KVS PGT Mathematics Mock Test - 1 - KVS PGT/TGT/PRT MCQ

The sentence has no error.

सही उत्तर है - ‘व्यष्टि’।

• समष्टि का विलोम व्यष्टि होगा।
• समष्टि का अर्थ : सामूहिकता।
• व्यष्टि का अर्थ : समष्टि का सदस्य या व्यक्ति।

Key Pointsअन्य विकल्प:

• अस्ति का विलोम : नास्ति।
• विशिष्ट का विलोम : साधारण।
• अशिष्ट का विलोम : शिष्ट।

Additional Information

• किसी शब्द का विलोम शब्द उस शब्द के अर्थ से उल्टा या विपरीत अर्थ वाला होता है।

विलोम शब्द के उदाहरण:-

• कृतज्ञ - कृतघ्न
• तुच्छ - महान्
• प्रगतिशील - प्रतिगामी
• देव - दानव

Key PointsBiogas:

• Biogas is an emerging renewable, non-conventional energy source that is obtained through the degradation of organic matter by bacteria under anaerobic conditions.
• The major constituent of biogas is Methane.
• Biogas is usually made up of around 50-70% methane (CH4) and 25-45% carbon dioxide (CO2), with other gases such as hydrogen (H2), hydrogen sulphide (H2S), watervapour (H2O), Nitrogen (N2), oxygen (O2), ammonia (NH3) making up the rest.
• It is released when Cow, Buffalo, and Pig manure is processed anaerobically i.e. in the absence of Oxygen.
• Biogas can be used for Space Heating, Generation of Electricity, Fuel for Cooking, etc.

Important Points

Advantages of Biogas - 

• ​Biogas burns without smoke; hence no harmful gas such as CO₂, CO, NO₂, and SO₂ are evolved.
• The slurry produced after the production of biogas is used as manure in fields.
• The method of disposal is safe and efficient and hence no space is wasted in the form of landfills.
• Biogas plants require very little installation costs and become self-sufficient in a span of 3-4 months.
• Work opportunity for thousands of people is created, especially in rural areas.

Thus, Biogas is a non-conventional type of natural resource.

Additional Information

There are basically two sources of energy:

The correct answer is Red.

Key Points

• Sulphuric acid is also known as the oil of vitriol.
• It is composed of sulfur, hydrogen, and oxygen element.
• The acid has a very strong acidic nature.
• It has several uses such as fertilizer manufacture, mineral processing, oil refining, and wastewater processing.
• It is also known by the name hydrogen sulfate.

Important Points

• The litmus solution is a purple dye solution.
• It is extracted from the plant called " Lichen".
• It is used as an acid-base indicator.

The meaning of synonym is Similar.

Similarly;

The meaning of Opposite is Adverse.

Hence, "Adverse" is the correct answer.

Additional Information

The approach is begun to deal with problems. It is the way that identifies the aptitude of the person to deal with things.

The topical approach gives mastery over the topic. It is organized around themes, topics, and units of the content or subject matter.

Key Points 
Topical Approach: 

• This approach is also known as the topic approach.
• The topical approach is based on the principle of totality.
• It specific topic is started in a particular class and finished in the same class.
• The topical approach is the opposite of the concentric approach.
• Topics are selected according to the mental level, capabilities, and interests of the student.
• Topics studied in the previous class received no attention.

Thus by all these references, we can conclude that The curriculum organization which gives scope for both ‘principle of difficulty’ and ‘principle of repetition’ in the same class is the Topical approach,

Important Points
Merits:

• The topical approach is psychological topics have been selected according to the interest, age group, mental levels, and needs of the students.
• Teaching is purposeful.
• Logical subject matter.
• In-depth knowledge.

Demerits:

• Destroys the continuity of subject matter.
• unsuitable for the same topics.
• Reading everything about one topic is very difficult.
• Knowledge attained is more bookish.

Additional Information

• Spiral approach: This approach helps students score better on tests and retain information longer than students who learn from curricula that take massed approach.
• Logical approach: Logical approach is very useful and significant to construct social studies curriculum. A sequential arrangement of the topics of the syllabus is known as a logical approach. It is based on logic.
• Concentric approach: In this approach, the topics will find a place in different classes of different years of the course in a progressive manner. the concentric approach takes into consideration the mental growth of pupils.

Early Childhood Education (also known as pre-primary or preschool education) traditionally refers to the education of children aged three to six years before entering the formal school setup.

Key Points

• NEP 2020 prescribed five years of the foundational stage of education from which 3 years of education include preschool or early childcare education and 2 years of early primary education which includes classes 1 and 2.
• It also suggests that there should be continuity between the ECE curriculum and Grade 1 and 2 curricula.
• The three years of pre-schooling is made mandatory to ensure Foundational Literacy and Numeracy among children.
• The highest priority of school education will be “Universal acquisition of Foundational learning skills by Grade 3.
• Foundational Literacy means the ability to read and write and comprehend. The key components in Foundational Language and Literacy are Oral Language Development, deciphering written words, Reading Fluency, Reading Comprehension, and competencies of writing.
• Foundational Numeracy means the ability to reason and to apply simple numerical concepts in daily life problem-solving. The major aspects and components of early mathematics are Pre-number concepts, Numbers and operations on numbers, space, and spatial understanding and measurement skills.

Hence, we conclude that 3 years of pre-schooling is mandatory for children according to NEP 2020.

The Play-way level school is based on the physiological principle of development and growth to keep the child fit and fight diseases. In these schools, there are no strict rules for learning, but education is learned by the way of playing.

• The aim of these schools is to remove the boring classroom environment by incorporating appropriate games to provide children with rich, meaningful, and balanced learning.
• It helps children to be socialized and enables the overall development of the children by helping them to reach full potential in all aspects of life.

• The play-way method is a complete package that enables the overall development of the child by developing in terms of feelings, intellect, and skills parameters. The Play-way method is mostly “Activity-based” or “Hands-on Experience”, children learn to cooperate in playing together. They learn to adjust their needs and desires to the behavior of their peers. In a very real sense, the child begins to develop a sense of self as distinct from the family. Thus, primary socialization takes place in infancy and childhood.
• It not only focuses on subjective development but the emotional development of the child as well.
• In this method, playing acts as the driving force as the entire learning method revolves around activity-based learning. It encourages expression and creative skills among children.

Key Points

Play way level is a method of teaching for lower classes that emphasize upon:

• enabling the overall development of the child.
• providing children with rich, meaningful, and balanced learning.

• removing the monotonous classroom environment by incorporating appropriate games.

• promoting the physiological principle of development and growth to keep the child fit and fight diseases.

Hence, we can conclude that there are/is no strict rules/methods to learn, but education is learned by the way of playing, which is correct regarding the play-way level.

The curriculum is the full set of subjects constituting a course of study / a program of study in a school or a college. Along with curricular subjects, it covers all scholastic and co-scholastic activities. Therefore, the curriculum comprises the totality of all educational experiences associated with a program of study.Key Points 

• The traditional curriculum was centered around subject-centered and teachers predominates in it.
• In Traditional curriculum, the greatest emphasis is on facts, principles, and skills in the subject concerned. 
• The purpose of traditional curriculum is to offer quality instruction and ensure active mode of learning in the classroom.
• In this curriculum, the teacher plays a pivotal role in scheduling and carrying out lectures, s/he carries out instructional planning and its implementation. 

Hence, we can conclude that 'Developing problem-solving and critical thinking skills' is not an advantage of the traditional perspective of curriculum.

Additional Information

• Competency-based curriculum emphasizes on the learner-centered approach with its focus on the changing needs of students, teachers, and society. The competencies like self-efficacy, citizenship, digital literacy, communication, and collaboration, learning to learn, imagination and creativity, critical thinking and problem-solving competencies could be developed through competency-based curriculum.

An exam is a formal test you take to demonstrate your expertise in a particular field or to get a certificate.

Key Points 

• If the results of two or more test takers are comparable, the exam is considered to be objective. 
• Objectivity examination has no place for discrimination.
• Recognizing and remembering topic knowledge is necessary for objective examinations.
• Questions of fact, sentence completion, true-false, analogy, multiple-choice, and matching are some of the different formats.
• They often cover a wider range of topics than essay examinations.
• Each question has a single, unchanging right response.

Hence, it is concluded that objectivity examination has no place for discrimination.

Community participation:
“An emphasis on participation has links with the interest in democracy in community organization and in self-help and political incorporation in the community developmental aspects.” 

The World Bank (2000b) describes participation as “a. process through which the stakeholders influence and share control over development initiatives and the decisions and resources which affect them”

In the educational history of education community participation in education is not new. It is important to discuss what community is in terms of educational points of view. 

• Communities can be defined by characteristics that members share, such as culture, language, tradition, law, geography, class, and race.
• Community participation in education is viewed as an effective means of promoting education both in qualitative and qualitative terms.
• Community is a group structure, whether formally or informally organized, in which members play roles that are integrated around goals associated with the problems from collective occupation and utilization of habitudinal space, second, members of the community have some degree of collective identification with the occupied space.
• Communities based on shared family or educational concerns, which include parents association and similar bodies that are based on families shared concern for the welfare of students.

Benefits of community participation in schooling:

1. Where communities participate, there are improved school facilities, increased accountability among school personnel, and improved capacity of participants.
2. Community participation in education helps to identify issues and problems in school education. 
3. According to a recent policy brief from the National Education Association (NEA), “when schools, parents, families, and communities work together to support learning, students tend to earn higher grades, attend school more regularly, stay in school longer, and enroll in higher-level programs”.

Conclusion: 

Community participation in education in India can be termed mostly as legislated participation, as people's participation is being promoted through constitutional provisions and program guidelines. The main objective of participatory development is to increase the involvement of socially and economically marginalized people in making decisions regarding their own lives. The assumption is that the participatory approach empowers people with the skills and confiden

Replacing x by -x, 


Subtracting and putting

Calculation:

The set X is given by

{2, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 58, 62, 66, 70, 74, 78, 82, 86, 90, 94, 98}.

We want to find the maximum size of a subset S of X such that no two

elements sum to 100.

The pairs in X that sum to 100 are

(2, 98), (6, 94), (10, 90), (14, 86), (18, 82), (22, 78), (26, 74), (30, 70), (34,

66), (38, 62), (42, 58), (46, 54).

Therefore, 

S = {2, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50}

∴ The maximum possible number of elements in S be 13.

then projection of vector a on vector b is given by :

If 2 tan^-1 (cos x) = tan ^-1(2 cosec x),

2tan^-1(cos x) = tan^-1 (2 cosec x)

= tan^-1(2 cosec x) 

= cot x cosec x = cosec x = x = π/4

(i.e. angle subtended at the centre of a circle is double the angle subtended in the alternate segment).
Hence (c) is the correct answer.

All the elements in set-A are presented in set-B. So "A" is a subset of "B".

Concept:

The null set is a subset of every set. (ϕ ⊆ A)

Every set is a subset of itself. (A ⊆ A)

The number of subsets of a set with n elements is 2ⁿ.

The number of proper subsets of a given set is 2n - 1

Calculation:

Statement I: If A = {x: x is an even natural number} and B = {y: y is a natural number}, A subset B.

A = {2, 4, 6, 8, 10, 12, ...} and A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, ...}.

It is clear that all the elements of set A are included in set B.

So, set A is the subset of set B.

Statement I is correct.

Statement II:  Number of subsets for the given set A = {5, 6, 7, 8) is 15.

Given: A = {5, 6, 7, 8}

The number of elements in the set is 4

We know that,

The formula to calculate the number of subsets of a given set is 2ⁿ

 = 2⁴ = 16

Number of subsets is 16

Statement II is incorrect.

Statement III: Number of proper subsets for the given set A = {5, 6, 7, 8) is 15.

The formula to calculate the number of proper subsets of a given set is 2ⁿ - 1

 = 2⁴ - 1

 = 16 - 1 = 15

The number of proper subsets is 15.

Statement III is correct.

∴ Statements I and III are correct.

 By formula 
Sn = n/2(a+l)

Slope of the normal is given to be -1. We know that, foot of the normal is (am², -2am). Here a = 2, m = -1. Hence the required point is (2, 4). 

Gen equation of a circle is (x−h)²+(y−k)²=r² (3,0),(1,−6),(4,−1) circle passes through these points
∴ These three points should satisfy the equation
of circle.
(3−h)²+k²=r² ___ (I)
(1−h)² +(−6−k)² = r²(1−h)²+(6+k)²=r²  ___ (II)
From (I) & (II)
(3−h)²+k² =(1−h)²+(6+k)²
9+h²−6h+k² =1+h² 2h+36+k²+12k
9−6h=1−2h+36+12k
9−37=4h+12k
−28=4h+12k
h+3k=−7
h=−7−3k ___ (III)
(4−h)²+(−1−k)²=r² ___ (IV)
From (I) & (IV)
(3−h)²+k² = (4−h)² +(1+k)²
9+h² −6h+k²
 =16+h² −8h+1+k²+2k
9−6h=17−8h+2k
9−17=−2h+2k
−8=−2h+2k
−h+k=−4
k=−4+h ___ (V)
Put (V) in (III)
h=−7−3(−4+h)
h=−7+12−3h
h=5/4,k=−11/4,r=170/16
Eq of circle: (x−5/4)² +(y+11/4)² =170/16
x²+25/16−10x/4+y² +121/16+22y/4=170/16
Simplifying, we get 2x²+xy²−5x+11y−3=0

z = -i
Comlex number z is of the form x + iy
x = 0, y = -1
arg(z) = π − tan−1|y/x|
⇒ π − tan−1|-1/0|
= π - (π/2)
⇒  π - π/2
⇒ π/2

n (P) = 5, n(Q) = 12 and n(PUQ) = 14
n(PUQ) = n(P) + n(Q) - n(P∩Q) 
14 = 5 + 12 - n(P∩Q)
n(P∩Q) = 3

Probability of not getting a head = 1/2
Probability of getting at least one head in n tosses is > 0.8 (given)
⇒ 1 -P (getting no head) > 0.8


Putting values for n, we see that the least value of n satisfying (1) is n=3.

The chord of a parabola through the focus and perpendicular to the axis is called the latus rectum.

Let original equation be  x² + ax + b = 0 from the given –a = 5, b = –6 

tan⁻¹ x = θ , so that  x=tanθ . We need to determine  cosθ .
sec²θ = 1 + tan²θ = 1 + x² 
∴s ecθ = ±√(1+x²) 
Then, cos(tan⁻¹x) = cosθ=1/secθ = ±1/√(1+x²)

Degree of a differential equation, when the equation is polynomial equation in y′ isHighest power (positive integral index) of the highest order derivative in the given differential equation.

n(A × B) = n(A) × n(B)