Solution for UGEE REAP Mock Test- 2 - Question 14

UGEE REAP Mock Test- 2 - Question 15
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Detailed Solution for UGEE REAP Mock Test- 2 - Question 15
Given Exp.

= x(b-c)(b+c-a)x(c-a)(c+a-b)x(a-2)(a+b-c)

= x0.x0 = 1

UGEE REAP Mock Test- 2 - Question 16
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If 2x+4 - 2 x+2 = 3, then x is equal to:

Detailed Solution for UGEE REAP Mock Test- 2 - Question 16
2x+4 -2x+2 =3

⇒2x+2(22 - 1) = 3

⇒ 2x+2 = 1 = 2.

∴ x + 2 = 0 or x = -2.

UGEE REAP Mock Test- 2 - Question 17
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The sum of the first 16 terms of an AP whose first term and third are 5 and 15 respectively is
Detailed Solution for UGEE REAP Mock Test- 2 - Question 17
a = 5, a + 2d = 15

So d = 5

now sum of 16 term will be 16/2[10 + 15 x 5] = 680

UGEE REAP Mock Test- 2 - Question 18
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A boy agrees to work at the rate of one rupee on the first day, two rupees on the second day, four rupees on the third day and so on. How much will the boy get if he starts working on the 1st of February and finishes on the 20th of February?

Detailed Solution for UGEE REAP Mock Test- 2 - Question 18
This sequence is in GP 1,2,4, 8, …. Now sum of first 20 term will be

UGEE REAP Mock Test- 2 - Question 19
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The seventh term of a GP is 8 times the fourth term, but will it be the first term when its fifth term is 48?
Detailed Solution for UGEE REAP Mock Test- 2 - Question 19
It is given that

ar6 = 8 ar3

R3 = 8, r = 2

Now ar4 = 48

A x 24 = 48, a = 3

UGEE REAP Mock Test- 2 - Question 20
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The sum of three numbers on a GP is 14, and the sum of their squares is 84. Find the largest number,
Detailed Solution for UGEE REAP Mock Test- 2 - Question 20
a, ar, ar2

Now a + ar +ar2 = 14 …(i)

Also, a2 + a2r2 + a2r4 = 84 …(ii)

only suitable combination is 2 , 4 , 8

So the largest term is 8.

UGEE REAP Mock Test- 2 - Question 21
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How many different numbers of six digits can be formed with the numbers 3, 1, 7, 0, 9, 5?

Detailed Solution for UGEE REAP Mock Test- 2 - Question 21
The numbers that can be formed, by taking all six digits together.

= 6P6 = 6!

But we have to neglect the numbers which begin with zero. Now the number in which zero comes in the 1st Place= 5!

Hence, the required number = 6! - 5!

= 720 - 120 = 600.

UGEE REAP Mock Test- 2 - Question 22
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How many three-digit numbers are there, with no digits repeated?
Detailed Solution for UGEE REAP Mock Test- 2 - Question 22
The required number of three-digit numbers = The permutations of the 10 objects 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 take 3 at a time, with the condition that 0 is not in the hundreds place.

= P(10, 3)-P(9, 2)

= 10 x 9 x 8 - 9 x 8

= 720 - 72 = 648

UGEE REAP Mock Test- 2 - Question 23
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In how many different ways, the letters of the word ALGEBRA can be arranged in a row if.

(i) The two As are together?

(ii) The two As are not together?
Detailed Solution for UGEE REAP Mock Test- 2 - Question 23
ALGEBRA has seven letters where 2-A, 1-L, 1-G, 1- E, 1-Band 1-R.

(i) Since two A’s are always together, we take both the A's as one letter.

If p is the number of arrangements, then p = 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720.

(ii) Total number of permutations

= 2520

In these permutations, in some permutations, two A's are together while in the rest they are not together Hence, the number of permutations in which two A's are not together in q - p = 2520 - 720 = 1800.

UGEE REAP Mock Test- 2 - Question 24
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A husband and wife appear in an interview for two vacancies in the same post. The probability of husband’s selection is 1/7 and that of wife's is 1/5.

What is the probability that none of them will be selected?
Detailed Solution for UGEE REAP Mock Test- 2 - Question 24
P(none of them will be selected)
UGEE REAP Mock Test- 2 - Question 25
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A man speaks the truth in 80% of the cases and another in 90% of the cases. While stating the same fact, what is the probability that they contradict?
Detailed Solution for UGEE REAP Mock Test- 2 - Question 25
Let the two men be A and B.

A: A speaks truth

B: B speaks truth

∴ Required probability

= (8+18)/100 = 26/100 = 13/50.

UGEE REAP Mock Test- 2 - Question 26
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A coin is tossed three times. Find the chance that head and tail show alternately.
Detailed Solution for UGEE REAP Mock Test- 2 - Question 26
Sample space S = |HHH: HHT, HTH. HTT, THT, TTH, THH, TTT}

Number of exhaustive cases = 8

Favourable cases are HTH, THT

The number of favorable = 2.

∴ Required probability = 2/8 = ¼.

UGEE REAP Mock Test- 2 - Question 27
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Akash said to Mohit, “The boy in the blue shirt is younger of the two brothers of the daughter of my father’s wife". How is the boy in the blue shirt related to Akash?
Detailed Solution for UGEE REAP Mock Test- 2 - Question 27

Hence brother.

UGEE REAP Mock Test- 2 - Question 28
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Pointing to a photograph, Vipul said, "She is the daughter of my grandfather's only son(and only child also)". How is Vipul related to the girl in the photograph?
Detailed Solution for UGEE REAP Mock Test- 2 - Question 28

Hence Vipui is the brother of the girl.

UGEE REAP Mock Test- 2 - Question 29
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A man said to a lady, "your mother's husband's sister is my aunt. How is the lady related to the man?
UGEE REAP Mock Test- 2 - Question 30
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If (i) M Is the brother of N

(ii) B is the brother of N and

(iii) M is the brother of D, then which of the following statements is true?
Detailed Solution for UGEE REAP Mock Test- 2 - Question 30

From the given information, we know that M is the brother of N and also the brother of D. This means that N and D are siblings and M is their common brother.

We also know that B is the brother of N. Since N and M are siblings, and M is the brother of B, this means that B is also a sibling of N and M. Therefore, option 3 is true: M is the brother of B.

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