KVS PGT Mathematics Mock Test - 3 - KVS PGT/TGT/PRT MCQ

'A house divided against itself cannot stand' means if there is no unity within an organization or group nothing can be achieved.

Option 3 states this meaning and is the correct option. All other options imply other ideas.

Example- The management never made peace with the players, hence there was complete chaos, and the team eventually lost. Truly a house divided against itself cannot stand in the long run.

The sentence indicates that the tribes believe in the 'vagueness' i.e the uncertainty of the after-life. Out of the given options, only 'obscurity' means unclear, uncertain or mysterious. The other options, 'totality', 'tenacity', 'severity' and 'lucidity' mean 'wholeness', 'persistence', 'seriousness' and 'clarity'. Hence, the correct answer is 2.

सज्जन- के लिए सही संधि विच्छेद: सत्+जन

• सज्जन का संधि विच्छेद = सत् + जन, जिन व्यंजनों में परिवर्तन के कारण संधि है = त्/द् + ज = ज्ज
• सज्जन - सत् + जन

Key Pointsयदि दन्त्य स् या त् वर्ग से पहले या बाद में तालव्य ‘श’ या च वर्ग का कोई एक वर्ण आये तो दन्त्य ‘स’ का तालव्य ‘श’ में और त् वर्ग को च् वर्ग में बदल देते हैं।

• व्यंजन संधि के उदाहरण :-
  • सत् + जन = सज्जन
  • जगत् + जननी = जगज्जननी
  • उद् + ज्वल = उज्जवल

Additional Information

सही उत्तर धर्मार्थ है।

Key Points

• धर्म + अर्थ= धर्मार्थ
• नियम- अ + अ= आ
• धर्मार्थ में "दीर्घ स्वर संधि" है।
• धर्मार्थ शब्द का अर्थ- धर्म हेतु किया गया।
• उदाहरण- सेठजी कोई भी काम धर्मार्थ करते हैं।

Additional Informationसंधि - दो शब्दों के मेल से जो विकार (परिवर्तन) होता है उसे संधि कहतेहैं।
संधि के तीन प्रकार हैं - 1. स्वर, 2. व्यंजन और 3. विसर्ग

International Literacy Day is celebrated every year on September 8. It was proclaimed by the United Nations Educational, Scientific and Cultural Organization (UNESCO) in 1966 to promote literacy worldwide. The theme of 2023 is 'Promoting literacy for a world in transition: Building the foundation for sustainable and peaceful societies.'

The correct answer is Six.

Key Points

​Therefore, The United Nation have Six organ body. 

Important Points

• ​The United Nations is an intergovernmental organization.
• The stated purposes are to maintain international peace and security, develop friendly relations among nations, and achieve international cooperation.
• The United Nations (UN) main organs are— the General Assembly, the Security Council, the Economic and Social Council, the Trusteeship Council and the Secretariat, and the International Court of Justice.
  • Founded: 24 October 1945
  • Headquarters: New York, New York, United States
  • Secretary general: António Guterres

There are 8 triangles in the figure. By counting the individual triangles, we can see that there are 2 large triangles, 4 medium triangles, and 2 small triangles, making a total of 8 triangles.

Principles of development define the basic process of human development. It will assess the role and importance of growth processes and levels and the principles of growth and behavior in the total life span. 

Key Points 
Importance of Understanding Principle of Development: It is necessary for the teachers to understand the need and importance to study them. 

• Knowledge of the development patterns for different age groups helps us to know what to expect of a child and when to expect it. We may often expect too much from a child too early. Your own experience in teaching will help you to understand this fact. For example- you know that trying to teach algebra to a III standard child will be a hostile exercise The concepts are too complicated for the child to comprehend.
• It helps parents and teachers to give timely guidance to children as they grow from one stage to the other. when a child is showing an increased curiosity in things around them, parents/teachers can facilitate this development by providing more opportunities. For example, answering the child's questions, giving suitable books to browse questions, daily book reading practice, etc. 
• It helps the teachers effectively cater to the different learning styles and diverse needs of learners.
• Normal development pattern makes it possible for parents and teachers to prepare children ahead of time for changes that will take place in their bodies, their interests or their behavior. For example, children can be prepared for what will be expected from them when they enter school. Similarly, older children call to be explained the reasons for physiological changes during puberty. 

Hence, we can conclude that Understanding the principles of the development of a child helps a teacher in effectively catering to the different learning styles of learners.

The development of child takes place through various place. Although each stage has an encompassing relationship to other stages, yet its has own unique characteristic needs and demands.

Key Points

Prenatal Period:

• The period from the day of conception to the birth of the baby.
• Life begins with the formation of zygote.
• The fertilized egg begins to divide within an hour or two after conception, into two cells.
• Ten hours later these two cells divide to make four cells, then four to make eight cells, then sixteen cells and so on.
• The cells continue to divide till eight weeks after conception ad this period is called Embryonic period.
• This is followed by fetal period of development which is from about 8 weeks when the embryo becomes a recognizable human beings, to the time of birth.
• The proper development of fetus depends upon many factors, such as health of mother, use of drugs and alcohol, smoking, nutritional status of mother, stress and emotional factors.

Hence, we can conclude that the period from the day of conception to the birth of the baby.

Additional Information

• Stages of Child Development:
  • Prenatal Period
    • Embryonic period: Conception to eight weeks
    • Period of fetus: 8 weeks to birth
  • Infancy period
    • Neonatal period: Birth to 15 days
    • Infancy period: 15 days to 2 years
  • Early Childhood (Preschool years): 2 to 5-6 years 
  • Middle Childhood (School age): 5-6 to 12 years
  • Adolescence
    • Puberty: 12 to 14 years
    • Adolescence: 14 to 18 years
  • Adulthood:
    • Early adulthood: 18 to 35/40 years
    • Middle adulthood: 40 to 60 years
    • Late adulthood: Early 60 and above

The term communication in Latin ‘communis’, means ‘to share’. It is the activity of conveying information through the exchange of thoughts, messages, or information through speech, visuals, signals, writing, or behavior.

Types of Communication:  

1. Verbal Communication:

• Verbal communication is the use of language to pass on information by speaking or writing formally.
• For example,  written instructions on a question paper, attending an online class and yoga instructor teaching yoga poses, etc.
• Verbal means the use of words in the communication process and in the design and formulation of messages.
• In oral communication, spoken words are used. 
• It is formal and precise because it often works in corporate, educational institutions, government organizations, etc.

Important Points

2. Non-Verbal Communication:

• It is understood as the process of communication through sending and receiving wordless messages. 
• It includes the use of visual cues such as body language (kinesics), distance (proxemics) and physical environments/appearance, of voice (paralanguage), and of touch (haptics).
• It involves the usage of gestures, touch, body language, postures, facial expressions, eye contact, or any actions depicting the universal meaning of such actions commonly understood.
• scholars argue that nonverbal communication can convey more meaning than verbal communication.
• It is informal because does not follow authority lines as in the case of formal communication. 
• Paralanguage is a non-verbal element that is found even in a speech which includes voice modulation, speaking style, rhythm, handwriting style, emotions, the spatial arrangement of words also comes under the ambit of nonverbal communication.
• Special symbols or infographic representing an ascertained message is also a medium of nonverbal communication.

Therefore The picture without dialogues is an example of Nonverbal communication because there are no words.

Additional Information

Interpersonal Communication:

• It is direct face-to-face communication between two people.
• It is personal, direct, and intimate, allowing for maximum interaction and exchange in word and gesture.
• It requires certain skills to interact effectively with others such as the knowledge of social norms, etiquette, willingness to listen, and respect for one another, willingness to share about oneself, etc.
• For example, talking to your friends or family, teacher and student interaction, etc.

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

• All these information technologies have mainly two types of communication technologies.
  • Satellite based communication and
  • Terrestrial based communication.
• Satellite based communication is the communication, which takes place between sender and receiver through a communication satellite whereas terrestrial based communication is the communication, which takes place through a network of transmitters spread across a geographical area, a country, or a state.
• This type of communication is used in the transmission of radio and television in India.
• However, with the launch of a series of satellites by Indian Space Research Organization (ISRO), satellite based communication is being used for telecommunication.

Important Points

• Communicating information effectively by making use of appropriate technology is called information and communication technology (ICT).
• In all, ICT is an umbrella term that includes many communication devices such as radio, television, cellular phones, computers and network, satellite systems and so on.
• ICTs are defined, as a “diverse set of technological tools and resources used to communicate, and to create, disseminate, store, and manage information.

It has been proved by research that there is a positive connection between parent’s involvement and student success. Effectively engaging parents and families in the education of their children has the potential to be far more transformational than any other type of education reform.

Key Points

•  Parent involvement is considered to be one of the most important educational goals. 
• Every school should promote partnerships that will increase parental involvement and participation in promoting the social, emotional, and academic growth of children.
• School education professionals can help parents with their changing roles in all of the following ways:-
  • ​To provide expertise.
  • To provide advice.
  • To provide educational support.

​Thus, it is concluded that School education professionals can help parents with their changing roles in all of the following ways, except to provide food and medicines.

Growth is an important attribute of childhood. The process of growth starts from the conception of the fetus and continues till adolescence when the child matures into adulthood. 

• The terms growth and development are closely interrelated and it is not possible to separate one from the other.

​Key Points

• Growth refers to an increase in the size of the body parts due to the multiplication of cells and an increase in the intercellular substance. It can be measured in inches or centimeters and in kilograms or pounds. It causes quantitative changes in the body. Each child has a different genetic potential for growth.
• Development refers to physiological maturation. It is a progressive increase in skill and capacity to function. It causes a qualitative change in a child's functioning.

Important Points
Lifespan and age are two major factors that explain the direction of the outcome of growth and development as both are dependent on these factors.

• ​ Life span refers to the ongoing process that we go through while growing up. It is the period of time from conception extending to death. Studying life span development is very important because it helps in describing and explaining the mysteries of human development.
• Life span development includes issues such as the extent to which development occurs through the gradual accumulation of knowledge versus stage-like development, or the extent to which children are born with innate mental structures versus learning through experience.

Thus, it is concluded that Lifespan and age are major factors explaining the direction and outcome of growth and development.

Diversity is everything that makes people different from each other. The term diversity indicates that a group of people is made up of individuals who are different from each other in some way or the other. For example, differences in culture, language, gender, appearance lifestyle, social and economic status, etc.

Key Points

• Diversity among students in education directly impacts their performance. Students work better in a diverse environment, enabling them to concentrate and push themselves further when there are people of other backgrounds working alongside them. This promotes creativity, as well as better education, as those with differing viewpoints are able to collaborate to create solutions.
• In a diverse class, teachers must teach according to diverse cultures and encourage students to share unique features of their culture.
• Teachers must bring diverse culture examples in the classroom teaching.
• Developing a curriculum and teaching style suitable to the dominant culture should be avoided by the teacher.

Thus, it is concluded that in a class comprising culturally diverse students, developing curriculum and teaching style suitable to dominant culture should be avoided by a teacher.

DIKSHA (Digital Infrastructure for Knowledge Sharing) is a national platform for school education, an initiative of the National Council for Educational Research and Training (NCERT), under the Ministry of Education (MoE). It was launched in 2017 by the Honourable Vice President of India Shri M. Venkaiah Naidu. 

Key Points

• The Committee observed that a large proportion of the students currently enrolled in elementary school (over five crores) have not attained foundational literacy and numeracy (the ability to read and understand the basic text and carry out basic addition and subtraction).
• It recommends that every student should attain foundational literacy and numeracy by grade three.  
• To achieve this goal, a National Mission on Foundational Literacy and Numeracy will be set up under the MHRD. 
• All state governments must prepare implementation plans to achieve these goals by 2025. 
• A national repository of high-quality resources on foundational literacy and numeracy will be made available on the government’s e-learning platform (DIKSHA). 
• DIKSHA has been adopted by almost all the States, Union Territories, and central autonomous bodies/boards including CBSE. 
• During the pandemic, the massive teacher’s professional development program NISHTHA 1.0 (National Initiatives for School Heads and Teacher’s Holistic Advancement) for Elementary grades was launched online through DIKSHA.

Thus, it is concluded that the national repository of high-quality resources on foundational literacy and numeracy will be  DIKSHA.

Hence ,slope of tangent at (a , b) = -b/a . Therefore , the equation of tangent at (a , b ) is ; 

f (x) is discontinuous when x² - 3|x| + 2 = 0
⇒ |x|² - 3|x| + 2 = 0 ⇒ |x| = 1, 2

When a is positive, the parabola is opening to the right and since directrix is x=-a, it gives the answer.

xy - 3x - 2y + λ = 0.
Then abc + 2fgh − af² − bg² − ch² = 0
⇒ 3/2 − λ/4 = 0
⇒ λ = 6
∴ Equation of asymptotes is xy-3x-2y+6=0
⇒ (x-2)(y-3)=0
⇒x - 2 = 0 and y - 3 = 0

Domain of sin^-1x is [-1,1]

Therefore, -1 ≤ log₃(x/3) ≤ 1

3^-1 ≤ x/3 ≤ 3

1 ≤ x ≤ 9

Therefore, the domain of sin^-1[log₃(x/3)] is [1,9]

Equation of tangents and normal with slope 'm' will be 

μ = (22 + 26 + 28 + 20 + 24 + 30)/6
= 150/6 
= 25
x(i) = (xi - μ)²
x(22) = (22-25)² = 9
x(26) = (26-25)² = 1
x(28) = (28-25)² = 9
x(20) = (20-25)² = 25
x(24) = (24-25)² = 1
x(30) = (30-25)² = 25
​
(xi - μ)²  = 70
Standard deviation : [(xi - μ)²]/N
= (70/6)^½
= 3.42

sin(A+B)-sin(A-B) = 2cosAsinB 
= 2cos(π/4)sinX
= 2 × 1/√2 sin X
= √2sinX

The given system of equation has a unique solution if : 

Mixed doubles includes 2 men and 2 women.
Since 2 men are selected of 6 men
⇒ number of ways = ⁶C₂
Also 2 women are selected of 4 women
⇒ number of ways = ⁴C₂
But they also can be interchanged in 2 ways
∴ Total no. of ways 

nth G.M. between a and b is
G_n = arⁿ
Where common ratio is r = (b/a)^(1/(n+1))
​So, to insert 3 geometric means between 1 and 256
 r = (b/a)^(1/(n+1))
r = (256/(1)^(1/(3+1))
r = (256)^1/4
r  = (4)^(4)1/4
r = 4
G_n = 1 * (4)ⁿ
G₁ = 1 * (4)¹ = 4
G₂ = 1 * (4)² = 16
G₃ = 1 * (4)³ = 64
The terms are  4, 16, 64

Probability that first critic favour is P(ε₁) = 5/7 
Similarly, P(ε₂) = 4/7  P(ε₃) = 3/7 
Majority are in favour if at least two favour 

LHS always positive RHS always negative LHS ≠ RHS