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


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30 Questions MCQ Test DSSSB PGT Mock Test Series 2024 - DSSSB PGT Mathematics Mock Test - 6

DSSSB PGT Mathematics Mock Test - 6 for DSSSB TGT/PGT/PRT 2024 is part of DSSSB PGT Mock Test Series 2024 preparation. The DSSSB PGT Mathematics Mock Test - 6 questions and answers have been prepared according to the DSSSB TGT/PGT/PRT exam syllabus.The DSSSB PGT Mathematics Mock Test - 6 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 - 6 below.
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DSSSB PGT Mathematics Mock Test - 6 - Question 1

A defective watch which gains uniformly, is 5 minutes slow at 8 o'clock in the morning on Sunday and it is 5 minutes 48 seconds fast at 8 pm on following Sunday. When was it correct?

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

Sunday 8 am to next Sunday 8 pm time duration 24 × 7 + 12 = 180 hrs.
In 180 hrs total gain = 10 min 48 s = 648 s
Gain of 5 min = 300 s will be obtained in  

Hence, Sunday 8 am + 83 h 20 min = Wednesday 7 : 20 p.m.

DSSSB PGT Mathematics Mock Test - 6 - Question 2

At what time between 5:30 and 6:00 will the hands of a clock be at right angles?

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

At 5 o'clock, the hands are 25 minute space apart.
To be at right angle, that too between 5:30 and 6:00, the minute hand has to gain (25 + 15) or 40 minute space.
55 minute space is gained in 60 minutes.
40 minute space is gained in 40 ×
Therefore, required time =  

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DSSSB PGT Mathematics Mock Test - 6 - Question 3

Statements:
Some fruits are mangos.
All mangos are guavas.
No guava is a banana.
Conclusions:
I. All guavas are fruits.
II. Some guavas are fruits

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

Some fruits are mangos.
All mangos are guavas.
I + A => I - type of conclusion
"Some fruits are guavas".
Conclusion II is Converse of it.
All mangos are guavas
No guava is a banana.
A + E => E - type of conclusion
"No mango is a banana

So Option B is correct

DSSSB PGT Mathematics Mock Test - 6 - Question 4

‘Kal Baisakhi’ gives rainfall to

Detailed Solution for DSSSB PGT Mathematics Mock Test - 6 - Question 4
  • During the hot weather period i.e from March to May the Eastern and North-eastern states of the subcontinent like West Bengal, Bihar, Assam, Odisha (parts) and Bangladesh experience a dramatic appearance of a special type of violent thunderstorm known as Nor’wester.

  • In Bengal it is known as ‘Kal Baisakhi’ Apart from its destructive effects like a sudden rise in wind speed, lightning, thunder and hail the rainfall associated with the storm although small in amount, is extremely helpful for the pre-Kharif crops like jute, paddy, summer till and a large number of vegetables and fruits and the sudden drop in temperature gives relief after unbearable midday heat.

DSSSB PGT Mathematics Mock Test - 6 - Question 5

South-West monsoon contributes to India’s total rainfall up to the extent of

Detailed Solution for DSSSB PGT Mathematics Mock Test - 6 - Question 5
Southwest Monsoon accounts for around 85% of India’s total rainfall.

DSSSB PGT Mathematics Mock Test - 6 - Question 6

The Supreme Court of India is located in which city?

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

The Supreme Court of India is located in New Delhi, the capital city of India.

DSSSB PGT Mathematics Mock Test - 6 - Question 7

During exhalation, the ribs move

Detailed Solution for DSSSB PGT Mathematics Mock Test - 6 - Question 7

During exhalation, i.e. releasing air during respiration, the ribs move downwards to reduce the volume of the thoracic cavity.
During exhalation, your diaphragm relaxes and moves upward into the chest cavity. The intercostal muscles between the ribs also relax to reduce the space in the chest cavity. As they relax they position the rib cage downwards and inwards.

DSSSB PGT Mathematics Mock Test - 6 - Question 8

Direction: Read the following passage carefully and answer the questions. Your answer to these questions should be based on passage only.
The last half of my life was spent at one of those painful epochs of human history, during which the world seemed to be getting worse; where past victories which had seemed to be definitive have turned out to be only temporary. When I was young, Victorian optimism was taken for granted. It was thought that freedom and prosperity would spread gradually through the world through an orderly process, and it was hoped that cruelty, tyranny, and injustice would continually diminish. Hardly anyone was hunted by the fear of great wars. Hardly any-one thought of the nineteenth century as a brief interlude between past and future barbarism.

Q. The author felt sad about the latter part of his life because:

Detailed Solution for DSSSB PGT Mathematics Mock Test - 6 - Question 8

The answer is (d). You can hit at the answer through inference. The clue is in the first sentence itself ---'the world is getting worse' . The whole passage also implies that the last half of the life of the author was a period of turmoil.

DSSSB PGT Mathematics Mock Test - 6 - Question 9

Direction: Despite promises of aid, the actual record of international aid to post-war reconstruction is deficient. Once the war ends, agencies involved in post-war relief efforts fail to understand how to start or restart economic development in a low income setting. They squander time, surplus aid funds and opportunities because they are not familiar with local conditions and don't understand their needs and viewpoints. There are distinct phases of outside help to end a conflict. In the first phase, focus is one providing instant food, water, shelter, medicine to refugees, this is the humanitarian. In the second phase emphasis is on the refugees' returning home while in the last phase long-term investments and strengthening of courts is the main focus.

Q. Where does the problem lie in implementing post-war relief measures?

Detailed Solution for DSSSB PGT Mathematics Mock Test - 6 - Question 9

Line 3 of the passage says, "because they are not familiar with local conditions and do not understand their needs and viewpoints", which implies that they do not have essential and qualified personnel. The other statements are neither mentioned nor implied in the passage.

DSSSB PGT Mathematics Mock Test - 6 - Question 10

Direction: Once a conflict gets over, aid agencies sanctioned by the world Bank send study groups instead of requisite personnel. There is a gap of several years before moving from humanitarian relief to economic development and hence political stability. By the time such help arrives the war has restarted. It is possible to restart economic development through targeted "quick impact" initiatives. Most economies in post-conflict countries are based on agriculture. Providing free packages of seeds, fertilizers and low-cost agricultural tools will ensure that former soldiers will return to their farms and establish their livelihood. But the window of opportunity closes quickly and one has to implement these measures almost immediately.

Q. What is the benefit of "Quick Impact" aid?

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

Lines 5 and 6 of the passage bring this out clearly as the correct choice. The other statement are not specifically mentioned in the passage.

DSSSB PGT Mathematics Mock Test - 6 - Question 11

Direction: Read the following passage carefully and answer the questions. Your answer to these questions should be based on passage only.
The last half of my life was spent at one of those painful epochs of human history, during which the world seemed to be getting worse; where past victories which had seemed to be definitive have turned out to be only temporary. When I was young, Victorian optimism was taken for granted. It was thought that freedom and prosperity would spread gradually through the world through an orderly process, and it was hoped that cruelty, tyranny, and injustice would continually diminish. Hardly anyone was hunted by the fear of great wars. Hardly any-one thought of the nineteenth century as a brief interlude between past and future barbarism.

Q. The word 'definitive' used in the passage means:

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

The answer is (b). Both information and simple inference suggest this answer.

DSSSB PGT Mathematics Mock Test - 6 - Question 12

निम्नलिखित शब्दों में से कौन-सा शब्द संज्ञा है?

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

दिए गए शब्दो में ‘क्रोध’ संज्ञा है क्योंकि यह भावना को दिखाता है। 
ऐसे सभी शब्द जो किसी स्थान, जाति, समूह, पदार्थ, भावना आदि का नाम व्यक्त करते हैं वे संज्ञा कहलाते हैं।
अतः सही विकल्प (B) है।

DSSSB PGT Mathematics Mock Test - 6 - Question 13

निर्देश: नीचे दिए गए शब्द के लिए उसके नीचे दिए गए विकल्पों में से सही पर्यायवाची शब्द चुनकर उत्तर दीजिए।
क्रोध

Detailed Solution for DSSSB PGT Mathematics Mock Test - 6 - Question 13
  • ‘अमर्ष’ का अर्थ है – क्रोध, कोप, अपने अपमान, तिरस्कार आदि से उत्पन्न क्षोभ।
  • 'घाम' का अर्थ है - सूर्यातप, धूप. कठिनाई, इत्यादि।
  • 'आलय' का अर्थ है - घर, आवास, गेह, गृह, निकेतन, निलय, निवास, भवन, वास, वास, स्थान, शाला, सदन, इत्यादि।
  • 'औक' का अर्थ है-  आलय, निवास, धाम, इत्यादि।

अतः सही विकल्प (B) है।

DSSSB PGT Mathematics Mock Test - 6 - Question 14

निर्देशः नीचे दिए गए अपठित गद्यांश को ध्यानपूर्वक पढ़ें एवं उस पर आधारित प्रश्न के उत्तर दें।
शिक्षा जीवन के सर्वांगीण विकास हेतु अनिवार्य है। शिक्षा के बिना मनुष्य विवेकशील और शिष्ट नहीं बन सकता। विवेक से मनुष्य में सही और गलत का चयन करने की क्षमता उत्पन्न होती है। विवेक से ही मनुष्य के भीतर उसके चहुँ ओर नित्य प्रति होते घटनाक्रमों के प्रति एक छिद्रान्वेषी दृष्टिकोण उत्पन्न होता है। शिक्षा ही मानव को मानव के प्रति मानवीय भावनाओं से पोषित करती है। शिक्षा से मनुष्य अपने परिवेश के प्रति जाग्रत होकर कर्तव्यविमुख हो जाता है। 'स्व' से 'पर' की ओर अग्रसर होने लगता है। निर्बल की सहायता करना, दुखियों के दु:ख दूर करने का प्रयास करना, दूसरों के दुःख से दु:खी हो जाना और दूसरों के सुख से स्वयं सुख का अनुभव करना जैसी बातें एक शिक्षित मानव में सरलता से देखने को मिल जाती हैं। इतिहास, साहित्य, राजनीतिशास्त्र, समाजशास्त्र, दर्शनशास्त्र इत्यादि पढ़कर विद्यार्थी विद्वान् ही नहीं बनता वरन् उसमें एक विशिष्ट जीवन दृष्टि, रचनात्मकता और परिपक्वता का सृजन भी होता है। शिक्षित सामाजिक परिवेश में व्यक्ति अशिक्षित सामाजिक परिवेश की तुलना में सदैव ही उच्च स्तर पर जीवन यापन करता है।
परन्तु आज शिक्षा का अर्थ बदल रहा है। शिक्षा भौतिक आकांक्षा की साध्य बनती जा रही है। व्यावसायिक शिक्षा के अन्धानुकरण में छात्र सैद्धान्तिक शिक्षा से दूर होते जा रहे हैं। रूस की क्रान्ति, फ्रांस की क्रान्ति, अमेरिकी क्रान्ति, समाजवाद, पूँजीवाद, राजनीतिक व्यवस्था, सांस्कृतिक मूल्यों आदि की सामान्य जानकारी भी व्यावसायिक शिक्षा ग्रहण करने वाले छात्रों को नहीं है। यह शिक्षा का विशुद्ध रोजगारकरण है। शिक्षा के प्रति इस प्रकार का संकुचित दृष्टिकोण अपनाकर विवेकशील नांगरिकों का निर्माण नहीं किया जा सकता। भारत जैसे विकासशील देश में शिक्षा रोजगार का साधन न होकर साध्य हो गई है। इस कुप्रवृत्ति पर अंकुश लगाना अनिवार्य है। जहाँ मानविकी के छात्रों को पत्रकारिता, साहित्य-सृजन, विज्ञापन, जनसम्पर्क इत्यादि कोर्स भी कराए जाने चाहिए ताकि उन्हें रोजगार के लिए न भटकना पड़े, वहीं व्यावसायिक कोर्स करने वाले छात्रों को मानविकी के विषय; जैसे-इतिहास, साहित्य, राजनीतिशास्त्र व दर्शन आदि का थोड़ा बहुत अध्ययन अवश्य कराना चाहिए ताकि समाज को विवेकशील नागरिक प्राप्त होते रहें, तभी समाज में सन्तुलन बना रहेगा।

Q. शिक्षा से मनुष्य स्व' से 'पर' की ओर अभिगमन करने लगता है, क्यों?

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

प्रस्तुत गद्यांश के अनुसार, “शिक्षा से मनुष्य अपने परिवेश के प्रति जाग्रत होकर कर्तव्यविमुख हो जाता है। 'स्व' से 'पर' की ओर अग्रसर होने लगता है। निर्बल की सहायता करना, दुखियों के दु:ख दूर करने का प्रयास करना, दूसरों के दुःख से दु:खी हो जाना और दूसरों के सुख से स्वयं सुख का अनुभव करना जैसी बातें एक शिक्षित मानव में सरलता से देखने को मिल जाती हैं।”
शिक्षा से मनुष्य स्व' से 'पर' की ओर अभिगमन करने लगता है, क्योंकि उसमें कर्त्वयपरायणता का बोध जागृत होता है।
अतः सही विकल्प (C) है।

DSSSB PGT Mathematics Mock Test - 6 - Question 15

नीचे दिए गए पद इक प्रत्यय लगाने से बने है, इनमें से कौन सा पद गलत है?

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

दैविक, सामाजिक तथा भौैमिक में 'इक' प्रत्यय लगा है।
नए शब्दों की रचना करने के क्रम में कुछ शब्दांशों को शब्दों के पीछे या उनके अंत में जोड़ दिया जाता है। इससे मूलशब्द के अर्थ में बदलाव या विशेषता आ जाती है। ये शब्दांश प्रत्यय कहलाते हैं।
अतः सही विकल्प (D) है।

DSSSB PGT Mathematics Mock Test - 6 - Question 16

‘दही’ शब्द है:

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

'दही' एक पुल्लिंग शब्द है।
जिन शब्दो से पुरुष जाति का बोध होता है, पुल्लिंग कहलाता है। ग्रहों, देशों, द्रव्य पदार्थो, अनाजो, पर्वतो आदि के नाम पुल्लिंग में आते हैं। जैसे- सूर्य, भारत, लोहा, घी, दही, पीपल, आदि।
अतः सही विकल्प (A) है।

DSSSB PGT Mathematics Mock Test - 6 - Question 17

If the coordinates of the mid-points of the sides of a triangle are (1,1), (2,-3) and (3,4). Find its centroid

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

Let P (1,1), Q (2,-3), R (3,4) be the mid-points of sides AB, BC and CA respectively, of triangle ABC. Let be the vertices of triangle ABC.

The midpoint of the line segment,

So, P is the mid-point of AB.

Q is the mid-point of BC.

R is the mid-point of AC.

From Above Equations,

The coordinates of the centroid of Δ ABC are

DSSSB PGT Mathematics Mock Test - 6 - Question 18

There are four numbers. Average of first three numbers is 14 and average of last three numbers is 16. If the first number is 11, what is the last number?

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

Given:

Average of first three numbers = 14

Average of last three numbers = 16

Total count of numbers = 4

Let, the last number = x

According to the question,

⇒3 × 14 + x = 11 + 3 × 16

⇒ x + 42 = 59

⇒ x = 17

∴ Last number = 17

DSSSB PGT Mathematics Mock Test - 6 - Question 19

Let , then the value of at is:

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

At

 does not exist.

DSSSB PGT Mathematics Mock Test - 6 - Question 20

The differential equation of all parabolas whose axis is y-axis is:

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

We know that, Standard formula of y-axis parabola is:

Let, Vertex of parabola be (0, k)

Taking derivative on both side,

We get, 

Again taking derivative on both side,

We get, 

DSSSB PGT Mathematics Mock Test - 6 - Question 21

The value of  is:

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

Given,

DSSSB PGT Mathematics Mock Test - 6 - Question 22

The lengths of the intercepts on the co-ordinate axes made by the plane 5x + 2y + z – 13 = 0 are:

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

Given:

Equation of plane 5x + 2y + z – 13 = 0

∴ Lengths of intercepts are unit

DSSSB PGT Mathematics Mock Test - 6 - Question 23

Consider the equation of a sphere .

Which of the following statements is/are correct?

1. z-axis is tangent to the sphere.

2. The centre of the sphere lies on the plane x + y + z - 9 = 0.

Select the correct answer using the code given below:

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

Equation of Tangent plane to the sphere at a point is given by:

When the equation of sphere is given by:

Given equation of sphere is

1. Lets find out the tangent of the given sphere.

For that, Comparing equation 2 i.e.,

with the given equation i.e.,

Now, putting the values of u,v,w and d in equation (1), we get,

, which is clearly not an equation of z-axis.

2. To find the equation of the plane passing through the centre of the sphere, we firstly need to find the centre of the sphere.

Given equation of the sphere is:

(Squaring 2,3 and 4 and adding both the sides)

The centre of the sphere is at (2,3,4)

i.e., x = 2, y = 3 and z = 4

Since, the question says the plane to be

Substituting the values of x,y and z, we get

2 + 3 + 4 - 9 = 0

0 = 0

which is true for the given values of centre (2,3,4) i.e. The centre of the sphere lies on the plane x + y +  z- 9 = 0.

DSSSB PGT Mathematics Mock Test - 6 - Question 24

Magnitude of the vector is:

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

Given,

Then,

DSSSB PGT Mathematics Mock Test - 6 - Question 25

Let R be the relation in the set {1, 2, 3, 4} given by  Choose the correct answer.

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

it is seen that for every .

∴R is reflexive.

It is seen that but

∴R is not symmetric.

Also, it is observed that

∴ R is transitive.

Thus, R is reflexive and transitive but not symmetric.

DSSSB PGT Mathematics Mock Test - 6 - Question 26

Distance between the two planes: and is:

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

The equations of the planes are:

.....(1)

and

It can be seen that the given planes are parallel as their direction ratios are equal. 

It is known that the distance between two parallel planes, and , is given by, 

Thus, the distance between the planes is units. 

Hence, the correct answer is (D).

DSSSB PGT Mathematics Mock Test - 6 - Question 27

tan54º can be expressed as:

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

Given,

tan54º

As we know,


DSSSB PGT Mathematics Mock Test - 6 - Question 28

A sequence is defined by letting and for all natural numbers Show that an  for all:

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

Given:

Let be true.

 is true when is true.

By Mathematical Induction is true.

∴ By Mathematical Induction is true for all natural numbers n.

DSSSB PGT Mathematics Mock Test - 6 - Question 29

If , then find the value of .

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



Since , n  can not be negative 
So, n = 8.

DSSSB PGT Mathematics Mock Test - 6 - Question 30

The multiplicative inverse of z = 4 + 3i is:

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

Let the multiplicative inverse be z'

So, by the definition

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