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DSSSB PGT Mathematics Mock Test - 4 - DSSSB TGT/PGT/PRT MCQ


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30 Questions MCQ Test DSSSB PGT Mock Test Series 2024 - DSSSB PGT Mathematics Mock Test - 4

DSSSB PGT Mathematics Mock Test - 4 for DSSSB TGT/PGT/PRT 2024 is part of DSSSB PGT Mock Test Series 2024 preparation. The DSSSB PGT Mathematics Mock Test - 4 questions and answers have been prepared according to the DSSSB TGT/PGT/PRT exam syllabus.The DSSSB PGT Mathematics Mock Test - 4 MCQs are made for DSSSB TGT/PGT/PRT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for DSSSB PGT Mathematics Mock Test - 4 below.
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DSSSB PGT Mathematics Mock Test - 4 - Question 1

The solution of the inequality 3(2-x)≥2(1-x) for real x is :

Detailed Solution for DSSSB PGT Mathematics Mock Test - 4 - Question 1

3(2 - x) ≥ 2(1 - x)
6 - 3x ≥ 2 - 2x
4 ≥ x

DSSSB PGT Mathematics Mock Test - 4 - Question 2

Directions: Study the following information carefully and answer the questions given below:

M, T, J, R, D, W and Q are seven friends traveling in three cars – X, Y, and Z with at least two persons in each car. There are three female members among them with at least one in each car. T travels only with her boyfriend Q in car Y. M travels in his car X. D, a male, and W do not travel in car Z. J is not a female member and W is a female.

Q. J travels in which car?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 4 - Question 2

M-travels in car X
T-+Q as given in Y
J-no female, and travels in Z
R-car X(sequential)
D-car Y
W-female with Z
Q-X
hence correct option is C.

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DSSSB PGT Mathematics Mock Test - 4 - Question 3

Swell writes: “Goa rose and fell simultaneously with the rise and fall of the Tuluva dynasty”.Why?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 4 - Question 3

C is the correct option.Swell writes: “Goa rose and fell simultaneously with the rise and fall of the Tuluva dynasty”. ... Goa was a part of the Vijayanagar empire. The city enjoyed protection and trade concessions. The Tuluva kings always had Goa as the last refuge after losing war.

DSSSB PGT Mathematics Mock Test - 4 - Question 4

Direction: Read the following passages carefully and answer the question that follows.
Although an Eco-friendly process and one of the important ways to save the environment, recycling is not gaining pace in the industry. The recycling undergoes many process. First is collecting and sorting of garbage. This required a lot of manpower and tools which are expensive. Another disadvantage of recycling which makes it unviable is that for the manufacturers economically, the recycled material is not highly demanded since its quality is not as good as the original material. So, if the marketing of recycled goods is not worthwhile then the whole process of recycling cannot be economically efficient. Recycled products face other disadvantage as well, such life, difficult in de-linking the dyed products and less durability etc.

Q. The authors highlights the problem of?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 4 - Question 4

The author highlights the problem that recycling is not an easy process and there are many obstacles in the way of recycling

DSSSB PGT Mathematics Mock Test - 4 - Question 5

Direction: Read the following passages carefully and answer the question that follows.
A new consciousness is to dawn. Science has not been able to demystify existence. This is now recognized not by ordinary technicians but by geniuses, because they are the pioneers; they can see the dawn very close by, they are the prophets. Albert Einstein said that science has failed in demystifying existence, that on the contrary, it has mystified things even more.

e.g., it was so easy-just 100 years ago-for the scientist to say that all is matter. Now matter has disappeared; in neon-physics there is no entity called matter. The deeper the physicist went into the world of matter, the less matter was found ; it is all pure energy . Can we define energy ? Energy can not be material; it is something totally different from matter . Matter is static, energy is dynamic; matter is a noun, energy is a verb. Matter is measurable. That is exactly, the meaning of the word 'matter'. It comes from 'measure', the root means 'measurable'. Matter can be measured, that's why it is called matter. Energy is immeasurable, it can not be called matter. Hence, physicists get more puzzled the more they probe into the world energy.

Q. What is the contrary thing that science has done?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 4 - Question 5

Instead of demystifying, it has mystified more, Other options (a), (c) and (d) are not correct.

DSSSB PGT Mathematics Mock Test - 4 - Question 6

(x2 + 1)2 - x2 = 0 has

Detailed Solution for DSSSB PGT Mathematics Mock Test - 4 - Question 6

DSSSB PGT Mathematics Mock Test - 4 - Question 7

The two numbers whose sum is 27 and their product is 182 are

Detailed Solution for DSSSB PGT Mathematics Mock Test - 4 - Question 7

Explanation:Let the one number be xx .As the sum  of numbers is 27 , then the other number will be (27−x)(27−x)                                                                                                                                    According to question

DSSSB PGT Mathematics Mock Test - 4 - Question 8

The average number of runs scored by Virat Kohli in four matches is 48. In the fifth match, Kohli scores some runs such that his average now becomes 60. In the 6th innings he scores 12 runs more than his fifth innings and now the average of his last five innings becomes 78. How many runs did he score in his first innings? (He does not remain not out in any of the innings)

Detailed Solution for DSSSB PGT Mathematics Mock Test - 4 - Question 8

Runs scored by Kohli in first 4 innings = 48*4 = 192
Average of 5 innings is 60, so total runs scored after 5 innings = 60*5 = 300
Hence runs scored by Kohli in fifth inning = 300 – 192 = 108
It is given that in 6th innings he scores 12 runs more than this, so he must score 120 in the sixth inning. Hence total runs scored in 6 innings = 300+120 = 420
Now average of last five innings is 78, so runs scored in last innings = 390
Hence runs scored in first inning = 420 – 390 = 30.

DSSSB PGT Mathematics Mock Test - 4 - Question 9

"पक्षी" का उचित पर्यायवाची शब्द है-

Detailed Solution for DSSSB PGT Mathematics Mock Test - 4 - Question 9

"पक्षी" का उचित पर्यायवाची शब्द "खग" है।
पक्षी के अन्य पर्यायवाची- चिडिया, गगनचर, पखेरू, विहंग, नभचर।
एक ही अर्थ में प्रयुक्त होने वाले शब्द, जो बनावट में भले ही अलग हों, को पर्यायवाची शब्द कहते है। 
पर्यायवाची शब्द को समानार्थी शब्द भी कहा जाता है।

DSSSB PGT Mathematics Mock Test - 4 - Question 10

निम्नलिखित विकल्पों में से "आलोक" का विलोम है-

Detailed Solution for DSSSB PGT Mathematics Mock Test - 4 - Question 10

एक-दूसरे के विपरीत अर्थ देने वाले शब्द, विलोम कहलाते है।

  • "आलोक" का विलोम "अंधकार" है।
  • आलोक का अर्थ- प्रकाश।
  • अंधकार का अर्थ- अँधेरा।
DSSSB PGT Mathematics Mock Test - 4 - Question 11

नीचे दिए गए वाक्य के लिए उपयुक्त एक शब्द का चयन कीजिए-
जिसका संबंध पृथ्वी से हो

Detailed Solution for DSSSB PGT Mathematics Mock Test - 4 - Question 11

जिसका संबंध पृथ्वी से हो, वह पार्थिव कहलाता है।

DSSSB PGT Mathematics Mock Test - 4 - Question 12

Let be a positive real number and let

If , then[ [k] is equal to:

Detailed Solution for DSSSB PGT Mathematics Mock Test - 4 - Question 12

DSSSB PGT Mathematics Mock Test - 4 - Question 13

Derivative of logxcosx with respect to x is:

Detailed Solution for DSSSB PGT Mathematics Mock Test - 4 - Question 13

Given,

Taking log on both sides, we get

Differentiate with respect to x, we get

DSSSB PGT Mathematics Mock Test - 4 - Question 14

Consider the proper subsets of {1, 2, 3, 4}. How many of these proper subsets are a superset of the set {3}?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 4 - Question 14

A proper subset is one that contains few elements of the original set.

A superset is one which contain all the element including elements of the original set.

The proper subsets of {1, 2, 3, 4} and supperset of set {3} are

{1, 3}, {2, 3}, {3, 4}, {1, 2, 3}, {2, 3, 4}, {1, 3, 4}, {1, 2, 3, 4}

DSSSB PGT Mathematics Mock Test - 4 - Question 15

If then :

Detailed Solution for DSSSB PGT Mathematics Mock Test - 4 - Question 15

Given:

If we take modulus on both sides,

Squaring both sides,

DSSSB PGT Mathematics Mock Test - 4 - Question 16

The coefficient of the term independent of x in the expansion of  is:

Detailed Solution for DSSSB PGT Mathematics Mock Test - 4 - Question 16

Given expression,

So required coefficient = .

DSSSB PGT Mathematics Mock Test - 4 - Question 17

The solution of the equation is:

Detailed Solution for DSSSB PGT Mathematics Mock Test - 4 - Question 17

DSSSB PGT Mathematics Mock Test - 4 - Question 18

The value of is :

Detailed Solution for DSSSB PGT Mathematics Mock Test - 4 - Question 18

To find the following:

Common Ratio

Here, the common ratio is the same so it is an example of a GP.

In the series 

first term , and

Now, we know the sum of an infinite number of terms of a GP.

DSSSB PGT Mathematics Mock Test - 4 - Question 19

The solution of the differential equation is:

Detailed Solution for DSSSB PGT Mathematics Mock Test - 4 - Question 19

Let

Differentiating with respect to x, we get

Now,

Integrating both sides, we get

DSSSB PGT Mathematics Mock Test - 4 - Question 20

Which one of the following statements is correct in respect of the function

Detailed Solution for DSSSB PGT Mathematics Mock Test - 4 - Question 20
Given:

Differentiating both sides, we get

Again differentiating both sides, we get

To find critical point,



At

Therefore, function neither maximum nor minimum at
DSSSB PGT Mathematics Mock Test - 4 - Question 21

Find the sum of the series whose nth term is n (n + 2).

Detailed Solution for DSSSB PGT Mathematics Mock Test - 4 - Question 21

Given, 

As we know that,

As we know

The sum of first n natural numbers,

S=

The sum of first n2 natural numbers,

S=

Then, we can write

DSSSB PGT Mathematics Mock Test - 4 - Question 22

Solve for , given .

Detailed Solution for DSSSB PGT Mathematics Mock Test - 4 - Question 22

In first-order linear differential equation;

Where and are functions of

Integrating factor

General solution:

Given the differential equation is;

∴ It is linear differential equation is of first order

Now,

Integrating,

Given  

or

For

 

DSSSB PGT Mathematics Mock Test - 4 - Question 23

Which of the following is true in the given figure where AD is the altitude to the hypotenuse of a right angled ΔABC?

I. ΔABD ~ ΔCAD

II. ΔABD ≅ ΔCDA

III. ΔADB ~ ΔCAB

Of these statements the correct ones are combination of:

Detailed Solution for DSSSB PGT Mathematics Mock Test - 4 - Question 23

Given:

ABC is a right angled triangle

AD is the altitude to the hypotenuse BC

∠A = 90°

Let ∠C = θ and ∠B = α  where α + θ = 90°

In ΔABD and ΔCAD, we have

⇒ ∠ADB = ∠CDA = 90°

⇒ ∠DCA = ∠DBA = α 

⇒ ∠BAD = DCA = θ

Two pairs of corresponding angles are equal, so

ΔABD ~ ΔCAD by Angle - Angle similarity

Now in  ΔABD and ΔCDA

The triangles are similar by AA similarity but no congruent.

Now in ΔADB and ΔCAB, we have

⇒ ∠ADB = ∠CAB = 90°

⇒ ∠ABC = ∠ABD = α

⇒ ∠ACB = ∠BAD = θ

Similarly, two pairs of corresponding angles are equal, so

= ΔADB ~ ΔCAB

∴ Only statements I and III are correct.

DSSSB PGT Mathematics Mock Test - 4 - Question 24

Direction: Consider the following data for the next three (03) items that follow :

The incidence of suffering from a disease among workers in an industry has a chance of

What is the probability that no one out of 6 workers suffers from a disease?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 4 - Question 24

Explanation:

Given :

of the workers have a chance of suffering from the disease

The formula for binomial distribution:

where,

probability of success of a trial

probability of failure of a trail

total no of trial

no of a successful trial for the given condition.

number of combinations of taken at a time

probability of success of trial.

Probability, where out of 6 , exactly 3 suffer from the disease is

The probability that no one out of 6 workers suffers from a disease is .

DSSSB PGT Mathematics Mock Test - 4 - Question 25

The coefficient of in is:

Detailed Solution for DSSSB PGT Mathematics Mock Test - 4 - Question 25

We know that

In the given binomial expression and .

For the term containing , we must have .

So, the coefficient of in is,


DSSSB PGT Mathematics Mock Test - 4 - Question 26

What is equal to?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 4 - Question 26

Let, G be the event that the first applicant interviewed is a graduate.

be the event that the first applicant interviewed has at least 3 years of experience.

is the event that the first applicant interviewed is not a graduate

is the event that the first applicant interviewed has less than three years of experience

Now, from the table we have,

Number of applicants who are not graduates,

Number of applicants who are not graduates and have less than three years of experience,

Total number of applicants

So the required probability is given by,

.

DSSSB PGT Mathematics Mock Test - 4 - Question 27

If (x – 4) and (x + 6) are the factors of equation x2 + ax + b = 0 then find the value of (a – b)?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 4 - Question 27

Given:

(x – 4) and (x + 6) are the factors of equation x2 + ax + b = 0

If (x – p) is the factors equation x2 + ax + b = 0 then ‘p’ will be the root of the equation.

Roots of equation x2 + ax + b = 0 will be: 4 and -6.

Putting the values of the roots we will get two equations as follows:

16 + 4a + b = 0

⇒ 4a + b = -16     ---- (1)

And

36 – 6a + b = 0

⇒ -6a + b = - 36     ---- (2)

Solving these two equations we get

⇒ a = 2 and b = -24

So,

(a – b) = 2 – (-24) = 26

DSSSB PGT Mathematics Mock Test - 4 - Question 28

If for , the derivative of is , then equals:

Detailed Solution for DSSSB PGT Mathematics Mock Test - 4 - Question 28

Let,

Differentiate the given function with respect to

Equating the derivative to

DSSSB PGT Mathematics Mock Test - 4 - Question 29

I.

II.

(Take )

Detailed Solution for DSSSB PGT Mathematics Mock Test - 4 - Question 29

From I,

Taking,

or

or

From II,

Taking,
or
or
Comparison between and (via Tabulation):

The relation between and cannot be established.  

DSSSB PGT Mathematics Mock Test - 4 - Question 30

Consider the following statements:

1. is divisible by 6 , where n > 3

2. is divisible by 7 , where n > 3

Which of the above statements is/are correct?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 4 - Question 30

Statement I: is divisible by 6 , where n > 3

Let n = 4

4 is not divisible by 6.

So, Statement I is incorrect.

Statement I: is divisible by 7 , where n > 3

Let n = 5

23 is not divisible by 7.

Statement II is incorrect.

∴ Neither statement I nor II is correct.

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