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

Here, a = x³y² and b = xy³.
⇒ a = x _* x _* x _* y _* y and b = xy _* y _* y
∴ LCM(a, b) = x _* x _* x _* y _* y _* y = x³ _* y³ = x³y³
LCM = x³y³

If  2k-1,k+2,2k are in AP, the difference of two consecutive terms will be same.
Therefore,

We have to find the value of

The probability of a sure event is always 1.

Mode is the most frequently occurring observation. Since it's not a grouped data the frequency is the occurrence of only one observation , So the highest no. of frequency is 7 . So the modal age is 13.

Let p(x) = 2x² − k
Since, (2x+5) is a factor of p(x), then by factor 
theorem,

Since, AC ⊥ BC, then ∠C = 90°

sin 30 =AC/AB = 4/AB  
1/2=4/AB
AB=8

= 1 x 4 / 8

= 1 / 2

p(x) = x² + (a + 1)x + b
Given: zeros of polynomial is 2, -3
For x = 2
(2)² + (a + 1)² + b = 0
⇒ 4 + 2a + 2 + b = 0
⇒ 2a + b = -6 ...(i)

For x = -3
(-3)² + (a + 1) (-3) + b = 0
⇒ 9 - 3a - 3 + b = 0
⇒ -3a + b = -6 ..(ii)

Solving (i) and (ii), we get 5a = 0
⇒ a = 0 and b = -6

Alternative method:

p(x) = x² + (a + 1)x + b
Given: zeros of polynomial is 2, -3

Sum of zeros: -(a+1) = 2-3
⇒ a = 0
Product of zeros: b = 2.(-3) = -6 

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.

x² - 0.09 = 0
x² = 0.09
x = √0.09
x = 0.3

 Given, ratio of angles of quadrilateral ABCD is 3 : 7 : 6 : 4.
Let angles of quadrilateral ABCD be 3x, 7x, 6x and 4x, respectively. We know that, sum of all angles of a quadrilateral is 360°.
3x + 7x + 6x + 4x = 360°
=> 20x = 360°
=> x=360°/20° = 18°

sum of root = -b/a
for (3) option sum of roots will be -(3)/(-1) = 3

Zeros of the polynomials are the values which gives zero when their value is substituted in the polynomial
When x=2,
x²+ax+b =(2)²+a*2+b=0
4+2a+b=0
b=-4-2a    ….1
When x=3,
(3)²+ 3a + b=0
9 + 3a + b=0
Substituting 
9 + 3a - 4 - 2a =0
5 + a =0
a = -5
b = 6

Suppose be all twelevth terms = x
Mean = Terms / Observation
19 . 25 = x / 12
x = 19.25 × 12
x = 231 .00

Now let thirteenth term will be y
Mean = 20
So, 20 = x + y / 13
20 = 231 + y / 13
20 × 13 = 231 + x
260 = 231 + x
260 - 231 = x
29 = x

The area should be 144π,
 ,Area of the circle= πr²
144π = πr²
r = 12cm
Circumference=2πr = 24πcm

The mode of a set of data values is the value that appears most often.it is the value that is most likely to be sampled This means mode is the observations whose frequency is highest. So it does not pay attention to what is the maximum value or the minimum value . So it is not affected either by maximum or minimum values and its not affected by both as well.

693 = 3×3×7×7
567 = 3×3×3×3×7
441 = 3×3×7×11
Therefore H.C.F of 693, 567 and 441 is 63.

Interpersonal communication is the process by which people exchange information, feelings, and meaning through verbal and non-verbal messages: it is face-to-face communication. Emotions result from outside stimuli or physiological changes that influence our behaviors and communication.

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.

If a teacher believes that each child is unique and a special individual, and therefore actively involves them in their own education and development.

The teacher is adopting a child-centric education. In this approach, the ‘learner’ or ‘child’ is the main focus of the educational programme. It emphasizes ‘learning’ rather than ‘teaching’.

Child-centric education advocates that-

• accommodate the individual difference and unique character of each individual learner
• each individual’s growth presents a different range of problems and requirements,
• at every stage from the womb to tomb” implying that the child’s individuality and dignity should be respected and his/her needs, interests, aptitude. So that two individual provided opportunities to grow and realise their potentials in the same class.
• Teacher adopts a variety of teaching-learning strategies to address the needs of all children at the same time.
• Varieties of activities/opportunities are available in the classroom, which enables each child to learn at her/his own pace and in tune with her/his own learning style. 

Here it is clear that if a teacher believes that each child is unique and a special individual, and therefore actively involves them in their own education and development. The teacher is adopting a child-centric approach to learning. 

Additional Information

In a child-centred classroom-

• The child is not a passive but an active participant in the classroom process.
• Reflects planning of teaching-learning and its monitoring jointly by teacher and children
• Evaluation of the child’s attainment is done to ensure the child’s progress and not as a means of passing judgement on the child’s abilities and achievement. it is diagnostic as well as remedial.

A learner-centered approach places the learner at the center of the learning process, emphasizing active engagement and personalized learning.

Key Points

• Activity-based scaffolding is an approach to teaching that involves breaking down complex tasks into smaller, more manageable parts and providing support as needed to help students develop the skills they need to complete those tasks independently.
• Activity-based scaffolding is particularly effective for helping students develop complex skills and knowledge.

Thus, it is based on  is based on the learner-centered approach of Education.

Additional Information

• Lecturing-demonstration is a teaching method in which the teacher presents information to the students, often using visual aids or hands-on demonstrations.
• Joyful method is not a commonly used term in education, but it may refer to teaching methods that emphasize fun and engagement in the learning process.
• Inductive method is a teaching method that involves presenting specific examples and then drawing general conclusions based on those examples.

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

Activity-based learning refers to learning through hands-on experience to develop an understanding of the environment around us. An activity is an action performed by the students to understand their environment and the environmental processes. 

Key Points

•  Activity-based learning is a form of Learner-centered approach. It stimulates curiosity and independent thinking, develops problem-solving skills, promotes planning and execution of projects, and develops self-learning involving the acquisition of knowledge through observation of phenomena, and creative thinking abilities.
• Tuition -Centric approach - This approach does not exist.
• Teacher-Centric approach - It emphasizes the importance of a teacher and ignores the active involvement of the learner in the teaching-learning process.
• Subject-Centric approach - It focuses on the subject matter and acquiring the subject knowledge through textbooks and resources available to be a master in the subject rather than the development of the child.

Hence, option 2 is the correct solution.

Important Points 

• In a learner-centered approach, the Learner is at the center of all activities and the teacher plays the role of a facilitator of the learning process and an organizer of the learning situation.
• The learner brings with him/her previous knowledge and experiences which influence the classroom learning process.
• In this approach, the focus is given on developmental stages, maturity, learning strategies, prior knowledge and experiences, interests, social context, and culture of the learner.
• The teacher must understand the learner and their learning styles to know in detail the characteristics of each and every learner in our classroom.