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JEE Exam  >  JEE Tests  >  VITEEE PCME Mock Test - 9 - JEE MCQ

VITEEE PCME Mock Test - 9 - JEE MCQ


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30 Questions MCQ Test - VITEEE PCME Mock Test - 9

VITEEE PCME Mock Test - 9 for JEE 2024 is part of JEE preparation. The VITEEE PCME Mock Test - 9 questions and answers have been prepared according to the JEE exam syllabus.The VITEEE PCME Mock Test - 9 MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for VITEEE PCME Mock Test - 9 below.
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VITEEE PCME Mock Test - 9 - Question 1
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For all real x, the minimum value of 1 - x + x2/1 + x + x2 is

VITEEE PCME Mock Test - 9 - Question 2
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AOB is the positive quadrant of the ellipse x2/a2 + y2/b2 = 1, where OA = a, OB = b. The area between the arc AB and the chord AB of the ellipse is

Detailed Solution for VITEEE PCME Mock Test - 9 - Question 2

 

Required area

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VITEEE PCME Mock Test - 9 - Question 3
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If |z| = 4 and arg z = (5π/6), then the value of z is

VITEEE PCME Mock Test - 9 - Question 4
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If z₁ and z₂ are two non-zero complex numberssuch that |z₁ + z₂| =|z₁| + |z₂|,then arg z₁ -arg z₂ is equal to
VITEEE PCME Mock Test - 9 - Question 5
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VITEEE PCME Mock Test - 9 - Question 6
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VITEEE PCME Mock Test - 9 - Question 7
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where [x] denotes the greatest integer less than or equal to x, is continuous at x = 2, then the value of a is equal to
VITEEE PCME Mock Test - 9 - Question 8
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VITEEE PCME Mock Test - 9 - Question 9
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The differential equation representing the family of curves y2 = 2c(x+√c), where c is a positive perimeter, is of
VITEEE PCME Mock Test - 9 - Question 10
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The differential equation | dy/dx | + | y | + 3 = 0 admits
VITEEE PCME Mock Test - 9 - Question 11
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Detailed Solution for VITEEE PCME Mock Test - 9 - Question 11

VITEEE PCME Mock Test - 9 - Question 12
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Find the degree of (y2)2  − √ y1  = y3
VITEEE PCME Mock Test - 9 - Question 13
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If x dy = y(dx + y dy), y > 0 and y (1) = 1, then y (-3) is equal to
VITEEE PCME Mock Test - 9 - Question 14
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If the function f(x) = cos2 x + cos2(π/3 + x) - cos x.cos(π/3 + x) is constant, then the value of this constant is
VITEEE PCME Mock Test - 9 - Question 15
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( d/dx )(x2 + cos x)4 =
Detailed Solution for VITEEE PCME Mock Test - 9 - Question 15

d/dx(x2 + cos x)4

= 4.(x2 + cos x)3 x d/dx (x2 + cos x)
= 4(x2 + cos x)3 x (2x - sin x)

VITEEE PCME Mock Test - 9 - Question 16
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VITEEE PCME Mock Test - 9 - Question 17
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∫[sin(logx) + cos(logx)] dx =
VITEEE PCME Mock Test - 9 - Question 18
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The domain of sin-1 x is
VITEEE PCME Mock Test - 9 - Question 19
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if f : R→R be such that f(1) = 4 and f'(1) = 12 then 

VITEEE PCME Mock Test - 9 - Question 20
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Which of the following is the converse of the statement: "If x > 4, then x + 2 > 5"?
Detailed Solution for VITEEE PCME Mock Test - 9 - Question 20

To form the CONVERSE of a statement, the "If" and the "then" sections of the statement switch places.

VITEEE PCME Mock Test - 9 - Question 21
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Directions: Study the following graph carefully and answer the question given below.

Q. The total number of units manufactured by companies R, S and U in the year 2006 is what percentage of the total number of units manufactured by Company P in all the years together?
Detailed Solution for VITEEE PCME Mock Test - 9 - Question 21

The total number of units manufactured by companies R, S and U in the year 2006 = 19.4 + 22.5 + 28.2 = 70.1 thousands
The total number of units manufactured by Company P in all the years together = 4.5 + 7.2 + 8.5 + 9.8 + 12.5 + 15.4 = 57.9 thousands
Required percentage = 70.1/57.9 x 100

= 121.07

≈ 121

VITEEE PCME Mock Test - 9 - Question 22
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Directions: Study the following graph carefully and answer the question given below.

Q. What is the average number of units sold by Company S in the years 2001, 2002, 2003, 2004 and 2005?
Detailed Solution for VITEEE PCME Mock Test - 9 - Question 22

The total number of units sold by Company S in the years 2001, 2002, 2003, 2004 and 2005 = 4.6 + 11.5 + 16.4 + 18.5 + 20.5 = 71.5 thousands = 71,500 units

Required average = 71,500/5 = 14,300

VITEEE PCME Mock Test - 9 - Question 23
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Directions: Study the following graph carefully and answer the question given below.

Q. What is the respective ratio of total number of units manufactured by companies Q and R together in the year 2001 to those manufactured by companies S and T together in the year 2003?
Detailed Solution for VITEEE PCME Mock Test - 9 - Question 23

The total number of units manufactured by companies Q and R together in the year 2001 = 6.5 + 6.5 = 13 thousands
The total number of units manufactured by companies S and T together in the year 2003 = 16.4 + 12.5 = 28.9 thousands
Required ratio = 13 : 28.9
= 130 : 289

VITEEE PCME Mock Test - 9 - Question 24
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Directions: Study the following graph carefully and answer the question given below.

Q. What is the average number of hard disks produced by Company 'X' over all the years together?
Detailed Solution for VITEEE PCME Mock Test - 9 - Question 24

Total number of hard disks produced by Company 'X' over all the years together = 6 + 10 + 18 + 15 + 30 + 28 + 38 + 35 = 180 (in thousand) = 1,80,000

Required average = 1, 80, 000/8 = 22,500

VITEEE PCME Mock Test - 9 - Question 25
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Rohan purchased some pens, pencils and erasers for his young brothers and sisters for the ensuing examinations. He had to buy atleast 11 pieces of each item in a manner that the number of pens purchased is more than the number of pencils, which is more than the number of erasers. He purchased a total of 38 pieces. If the number of pencils cannot be equally divided among his 4 brothers and sisters, how many pens did he purchase?
Detailed Solution for VITEEE PCME Mock Test - 9 - Question 25
  • Different possibilities for the number of pencils = 12 or 13.
  • Since it cannot be divided into his 4 brothers and sisters, it has to be 13.
  • The number of erasers should be less than the number of pencils and greater than or equal to 11. So the number of erasers can be 11 or 12.
  • If the number of erasers is 12, then the number of pens = 38 - 13 - 12 = 13, which is not possible as the number of pens should be more than the number of pencils.
  • So the number of erasers = 11 and therefore the number of pens = 14 
VITEEE PCME Mock Test - 9 - Question 26
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A nursery has 363, 429 and 693 plants respectively of 3 distinct varieties. It is desired to place these plants in straight rows of plants of 1 variety only so that the number of rows required is the minimum. What is the size of each row and how many rows would be required?

 
Detailed Solution for VITEEE PCME Mock Test - 9 - Question 26

The size of each row would be the HCF of 363, 429 and 693. Difference between 363 and 429 =66.

Factors of 66 are 66, 33, 22, 11, 6, 3, 2, 1.

66 need not to be checked as it is even and 363 is odd. 33 divides 363, hence would automatically divide

429 and also divides 693. Hence, 33 is the correct answer for the size of each row.

For how many rows would be required we need to follow the following process:

Minimum number of rows required = 363/33 + 429/33 + 693/33 = 11 + 13 + 21 = 45 rows.

Therefore, the correct answer is A

VITEEE PCME Mock Test - 9 - Question 27
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Write three rational numbers between 4 and 5?
Detailed Solution for VITEEE PCME Mock Test - 9 - Question 27
  • There are several rational numbers between 4 and 5. The numbers are between 16/4 and 20/4. 
  • Therefore, the answer is c, that is, 17 / 4, 18 / 4, 19 / 4.
VITEEE PCME Mock Test - 9 - Question 28
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Shyam visited Ram during his brief vacation. In the mornings they both would go for yoga. In the evenings they would play tennis. To have more fun, they indulge only in one activity per day, i.e. either they went for yoga or played tennis each day. There were days when they were lazy and stayed home all day long. There were 24 mornings when they did nothing, 14 evenings when they stayed at home, and a total of 22 days when they did yoga or played tennis. For how many days Shyam stayed with Ram?
Detailed Solution for VITEEE PCME Mock Test - 9 - Question 28

Let the number of days in the vacation be x
They played tennis for x - 14 days
They did yoga for x - 24 days
So, they did yoga or played tennis for x - 14 + x - 24 = 2x - 38 days
2x – 38 = 22
=> x = 30

VITEEE PCME Mock Test - 9 - Question 29
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How many even integers n, where 100 ≤ n ≤ 200, are divisible neither by seven nor by nine?
Detailed Solution for VITEEE PCME Mock Test - 9 - Question 29

Between 100 and 200 both included there are 51 even nos.

There are 7 even nos which are divisible by 7 and 6 nos which are divisible by 9 and 1 no divisible by both ie 42.

Hence in total 51 – (7+6-1) = 39

There is one more method through which we can find the answer.

Since we have to find even numbers, consider the numbers which are divisible by 14, 18 and 126 between 100 and 200.

These are 7, 6 and 1 respectively.

VITEEE PCME Mock Test - 9 - Question 30
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There are 3 clubs A, B & C in a town with 40, 50 & 60 members respectively. While 10 people are members of all 3 clubs, 70 are members in only one club. How many belong to exactly two clubs?
Detailed Solution for VITEEE PCME Mock Test - 9 - Question 30

We know that x + y + z = T and x + 2y + 3z = R, where
x = number of members belonging to exactly 1 set = 70
y = number of members belonging to exactly 2 sets
z = number of members belonging to exactly 3 sets = 10
T = Total number of members
R = Repeated total of all the members = (40 + 50 + 60) = 150
Thus we have two equations and two unknowns. Solving this we get y = 25

So, 25 people belong to exactly 2 clubs.

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