Bihar STET Paper 1 Mathematics Mock Test - 6 - Bihar PGT/TGT/PRT MCQ

A circle divides the plane on which it lies into three parts:
(i) Inside the circle, which is also called the interior of the circle.
(ii) The circle
(iii) Outside the circle, this is also called the exterior of the circle.

The circle and its interior make up the circular region.
 

Since if a circle inscribed a square. then the radius of the circle is half of to side of square.
∴  Radius = 10/2 = 5 cm
∴ Area of the circle = πr² = π(5)² = 25π sq. cm 

if a,b,c are in AP, then b − a = c − b

a + c = 2b

For 1/bc, 1/ac, 1/ab ​

= 1/ac - 1/bc = b - a / abc

1/ac - 1/ac = c - a/abc

From above two equations,

1/bc, 1/ac, 1/ab ​ are also in AP.

And their common difference is divided by abc since numbers are also divided by abc.

So, if a,b,c are in AP and you divide the numbers by their product abc they will remain in AP.

The denominator 2⁶ x 5² is of the form 2^m x 5ⁿ, where m and n are non-negative integers. Hence, it is a terminating decimal expansion.

d=60
so r=30
l=√r²+h²
l= √30²+40²
l=50

Given: Angle of elevation θ = 60°
Let the height of the tower AB be hmeters.
And the length of the shadow BC is 30 meters.

Therefore the hieght of the tower is 30√3 meters.

It is given that,
∠POQ =110°
Since, the Iangent at any point of a circle is perpendicular to the radius through the point of contact.
∴ ∠OPT = 90°
and ∠OQT = 90°
Now, in quadrilateral POQT.
∠POQ + ∠OQT + ∠PTQ + ∠OPT = 360°
(angle sum property of quadrilateral)
⇒ 110° + 90° + ∠PTQ + 90° = 360°
⇒ ∠PTQ + 290° = 360°
⇒ ∠PTQ = 70°
Hence, right option is (B).

p(x) = ax
p(x) = 0
ax = 0
x = 0/a
x = 0
{0 by something is equals to 0}
Therefore,0 is the zero of the polynomial. 
Checking:-
p(0) = a(0)
= 0

∠BOA = 120° (Given)
∠AOC = 60° (Linear Pair)

In triangle OAC,
OA = OC (Radii of same circle)
∠OAC = ∠ OCA = x (angle opposite to equal sides are equal)
∵ ∠A + ∠C +∠O = 180°
⇒ x + x + 60 = 180°
⇒ 2x = 120°
⇒ x =60^o

Let,angle= θ
(asinθ + bcosθ)/(asinθ - bcosθ)
Dividing both numerator and denominator from cosθ
We get,
atanθ +b/atanθ - b
= ( a.a/b + b) /(a.a/b - b) =(a²/b +b)/(a²/b - b)
=(a² + b²/a²- b²) 

⇒ cos A = cos 60°

⇒ A = 60°

Then, 9 cot² A – 1 = 9(cot 60°)² – 1

= 2

We have as the roots which means x + and x- are the factors of the quadratic equation. Multiplying x+ and x- and applying a²-b² we get the equation x²-5.

-3 is root of both

2(9) -3p -15 = 0

p = 1

and

second equation has two equal roots so, 

b²-4ac = 0

p² = 4pq

p = 4q

q = 1/4

 Let p (x) = 5x – 4x2 + 3 …(i)
On putting x = -1 in Eq. (i), we get
p(-1) = 5(-1) -4(-1)2 + 3= - 5 - 4 + 3 = -6

Inclusion as a philosophy or practice cannot be discussed meaningfully unless it is situated in the context of diversity across the members of the group, especially in the framework of inclusive education. 

Key Points

• Inclusive education means creating effective classrooms where the educational needs of all children are addressed irrespective of ability or disability.
• It implies all learners, young people - with or without disabilities being able to learn together through access to common pre-school provisions, schools, and community educational settings with an appropriate network of support services.
• Social inclusion refers to a process by which efforts are made to ensure equal opportunities for all, regardless of their background, be it money, class, ethnicity, gender, race, or whatever the index of diversity be, to enable full and active participation in all aspects of life, including civic, social, economic, and political activities, as well as participation in decision-making processes.
• Social inclusion can be approached as a goal, an objective, and a process. Its process affects almost all societal activities, and should therefore be approached from various dimensions.
• Hence, the effort for quality-based inclusive education for all should be a Child-centered, relevant, and justified process of learning in a social context so that is not affected by social barriers and get an equal opportunity to learn and develop in life.

​Thus, it is concluded that a Child-centered, relevant, and justified process of learning in a social context will be the effort for quality-based inclusive education for all.

Hint

• Sensitivity towards all the needs of the children comes under child-centered education. The teacher must take care and be sensitive towards the children.
• Improvement in self qualification and teaching methodology: Teacher will improve themselves and their methodologies to impart quality education to children. This is also a part of child-centered education.
• School should be complete with all the high technology instruments to impart quality, relevant and justified education to children.

Playing games along with studies in school is very important for the physical growth and balance of the children. It also develops in them qualities like cooperation and spirit of teamwork to work with each other.

The rate of development of an individual child is different from that of another child. This principle is known as the ‘principle of individual differences’. For instance, some children may learn to walk in 8 months, while some may take more than a year to start walking. 

It is important for teachers to know variables such as physical characteristics, intelligence, perception, gender, ability, learning styles, which are individual differences of learners. An effective and productive learning-teaching process can be planned by considering these individual differences of students.

Learning takes place by comparing previous knowledge and experience with the present learning experience through thinking and activities. Learning is a universal skill seen in all species. Thinking and Learning are two interwoven activities that help to develop knowledge, critical thinking, and creative thinking.

Key Points

•  Despite the addition of more specialized disciplines and subject instructors, experiential learning within each subject and investigations of relationships among different subjects will be encouraged and highlighted.
• Experiential learning will be implemented at all levels, with investigations of the connections between various disciplines as well as hands-on learning, education that incorporates the arts and sports, and pedagogy centered on telling stories, among others, as normal practices within each subject.
• Classroom activities will change to competency-based learning and teaching to address the achievement gap in learning outcomes. Additionally, the assessment instruments—including assessment "as," "of," and "for" learning—will be in line with the learning objectives, skills, and attitudes that are listed for each subject in a given class.
• Each subject's curriculum will be edited down to the fundamentals in order to allow room for critical thinking and more all-encompassing, inquiry-based, discovery-based, discussion-based, and analysis-based learning.

Hence, National Education Policy 2020 proposes that experiential learning should be encouraged to promote critical thinking. 

The NRF (National Research Foundation) will be governed, independently of the government, by a rotating Board of Governors consisting of the very best researchers and innovators across fields.

Key Points

•  The goal of the NRF will be to enable a culture of research to permeate through our universities.
• The primary activities of the NRF will be to:
  •  fund competitive, peer-reviewed grant proposals of all types and across all disciplines.
  •  seed, grow and facilitate research at academic institutions.
  • act as a liaison between researchers and relevant branches of government as well as industry; so as to allow breakthroughs to be optimally brought into policy and/or implementation.
  • recognize outstanding research and progress.

Thus, it is concluded that According to NEP‐2020, National Research Foundation (NRF) may be established to enable a culture of research to permeate through universities.

Multiple means of discrimination is not a part of universal design for learning guidelines.

NEP 2020 emphasizes a flexible and creative National Curriculum Framework (NCF) to promote a more innovative and engaging learning experience.

Brainstorming is a creative group work in which group members produce large number of ideas quickly on a given topic or problems for subsequent evaluation. In this method, anyone can exchange remarks with anyone except that the participants are not allowed to criticize the ideas. Sometimes, quantity of ideas is more important than quality. Spontaneity is the hallmark of brainstorming sessions. On the spot ideas are expected.

Action research in education can be defined as the process of studying a school situation to understand and improve the quality of the educative process. It is an attractive option for teacher researchers, school administrative staff, and other stakeholders in the teaching and learning environment to consider. . It provides practitioners with new knowledge and understanding about how to improve educational practices or resolve significant problems in classrooms and school. 

The National Medical Commission (NMC) is all set to launch its “one nation, one registration platform” for doctors across India. The NMC will unveil a patch pilot of the National Medical Register (NMR) in the next six months, where doctors will be allotted a unique identification number.

x% of a = y% of b
z × x% of a = z × y% of b

Hence, Option C is correct.

(The volume of cube = side³)
The ratio of sides = ∛8 : ∛27 = 2 : 3
Hence, Option B is correct.

According to the sequence in the dictionary: 

The correct order of the given words is:

2. Arrange

1. Arrest

3. Arrogant

4. Arrow

Hence, the correct answer is "2, 1, 3, 4".

Additional Information

1. First of all, check the common letter in all.

2. Arrange them according to the alphabet they come first. 

3. When common letters are arranged, then go for the rest.