Bihar STET Paper 1 Mathematics Mock Test - 8 - Bihar PGT/TGT/PRT MCQ

a₁=-3,
a₂=4,
d=4-(-3)=7,
a₂₁=?,
a₂₁=a+(n-1)d
=-3+(21-1)7
= -3+(20)(7)
= -3+140
=137

We have circumference which is equal to the boundary of the circle. So we have one revolution equal to circumference of the circle which is equal to 4
Distance covered by the roller=circumference of the roller*number of revolutions
⇒ number of revolutions = distance covered by the roller/circumference of the roller
= 40/4 = 10

cos²θ = 3(cot²θ-cos²θ)
4cos²θ = 3cot²θ
4=3(1/sin²θ)
sin²θ = 3/4
sinθ = √3/2
θ = 60

a₃ = a + 2d = 600 …(i)

a₇ = a + 6d = 700 …(ii)

Subtracting (i) from (ii),

d = 25

Put value of d in (i), we get

a = 550

Boundaries of surfaces are known as curves whereas boundaries of solids are known as surfaces. Therefore, the boundaries of surfaces are curves.

∠LQ = ∠MNR,

∠Q = ∠R

QM = MR,

Hence, ΔQLM ≅ ΔMNR (by AAS)

There are 366 days in a leap year, i.e, 1 more than a normal year.

Now, 52 weeks make up 344 days (52 x 7 = 344)
That means that we already have 52 sundays for sure.

Then, we are left with 2 days. Now, these days can be any from a pair of- mon-tues,tues-wed,wed-thurs,thurs-fri,fri-sat,sat-sun,sun-mon. Here favourable cases are sat-sun and sun-mon i.e, 2 cases and total number of cases is 7.

So, Probability=number of favourable cases/Total number of cases.

Therefore, Probability= 2/7.

Let, p(x) = x²-10x+k
since, 8 is the root of p(x)
∴ p(8) = 0
8²-10(8)+k = 0
64-80+k = 0
-16+k = 0
⇒ k = 16 .

k(x – 10) (x + 10) =0
⇒ either k=0
Or x-10=0
Or x+10=0
Since we don’t know the value of k 
So either x-10=0
x=10
Or x+10=0
x=-10
So values of x can be 10,-10

Arithmetic progression is a sequence of numbers such that the difference of any two successive members is a constant,d
AP is x, y, 2, 4, 6, 8,…
So we have 4-2=2,6-4=2 so we have d=2
So y=2-2=0
And x=0-2=-2

The way in which students bring their finding to others and apply their understanding to new and unfamiliar circumstances, grows out of excitement for what they have accomplished. Student would be excited to reveal his finding.

By physically conducting experiments and recording outcomes, students actively participate in the learning process, making it more meaningful and memorable.

Key Points

• Through this hands-on approach, students develop a concrete understanding of probability concepts like sample space, equally likely outcomes, and relative frequency.
• They observe patterns and begin to grasp the concept of probability intuitively.
• This activity also encourages critical thinking as students analyze the data they collect and draw conclusions about the likelihood of different outcomes.
• Moreover, the activity promotes teamwork and communication skills as students discuss their findings and observations with their peers.
• It creates an interactive and dynamic learning environment, fostering curiosity and a deeper appreciation for mathematics.

Hence, it can be concluded that Asking students to throw a dice or flip a coin and note down the number of times each possibility occurs is the best approach.

Learners Characteristics:

• The concept of learner's characteristics is used in the science of learning and cognition to designate a target group of learners and define those aspects of their persona, the academic, social, or cognitive self that may influence how and what they learn.
• Learners' Characteristics are important for an instructional designer as they allow them to design and create tailored instruction for a target group. It is expected by taking into account of the characteristics of learners, more efficient, effective, and/or motivating instructional materials can be designed and developed.
• Learners' Characteristics can be: Personal, Academic, Social and emotional, and Cognitive.

Important Points

One of the important characteristics that is highly related to the effectiveness of teaching is

1. Prior experience of the learner:

• Prior experience of the learner is based on the learner's Academic characteristics. 
• To facilitate learning, one of the fundamental principles instructors employ is understanding students' prior knowledge.
• It is also important to assess prior knowledge and skills early since such information could be used to help foster student engagement and critical thinking in the course.

​Key Points

Other characteristics that affect the learning experience of the learner are:

1. Educational status of the parents of the learner:

• This is based on the learner's characteristics.
•  Parents play an important role in their children's learning.
• Aside from being actively involved in their children's education, parents also provide a home environment that can affect learning.

​2. Peer groups of the learner: 

• The term peer learning refers to situations where peers support each other in learning processes.
• Peer learning occurs among peers from similar social groupings, who are not professional teachers, helping each other to learn and in doing so, learning themselves.

​3.  Family size from which the learner comes:  

• Large numbered families whether rich or poor are difficult to maintain, they are characterized by a high number of children this does not create convenience for learning.
• They also create in the upbringing of children some identified problems such as feeding, poor clothing, insufficient funds, lack of proper attention for children, disciplinary problems, and malnutrition which impact negatively children's academic performance.​

Therefore, the prior experience of the learner is highly related to the effectiveness of teaching.

Learning is defined as a process of behavior modification through experiences, exercise, and efforts. Learning occupies a very important place in our life. It provides a key to the structure of our personality and behavior. Experience, direct or indirect, plays a very important and dominating role in molding and shaping the behavior of the individual from the very beginning.

Students feel humiliated being criticised by a teacher in front of their peers. So, handling discipline issues without an audience allows for better, more genuine exchanges, since the student responses will not be witnessed by classmates.

Teachers play the most crucial role in moulding the behaviour of learners. This shaping of behaviour is achieved through planning and dedication.

The Primary duties of a teacher include:

• to achieve all-round development of students by guiding the students in their learning process.
• to provide motivation for learning.
• to stimulate learners in order to realize their optimum potential.
• to plan the teaching and learning process to suit the needs of the students.
• to promote learning by providing a conducive environment.
• to encourage learners to become active learners.

​Although imparting knowledge and values into the students are important duties of a teacher. However all round development of students is the most important and vital duty of a teacher.

Thus, the primary duty of the teacher is to help in all round development of the students.

Mrs. Sharma makes her assessment useful and interesting by using various ways to collect the information. Each way provides a different piece of information or same information with some additional inputs. For example, a written question paper gives us the idea of the person's knowledge, an oral assessment gives us an idea of the person's verbal ability and articulation, and activities may prove useful in testing child's ability to apply the knowledge practically. Activities also make assessment interesting for children.

Learning disabilities are neurologically-based processing problems. These processing problems can interfere with learning basic skills such as reading, writing and/or math. They can also interfere with higher level skills such as organisation, time planning, abstract reasoning, long or short term memory and attention. They are not caused due to the method of teaching used by the teacher. They may be present due to improper brain development, or infection in brain, etc. Constant fights amongst parents also lead to mental strain and anxiety in students, which may lead to learning disabilities.

Kinesthetic/tactile persons learn best through a hands-on approach, actively exploring the physical world around them. Thus, using the hands-on approach may not help Sita much.

The Correct Answer is Option 1 i.e Tomara Rajputs.

• Tomara Rajputs (8th Century -12th Century):
  • Anangapala was considered to be the founder of this dynasty.
  • Delhi became the capital of a kingdom for the first time under the Tomara Rajputs.
  • They were defeated by Chauhans in the middle of the twelfth century.
  • The name of Anangpala is inscribed in the Iron Pillar of Delhi. 
• Chauhans (1165-1192):
  • Prithviraj Chauhan was the most important ruler of this dynasty.
  • In the first battle of Tarain 1191 AD, he defeated Muhammad Ghori.
  • In the second battle of Tarain 1192 AD, he was defeated by Muhammad Ghori.
•  Aurangzeb (1658-1707):
  • He was the sixth Mughal Emperor.
  • He executed the ninth Sikh guru Guru Tegh Bahadur in 1675 AD.
  • He re-imposed Jaziya in 1679 AD.

South Korea experienced a further decline in its fertility rate, reaching a record low of 0.72 in 2023. This exacerbates concerns about population decline and highlights socio-economic factors influencing birth rates, such as career advancement concerns and financial burdens.

The activity will help the students to gain first-hand experience. This helps in better retention of the concepts.

Complement of 30°20′ = 90° – ( 30°20′ ) = 90° – ( 30° + 20′ )
= (89° – 30°) + (1° – 20′)
= 59° + 60′ – 20′ [ ∴ 1° = 60°′]
= 59° + 40′ = 59°40′.