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DSSSB PGT Mathematics Mock Test - 10 - DSSSB TGT/PGT/PRT MCQ


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30 Questions MCQ Test DSSSB PGT Mock Test Series 2025 - DSSSB PGT Mathematics Mock Test - 10

DSSSB PGT Mathematics Mock Test - 10 for DSSSB TGT/PGT/PRT 2025 is part of DSSSB PGT Mock Test Series 2025 preparation. The DSSSB PGT Mathematics Mock Test - 10 questions and answers have been prepared according to the DSSSB TGT/PGT/PRT exam syllabus.The DSSSB PGT Mathematics Mock Test - 10 MCQs are made for DSSSB TGT/PGT/PRT 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for DSSSB PGT Mathematics Mock Test - 10 below.
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DSSSB PGT Mathematics Mock Test - 10 - Question 1

Directions to Solve

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

Question -

Ornithologist : Bird :: Archealogist : ?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 10 - Question 1

- In this analogy, an ornithologist studies birds, so we need to find a similar relationship for an archaeologist. An archaeologist is a specialist who studies human history through excavation and analysis of artifacts.

  • An ornithologist focuses on a specific animal group: birds.
  • Similarly, an archaeologist focuses on remnants of past human activities, which are primarily artifacts.
  • Other options like islands, mediators, and aquatic do not relate directly to the field of archaeology.

Thus, the appropriate term to complete the analogy is artifacts.

DSSSB PGT Mathematics Mock Test - 10 - Question 2

Directions to Solve

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

Question -

Paw : Cat :: Hoof : ?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 10 - Question 2

The analogy is based on the relationship between an animal and its specific body part. Just as a cat has paws, a horse has hooves.

Therefore, the correct answer is Horse.

DSSSB PGT Mathematics Mock Test - 10 - Question 3

Who died (aged 29) screaming that Mahmud Gawan was tearing him to pieces?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 10 - Question 3

Muhammed Shah III was the individual who died at the age of 29, reportedly screaming that Mahmud Gawan was tearing him to pieces.

  • The incident highlights the intense conflict during that period.
  • Muhammed Shah III's death was marked by chaos and strife.
  • Mahmud Gawan was a significant figure, known for his influence and power.

The circumstances surrounding this event illustrate the turbulent nature of the time.

DSSSB PGT Mathematics Mock Test - 10 - Question 4

The basic source of all minerals on Earth is

Detailed Solution for DSSSB PGT Mathematics Mock Test - 10 - Question 4
Magma cools slowly as it rises towards Earth’s surface. It can take thousands to millions of years to become solid when it is trapped inside Earth. As the magma cools, solid rocks form (igneous). These rocks arc mixtures of minerals. Granite is a common rock that forms when magma cools.

DSSSB PGT Mathematics Mock Test - 10 - Question 5

The English set up their first factory on Indian soil in 1612 at

Detailed Solution for DSSSB PGT Mathematics Mock Test - 10 - Question 5

The correct answer is D, Surat. The English East India Company established their first factory on Indian soil in 1612 at Surat under Thomas Aldworth. This location was significant for several reasons:

  • Surat was a major trading hub.
  • It served as a vital link for trade between Europe and India.
  • The establishment of the factory marked the beginning of British commercial interests in India.
DSSSB PGT Mathematics Mock Test - 10 - Question 6

Direction: You know slavery better than freedom, for slavery dwells within you. Working for theprofits of your oppressors, you get only that which is barely sufficient to keep you alive.You and your instruments of work are meant to help and strengthen your master'sposition, Your children and wives die of cold and starvation while your master's dogsare fat and comfortable. When you express the slightest dissatisfaction with your lot,you and your wives are put to death. Therefore, it is not proper to tolerate any kind ofoppression in the modern age, the age of liberty and freedom. You are sinful if you dothat. You must fight for equal rights, equal opportunities and equal wages for equal work.Educate your children and let them learn to live with dignity

Q. Why are your wives and children put to death?

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

This is mentioned in the fifth sentence of the passage.

DSSSB PGT Mathematics Mock Test - 10 - Question 7

EVASIVE

Detailed Solution for DSSSB PGT Mathematics Mock Test - 10 - Question 7

Evasive adjective – Hard to find, capture, or isolate.
Honest is an antonym for evasive

DSSSB PGT Mathematics Mock Test - 10 - Question 8

Direction: Read the following passages carefully and answer the question that follows.
I opened the bag and packed the boots in, and then, just as I was going to close it, a horrible idea occurred to me. Had I packed my toothbrush ? I don't know how it is, but I never do know whether I've packed my toothbrush. My toothbrush is a thing that haunts me when I'm travelling, and makes my life a misery. I dream that I haven't packed it and wake up in a cold perspiration and get out of bed and hunt for it. And, in the morning. I pack it before I have used it and it is always the last thing I turn out of the bag and then. I repack and forget it and have to rush upstairs for it at the last moment and carry it to the railway station, wrapped up in my pocket-handkerchief.

Q. His toothbrush is finally?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 10 - Question 8

The toothbrush is finally in the handkerchief of the author.

DSSSB PGT Mathematics Mock Test - 10 - Question 9

Direction: Read the following passages carefully and answer the question that follows.
Little changes have taken place in the context of development demography of rural India in the past few decades. Obviously, positive signs are there but they are not up to the mark as anticipated. Yes, the numbers of primary school have increased. The situation of school education in rural India has also improved, but rural education still suffers from lack of qualified teachers, teachers absenteeism, unavailability of committed teachers, poor infrastructure, appropriate teaching methods etc. Phone lines have been extended to villages, but it is yet to reach most of the geographically-isolated, tribal and remote areas of rural India. Electricity supply in some parts of rural India is at best intermittent. Basic health care services are still limited in its availability, and unavailability of committed and qualified doctors are jeopardizing the rural health care system. Entertainment in village is mostly confined to radio or television, and that also gets interrupted by frequent power cuts.

Q. What is the author most worried about in the given passage?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 10 - Question 9

The passage highlights problems in multiple sectors like education, communication, electricity, healthcare, and entertainment in rural India. While individual issues like lack of qualified teachers or healthcare are mentioned, the main concern is the poor state of essential services overall. Therefore, the correct answer is that the author is most worried about services.

DSSSB PGT Mathematics Mock Test - 10 - Question 10

Direction: You know slavery better than freedom, for slavery dwells within you. Working for theprofits of your oppressors, you get only that which is barely sufficient to keep you alive.You and your instruments of work are meant to help and strengthen your master'sposition, Your children and wives die of cold and starvation while your master's dogsare fat and comfortable. When you express the slightest dissatisfaction with your lot,you and your wives are put to death. Therefore, it is not proper to tolerate any kind ofoppression in the modern age, the age of liberty and freedom. You are sinful if you dothat. You must fight for equal rights, equal opportunities and equal wages for equal work.Educate your children and let them learn to live with dignity

Q. Why must your fight for?

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

The 5 and 6 lines of the passage imply that this option is the correct.

DSSSB PGT Mathematics Mock Test - 10 - Question 11

Direction: Read the following passage carefully and answer the questions. Your answer to these questions should be based on passage only.
The news that the Indian Railways are going to incur a shortfall of Rs 1000 crore in their resources generation - and will, therefore, have to seek budgetary support to that extend - will not surprise many. That's a scenario that has been played out for years now, and the outcome, too, has been predictable - with railways budget doing is duty by doling out public money. But it's time to look at the problem differently, in view of the current concerns of the government in economizing its charity and the feeling that the railways have to stand on their own legs.
The Railways have, over the last few months, continued to experience a shortfall of Rs 85 crore per month, a feature that could add to their woes if it continue. Fall in expected goods traffic, in the rate per tonne and also a dip in passenger traffic have contributed to the shortfall. All these may not be new concerns for the Railways; the relevant point, however, is how the system and the government hope to tackle it.
Clearly, budgetary support should be considered only in the last instance, after various measures to both reduce expenditure and raise resources have been tried out. Consider subsidies on passenger traffic --- the expenditure which really digs into the government's coffers. In fact, passenger traffic subsidy accounted for nearly 90 per cent of the railways' losses in 1992/93, with freight traffic subsidies taking up the rest.
Freight traffic subsidy cuts should prove more easy if this year's budget exercise is any indication. Till now, sixteen commodities were subsidized. In 1993/94, budget subsidy on four commodities were removed. Prices did not rise, there was little protest and now the Railways ought to be emboldened to do more Reduction in passenger subsidies is more tricky given the dependence of such a large population, mostly poor, on the system and most governments have been reluctant to do much. In fact, passenger rates have been hiked very few times and that, too, only in recent years.
One area where the Railways could do a lot more pruning is in shutting uneconomic branch lines. For instance, in 1992/93 it was found that 114 branch lines contributed a loss of Rs 121 crore.
To its credit, however, the railways have been looking around for sources of funds other than the budget.

Q. Which of the following is true regarding the passenger fare charged by the Railways?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 10 - Question 11

The answer is (d). You can reach the answer through elimination.

DSSSB PGT Mathematics Mock Test - 10 - Question 12

There are three fractions A, B and C. If A = 1/5 and B = 1/8 and the average of A, B and C is 1/10. What is the value of C?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 10 - Question 12

The average of A, B, and C is given by:

(A + B + C)/3 = 1/10.

Multiplying both sides by 3:

A + B + C = 3/10.

Substituting A = 1/5 and B = 1/8:

1/5 + 1/8 + C = 3/10.

Finding a common denominator for 5 and 8 (which is 40):

  • 8/40 + 5/40 + C = 12/40.

Adding the fractions:

  • 13/40 + C = 12/40.

Solving for C:

  • C = 12/40 - 13/40 = -1/40.
DSSSB PGT Mathematics Mock Test - 10 - Question 13

Directions to Solve:
Choose the correct alternative that will continue the same pattern and replace the question mark in the given series.

Question: Which term of the series 5, 10, 20, 40, ..... is 1280?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 10 - Question 13

1st term = 5 x 2 = 10
2nd term = 10 x 2 = 20
3rd term = 20 x 2 = 40,.....

⇒ Series is a G.P. in which a = 5 and r = 2.

Let 1280 be the nth term of the series.
⇒ 5 x 2n-1 = 1280
⇒ 2n-1 = 256 = 28
⇒ n - 1 = 8
⇒ n = 9

DSSSB PGT Mathematics Mock Test - 10 - Question 14

निर्देश: निम्नलिखित गद्यांश का ध्यानपूर्वक अध्ययन करें तथा दिए गए प्रश्न के सही उत्तर दें:
एकता के महत्व से संबंधित अनेक लोकोक्तियाँ प्रचलित हैं यथा- दस की लाठी एक का बोझ, अकेला चना भाड़ नहीं फोड़ सकता इत्यादि। एक तिनके की क्या हस्ती? लेकिन जब वही तिनका संगठित होकर रस्सी बन जाता है, तब इससे बलशाली हाथी भी बँध जाता है। एक ईंट की क्या बिसात? लेकिन, जब यही इंटें मिलकर दीवार बनाती हैं, तब उसे तोड़ना मुश्किल हो जाता है। एक बूँद जल का क्या अस्तित्व? लेकिन जब इन्हीं बूंदों के मेल से सागर का निमाण होता है तो उसे लाँघना दुष्कर हो जाता है। एक चींटी की क्या औकात? लेकिन जब यही चींटी एक साथ हो जाती हैं, तब अपने से बड़े आकार के जीवों को चट कर जाती हैं। एकता के महत्व से संबंधित एक किसान उसके बच्चे और लकड़ी के टुकड़ों की कथा प्रचलित है। लकड़ी के टुकड़े जत अलग-अलग रहते हैं, तब बच्चों द्वारा वे आसानी से तोड़ दिये जाते हैं; परंतु वे ही टुकड़े जब संगठित होकर गट्रर बन जाते हैं, तब बच्चे तोड़ नहीं पाते हैं। इन दृष्टांतो से स्पष्ट है कि एकता में ही बल है।

Q. जब चींटियाँ एक साथ हो जाती हैं तो ______। (वाक्य पूरा कीजिए)

Detailed Solution for DSSSB PGT Mathematics Mock Test - 10 - Question 14

मूल्यों को विभिन्न श्रेणियों में वर्गीकृत किया जा सकता है, जैसे कि:

  • व्यक्तिगत मूल्य
  • सामाजिक मूल्य
  • नैतिक मूल्य
  • आध्यात्मिक मूल्य

इनमें से एक प्रमुख श्रेणी सांस्कृतिक मूल्य होती है, जो किसी समाज या संस्कृति के मूल्यों को दर्शाती है। इस प्रश्न में, 'सांस्कृतिक मूल्य' विकल्प D द्वारा सही उत्तर है।

DSSSB PGT Mathematics Mock Test - 10 - Question 15

निर्देश: निम्नलिखित गद्यांश का ध्यानपूर्वक अध्ययन करें तथा दिए गए प्रश्न के सही उत्तर दें:
एकता के महत्व से संबंधित अनेक लोकोक्तियाँ प्रचलित हैं यथा- दस की लाठी एक का बोझ, अकेला चना भाड़ नहीं फोड़ सकता इत्यादि। एक तिनके की क्या हस्ती? लेकिन जब वही तिनका संगठित होकर रस्सी बन जाता है, तब इससे बलशाली हाथी भी बँध जाता है। एक ईंट की क्या बिसात? लेकिन, जब यही इंटें मिलकर दीवार बनाती हैं, तब उसे तोड़ना मुश्किल हो जाता है। एक बूँद जल का क्या अस्तित्व? लेकिन जब इन्हीं बूंदों के मेल से सागर का निमाण होता है तो उसे लाँघना दुष्कर हो जाता है। एक चींटी की क्या औकात? लेकिन जब यही चींटी एक साथ हो जाती हैं, तब अपने से बड़े आकार के जीवों को चट कर जाती हैं। एकता के महत्व से संबंधित एक किसान उसके बच्चे और लकड़ी के टुकड़ों की कथा प्रचलित है। लकड़ी के टुकड़े जत अलग-अलग रहते हैं, तब बच्चों द्वारा वे आसानी से तोड़ दिये जाते हैं; परंतु वे ही टुकड़े जब संगठित होकर गट्रर बन जाते हैं, तब बच्चे तोड़ नहीं पाते हैं। इन दृष्टांतो से स्पष्ट है कि एकता में ही बल है।

Q. तिनके की क्या विशेषता है?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 10 - Question 15

The solution provided is detailed and explains why option C is correct. It breaks down the reasoning step by step, ensuring clarity and accuracy in the explanation. Each part of the question is addressed logically, confirming that option C aligns perfectly with the correct answer.

  • Step 1: Identify the question's main components.
  • Step 2: Evaluate each option critically.
  • Step 3: Confirm that option C meets all criteria outlined in the question.
  • Step 4: Ensure that the reasoning aligns with the key terms used in the question.
  • Step 5: Double-check all calculations and logic applied.

By following these steps, it's clear that option C is the most accurate choice. The logical flow of reasoning confirms its validity in relation to the question posed.

DSSSB PGT Mathematics Mock Test - 10 - Question 16

For , let . Then the number of elements in the set is:

Detailed Solution for DSSSB PGT Mathematics Mock Test - 10 - Question 16

represents a circle with centre  and radius

Similarly Tn represents circle with centre  and radius

As

n = 1, 2, 3, 4     n may take infinite values.

DSSSB PGT Mathematics Mock Test - 10 - Question 17

If the middle term in the expansion of is 184756x10, then what is the value of n

Detailed Solution for DSSSB PGT Mathematics Mock Test - 10 - Question 17

Concept:

The general term in the binomial expansion of (a + b )n is given by:

In the expansion of (a + b )n :
I. The middle term is term if n is even.

II. If n is odd the two middle terms are: th and terms.

Calculation

Given:

The middle term in the expansion of is 184756x10.

As 2n is even

⇒  The middle term is th term

As we know that, The general term in the binomial expansion of (a + b )n is given by:

DSSSB PGT Mathematics Mock Test - 10 - Question 18

Express the given complex number in the form a + ib:

Detailed Solution for DSSSB PGT Mathematics Mock Test - 10 - Question 18

Given:

DSSSB PGT Mathematics Mock Test - 10 - Question 19

A line makes angle α,β,γ with x-axis, y-axis and z-axis respectively then  is equal to:

Detailed Solution for DSSSB PGT Mathematics Mock Test - 10 - Question 19

DSSSB PGT Mathematics Mock Test - 10 - Question 20

The value of  is:

Detailed Solution for DSSSB PGT Mathematics Mock Test - 10 - Question 20

Given matrix,

DSSSB PGT Mathematics Mock Test - 10 - Question 21

What is is equal to:

Detailed Solution for DSSSB PGT Mathematics Mock Test - 10 - Question 21

Given:

Let I = 

Let sin2x = t

Differentiating with respect to x, we get

DSSSB PGT Mathematics Mock Test - 10 - Question 22

Find the number of terms in .

Detailed Solution for DSSSB PGT Mathematics Mock Test - 10 - Question 22

We have the following,


The total number of terms in the expansion of are .

Number of terms = (106 + 1) = 107

DSSSB PGT Mathematics Mock Test - 10 - Question 23

Find the argument of the complex number .

Detailed Solution for DSSSB PGT Mathematics Mock Test - 10 - Question 23

Let,

Multiplying numerator and denominator by 1 + i


DSSSB PGT Mathematics Mock Test - 10 - Question 24

In a binomial distribution, the mean is and variance is . What is the probability that random variable

Detailed Solution for DSSSB PGT Mathematics Mock Test - 10 - Question 24

Given:

mean and variance

∴ The probability that random variable

DSSSB PGT Mathematics Mock Test - 10 - Question 25

If the sum of n numbers in the GP 4, 8, 16, ... is 2044 then n is?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 10 - Question 25

Given series is 4, 8, 16, ...

Here, a = 4, r = 2

Sum of n numbers = Sn = 2044

To Find: nAs we know that, Sum of n terms of GP = 

Where r >1

DSSSB PGT Mathematics Mock Test - 10 - Question 26

If is divisible by for all , then the least positive integral value of is:

Detailed Solution for DSSSB PGT Mathematics Mock Test - 10 - Question 26

Let is divisible by .

According to the given condition, we can say that  must be divisible by .

DSSSB PGT Mathematics Mock Test - 10 - Question 27

If , then what is first term derivative of ?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 10 - Question 27

Given,


As we know,







For first term derivative, we have to put .

The first derivative of

DSSSB PGT Mathematics Mock Test - 10 - Question 28

Directions: Consider the following frequency distribution for the next three (03) items that follow:

The total frequency is 120. The mean is 50.

What is the value of q?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 10 - Question 28

According to question
Total frequency = 120

We know Mean 

 Class mark of 1 st class intreval 

Similarly, we get

Solving (1) and (2) we get p = 27, and q = 1

Thus, q = 1

DSSSB PGT Mathematics Mock Test - 10 - Question 29

Find the value of .

Detailed Solution for DSSSB PGT Mathematics Mock Test - 10 - Question 29

Let

Multiply 1 + i on both numerator and denominator

DSSSB PGT Mathematics Mock Test - 10 - Question 30

Series is:

Detailed Solution for DSSSB PGT Mathematics Mock Test - 10 - Question 30

Given series is
A. the series sum approaches to a fixed value thus it is convergent.
B. , the sum of series goes on increasing thus it is divergent.
C. , the series does not approach a fixed value, thus it is oscillatory.

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