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HSSC TGT Math Mock Test - 8 - HSSC PGT/TGT MCQ


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30 Questions MCQ Test - HSSC TGT Math Mock Test - 8

HSSC TGT Math Mock Test - 8 for HSSC PGT/TGT 2024 is part of HSSC PGT/TGT preparation. The HSSC TGT Math Mock Test - 8 questions and answers have been prepared according to the HSSC PGT/TGT exam syllabus.The HSSC TGT Math Mock Test - 8 MCQs are made for HSSC PGT/TGT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for HSSC TGT Math Mock Test - 8 below.
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HSSC TGT Math Mock Test - 8 - Question 1

Which is the most abundant gas in the earth’s atmosphere?

Detailed Solution for HSSC TGT Math Mock Test - 8 - Question 1

The correct answer is Nitrogen.

Key Points

  • Nitrogen is the most abundant gas in Earth's atmosphere.
  • The composition of gases in Earth's atmosphere:
    • Nitrogen(78.08%)
    • Oxygen(20.95%)
    • Argon(0.93%)
    • Carbon dioxide(0.036%)

Hint

  • Code to remember the composition of gases in Earth's atmosphere is NO AC(Nitrogen, Oxygen, Argon, Carbon dioxide).

Confusion Points  

  • Hydrogen is the most abundant element in the universe.
HSSC TGT Math Mock Test - 8 - Question 2

What CANNOT be replaced by ICT?

Detailed Solution for HSSC TGT Math Mock Test - 8 - Question 2

IT and ICTs are very often interchangeably used in the context of modern technology infrastructure. ICT is a broad and comprehensive term, which comprises information technology and communication technology. Information technology includes radio, television, computer and internet, teleconferencing and mobile technology. 

Key Points

The ICTs are needed at school level for the following activities:

  • Teaching-learning
  • Diagnostic Testing and Remedial teaching
  • Evaluation activities
  • Psychological analysis of learners
  • Development of reasoning and thinking abilities among students
  • Instructional material development

Important Points

  • Computer is being used in teaching-learning process frequently now-a-days. We have new tablets like Akash launched by Ministry of Human Resource Development (MHRD), Govt. of India. Teacher can be equipped with skills to use these new technologies as students are becoming familiar with them. Use of interactive white boards, digital projectors is very effective ICT application in education. Teachers and students enjoy them. Mobile is also very effective tool.
  • Teacher's responsibilities are not only to understand these technologies but also to use them as a helping tool in the teaching learning process. ICT is used for effective teaching process but can not replace teacher's motivation. It is important to motivate students time to time by rewarding, creating learning environment, giving feedback and chances to improve. Teacher can engage and motivate students to participate in classroom activities as the use of multimedia in teaching-learning makes it more interesting.

Hence, it can be concluded that," Teachers Motivation" cannot be replaced by ICT.

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HSSC TGT Math Mock Test - 8 - Question 3

Match the contents of Column A with that of Column B.

Detailed Solution for HSSC TGT Math Mock Test - 8 - Question 3

Concept:

Ecosystem: 

  • All organisms such as plants, animals, microorganisms and human beings as well as the physical surroundings interact with each other and maintain a balance in nature.
  • All the interacting organisms in an area together with the non-living constituents of the environment form an ecosystem.
  • The term ecosystem was coined by Tansley.

Explanation:

Components of an ecosystem:

Biotic Components: 

  • It includes producers, consumers and decomposers.
  • All living things have a direct or indirect influence on other organisms in an environment.
  • Example: plants, animals, humans, microorganisms etc.

Abiotic components: 

  • All the inorganic components of the ecosystem, non-living physical and chemical composition of nature are abiotic components.
  • The biotic constituent of the environment includes soil, water, air, climate, temperature, light etc.
  • This part of the environment mainly determines the type of habitat or living conditions of the living population.

Important Points

The abiotic constituent of the environment is again divided into three parts. These are: 

Thus, the correct match is:

HSSC TGT Math Mock Test - 8 - Question 4
Solution of energy crises is
Detailed Solution for HSSC TGT Math Mock Test - 8 - Question 4

Concept:

Energy:

  • Energy is the capacity or ability to perform work.
  • It could exist in several different forms, such as potential, kinetic, thermal, electrical, chemical, radioactive, etc.

Energy crisis:

  • Any significant disruption in the supply of energy resources in an economy is considered an energy crisis.

Explanation:

Alternative energy:

  • Alternative energy comes from sources other than fossil fuels, and as a result, it emits little or no greenhouse emissions like carbon dioxide (CO2).
  • This indicates that energy is generated from several sources.
  • Examples of alternative energy are solar power, wind power, hydropower etc.
  • The wisest course of action to solve the energy crisis is to reduce global reliance on non-renewable resources while enhancing the use of alternative energy.

Thus, the solution to energy crises is alternative energy.

Additional Information Hydroelectric energy:

  • This source of energy is the kinetic energy of flowing water or the potential energy of water at a height.
  • Hydropower plants convert the potential energy of falling water into electricity.

Petroleum:

  • Petroleum is a dark oily liquid.
  • It has an unpleasant odour.
  • It is a mixture of various constituents such as petroleum gas, petrol, diesel, lubricating oil, paraffin wax, etc.

Coal:

  • Coal is one of the fuels used to cook food.
  • Earlier, it was used in railway engines to produce steam to run the engine.
  • It is also used in thermal power plants to produce electricity. 
HSSC TGT Math Mock Test - 8 - Question 5

For classroom discussion sessions which of the following is the most appropriate in encouraging reflection amongst learners?

Detailed Solution for HSSC TGT Math Mock Test - 8 - Question 5

Reflection

  • "reflection’ that means a continuous thought process by teachers on understanding their various activities and how they perform in the classrooms, reflecting on their classroom practices.
  • Reflection is one of the crucial aspects of the teaching-learning process that helps the teachers to analyze their own practices and improve upon them. In fact, reflecting on different aspects of teaching is fairly instinctive for most of the teachers
  • Reflection on activities taken up in the school and generating discussion on key issues of concern that require to be addressed. It prompts us to evaluate our own instructional practices in the classrooms.

Think-pair-share

  • The teacher introduces a problem related to higher-order thinking ability like analysis, synthesis, evaluation, and construction, etc. before learners.
  • All learners are provided five minutes so that they can respond properly to the solution of the problem. After it, they are given time for sharing their thinking with peers in small groups.
  • Also, they have to listen to others and discuss it with other classmates. At least, they have to have a consensus on the appropriate method for the solution of the problem.
  • At the end of the class, all groups share related processes and outcomes of discussion during a follow-up discussion.
  • This is the most suitable and appropriate strategy for collaborative learning in encouraging reflection amongst learners.

Individual and Group interactive sessions

  • An individual interactive session where the individual discusses his/her views on the theme or topic assigned by the teacher.
  • Group interactive sessions a theme or topic is presented or initiated by someone, either by a member of the group or a teacher.
  • Elements of interactive sessions:
    • Chairperson
    • Speaker
    • Participants
    • Recorder 

Question and Anser session

  • In this session, the teacher posses question, and the students answer the question. It is an oral activity in the class which enhances the speaking skills of students.
  • Realize the relevance and importance of activities that enhance oral skills and translate this realization into actual classroom practice. Thus every classroom should provide numerous opportunities for oral language practice through discussion, reporting, and question and answer sessions. 

Individual - work assignment based sessions

  • In this session, the teacher assigns work assignment individually, and the student has to work on assigned topics. In this session, the student discusses his/her assignment and discloses his/her work.
  • These assignments develop understanding and critical thinking in the student.
  • It is essential to keep in mind that class-appropriate assignments may be chosen for your students.
HSSC TGT Math Mock Test - 8 - Question 6
Which songs are sung on the birth of male child in Haryana?
Detailed Solution for HSSC TGT Math Mock Test - 8 - Question 6

The correct answer is All of these.

Key Points

  • Sovar, Pilia and Ashish songs are sung on the birth of male child in Haryana.

Important Points

  • On the birth of a baby boy, the family of the lactating mother visit her marital home with sweets, toys, jewellery, and clothes of boy's baby and family.
  • This tradition, in Haryana, is known as ‘Piliya’.
HSSC TGT Math Mock Test - 8 - Question 7
Deenbandhu Chhotu Ram Thermal Power Plant, is located in which district of Haryana?
Detailed Solution for HSSC TGT Math Mock Test - 8 - Question 7

The correct answer is Yamunanagar.

  • Deenbandhu Chhotu Ram Thermal Power Plant is located in the Yamunanagar district of Haryana.
  • It has a total installed capacity of 2x300 MW.
  • It spreads in the area of 1107 acres.
  • It is the first Power Project in the State Haryana to be awarded to Private Developer i.e. M/s Reliance Energy Ltd.
  • It is the first Project in the Country where BTG equipment was supplied by M/s Shanghai Electric Corp. China.
  • The first Unit of the plant was commissioned in a record period of 27 months which is the lowest for any coal-based greenfield project in the Country.
  • The Source of coal for the generation of power in the thermal power plant is from Central coalfields.

HSSC TGT Math Mock Test - 8 - Question 8
According to census 2011, which of the following percentage depict the level of urbanization in India ?
Detailed Solution for HSSC TGT Math Mock Test - 8 - Question 8

The Correct Answer is 31.16%.

Key Points

  • Currently, India’s population stood at 1210 million in 2011, with an urbanisation level of 31.1% (Census of India 2011).
  • Number of Persons Living in Urban Areas:
    • Over 75% of the urban population of the country is in 10 States: Maharashtra, Uttar Pradesh, Tamil Nadu, West Bengal, Andhra Pradesh, Gujarat, Karnataka, Madhya Pradesh, Rajasthan, and Kerala.
    • Maharashtra leads with 50.8 million persons (13.5% of the total urban population of the country).
    • Uttar Pradesh accounts for about 44.4 million, followed by Tamil Nadu at 34.9 million.
  • High-Scoring States: Goa is the most urbanised State with a 62.2% urban population.

Additional Information

  • Schemes/Programmes Related to Urban Development:
    • Smart Cities.
    • AMRUT Mission.
    • Swachh Bharat Mission-Urban.
    • HRIDAY.
    • Pradhan Mantri Awas Yojana-Urban.
  • Government Initiatives for Slum Dwellers/Urban Poor:
    • Pradhan Mantri Garib Kalyan Yojana.
    • Atmanirbhar Bharat Abhiyan (self-reliant India).
HSSC TGT Math Mock Test - 8 - Question 9
Recently in March 2021, Who has been appointed as the Managing director of Haryana State Cooperative APEX Bank Limited (HARCO)?
Detailed Solution for HSSC TGT Math Mock Test - 8 - Question 9

The correct answer is Rahul Uppal.

Key Points

  • Shri Rahul Uppal replaced Dr Shaleen as the Managing Director of the Haryana State Cooperative APEX Bank Limited (HARCO).
    • Haryana State Cooperative Apex Bank Limited (HARCO BANK) occupies a vital position in the State economy and has been financing farmers, rural artisans agricultural labourers, entrepreneurs etc.
    • The Short Term Cooperative Credit Structure consists of three tiers:
      • HARCO BANK at State Level has 13 branches and two Extension Counters at Chandigarh and Panchkula.
      • 19 Central Cooperative Banks at district headquarters with their 594 branches.
      • 718 PACS i.e. Patwar Circle level (Mini Banks).
    • Arvind Yadav is the chairman of the HARCO. (As of September 2021)
    • Headquarters- Chandigarh

Source:-https://harcobank.org.in/index

HSSC TGT Math Mock Test - 8 - Question 10
Who among the following has recently been honored with the Panjabrao Deshmukh Outstanding Women Scientist Award 2021?
Detailed Solution for HSSC TGT Math Mock Test - 8 - Question 10

The correct answer is Sushila Mann.

Key Points

  • Dr. Sushila Mann -
    • She is a scientist at Lala Lajpat Rai University of Veterinary and Animal Sciences (LUVAS).
    • She has been awarded the 'Punjabrao Deshmukh Outstanding Women Scientist Award 2021 on the 94th Foundation Day of the Indian Council of Agricultural Research.

Additional Information

  • ​This award was given by Union Agriculture and Farmers Welfare Minister Narendra Singh Tomar.
  • Dr. Maan is holding the responsibility of the Head of the Department in the Animal Biotechnology Department of Luvas.
  • The award was given to Dr. Mann for his outstanding research work in the biotechnology area of veterinary science.
  • This award is a special honor. Under this, he was given a certificate and a memento, and cash prize money.
  • She has also been honored with the Haryana Vigyan Ratna Award in 2020 by the Haryana Government.
HSSC TGT Math Mock Test - 8 - Question 11
If the driver takes out his right palm by bending it and moves his arm up and down several times, then you will understand-
Detailed Solution for HSSC TGT Math Mock Test - 8 - Question 11

The correct answer is He is slowing down the speed of the vehicle.

Key Points

  • Hand gestures :
    • These are additional signals given by other drivers as this lets the traffic know exactly what the vehicle's next move is.
    • This ensures a safe drive for everyone on the road.
  • Common hand gestures:
  • To slow down: 
    • When the driver is slowing down his vehicle, he or she has to extend the right arm and swing it up and down gently.

Additional Information

  • To turn right:
    • If the driver is turning right or switching to a lane on the right side, he or she has to extend the arm straight out with the palm facing front.

 

  • To overtake: Extend the right hand with palm facing forward below the level of the shoulder, and wave it forward and backwards.
    • Once the vehicle is close enough, firmly pull your hand back in the car and let the driver pass you. 

  • To turn left:
    • Extend your right arm horizontally from the window with your forearm pointing towards the ground.
    • Now that you are clearly visible to the motorist behind, turn your forearm in an anti-clockwise motion until you feel it is time to brake and turn.

HSSC TGT Math Mock Test - 8 - Question 12
‘Ghagghar Ka Maidan’ is situated at
Detailed Solution for HSSC TGT Math Mock Test - 8 - Question 12

The correct answer is In the districts of Ganganagar & Hanumangarh.

Key Points

  • 'Ghagghar ka Maidan' is situated in the districts of Ganganagar and Hanumangarh.
  • The Ghaggar-Hakra River is an intermittent river in India and Pakistan that flows only during the monsoon season.
    • The river is known as Ghaggar in India, before the Ottu barrage, and as the Hakra in Pakistan, downstream of the barrage, ending in the Thar desert.
  • In pre-Harappan times the Hakra was a tributary of the Sutlej.
    • It is still connected to this paleochannel of the Sutlej, and possibly the Yamuna, which ended in the Nara River, presently a delta channel of the Indus River joining the sea via Sir Creek.

Additional Information

  • The Ghaggar is an intermittent river in India, flowing during the monsoon rains.
    • It originates in the village of Dagshai in the Shivalik Hills of Himachal Pradesh at an elevation of 1,927 meters (6,322 ft) above mean sea level and flows through Punjab and Haryana states into Rajasthan just southwest of Sirsa, Haryana, and by the side of Talwara Lake in Rajasthan.
    • Dammed at Ottu barrage near Sirsa, Ghaggar feeds two irrigation canals that extend into Rajasthan.
  • The main tributaries of the Ghaggar are the Kaushalya river, Markanda, Sarsuti, Tangri and Chautang.
  • The Kaushalya river is a tributary of Ghaggar river on the left side of Ghaggar-Hakra,
  • It flows in the Panchkula district of Haryana state of India and confluences with Ghaggar river near Pinjore just downstream of Kaushalya Dam.
HSSC TGT Math Mock Test - 8 - Question 13
CNG engines are 
Detailed Solution for HSSC TGT Math Mock Test - 8 - Question 13

The correct answer is Spark ignited.

Key Points

  • CNG engines are Spark ignited.
  • Compressed natural gas (CNG) vehicles operate much like gasoline-powered vehicles with spark-ignited internal combustion engines.
  • Compressed natural gas (CNG) is a fuel gas composed of methane (CH4).
  • CNG plays an important role in reducing greenhouse gas emissions from vehicles.
  • It is very environmentally friendly and helps to reduce air pollution.

Additional Information

  • Hot spot ignition engine:
    • The hot spot ignition engine is any unwanted overheated area inside the engine combustion chamber that dramatically effects the efficiency of the engine.
  • Compression ignition:
    • It is an internal-combustion engine in which high temperature is produced by compressing air in the cylinder before the admission of the fuel.
HSSC TGT Math Mock Test - 8 - Question 14
A wise teacher will permit the class-room group to decide
Detailed Solution for HSSC TGT Math Mock Test - 8 - Question 14
Classrooms are social settings; teaching and learning occur through social interaction between teachers and students. As teaching and learning take place, they are complicated processes and are affected by peer-group relationships. The interactions and relationships between teachers and students, and among students, as they work side by side, constitute the group processes of the classroom.
Important Points A group is a collection of interdependent, interacting individuals with reciprocal influence over one another.
  • Interdependent means the participants mutually depend on one another to get work done; the teacher's part is to teach as the students strive to learn. 
  • Reciprocal influence refers to mutual effects exchanged and felt by the same people.
  • Classroom group allows students to interact with each other. They build a strong impact on the confidence level of each individual.
  • A wise teacher allows the class group to discuss about the academic issues where the pupil's choice leads to more desired goals.
  • Classroom groups can solve the issues related to academics with each other.

Thus, it is concluded that A wise teacher will permit the classroom group to decide academic issues, where pupil choice of the means will lead to more effective attainment of desired ends.

Hint

  •  The classroom groups cannot decide all classroom issues as they are not incharge of the class. It is the teacher's duty to solve the issues of the class.
  • The classroom group is not allowed to solve all issues in which they alone are involved and in which all the decisions-right or wrong will not matter much but they need to address the academic issues.
HSSC TGT Math Mock Test - 8 - Question 15
Let us assume that a teacher wishes students to gain some understanding of the horrors of war and to be able to suggest peaceful alternatives to international conflicts. This objective can be fulfilled by
Detailed Solution for HSSC TGT Math Mock Test - 8 - Question 15

A variety of ways and approaches to organising a social studies curriculum have been tried out. Each one of these has some limitations and strengths. It is the responsibility of the teacher to ensure the achievement of objectives according to learners' needs, age level as well as societal and national-international demands. Rigidity in organising the curriculum in a singular manner will generate an imbalance in achieving the goals earlier stated. The following section will focus on the various approaches of curriculum organisation of social studies and the governing factors in adopting alternative approaches too.

Key Points Integrated Approach:

  • It responds to the changing nature of the scientific study. An integrated approach can design the instruction in consonance with children's stages of mental growth.
  • Secondly, it is more likely to maintain focus on enhancing individual goals and promoting social goals. Thirdly, advances in scientific knowledge have broken boundaries between traditional academic disciplines and new disciplines.
  • For example, areas such as political behaviour, economic history and cultural geography have taken the place of old singular disciplines, and new fields of studies like population studies, environmental studies, global studies, etc., have emerged and they draw their content from various traditional disciplines. Hence, the integrated approach is being justified on the above grounds.

Integration in the organisation of content can be achieved in many ways but at least three alternatives that are significant should be noted:

  • Integrating while preserving discipline identification
  • Integration through social science concepts and generalisations
  • Integration through unification

Thus from the above-mentioned points, it is clear that the objective can be fulfilled by an integrated approach. 

HSSC TGT Math Mock Test - 8 - Question 16
What role will you play as a teacher when some students are deliberately trying to break the discipline of the class by doing mischief?
Detailed Solution for HSSC TGT Math Mock Test - 8 - Question 16

Maintaining discipline in the classroom is one of the important task which should be done by the teacher during teaching learning process because indiscipline in classroom may cause disturbance for all the students and even the students which who are in the other classrooms also.Key Points

When I see some students are deliberately trying to break the discipline of the class by doing mischief I will

  • Teach them some moral values and teach them disciplined behaviour and also specify the disadvantages of indiscipline behaviour and mischief.
  • Closely follow them and find out the reasons for their indiscipline behaviour and mischief and try to solve them in their own way.
  • Will give them an opportunity to introspect and improve their behaviour after teaching them some moral values and making them change their path regarding their behaviour.
  • Design interesting and curious activities for this kind of student so that they stop the mysterious behaviour and divert their concentration towards learning.

Hence I will give them an opportunity to introspect and improve their behaviour.

HSSC TGT Math Mock Test - 8 - Question 17

Which of the following will not come under collaborative teaching-learning process ?

Detailed Solution for HSSC TGT Math Mock Test - 8 - Question 17

The teaching-learning process is aimed to bring permanent change in the behavior of an individual (knowledge, skill, and attitude) that can be acquired consciously.

  • It involves planning and execution of several activities and experiences to bring the desired outcomes.
  • If the outcomes are not achieved as per expectations or much lower than that it is considered as the "failure" of the system.

Important Point

The collaborative teaching-learning process is a synchronized process in which students attempt to learn something together.

  • They work as a team that develops the team spirit, feeling of collaboration, and make them good communicators as well.
  • The use of a collaborative learning approach will help a teacher to develop social interdependence and participation among students and will help in removing the communication gap among students.

Key Points 

Therefore, it is concluded that programmed learning does not come under the collaborative teaching-learning process.

HSSC TGT Math Mock Test - 8 - Question 18
The four 'D' model of dream, discover, design and deliver will be the best fit with which of the following models of teacher education?
Detailed Solution for HSSC TGT Math Mock Test - 8 - Question 18

Teacher Education

  • Teacher Education programs produce teachers, who in turn educate generations of pupils and students.
  • Teachers who transform the knowledge and skills acquired in school, college, or university during the rest of their lives and work.
  • It is an education program which has the policies, procedures, and provision designed to equip teachers with the knowledge, attitudes, behaviors, and skills a teacher require to perform tasks effectively in the classroom, school, and wider community.
  • The 4-D's
    • DISCOVERY: It involves Identification and appreciation of what works.
    • DREAM: It involves Imagining what might be.
    • DESIGN: It involves Developing systems, structures leveraging the best of what was and what might be.
    • DESTINY: It involves Implementing or delivering the proposed design.

Competency-Based Model:

  • A competency model is a guideline developed by a Human Resource department that sets out the specific skills, knowledge, and behavioral requirements that enable an employee to perform their job successfully.

Hence, From the above-explained points, we can conclude that The four ‘D’ model of a dream, discover, design, and deliver the best fit with the competency-based model of teacher education. It enables the student teacher to make decisions by exploring and discovering. The 4 -D's help in creating an environment of proving, exploring, and discovering one's abilities.

Additional Information

Concept Attainment model:

  • The Concept Attainment model is an instructional strategy founded on the works of Jerome Bruner. 
  • Built on the principle of concept formation, the Concept Attainment model promotes student learning through a process of structured inquiry.
  • The model helps students to understand and learn concepts by identifying attributes or key features through a process of analysis, comparison, and contrasting examples. 
  • Two sets of examples are used in this strategy – Yes (examples that have attributes of the concept) and No (examples that do not have attributes of the concept) examples.

Inquiry oriented teacher education model:

  • The inquiry is the systematic, intentional study of one's own professional practice. It is a stance, a way of learning about teaching and from teaching, and genuine inquiry is conceptualized as a transformative force for teacher development, student learning, and school change.
  • The conceptual scholarship on inquiry-oriented teacher education is extensive, and over the last 25 years, a growing number of teacher education programs around the world are describing themselves as inquiry-oriented.

​The jurisprudence model used principally in analyses of individual values regarding domestic laws helps to explain these beliefs.

HSSC TGT Math Mock Test - 8 - Question 19
Which one of the following is NOT the common speech disorder of childhood?
Detailed Solution for HSSC TGT Math Mock Test - 8 - Question 19

Learners face significant difficulties in acquiring and rising their abilities in speaking, acquiring and their abilities for speaking, listening with understanding, reading, writing, paying attention, and motor abilities disabilities.

Key Points Speech disorders may range from problems with expression or voice strength to complete voicelessness, chronic hoarseness, stuttering, or stammering, defect in pronunciation, defect in speaking sentences correctly, slurring, and lisping.

  • Speech difficulties can also be associated with cerebral palsy, hearing impairment, and brain injury.
  • Children with speech difficulties may have difficulty understanding and have difficulty in expressing ideas.
  • Mental Retardation hearing Impairment and behavioral disorders may cause delayed speech.
  • Auditory and speech training will be given to the child in the resource room.
  • Avoid criticizing them for speaking faulty language. They should be gently encouraged to speak correctly.
  • Use linguistic scaffolding techniques that involve a series of questions.
  • Most such defects can be cured if early action is taken.
  • Teachers should focus on interactive communication.

Thus, it is concluded that depletion of energy is not a common speech disorder in childhood.

HSSC TGT Math Mock Test - 8 - Question 20

In the given figure, what is the measurement of YXZ?

Detailed Solution for HSSC TGT Math Mock Test - 8 - Question 20

The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.

HSSC TGT Math Mock Test - 8 - Question 21

An AP consists of 31 terms. If its 16th term is m, then sum of all the terms of this AP is

Detailed Solution for HSSC TGT Math Mock Test - 8 - Question 21

S31 = 31/2(2a + 30d)
a16 = a + 15d = m
⇒ S31 = (31/2) x 2(a + 15d) ⇒ S31 = 31 m

HSSC TGT Math Mock Test - 8 - Question 22

In the figure, O is the centre of eh circle and ∠AOB = 80o. The value of x is :

Detailed Solution for HSSC TGT Math Mock Test - 8 - Question 22

the angle subtend at center is double of the angle at the arc

so:    2x=80

so x=40 

HSSC TGT Math Mock Test - 8 - Question 23

Every positive even integer is of the form ____ for some integer ‘q’.

Detailed Solution for HSSC TGT Math Mock Test - 8 - Question 23

Let a be any positive integer and b = 2
Then by applying Euclid’s Division
Lemma, we have, a = 2q + r where 0 ⩽ r < 2 r = 0 or 1
Therefore, a = 2q or 2q+1 
Therefore, it is clear that a = 2q i.e., 
a is an even integer in the form of 2q

HSSC TGT Math Mock Test - 8 - Question 24

The true set of real values of x for which the function, f(x) = x ln x – x + 1 is positive is

Detailed Solution for HSSC TGT Math Mock Test - 8 - Question 24

f(x)=xlnx−x+1
f(1)=0
On differentiating w.r.t x, we get
f′(x)=x*1/x+lnx−1
=lnx
Therefore,f′(x)>0 for allx∈(1,∞)
f′(x)<0 for allx∈(0,1)
lim x→0 f(x)=1
f(x)>0
for allx∈(0,1)∪(1,∞)

HSSC TGT Math Mock Test - 8 - Question 25

Three unbiased coins are tossed. What is the probability of getting at most two heads?

Detailed Solution for HSSC TGT Math Mock Test - 8 - Question 25

HSSC TGT Math Mock Test - 8 - Question 26

If 3 sin(xy) + 4 cos (xy) = 5, then   = .....

Detailed Solution for HSSC TGT Math Mock Test - 8 - Question 26

3sinxy + 4cosxy = 5
⇒ 5(3/5 sinxy + 4/5 cosxy) = 5 
⇒ (3/5 sinxy + 4/5 cosxy) = 1
now (3/5)²+(4/5)² = 1
    so let, 3/5 =   cosA
             ⇒ 4/5 = sinA
So , (3/5 sinxy + 4/5 cosxy) = 1
     ⇒ (cosAsinxy + sinAcosxy) = 1
     ⇒ sin(A+xy) = 1
     ⇒ A + xy = 2πk + π/2 (k is any integer)
     ⇒ sin⁻¹(4/5) + xy = 2πk + π/2
     differenciating both sides with respect to x
   0 + xdy/dx + y = 0
      dy/dx = -y/x

HSSC TGT Math Mock Test - 8 - Question 27

The co – ordinates of the mid – point of the line segment joining the points (– 2, 3) and (4, – 5) are

Detailed Solution for HSSC TGT Math Mock Test - 8 - Question 27

Let the coordinates of midpoint C(x,y) of the line segment joining the points A(−2,3) and B(4,−5).

HSSC TGT Math Mock Test - 8 - Question 28

If P = {1, 2, 3, 4}, then the number of elements in its power set will be:

Detailed Solution for HSSC TGT Math Mock Test - 8 - Question 28

Number of elements in a power set = 2n, where n = number of elements in the set P.
Hence, 2= 16.

HSSC TGT Math Mock Test - 8 - Question 29

If A = {1, 2, 3, 4} and B = {4, 5, 6, 7, 8}, then A U B = ?

Detailed Solution for HSSC TGT Math Mock Test - 8 - Question 29

 In set theory, if A and B are sets, then the union of A and B , written A ⋃ B, is {x: x ∈ A or x ∈ B}. By asserting that x ∈ A or x ∈ B, we do not exclude the possibility that x is a member of both A and B. Further, if the same object/element is member of both A and B, then that element is counted only once in the new set formed by the union of A and B.
Given, A = {1,2,3,4} and B = {4,5,6,7,8}.
∴ By definition, A ⋃ B = {1,2,3,4,5,6,7,8}

HSSC TGT Math Mock Test - 8 - Question 30

On the interval [0, 1] the function x25(1 – x)75 takes its maximum value at

Detailed Solution for HSSC TGT Math Mock Test - 8 - Question 30

Let f(x)=x25(1−x)75,xϵ[0,1]
⇒f′(x)=25x24(1−x)75−75x25(1−x)74
=25x24(1−x)74{(1−x)−3x}
=25x24(1−x)74(1−4x)
We can see that f′(x) is positive for x<1/4 and f'(x) is negative for x>1/4
Hence, f(x) attains maximum at x= 1/4

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