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DSSSB TGT Mathematics Mock Test - 6 - DSSSB TGT/PGT/PRT MCQ


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30 Questions MCQ Test DSSSB TGT Mock Test Series 2025 - DSSSB TGT Mathematics Mock Test - 6

DSSSB TGT Mathematics Mock Test - 6 for DSSSB TGT/PGT/PRT 2025 is part of DSSSB TGT Mock Test Series 2025 preparation. The DSSSB TGT Mathematics Mock Test - 6 questions and answers have been prepared according to the DSSSB TGT/PGT/PRT exam syllabus.The DSSSB TGT Mathematics Mock Test - 6 MCQs are made for DSSSB TGT/PGT/PRT 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for DSSSB TGT Mathematics Mock Test - 6 below.
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DSSSB TGT Mathematics Mock Test - 6 - Question 1

The first Indian to swim across English channel was

Detailed Solution for DSSSB TGT Mathematics Mock Test - 6 - Question 1

Mihir Sen (16 November 1930 - 11 June 1997) was a famous Indian long distance swimmer and businessman. He was the first Indian to conquer the English Channel from Dover to Calais in 1958, and did so in the fourth fastest time (14 hrs & 45 mins). He was the only man to swim the oceans of the five continents in one calendar year (1966). These included the Palk Strait, Dardanelles, Bosphorus, Gibraltar, and the entire length of the Panama Canal.

DSSSB TGT Mathematics Mock Test - 6 - Question 2

Who is the author of the book 'The Future of Freedom'?

Detailed Solution for DSSSB TGT Mathematics Mock Test - 6 - Question 2

'The Future of Freedom: Illiberal Democracy at Home and Abroad' is a book by Fareed Zakaria analyzing the variables that allow a liberal democracy to flourish and the pros and cons of the global focus on democracy as the building block of a more stable society rather than liberty.

DSSSB TGT Mathematics Mock Test - 6 - Question 3

The major towns namely Fatehabad, Hissar, Firozpur, Jaunpur and Firozabad were founded by :

Detailed Solution for DSSSB TGT Mathematics Mock Test - 6 - Question 3

The major towns namely Fatehabad, Hissar, Firozpur, Jaunpur and Firozabad were founded by Firoz Shah Tughlaq.

DSSSB TGT Mathematics Mock Test - 6 - Question 4

A man walks 30 metres towards South. Then, turning to his right, he walks 30 metres. Then, turning to his left, he walks 20 metres. Again, he turns to his left and walks 30 metres. How far is he from his initial position?

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

The movements of the man are as shown in figure.
Man's distance from initial position A = AE = (AB + BE) = (AB + CD) = (30 + 20) m = 50 m.

DSSSB TGT Mathematics Mock Test - 6 - Question 5

Select the correct figure from the given Answer Figure that would complete the Question figure.

​​​​

Detailed Solution for DSSSB TGT Mathematics Mock Test - 6 - Question 5

Figure (c) will complete the figure if you check carefully.

DSSSB TGT Mathematics Mock Test - 6 - Question 6

Directions to Solve

In each of the following questions find out the alternative which will replace the question mark.

Question -

3 : 12 :: 5 : ?

Detailed Solution for DSSSB TGT Mathematics Mock Test - 6 - Question 6

DSSSB TGT Mathematics Mock Test - 6 - Question 7

Select the option that expresses the given sentence in passive voice.
They will have brought the toy.

Detailed Solution for DSSSB TGT Mathematics Mock Test - 6 - Question 7
  • The given sentence is in Future Perfect Tense and in Active Voice.
  • The rule for changing a Future Perfect Tense from Active voice to Passive voice:
    • Interchange the object and subject with each other, i.e. object of the active sentence become the subject of the passive sentence.
    • ​Structure: Subject + will + have + v3 + Object (Active Voice) 
  • Object + will + have + been + V3 + by + Subject (Passive Voice)
  • Example: I will have sung different songs. (Active Voice)
    • Different songs will have been sung by me. (Passive Voice)

Therefore, the correct answer is 'The toy will have been brought by them.​'

DSSSB TGT Mathematics Mock Test - 6 - Question 8

Direction: Read the passage carefully and answer the following questions.
We are living in truly challenging times. The loss of near and dear ones in the second surge of the Covid pandemic is painful. Those who have died include not only ordinary people but also eminent doctors, academics, business leaders, literary and public figures, editors and journalists, civil servants, and people from the judicial fraternity. Their grief has to be our grief, too, because only by sharing sorrow can we develop a true national resolve.
Yet, there is a glimmer of hope. The positivity rate is declining, and new cases are down in 200 districts. The rate of recovery is a satisfying 86.7 percent. As on May 19, nearly 18.58 crore doses of vaccine have been administered. There is a well-laid-out plan to increase the production capacity of vaccines. Covaxin production is projected to increase from 1.5 crore doses per month to 10 crore doses by September. Similarly, Covishield is projected to increase its production up to 10 crore doses per month by August. This, along with Sputnik and many other vaccines in the pipeline, implies that the government has a clear roadmap for the production of 216 crore vaccines before the end of this year.
It is necessary to understand the scale of the challenge. In the first wave of Covid, the total number of cases in one year — from March 31, 2020, to March 31, 2021 — as per WHO data, was 1.20 crore approximately. The fatality percentage was 1.34 percent. In contrast, in the second wave, within a short span of 49 days — from April 1 to May 19 — the total number of Covid cases reported was 1.31 crore and the fatality percentage was 1.10 percent. Yet, there is hope in this WHO data. Deaths per lakh population in India was 21, whereas it was 181 in the USA, 166 in France, 195 in the UK, 209 in Italy, 171 in Spain, and 106 in Germany. I must clarify that any death anywhere is very painful.

Q. Which one of the following statements is TRUE according to the passage?

Detailed Solution for DSSSB TGT Mathematics Mock Test - 6 - Question 8
  • In the last sentence of the 1st paragraph that 'Their grief has to be our grief, too, because only by sharing sorrow can we develop a true national resolve'.
  • Thus, it is clear that the only statement which is true is Option 4.
  • Option 1 is incorrect as the correct statement is 'We are living in truly challenging times'.
  • Option 2 is incorrect because the correct statement is 'The loss of near and dear ones in the second surge of the Covid pandemic is painful'.
  • Option 4 is incorrect because the correct statement is 'Those who have died include not only ordinary people.

Therefore, the statement which is true according to the given passage is We can develop a true national resolve by sharing each others sorrow.

DSSSB TGT Mathematics Mock Test - 6 - Question 9

Direction: Change the Narration.

Q. He said, “She has finished her homework“.

Detailed Solution for DSSSB TGT Mathematics Mock Test - 6 - Question 9
  • The given sentence is in Present Perfect Tense.
  • The rule for changing Direct Speech to Indirect Speech:
    • Present Perfect Tense Changes to Past Perfect Tense.
    • Change the reporting verb according to the reported speech.
    • Remove the inverted comma’s from the direct speech and replace them with an appropriate conjunction.
    • The third person of direct speech doesn’t change.
      • ​Example: She said, " He has written five letters." (Direct Speech)
        • She said that he had written five letters.  (Indirect Speech)

Therefore, the correct answer is 'He said that she had finished her homework.'

DSSSB TGT Mathematics Mock Test - 6 - Question 10

‘वर्षा’ शब्द का उचित बहुवचन ज्ञात करें।

Detailed Solution for DSSSB TGT Mathematics Mock Test - 6 - Question 10

'वर्षा' शब्द सदैव एकवचन में प्रयोग किया जाता है। जैसे - इस बार आगरा में बहुत कम वर्षा हुई। इस प्रकार 'वर्षा' का बहुवचन 'वर्षा' ही रहेगा। अतः सही विकल्प ‘वर्षा’ है।
विशेष -

DSSSB TGT Mathematics Mock Test - 6 - Question 11

निम्न में से अशुद्ध वर्तनी वाला विकल्प चुनिए।

Detailed Solution for DSSSB TGT Mathematics Mock Test - 6 - Question 11

DSSSB TGT Mathematics Mock Test - 6 - Question 12

निम्नलिखित पर्यायवाची में से विछोह का पर्यायवाची शब्द बताओ ?

Detailed Solution for DSSSB TGT Mathematics Mock Test - 6 - Question 12

इनमें से विछोह का पर्यायवाची हिज्र है। अत: विकल्प हिज्र  इसका सही उत्तर है। अन्य विकल्प असंगत हैं।
विछोह के अन्य पर्यायवाची:-  अलगाव, बिलगाव, जुदाई, दूरी, विछोह, पार्थक्य, वियुक्तता, विच्छेद, तालाक,पृथकता, विभाजन, निस्संगता, पृथक्करण
अन्य विकल्प

DSSSB TGT Mathematics Mock Test - 6 - Question 13

निर्देश: निम्नलिखित गद्यांश को ध्यानपूर्वक पढ़िए व प्रश्नों के उतर दीजिये:
जन्‍मजात लोकतंत्रवादी वह होता है, जो जन्‍म से ही अनुशासन का पालन करने वाला हो। लोकतंत्र स्‍वाभाविक रूप में उसी को प्राप्‍त होता है, जो साधारण रूप में अपने को मानवीय तथा दैवीय सभी नियमों का स्‍वेच्‍छापूर्वक पालन करने का अभ्‍यस्‍त बना ले। जो लोग लोकतंत्र के इच्‍छुक हैं उन्‍हें चाहिए कि पहले वे लोकतंत्र की इस कसौटी पर अपने को परख लें। इसके अलावा, लोकतंत्रवादी को नि:स्‍वार्थ भी होना चाहिए। उसे अपनी या अपने दल की दृष्टि से नहीं बल्कि एकमात्र लोकतंत्र की ही दृष्टि से सब-कुछ सोचना चाहिए। तभी वह सविनय अवज्ञा का अधिकारी हो सकता है। व्‍यक्तिगत स्‍वतंत्रता की मैं कदर करता हूँ, लेकिन आपको यह हरगिज नहीं भूलना चाहिए कि मनुष्‍य मूलत: एक सामाजिक प्राणी ही है। सामाजिक प्रगति की आवश्‍यकताओं के अनुसार अपने व्‍यक्तित्‍व को ढालना सीखकर ही वह वर्तमन स्थिति तक पहुँचा है। अबाध व्‍यक्तिवाद वन्‍य पशुओं का नियम है। हमें व्‍यक्तिगत स्‍वतंत्रता और सामाजिक संयम के बीच समन्‍वय करना सीखना है। समस्‍त समाज के हित के खातिर सामाजिक संयम के आगे स्‍वेच्‍छापूर्वक सिर झुकाने से व्‍यक्ति और समाज, जिसका कि वह एक सदस्‍य है, दोनों का ही कल्‍याण होता है।

Q. लोकतंत्र में एक लोकतंत्रवादी को कैसा होना चाहिए?

Detailed Solution for DSSSB TGT Mathematics Mock Test - 6 - Question 13
  • जो लोग लोकतंत्र के इच्‍छुक हैं उन्‍हें चाहिए कि पहले वे लोकतंत्र की इस कसौटी पर अपने को परख लें।
  • इसके अलावा, लोकतंत्रवादी को नि:स्‍वार्थ भी होना चाहिए। उसे अपनी या अपने दल की दृष्टि से नहीं बल्कि एकमात्र लोकतंत्र की ही दृष्टि से सब-कुछ सोचना चाहिए।
  • तभी वह सविनय अवज्ञा का अधिकारी हो सकता है। 
DSSSB TGT Mathematics Mock Test - 6 - Question 14

Find the value of .

Detailed Solution for DSSSB TGT Mathematics Mock Test - 6 - Question 14

Given,

Applying , we get

As we know,

Taking out (b - a), (c - a) common from C2 and C3 respectively, we get

DSSSB TGT Mathematics Mock Test - 6 - Question 15

The product of two consecutive positive integers is 360. To find the integers, this can be represented in the form of quadratic equation as:

Detailed Solution for DSSSB TGT Mathematics Mock Test - 6 - Question 15

Let x and (x + 1) be the two consecutive integers.

According to the given question,

DSSSB TGT Mathematics Mock Test - 6 - Question 16

Find the quadratic equation whose one root is .

Detailed Solution for DSSSB TGT Mathematics Mock Test - 6 - Question 16

Given:

One root of the equation is 

Concept: 

If one root of the quadratic equation is in this form  then the other roots must be conjugate  and vice-versa.

Quadratic equation: x2 - (sum of root) + (product of root) = 0

Calculation: 

Let and

sum of root

Product of root

Now, Quadratic equation

So, required quadratic equation is .

DSSSB TGT Mathematics Mock Test - 6 - Question 17

Let two events and be such that and . Which one of the following is correct?

Detailed Solution for DSSSB TGT Mathematics Mock Test - 6 - Question 17

Given: and

Here  (∵ Max value of probability is 1)


DSSSB TGT Mathematics Mock Test - 6 - Question 18

A man wants to cut three lengths from a single piece of board of length . The second length is to be longer than the shortest and the third length is to be twice as long as the shortest. What are the possible lengths of the shortest board if the third piece is to be at least longer than the second?

Detailed Solution for DSSSB TGT Mathematics Mock Test - 6 - Question 18

Let us assume the length of the shortest piece be .

According to the question, length of the second piece .

And, length of third piece .

As all the three lengths are to be cut from a single piece of board having a length of .

Also, it is given in the question that, the third piece is at least longer than the second piece.

Thus, from equation (i) and (ii) we have:

Hence, it is clear that the length of the shortest board is greater than or equal to and less than or equal to .

DSSSB TGT Mathematics Mock Test - 6 - Question 19

In a class, 54 students are good in Hindi only, 63 students are good in Mathematics only and 41 students are good in English only. There are 18 students who are good in both Hindi and Mathematics. 10 students are good in all three subjects.
What is the number of students who are good in Hindi and Mathematics but not in English?

Detailed Solution for DSSSB TGT Mathematics Mock Test - 6 - Question 19

Let denote the set of students studying Hindi, Mathematics and English.

 

DSSSB TGT Mathematics Mock Test - 6 - Question 20

Given that N = {1, 2, 3, …, 100}, then write B, the subset of N whose elements are represented by x + 2, where x is ∈ N.

Detailed Solution for DSSSB TGT Mathematics Mock Test - 6 - Question 20

Given,

N = {1, 2, 3, …, 100}

B = {y | y = x + 2, x ∈ N}

Hence, for 1 ∈ N

y = 1 + 2 = 3 

For 2 ∈ N  

y = 2 + 2 = 4 etc

Therefore, B = {3, 4, 5, 6, … , 100}

DSSSB TGT Mathematics Mock Test - 6 - Question 21

is equal to:

Detailed Solution for DSSSB TGT Mathematics Mock Test - 6 - Question 21

Given,

...(1)

Let ...(2)

Then,

By pythagoras theorem,

From equation (1) and (2), we get

DSSSB TGT Mathematics Mock Test - 6 - Question 22

If the magnitude of the sum of two non-zero vectors is equal to the magnitude of their difference, then which one of the following is correct?

Detailed Solution for DSSSB TGT Mathematics Mock Test - 6 - Question 22

Let and be two non-zero vectors.

It is given that the magnitude of the sum of two non-zero vectors is equal to the magnitude of their difference.

As we know that, if be a vector then 

 


 and be two non-zero vectors

So, and are perpendicular to each other.

DSSSB TGT Mathematics Mock Test - 6 - Question 23

There are people in a group. If all shake hands with one another, how many handshakes are possible?

Detailed Solution for DSSSB TGT Mathematics Mock Test - 6 - Question 23

There are people 

A handshake needs people

This simply means in how many ways people can be selected out of So the answer is

Number of handshakes

DSSSB TGT Mathematics Mock Test - 6 - Question 24

Consider the following statements:

I. A' ∪ B = (A ∩ B)'

II. (ϕ')' = ∪

III. A ∩ (B ∪ C) = (A ∩  B) ∪ (A ∩ C)

Which of the statement(s) given above is/are correct?

Detailed Solution for DSSSB TGT Mathematics Mock Test - 6 - Question 24

Given:

Three statements,

I. A' ∪ B = (A ∩ B)'

II. (ϕ')' = ∪

III. A ∩ (B ∪ C) = (A ∩  B) ∪ (A ∩ C)

Concept:

De Morgan's law:

(A ∩ B)' = A' ∪ B' 

Distributive law:

A ∩ (B ∪ C) = (A ∩  B) ∪ (A ∩ C)

Universal Law:

(ϕ)' = ∪

Explanation:

I. A' ∪ B = (A ∩ B)'

⇒ (A ∩ B)' = A' ∪ B' [by De Morgan's law]

So, statement (l) is not correct.

II. (ϕ')' = ∪

⇒ (ϕ)' = ∪ and (∪)' = ϕ   [by universal law]

So, statement (II) is not correct.

III.  A ∩ (B ∪ C) = (A ∩  B) ∪ (A ∩ C)

⇒  A ∩ (B ∪ C) = (A ∩  B) ∪ (A ∩ C)   [by Distributive law]

∴ Statement (III) is correct.

DSSSB TGT Mathematics Mock Test - 6 - Question 25

Let be a non-empty set and let be subsets of , consider the following statements:

1.

2. for all sets

3. for all sets

Which of the above statements is/are correct?

Detailed Solution for DSSSB TGT Mathematics Mock Test - 6 - Question 25

Given: 

be subsets of

Statement 1:

Now, if then is true.

Statement 1 is true.

Statement for all sets

Let and

but is not true.

Statement 2 is false.

Statement 3: for all sets

This is true as for all sets

DSSSB TGT Mathematics Mock Test - 6 - Question 26

There are 2 shirts, 3 jeans, 3 socks and 2 skirts. In how manys ways a shopkeeper can arrange these things so that all the socks come together and all the skirts come together?

Detailed Solution for DSSSB TGT Mathematics Mock Test - 6 - Question 26

As given,

There are 2 shirts, 3 jeans, 3 socks and 2 skirts.

Take all the socks as 1 and all the skirts as 1.

Total elements becomes = 7

For total elements = 7!

For socks = 3!

For shirts = 2!

Total ways = 7! × 3! × 2! = 60,480

DSSSB TGT Mathematics Mock Test - 6 - Question 27

If is an isosceles triangle and is an equilateral triangle then find

Detailed Solution for DSSSB TGT Mathematics Mock Test - 6 - Question 27

Given:

is an isosceles triangle and is an equilateral triangle

We know that:

Every equilateral triangle is isoceles triangle.

It is clear that:

An isosceles triangle has 2 equal sides

The Equilateral triangle has 3 equal sides.

Then each element of B is also an element of A.

Therefore, B is a proper subset of A.

DSSSB TGT Mathematics Mock Test - 6 - Question 28

If A and B are two events such that and , then consider the following statements:

Which of the statements is/are correct?

Detailed Solution for DSSSB TGT Mathematics Mock Test - 6 - Question 28

It is given that

We can calculate the probability of complementary events as follows 

We know that

Note that 

Therefore in the given case:

Using this we write:

Therefore, the first statement is wrong.

Using the formula for conditional probability we write:

We know that  .

Using the given data we will first determine the value of

Now using the complementary event formula we get:

Substituting in the formula for the conditional formula:

Therefore, the second statement is correct.

DSSSB TGT Mathematics Mock Test - 6 - Question 29

Solve:

Detailed Solution for DSSSB TGT Mathematics Mock Test - 6 - Question 29

Let

The Product Rule is,

Using the Product Rule Differentiating with respect to x, we get

As we know,

DSSSB TGT Mathematics Mock Test - 6 - Question 30

If x =, y =, z =where a, b, c are in AP and |a| < 1, |b| < 1, |c| < 1, then x, y, z are in

Detailed Solution for DSSSB TGT Mathematics Mock Test - 6 - Question 30

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