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VITEEE PCME Mock Test - 13 - JEE MCQ


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30 Questions MCQ Test - VITEEE PCME Mock Test - 13

VITEEE PCME Mock Test - 13 for JEE 2024 is part of JEE preparation. The VITEEE PCME Mock Test - 13 questions and answers have been prepared according to the JEE exam syllabus.The VITEEE PCME Mock Test - 13 MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for VITEEE PCME Mock Test - 13 below.
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VITEEE PCME Mock Test - 13 - Question 1
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If the slope of the normal to the curve x3 = 8a2y, a > 0, at a point in the first quadrant is - 2/3, then the point is

VITEEE PCME Mock Test - 13 - Question 2
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Area bounded by parabola y2 = x and st.line 2 y = x is

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VITEEE PCME Mock Test - 13 - Question 3
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If ω is a cube of unity and equation  has one root . Then

Detailed Solution for VITEEE PCME Mock Test - 13 - Question 3


⇒ x = 0
∵ x2 + 5 = 0. Not possible ∀ x ∈ R

VITEEE PCME Mock Test - 13 - Question 4
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If 1 + i is the conjugate of (x+iy)(1-2i), then
VITEEE PCME Mock Test - 13 - Question 5
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Let y = | x | + | x − 2 | . Then dy/dx at x = 2 is
VITEEE PCME Mock Test - 13 - Question 6
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If | z1 − 1 | < 1 , | z2 − 2 | < 2 , | z3 − 3 | < 3 then | z1 + z2 + z3 |
VITEEE PCME Mock Test - 13 - Question 7
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If f: R → R defined by  is continuous function, then
VITEEE PCME Mock Test - 13 - Question 8
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The value of   
VITEEE PCME Mock Test - 13 - Question 9
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The order of the differential equation y(dy/dx)=x/(dy/dx)+(dy/dx)3 is
VITEEE PCME Mock Test - 13 - Question 10
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Detailed Solution for VITEEE PCME Mock Test - 13 - Question 10

VITEEE PCME Mock Test - 13 - Question 11
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The solution of differential equation (xdy/dx) = y+x2 is
VITEEE PCME Mock Test - 13 - Question 12
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The solution of the equation xdy-ydx=0 is
VITEEE PCME Mock Test - 13 - Question 13
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The order of differential equation (d2y/dx2)2 = (1+dy/dx)1/2 is
VITEEE PCME Mock Test - 13 - Question 14
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If f x = x − x2 + x3 − x4 + … ∞ , | x | < 1, then f′(x) =
VITEEE PCME Mock Test - 13 - Question 15
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If f(x) = log (1 + x/1 - x), then f(2x/1 + x2) is equal to
VITEEE PCME Mock Test - 13 - Question 16
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VITEEE PCME Mock Test - 13 - Question 17
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VITEEE PCME Mock Test - 13 - Question 18
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sin(sin-1(1/2) + cos-1(1/2))=
VITEEE PCME Mock Test - 13 - Question 19
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VITEEE PCME Mock Test - 13 - Question 20
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VITEEE PCME Mock Test - 13 - Question 21
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Look at this series: 2, 1, (1/2), (1/4),...so on. What number should come next?
Detailed Solution for VITEEE PCME Mock Test - 13 - Question 21

This is a simple division series, each number is one-half of the previous number.

In other terms to say, the number is divided by 2 successively to get the next result.

► 4/2 = 2
► 2/2 = 1
► 1/2 = 1/2
► (1/2) / 2 = 1/4
► (1/4) / 2 = 1/8 and so on.

VITEEE PCME Mock Test - 13 - Question 22
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Look at this series: 7, 10, 8, 11, 9, 12,...so on. What number should come next?
Detailed Solution for VITEEE PCME Mock Test - 13 - Question 22

This is a simple alternating addition and subtraction series.

In the first pattern, 3 is added. In the second, 2 is subtracted.

► 7 + 3 = 10,
► 10 - 2 = 8,
► 8 + 3 = 11,
► 11 - 2 = 9,
► 9 + 3 = 12,
► 12 - 2 = 10.

VITEEE PCME Mock Test - 13 - Question 23
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3, 9, 24, 57, ?, 267, 552. What number should come? 
Detailed Solution for VITEEE PCME Mock Test - 13 - Question 23

 

VITEEE PCME Mock Test - 13 - Question 24
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Look at this series: 4, 6, 12, 30, 90,  ?, 1260. What number should come?
Detailed Solution for VITEEE PCME Mock Test - 13 - Question 24

Logic is:

► 4 × 1.5 = 6,
► 6 × 2 = 12,
► 12 × 2.5 = 30,
► 30 × 3 = 90,
► 90 × 3.5 = 315,
► 315 × 4 = 1260. 

VITEEE PCME Mock Test - 13 - Question 25
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Directions: Read the following to answer the question.

The following table shows the results of Triangular Hockey Series played among the teams of India, Australia and England. The matches were played in such a manner that each team played against another at least once. The table has a few missing pieces of information.

Q. Calculate the total number of matches played in the whole series.
Detailed Solution for VITEEE PCME Mock Test - 13 - Question 25

There are three teams playing in the hockey series. They are India, Australia and England.
According to the given condition, the matches were played in such a manner that each team played against another at least once, each team should play in 2 matches.


i.e. India Vs Australia, Australia Vs England and India Vs England.
Therefore, total 3 matches were played in the series.

VITEEE PCME Mock Test - 13 - Question 26
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Directions: Read the following to answer the question.

The following table shows the results of Triangular Hockey Series played among the teams of India, Australia and England. The matches were played in such a manner that each team played against another at least once. The table has a few missing pieces of information.

Q. Identify the score card reading during India-England match, favouring India.
Detailed Solution for VITEEE PCME Mock Test - 13 - Question 26

Checking the inning details of the given score board of the series, we have a clue i.e. India has drawn in one match, which means either won or lost in second match.
In the score board, India has scored 2 goals.
So, the possibilities for match drawn will be 0 - 0, 1 - 1 and 2 - 2.
As we know that total goals scored by all three teams are 12, so the total goals scored by England = 12 - (2 + 3) = 7

Possibility case 0 - 0:
Case 1:
1st match: India Vs Australia: 0 - 0
2nd match: India Vs England: 2 - 4
The score card 2 - 4 shows that India scored 2 goals and England scored 4 goals.
So, second match would be lost.

Case 2:
1st match: Australia Vs India: 0 - 0
2nd match: Australia Vs England: 3 - 7
The score card 3 - 7 shows that Australia scored 3 goals and England scored 7 goals.
As one of the matchs is drawn with India i.e. 0 - 0, second match would be lost against England i.e. 3 - 7.

Case 3:
1st match: India Vs England: 2 - 4
2nd match: Australia Vs England: 3 - 7
This case is not matched with the first 2 cases of 0 - 0, so the possibility case for 0 - 0 is wrong.

Possibility case 1 - 1:
Case 1:
1st match: India Vs Australia: 1 - 1
2nd match: India Vs England: 1 - 1
So, second match would be drawn. But, it is not given in favour of India.
Therefore, the possibility case for 1 - 1 is also wrong.

Possibility case 2 - 2:
Case 1:
1st match: India Vs Australia: 2 - 2
2nd match: India Vs England: 0 - 2
So, the second match would be lost to India and England scored 2 goals against India.

Case 2:
1st match: Australia Vs India: 2 - 2
2nd match: Australia Vs England: 1 - 5
It shows that Australia has lost in second match with 1 goal and England scored 5 goals against Australia.
From cases 1 and 2, we can clearly say that England scored 2 + 5 = 7 goals in total. It is completely matched with the given table.
Meanwhile, India and Australia have scored together = 0 + 1 = 1 goal against England.
Thus, the possibility case 2 - 2 is perfectly correct.
So, the table can be filled as follows.

During India Vs England match, the score card reading in favour of India is 0 - 2.

VITEEE PCME Mock Test - 13 - Question 27
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Directions: Read the following to answer the question.

The following table shows the results of Triangular Hockey Series played among the teams of India, Australia and England. The matches were played in such a manner that each team played against another at least once. The table has a few missing pieces of information.

Q. What is the mean average of goals scored by all three teams in the whole series?
Detailed Solution for VITEEE PCME Mock Test - 13 - Question 27

From the given information, we can find that total number of goals scored by all teams is same as total number of goals against all teams.
Therefore, total number of goals against all teams = 4 + 7 + 1 = 12
Thus, total number of goals scored by all teams = 12
So, the mean average of goals scored by all three teams = 12/3 = 4

VITEEE PCME Mock Test - 13 - Question 28
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Directions: Read the data and answer the following question.

Dance, music, cooking, karate, swimming and drawing classes are to be scheduled from 3rd April to 9th April, not necessarily in the same order. Each of them is held for 50 mins, 60 mins, 70 mins, 85 mins, 100 mins and 110 mins, but not necessarily in the same order. A class of 50 mins is scheduled on 9th April which is not Sunday as it is an off day. Dance class is for less than 70 mins and is scheduled immediately before karate class. There are two classes scheduled between swimming class, which is for 110 mins and cooking class, which is for 70 mins. Karate class is before Sunday and there are two days between Sunday and the dance class. Drawing class, which is for 85 mins, is not scheduled on 3rd April. Saturday's class is of 110 mins.

Q. On which of the following days is the drawing class scheduled?
Detailed Solution for VITEEE PCME Mock Test - 13 - Question 28

VITEEE PCME Mock Test - 13 - Question 29
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A premier B-school, which is in process of getting an AACSB accreditation, has 360 second year students. To incorporate sustainability into their curriculum, it has offered 3 new elective subjects in the second year namely Green Supply Chain, Global Climate Change & Business and Corporate Governance. Twelve students have taken all the three electives, and 120 students study Green Supply Chain. There are twice as many students who study Green Supply Chain and Corporate Governance but not Global Climate Change and Business, as those who study both Green Supply Chain and Global Climate Change & Business but not Corporate Governance, and 4 times as many who study all the three. 124 students study Corporate Governance. There are 72 students who could not muster up the courage to take up any of these subjects. The group of students who study both Green Supply Chain and Corporate Governance but not global Climate Change & Business is exactly the same as the group made up to the students who study both Global Climate Change & Business and Corporate Governance. How many students study Global Climate Change & Business only?
Detailed Solution for VITEEE PCME Mock Test - 13 - Question 29

The number of students who study each combination of subjects (based on the direct data) given is as shown below:

It is given that: (GSC and CG but not GCCB) = 4 times (all three electives)

∴ 2x = 4(12) i.e. x = 24

Also: (GSC and CG but not GCCB) = (all three electives) + (GCCB and CG but not GSC) 

∴ (GCCB and CG but not GSC) = 2x − 12 = 2(24) − 12 = 36

So, the figure becomes:

Now, CG only = 124 − (48 + 12 + 36) = 28 

∴ GCCB alone = 360 − 120 − 36 − 28 − 72 = 104

Hence, option (b).

VITEEE PCME Mock Test - 13 - Question 30
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In an amusement park along with the entry pass a visitor gets two of the three available rides (A, B and C) free. On a particular day 77 opted for ride A, 55 opted for B and 50 opted for C; 25 visitors opted for both A and C, 22 opted for both A and B, while no visitor opted for both B and C. 40 visitors did not opt for ride A and B, or both. How many visited with the entry pass on that day?
Detailed Solution for VITEEE PCME Mock Test - 13 - Question 30

Let the Venn diagram be as shown in the figure,

No one can take all three rides, hence g = 0.

22 people take rides A and B, 
∴ d = 22

25 people take rides A and C, 
∴ f = 25

50 people take ride C, 
∴ c = 50 – 25 = 25.

40 people don’t take A or B or both,
∴ 40 = c + h
⇒ h = 40 – 25 = 15

∴ Total number of people visiting the park = (77 + 55 + 50 – 25 – 22) + 15 = 150.

Hence, option (d).

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