Bihar STET Paper 1 Mathematics Mock Test - 10 - Bihar PGT/TGT/PRT MCQ

The given AP is x – 7, x – 2, x + 3 …
So a= x-7, d=x - 2- x + 7 = x + 3 - x +2 = 5
l = a + (n - 1)d
=x - 7 + (15 - 1)5
=x - 7 + 70 = x + 63

The degree of zero polynomial is not defined, because, in zero polynomial, the coefficient of any variable is zero i.e., Ox² or Ox⁵, etc. Hence, we cannot exactly determine the degree of the variable.  

 The correct answer is a.

Distance between two points (x1,y1) and (x2,y2) can be calculated using the formula −

Distance between the points (p,−5) and (2,7)=

(2−p)2  +(7−(−5)) 2 =13 

(2-p)2 + 144 = 13

(2-p)2 + 144 = 169

(2-p)2  = 25

2-p = 5  or 2-p = -5

p = -3 or p = 7

For forming a triangle sum of any two sides must be greater than the third side.

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

so:    2x=80

so x=40 

⇒

⇒

⇒ r = 21 cm, which is true.

The reason is also true but it doesn’t explain the assertion as the formula given is of cylinder.

Therefore, Both A and R are true and R is not correct explanation for A.

X+ 1/x = 7 then,
cubing both side
= (x +1/x)³ = (7)³
= x³ + 1/x³ + 3×x×1/x×(x+1/x) = 343
= x³ +1/x³ +3(7) = 343
= x³ +1/x³ +21 =343
= x³ +1/x³ =343 - 21
= x³ +1/x³ = 322

The degree refers to the highest power of the polynomial. In this polynomial X has highest power 4.So the degree of polynomial is 4.

2. Coincident

• Coincident Lines: Two lines are coincident if they are exactly the same line, meaning they have the same slope and y-intercept. In other words, they overlap completely.
• For the given equations:

•  Because the y-intercepts are different, the lines are not coincident.

3. Intersecting

• Intersecting Lines: Two lines are intersecting if they cross each other at exactly one point. This happens when the lines have different slopes.
• 

4. Perpendicular to Each Other

• Perpendicular Lines: Two lines are perpendicular if the product of their slopes is −1-1−1. In other words, if the slopes are negative reciprocals of each other.

Let the number of wickets taken by Srinath be x then the number of wickets taken by Kumble will be 2x−3

According to question, x (2x−3) = 20

⇒ 2x²−3x−20 = 0

⇒ 2x²−8x+5x−20 = 0

⇒ 2x(x−4)+5(x−4) = 0

⇒ (x−4)(2x+5) = 0

⇒ x−4 = 0and 2x+5 = 0

Therefore, number of wickets taken by Srinath is 4.
Then number of wickets taken by Kumble = 2 x 4 - 3 = 5 

a₆ = a + 5d = 30

= 11 × 30 = 330

Also, Sum of first n terms of an A.P is given by is last term(Here we can’t apply this formula as no last term is mentioned in the statement.)

Therefore, A is true but R is false.

Slow learners learn the concepts at a lower pace than other students leading to delay in their work. One of the best methods that can help them is self exploring the things. This will lead them to understand things better.

Questions take learning forward by interactions and lead to conceptual clarity. Thus, students should be encouraged to ask the questions. Question-asking puts advanced cognitive demand on students. It encourages students to think beyond literal questions.

It is very important that the teacher has complete understanding of her subject so that each concept can be clearly explained to the students.

The term 'micro teaching' was coined by Dwight Allen of the Stanford University. This is an innovative teacher training technique and focuses on developing teaching skills. This is highly individualised training skill. Micro teaching can also be defined as a teaching technique especially used in teachers' pre-service education to train them systematically by allowing them to experiment main teacher behaviours. By the help of this technique, teacher candidates can experiment and learn each of the teaching skills by breaking them into smaller parts and without encountering chaotic environment of the crowded classes.
In the original process, a teacher is asked to prepare a short lesson (usually 20 minutes) for a small group of learners who may not have been his/her own students. This is then recorded on video. After the lesson, the teacher, teaching colleagues, a master teacher and the students together view the video recording and comment on what they see happening, referencing the teacher's learning objectives. Watching the video and getting comments from colleagues and students provide teachers with an often intense "under the microscope" view of their teaching.

Creative Learner:

• Creative children are those who exhibit creativity. Creativity is the ability to adopt an innovative approach to solving a problem, to cope with ideas that are both relevant and unusual, to go beyond the immediate situation to redefine the problem. 
• The creative children are those who show high-performance capability in several areas such as artistic and creative work, leadership quality, keen power of observation, etc.

Key Points

Characteristics of Creative learner:

• A creative learner can make unusual associations or connections between seemingly unrelated or remote ideas They can rearrange elements of thought to create new ideas or products.
• Also, they pose many ideas or solutions to problems.
• They display intellectual playfulness, fantasize, imagine, and daydream. Also, a creative learner doesn't need to have a high IQ. 
• They are good at lateral thinking and problem-solving. Creativity is associated with lateral thinking for the generation of new ideas.
• These children have divergent thinking and are very curious in nature that's why sometimes the classroom seems monotonous to them because they grab things fastly than their age-peers.
• Divergent thinking in creativity leads to a broadening of the definition and criteria of the problem to generate a wide variety of possible solutions. 
• The creative learner has personality traits such as sensitivity to problems, fluency, flexibility, originality, ability to transform meaning, and ability to elaborate.

Hence, we can conclude that a creative learner refers to one who is good at lateral thinking and problem-solving.

The child with Special Need: Also known as a specially-abled child, a child with special needs is the one who needs special attention and requires necessities that other children do not. There are many types of special needs one of which is for visually impaired children.

• A visually challenged child is the one who has a problem seeing with the naked eyes or is not able to see completely.

Important Points

Instruction adaptations that a teacher can follow while working with students who are ‘visually challenged’ are:

• Should speak clearly and audibly to help them learn through listening or auditory learning
• Use a lot of touches and feel materials.
  • Make use of material adaptations according to the individual needs, the actual degree of functional vision, presence of any other disabilities
  • Using a variety of tactile materials like rough or smooth, cold or hot, wet or dry, vibrate or stationary helps the students to touch, feel, and understand the differences between the materials
• Break the entire learning process into smaller units
• Provide ample time for the challenged learner to learn in his/her own way
• Provide support and independence wherever necessary
• Braille, tactile symbols, large prints, recorded materials, etc. can be used as teaching aids for visually challenged learners
• A touch and feel tool for the visually challenged person

Hence, we can conclude that a teacher should speak clearly and use a lot of touches and feel materials while working with students who are ‘Visually Challenged’.

Cooperation teaches the values of committing oneself to the common good, seeing success as depending on the efforts of all participants, feeling happy when others succeed, seeing others as resources to help one succeed, viewing worth as unconditional, and viewing diverse others in positive ways.
Cooperative learning is a teaching way for students to learn essential interpersonal life-skills and develop the ability to work collaboratively, a skill now greatly in demand in the workplace. Thus, it provides faster and efficient learning. In cooperative learning, the diverse students in the school are to be transformed into a symphony. Students need positive self-esteem, the psychological health to face conflict and challenge, and the social competencies required to work effectively with diverse peers. Personal and superordinate identities are developed through group processes.

Herbart advocated five formal steps in teaching:

1. Preparation—a process of relating new material to be learned to relevant past ideas or memories in order to give the pupil a vital interest in the topic under consideration;
2. Presentation—presenting new material by means of concrete objects or actual experience;
3. Association—thorough assimilation of the new idea through comparison with former ideas and consideration of their similarities and differences in order to implant the new idea in the mind;
4. Generalisation—a procedure especially important to the instruction of adolescents and designed to develop the mind beyond the level of perception and the concrete;
5. Application—using acquired knowledge not in a purely utilitarian way but so that every learned idea becomes a part of the functional mind and an aid to a clear, vital interpretation of life. This step is presumed possible only if the student immediately applies the new idea, making it his own.

A teacher should take care of each child irrespective of their disabilities. He/she should ensure the students' maximum potential. Everyone has the right to education. A teacher should ensure that his/her students derive maximum benefit from education. 
Teachers must be aware of the fact that every child is different from each other. The differences occur from physical characteristics to learning styles. The objective of education is to provide the fullest possible development of learners. The teachers should find out the different strengths and weaknesses of students before their disabilities.
Hence, the correct answer is, 'Mohan, why don't you use your crutches to go to the playground?'

Best speech habits are developed in language labs. Thus, to develop good speech habits in the learners, he should exploit language labs. Language labs involve students in language learning exercises more actively and also let them participate more as compared to a traditional classroom setting.

Activity-based learning is a ‘learner-centred’ approach in the teaching-learning process. In this approach, the ‘learner’ or ‘child’ and not the ‘teacher’ is the main focus of the educational program. It emphasizes ‘learning’ rather than ‘teaching’.

• Activity-based learning integrates multiple methods of teaching like Demonstration, Role-play, Brainstorming, Project method, Debate, etc.
• Activity-based learning brings the real issues and problems from day-to-day life in classroom settings.
• It provide provides opportunities to apply multiple senses.
• It includes all objects, events, natural phenomena and social surroundings in the teaching-learning process.
• It clarifies abstract concepts, develops concrete thinking and brings reality in real settings.
• During activity-based learning, the learners use his/her multiple senses to understand the concepts and enhance learning.
• It arouses the child’s interests, abilities, and needs during the learning process.

Hence, we conclude that all the above points are the advantages of the activity-based learning.

Practice-based learning is more than 'learn the theory then go to work. ' With practice-based learning, students combine theory and work experience with a strategic, reflective process throughout the duration of your learning. Students don't just learn the theory first, then jump into the classroom and apply it afterward. Key Points

Advantages of practical teaching method

• Practical-Learning assists students in identifying their real interests and choose a career accordingly.
• Makes the learner practically work to achieve the goal.
• Provides Basic Skills for Students. Practice and drills give students an opportunity to learn certain concepts quickly and effectively.

Hence, we can conclude that in practical teaching method does the learner practically work to achieve the goal.Additional Information

An Se-young of South Korea won the gold medal in the women's singles event at the 2023 World Badminton Championships, defeating Carolina Marín of Spain in the final, 21-12, 21-10. An Se-young, aged 21, became the first woman from South Korea to win the world singles title. She had a dominant tournament, winning all of her matches in straight games, including victories over Olympic champion Chen Yufei and two-time world champion Akane Yamaguchi.

18% of x = 13.50% of y

50% of x = 37.50% of y
Hence, Option D is correct.

Preparing the family tree using the following symbols:

On decoding L θ Z β T means L is the mother of Z and Z is the sister of T.

i) L is mother of T → True
ii) L is father of T → False (as L is mother of T) 
iii) T is father of L → False (as T is either son or daughter of L)
iv) Z is daughter of T → False (as Z is sister of T)
Hence, 'L is mother of T' is the correct answer.