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JEE Exam  >  JEE Tests  >  VITEEE PCME Mock Test - 7 - JEE MCQ

VITEEE PCME Mock Test - 7 - JEE MCQ


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30 Questions MCQ Test - VITEEE PCME Mock Test - 7

VITEEE PCME Mock Test - 7 for JEE 2024 is part of JEE preparation. The VITEEE PCME Mock Test - 7 questions and answers have been prepared according to the JEE exam syllabus.The VITEEE PCME Mock Test - 7 MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for VITEEE PCME Mock Test - 7 below.
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VITEEE PCME Mock Test - 7 - Question 1
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The sides of an equilateral triangle are increasing at the rate of 2 cm/sec. The rate at which the area increases, when the side is 10 cm is

VITEEE PCME Mock Test - 7 - Question 2
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The area bounded by the parabola x = 4 − y2 and the y-axis, in square units is

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VITEEE PCME Mock Test - 7 - Question 3
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VITEEE PCME Mock Test - 7 - Question 4
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The argument and modulus of [(1+i)/(1-i)] are respectively
VITEEE PCME Mock Test - 7 - Question 5
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If a is real number such that | z − a i | = | z + a i | , then the locus of z is
VITEEE PCME Mock Test - 7 - Question 6
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 for x ≠ 0, f 0 = 0, then f(x) at  x = 0 is
VITEEE PCME Mock Test - 7 - Question 7
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VITEEE PCME Mock Test - 7 - Question 8
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If - 9 is the root of the equation , then other two roots are
VITEEE PCME Mock Test - 7 - Question 9
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Let f(x) = log |x - 1|, x ≠ 1. The value of f ′(1/2)      is
Detailed Solution for VITEEE PCME Mock Test - 7 - Question 9

VITEEE PCME Mock Test - 7 - Question 10
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The order and degree of the differential equation (1 + 3dy/dx)2/3 = 4d3y/dx3 are
VITEEE PCME Mock Test - 7 - Question 11
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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 - 7 - Question 12
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The general solution of the differential equation  is given by
VITEEE PCME Mock Test - 7 - Question 13
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The differential equation of all circles which pass through (0,0) and having centre on y-axis, is
VITEEE PCME Mock Test - 7 - Question 14
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  then f'(1) is ?
VITEEE PCME Mock Test - 7 - Question 15
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VITEEE PCME Mock Test - 7 - Question 16
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∫tan-1x dx =
VITEEE PCME Mock Test - 7 - Question 17
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The domain of sin-1x is
VITEEE PCME Mock Test - 7 - Question 18
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∫ tan5θ dθ =
VITEEE PCME Mock Test - 7 - Question 19
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If f'(2) = 4 and f ' (1) = 2 then 

Detailed Solution for VITEEE PCME Mock Test - 7 - Question 19

Explanation:

- Given that f'(2) = 4 and f'(1) = 2
- The derivative of a function represents the rate of change of the function at a specific point.
- Therefore, f'(2) = 4 means that the rate of change of the function at x = 2 is 4.
- Similarly, f'(1) = 2 means that the rate of change of the function at x = 1 is 2.
- To find the value of f(x) when the derivative is given, we need to integrate the derivative function.
- Since the derivative of f(x) is given, we can integrate it to find f(x).
- Integrate f'(x) = 4 with respect to x, we get f(x) = 4x + C (where C is the constant of integration)
- Integrate f'(x) = 2 with respect to x, we get f(x) = 2x + D (where D is the constant of integration)
- Since both expressions represent the same function f(x), we can equate them: 4x + C = 2x + D
- Solving for x, we get x = (D - C) / 2
- Therefore, the answer is B: 4.

VITEEE PCME Mock Test - 7 - Question 20
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The value of 

VITEEE PCME Mock Test - 7 - Question 21
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Directions: Read the table given below and answer the questions accordingly.

Shares traded in Chandigarh, Punjab, Haryana (In Rupees)

Q. Total of high for all the companies in all the States/UT are more than the lows for all the states/UT by how much?
Detailed Solution for VITEEE PCME Mock Test - 7 - Question 21

The total of high for all the given places is 2973.25 whereas the low totals to 2693.

So the given data differ by 280.25.

VITEEE PCME Mock Test - 7 - Question 22
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Directions: Study the following graph carefully and answer the questions given below:

Production (in Lakhs) of  Widgets  & Percentage defect over the years in five factories A, B, C, D, E.

Q. The average production for the given data will be maximum for which factory?
Detailed Solution for VITEEE PCME Mock Test - 7 - Question 22

If we look closely then we will find that the production of factory A happens to be maximum and thus its average will also be highest.

We can also verify this by calculating the number of widgets individually and dividing it by the number of given years i.e. 6.

VITEEE PCME Mock Test - 7 - Question 23
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Directions: Study the following graph carefully and answer the questions given below:

Production (in Lakhs) of  Widgets  & Percentage defect over the years in five factories A, B, C, D, E.

Q. What was the difference in defected widgets of factory C for the year 2006 and defected widgets of factory E for the year 2003?
Detailed Solution for VITEEE PCME Mock Test - 7 - Question 23

Reqd. No. = (15% of 420000) - (8% of 400000) = 63000 - 32000 = 31000

VITEEE PCME Mock Test - 7 - Question 24
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All the page numbers from a book are added, beginning at page 1. 

However, one page number was added twice by mistake. The sum obtained was 1000. Which page number was added twice?
Detailed Solution for VITEEE PCME Mock Test - 7 - Question 24

The Correct Answer is C: 10

Let the total pages be ‘n’ and the number which is added twice is x;

∴ {n(n + 1)}/2 = 1000 – x

⇒ n(n + 1) = 2000 – 2x

Now, by hit and trial, we can say that the value of n = 44 i.e. initially there were 44 pages and their sum was (44 × 45)/2 = 990

Since the given sum is 1000, so we can say that the page number 10 was added twice.

VITEEE PCME Mock Test - 7 - Question 25
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The integers 34041 and 32506 when divided by a three-digit integer n leave the same remainder. What is n?
Detailed Solution for VITEEE PCME Mock Test - 7 - Question 25

Let the common remainder be x.

32506 – x is divisible by n.

34041 – x is divisible by n.

Difference of (32506 – x) and (34041 – x) = (32506 – x) – (34041 – x)

⇒ 32506 – x – 34041 + x

⇒ 32506 – 34041

⇒ 1535 

Factors of 1535 = 1 × 5 × 307 × 1535

3-digit number = 307

⇒ n = 307

∴ The value of n is 307.

VITEEE PCME Mock Test - 7 - Question 26
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What is the least number of soldiers that can be drawn up in troops of 12, 15, 18 and 20 soldiers and also in form of a solid square?
Detailed Solution for VITEEE PCME Mock Test - 7 - Question 26

In this type of question, We need to find out the LCM of the given numbers.
LCM of 12, 15, 18 and 20:

⇒ 12 = 2 x 2 x 3
⇒ 15 = 3 x 5
⇒ 18 = 2 x 3 x 3
⇒ 20 = 2 x 2 x 5

∴ LCM = 2 x 2 x 3 x 5 x 3
Since the soldiers are in the form of a solid square. Hence, LCM must be a perfect square.
To make the LCM a perfect square, We have to multiply it by 5, hence, the required number of soldiers: 

= 2 x 2 x 3 x 3 x 5 x 5
= 900

VITEEE PCME Mock Test - 7 - Question 27
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How many factors of 1080 are perfect squares?
Detailed Solution for VITEEE PCME Mock Test - 7 - Question 27
  • The factors of 1080 which are perfect square:
  • 1080 → 23 × 33 × 5
  • For, a number to be a perfect square, all the powers of numbers should be even number.
  • Power of 2 → 0 or 2
  • Power of 3 → 0 or 2
  • Power of 5 → 0 
  • So, the factors which are perfect square are 1, 4, 9, 36.
  • Hence, Option B is correct.
     
VITEEE PCME Mock Test - 7 - Question 28
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Directions: In this type of questions, some particular words are assigned certain substituted names. Then a question is asked that is to be answered in the substituted code language.

If 'bat' is 'racket', 'racket' is 'football', 'football' is 'shuttle', 'shuttle' is 'ludo' and 'ludo' is 'carrom', what is cricket played with?
Detailed Solution for VITEEE PCME Mock Test - 7 - Question 28

Cricket is played with a 'bat' and 'bat' is called 'racket'. So, cricket is played with 'racket'.

Hence, option A is correct

VITEEE PCME Mock Test - 7 - Question 29
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Directions: In this type of questions, some particular words are assigned certain substituted names. Then a question is asked that is to be answered in the substituted code language.

If 'sand' is called 'air', 'air' is called 'plateau', 'plateau' ia called 'well', 'well' is called 'island' and 'island' is called 'sky', then from where will a woman draw water?
Detailed Solution for VITEEE PCME Mock Test - 7 - Question 29

A woman shall draw water from a 'well' but a 'well' is called 'island' . So, the woman will draw water from an 'island'.

Hence, option B is correct.

VITEEE PCME Mock Test - 7 - Question 30
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Directions: In this type of questions, some particular words are assigned certain substituted names. Then a question is asked that is to be answered in the substituted code language.

If 'cushion' is called 'pillow', 'pillow' is called 'mat', 'mat' is called 'bedsheet' and 'bedsheet' is called 'cover', which will be spread on the floor ?
Detailed Solution for VITEEE PCME Mock Test - 7 - Question 30

'mat' will be spread on the floor But 'mat' is called 'bedsheet'.So, a 'bedsheet' will be spread on the floor.

Hence, option B is correct.

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