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UGEE REAP Mock Test- 6 - JEE MCQ


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30 Questions MCQ Test - UGEE REAP Mock Test- 6

UGEE REAP Mock Test- 6 for JEE 2024 is part of JEE preparation. The UGEE REAP Mock Test- 6 questions and answers have been prepared according to the JEE exam syllabus.The UGEE REAP Mock Test- 6 MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for UGEE REAP Mock Test- 6 below.
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UGEE REAP Mock Test- 6 - Question 1
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Nishu and Archana can do a piece of work in 10 days and Nishu alone can do it in 12 days. In How- many days can Archana do it alone?

Detailed Solution for UGEE REAP Mock Test- 6 - Question 1

One day work of both 1/10

and Nishu’s day -work = 1/12

So, Archana’s one day work = 1/10 - 1/12 = 2/120 = 1/60

So, 60 days required to finish the work by Archana.

UGEE REAP Mock Test- 6 - Question 2
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A can do a piece of work in 10 days and B can do the same work in 20 days. With the help of C, they finish the work in 5 days. How long will It take for C alone to finish the work?

Detailed Solution for UGEE REAP Mock Test- 6 - Question 2
⅕ - 1/10 - 1/20 = 1/20

This is C’s one day work so 20 days are required for C alone to finish the task.

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UGEE REAP Mock Test- 6 - Question 3
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Twenty workers can finish a piece of work in 30 days. After how many days should 5 workers leave the job so that the work is completed in 35 days?

Detailed Solution for UGEE REAP Mock Test- 6 - Question 3
Man x Day = Man . Day

20 x 30 = 600

Let 5 workers leave after x days then 20 + 15 (35 - x) = 600

5x + 525 = 600

5x = 75, x = 15

UGEE REAP Mock Test- 6 - Question 4
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Akshay borrowed Rs 2100 at compound interest of 5% per annum for 2 years. What is the total the amount due after two years?
Detailed Solution for UGEE REAP Mock Test- 6 - Question 4

Here P = 2100, R = 5%, T = 2 years

UGEE REAP Mock Test- 6 - Question 5
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What is the difference between the simple interest on a principal of Rs. 500 being calculated at 5% per annum for 3 years and 4% per annum for 4 years?
Detailed Solution for UGEE REAP Mock Test- 6 - Question 5
P = Rs. 500, R1 = 5%, R2 = 4%, T1 = 3 years, T2 = 4 years

Difference = PR1T1/100 - PR2T2/100 = Rs. 5.

UGEE REAP Mock Test- 6 - Question 6
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Find the compound interest on Rs. 1000 at the rate of 20% per annum for 18 months when interest is compounded half-yearly.
Detailed Solution for UGEE REAP Mock Test- 6 - Question 6

Here P = Rs. 1000, R = 20%, T = 18 months or 1(½) years.

Compound interest when interest is compounded annually

hence interest is= 1331-1000=331

UGEE REAP Mock Test- 6 - Question 7
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A train is moving at a speed of 132 kmph. If the length of the train is 110 metres, how long will it take to cross a railway platform 165 m long?
Detailed Solution for UGEE REAP Mock Test- 6 - Question 7

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UGEE REAP Mock Test- 6 - Question 8
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A train 300 m long crossed a platform 900 m long in 1 minute 12 seconds. The speed of the train (in km/hr) is
Detailed Solution for UGEE REAP Mock Test- 6 - Question 8
Total distance covered = (300 + 900)m = 1200m.

Time taken = 1 min. 12 sec = 72 sec,

∴ Speed = (1200/72)m/sec.

= (1200/72 x 18/5) km/hr = 60km/hr

UGEE REAP Mock Test- 6 - Question 9
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A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is
Detailed Solution for UGEE REAP Mock Test- 6 - Question 9
Let foe length of train be x metres and its speed by y metres/sec.

Then, x/y = 15 ⇒ y = x/15

⇒ x = 150 m/s

UGEE REAP Mock Test- 6 - Question 10
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Choose the correct alternative that will continue the same pattern and fill in the blank spaces. 2, 7, 14, 23, ___, 47
Detailed Solution for UGEE REAP Mock Test- 6 - Question 10
Difference between No. is in AP, i.e., Difference between No is 7,9,11,13.
UGEE REAP Mock Test- 6 - Question 11
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A known positive charge is located at point P between two unknown charges, Q1 and Q2. P is closer to Q2 than Q1. If the net electric force acting on the charge at P is zero, it may correctly be concluded that:
Detailed Solution for UGEE REAP Mock Test- 6 - Question 11

To Balance the Forces, it is clear that Q1, Q2 must have the same sign of charges by which Both will Attract or Both will Repel to Balance the forces.

As Distance is not Same so, Their Magnitude be different. F = kq1q2/d as F ~ 1/d (Inversely Proportion) so in between Q2 & P as d is Less Hence F is more to Balance it so, Q2 must be more.

UGEE REAP Mock Test- 6 - Question 12
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Which of the following solutions, when mixed, will not form a buffer solution?
Detailed Solution for UGEE REAP Mock Test- 6 - Question 12
Buffer Solution is a Solution which Resist change in pH

For a Buffer Solution: Existence of both weak part & its Conjugate is Required.

In (A) As NaOH is more than CH3COOH so, CH3COOH will be the LR (Limiting Reagent) & No Conjugate Part Will Remain.

UGEE REAP Mock Test- 6 - Question 13
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Three identical masses are at the three corners of the triangle, connected by massless identical springs (rest length 10) forming an isosceles right-angle triangle. If the two sides of equal length (of length 210) lie along positive x-axis and positive y-axis, then the force on the mass that is not at the origin but on the x-axis is given by with
Detailed Solution for UGEE REAP Mock Test- 6 - Question 13
Que Directly from NCERT Exemplar Available on IIITprep.com SUPR Book

Mainly 2 types of forces are Considered here

1. Gravitational Force

2. Spring Force

The Spring force is kx2 where x is Elongation. Now take the Proper Direction of Forces. Resolve its Component along x axis & y axis i.e. so, a = -2 & b = 1

UGEE REAP Mock Test- 6 - Question 14
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Consider a rope fixed at both ends under tension so that it is horizontal (i.e., assume the rope is along the x-axis, with gravity acting along the z-axis). Now the right end is continually oscillated at high frequency n (say n=100 Hz) horizontally and in a direction along the rope; amplitude of oscillation is negligible. The oscillation travels along the rope and is reflected at the left end.

Let the total length of rope be I, total mass be m and the acceleration due to gravity be g.

After initial phase (say a minute or so), the rope has (BLANK-1)_ wave, which is_(BLANK-2)__in nature. It results from superposition of left travelling and right traveling _(BLANK-3) waves. This resulting wave has a frequency__(BLANK-4) _ that of oscillation frequency nu, Simpy&fmensional analysis indicates that the frequency of can be of the form:___(BLANK-5)__.
Detailed Solution for UGEE REAP Mock Test- 6 - Question 14

Answer:

1. Nature of the resulting wave
The resulting wave on the rope after the initial phase is a transverse wave.

2. Frequency of the resulting wave
The frequency of the resulting wave is equal to the oscillation frequency n.

3. Superposition of waves
The resulting wave is formed due to the superposition of left traveling and right traveling waves.

4. Form of the frequency of the resulting wave
The frequency of the resulting wave can be expressed in the form:

(sqrt(g/l))

Explanation:

Let's analyze the given scenario step by step to understand the nature of the wave and its frequency.

1. As the right end of the rope is oscillated horizontally at a high frequency n, a wave is generated that travels along the rope. This wave can be considered as a right traveling wave.

2. When this wave reaches the left end of the rope, it gets reflected. The reflected wave can be considered as a left traveling wave.

3. The resulting wave on the rope is formed due to the superposition of the left and right traveling waves. Since the rope is fixed at both ends, the resulting wave is a standing wave.

4. The standing wave on the rope has a frequency that is equal to the oscillation frequency n. This means that the frequency of the resulting wave is equal to the frequency of the oscillation applied at the right end of the rope.

5. Dimensional analysis suggests that the frequency of the resulting wave can be expressed in terms of the acceleration due to gravity (g) and the length of the rope (l). The only combination that gives a frequency is sqrt(g/l).

Therefore, the answer is: stationary, transverse, regular, equal to, sqrt (g/l)

UGEE REAP Mock Test- 6 - Question 15
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The value of (√8)⅓ is:

Detailed Solution for UGEE REAP Mock Test- 6 - Question 15

UGEE REAP Mock Test- 6 - Question 16
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(1/216)-⅔ / (1/27)-4/3 = ?
Detailed Solution for UGEE REAP Mock Test- 6 - Question 16

UGEE REAP Mock Test- 6 - Question 17
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If √2n = 64, then the value of n is:

Detailed Solution for UGEE REAP Mock Test- 6 - Question 17
√2n = 64 ⇒ 2n/2 = 64 = 26.

∴ n/2 = 6 or n = 12

UGEE REAP Mock Test- 6 - Question 18
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If  then n equals:
Detailed Solution for UGEE REAP Mock Test- 6 - Question 18

Or 32n + 14 = 320

∴ 2n + 14 = 20

Or 2n = 6 or n = 3.

UGEE REAP Mock Test- 6 - Question 19
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How many terms are there in the AP 20, 25, 30, .............. 130.
Detailed Solution for UGEE REAP Mock Test- 6 - Question 19
In series 20, 25, 3 0 .............. 130.

a = 20, d = 5

nth term is 130

⇒ 20 + (n - 1) 5 = 130

⇒ 5n = 115, n = 23

UGEE REAP Mock Test- 6 - Question 20
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Find the 1st term of an AP whose 8th and 12 m terms are respectively 39 and 59.

Detailed Solution for UGEE REAP Mock Test- 6 - Question 20
Here a + 7d = 39 …(i)

a + 11d = 59

So, 4d = 20

d = 5

a + (7 x 5) = 39

So, a = 4

UGEE REAP Mock Test- 6 - Question 21
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Find the 15th term of the sequence 20, 15, 10 .......
Detailed Solution for UGEE REAP Mock Test- 6 - Question 21
AP 20,15,10

Here a = 20

d = - 5

15th term will be a + 14d which is equal to 20 + (-5) x 14 = -50

UGEE REAP Mock Test- 6 - Question 22
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A number 15 is divided into three parts which are in AP and the sum of their squares is 83. Find the smallest number.
Detailed Solution for UGEE REAP Mock Test- 6 - Question 22
Let numbers are

a - d, a and a + d

now it is given that sum = 15 & sum of there square is 83 i.e,

3a = 15 …(i)

(a - d)2 + a2 + (a + d)2 = 83 …(ii)

3a2 + 2d2 = 83

75 +2d2 = 83

2d2 = 8

d2 = 4, d = 2

So, least term is a - d = 3

UGEE REAP Mock Test- 6 - Question 23
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How many different words can be formed with the letters of the word ‘BHARAT’?

In how many of these B and H are never together?
Detailed Solution for UGEE REAP Mock Test- 6 - Question 23
Out of letters in the word ‘BHARAT' two letters, that is, A's are alike.

∴ Number of permutations = 6!/21 = 360.

Number of words in which B and H are never together = Total number of words - number of words in which B and H are together

= 360 - (5!/2!).2! = 360 - 120 = 240.

UGEE REAP Mock Test- 6 - Question 24
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There are 15 buses running between Delhi and Mumbai. In how many ways can a man go to Mumbai and return by a different bus?
Detailed Solution for UGEE REAP Mock Test- 6 - Question 24
The first event of going from Delhi to Mumbai can be performed in 15 ways as he can go by any of the 15 buses. But the event of coming back from Mumbai can be performed in 14 ways ( a different bus is to be taken).

Hence, both the events can be performed in 15 x 14 = 210 ways.

UGEE REAP Mock Test- 6 - Question 25
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A teacher of a class wants to set one question from each of two exercises in a book. If there are 15 and 12 questions in the two exercises respectively, then in how many ways can the two questions be selected?
Detailed Solution for UGEE REAP Mock Test- 6 - Question 25
Since the first exercise contains 15 questions, the number of ways of choosing the first question In 15.

Since the second exercise contains 12 questions, the number of ways of choosing the second question is 12. Hence, by the fundamental principle, two questions can be selected in 15 x 12 = 180 ways.

UGEE REAP Mock Test- 6 - Question 26
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Find the probability that in a random arrangement of the letters of the word DAUGHTER, the letter D occupies the first place.
Detailed Solution for UGEE REAP Mock Test- 6 - Question 26
If D occupies the first place n(A) = 7!, Total words = n(S) = 8!

∴ Required probability

UGEE REAP Mock Test- 6 - Question 27
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Find the probability that in a random arrangement of letter of the words “UNIVERSITY” two ‘I’s do not come together.
Detailed Solution for UGEE REAP Mock Test- 6 - Question 27
Out of theTetters in the word ‘UNIVERSITY’ two letters ‘I’ are alike.

∴ Number of permutations = 10!/2 …(i)

Number of words in which two ‘I’ are never together = Total number of words - Number of words in which two ‘I’ are together

∴ Required probability =

= 8/10 = ⅘.

UGEE REAP Mock Test- 6 - Question 28
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A and B are mutually exclusive events of an experiment. If P ('not A’) = 0.65, P(A∪B) = 0.65 and P(B) = P, find the value of p.
Detailed Solution for UGEE REAP Mock Test- 6 - Question 28
We know P(A) = 1-P(A)

= 1 - 0.65 = 0.35 and

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

⇒ 0.65 = 0.35 + P(B) - 0

[∵ A and B are mutually exclusive events]

⇒ P(B) = 0.65 - 0.35 = 0.30.

UGEE REAP Mock Test- 6 - Question 29
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Direction: Read the following information carefully and answer the questions given below it P is the son of Q. R, Q’s sister has a son S and daughters T. U is the maternal uncle of S.

Q. How is P related to S?

UGEE REAP Mock Test- 6 - Question 30
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Direction: Read the following information carefully and answer the questions given below it P is the son of Q. R, Q’s sister has a son S and daughters T. U is the maternal uncle of S.

Q. How is T related to U?

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