DSSSB TGT Mathematics Mock Test - 3 - DSSSB TGT/PGT/PRT MCQ

Explanation:

• Matching Type Terms: In matching type questions, the number of choices to select from is limited, which reduces the probability of guessing correctly. This makes it less likely to guess the correct answer by chance.



• True-False Terms: In true-false questions, there are only two possible answers, making it easier to guess the correct answer by chance. The probability of guessing correctly in true-false terms is 50%, which is higher compared to other question types.



• Multiple Choice Terms: In multiple choice questions, the number of options to choose from varies, but it generally provides more choices than true-false questions. However, the probability of guessing correctly in multiple choice terms is lower than in true-false terms.



• None of these: This option suggests that none of the given choices have a higher possibility of guessing correctly. It implies that the correct answer may not be related to the question type but rather the knowledge and understanding of the subject matter.

Based on the explanations above, the most possibility of guessing correctly is in true-false terms due to the limited options and higher probability of guessing the correct answer by chance.

Explanation:

• Preponderate of nation: This term refers to a person who holds a position of influence or power in a nation.


• Guardian: A guardian is someone who is legally responsible for taking care of another person, typically a child. This role does not necessarily involve holding a position of influence over a nation.


• School inspector: A school inspector is responsible for evaluating the performance of schools and ensuring they meet educational standards. This role is specific to the education sector and does not relate to holding a position of influence over a nation.


• Teacher: While teachers play a crucial role in shaping the minds of students, they do not typically hold a position of influence over a nation as a whole.


• None of these: This option is incorrect as the correct answer is Teacher.

Therefore, the correct answer is Teacher as none of the other options accurately represent the term "Preponderate of nation."

Explanation:

• Herbart: The five stepped system of lesson planning was started by Herbart. This system consists of five steps: Preparation, Presentation, Association, Generalization, and Application.


• Kilpatrick: Kilpatrick is known for his project method of teaching, which emphasizes learning through projects and hands-on experiences.


• Morrison: Morrison is not directly associated with the five stepped system of lesson planning.


• None of them: While Kilpatrick and Morrison have made significant contributions to education, the five stepped system of lesson planning was actually started by Herbart.

Explanation:

• Heurisco is a Greek word that means 'to find out' or 'to discover'.


• It is often used in the context of searching for or uncovering information or knowledge.


• When someone is trying to heurisco something, they are actively seeking to uncover new information or insights.


• It implies a process of exploration and investigation to arrive at a new understanding or solution.


• Unlike simply knowing or learning, heurisco involves a sense of discovery and excitement in the pursuit of knowledge.

Why a text-book is useful for all types of students

• Backward children: Text-books provide a structured and organized way of learning, which can be especially beneficial for children who may need extra support and guidance in their studies.


• Gifted children: Text-books offer a comprehensive overview of a subject, allowing gifted children to deepen their understanding and explore advanced concepts at their own pace.


• Average students: Text-books serve as a valuable resource for average students to reinforce their learning, clarify doubts, and improve their overall academic performance.


• All the above: Text-books cater to the diverse learning needs of students, making them an essential tool for educational success regardless of the student's academic level.

Exceptional Children

• Gifted in Nature: Some exceptional children display exceptional abilities or talents in specific areas such as academics, arts, music, or sports.


• Orthopedically Handicapped: Some exceptional children may have physical disabilities that affect their mobility or motor skills.


• Learning Disabled: Some exceptional children may have difficulties with learning or academic skills, such as reading, writing, or math.

Solution

• Exceptional children encompass a wide range of abilities and disabilities.


• Gifted children may excel in certain areas and require advanced educational opportunities.


• Orthopedically handicapped children may need physical accommodations or support to fully participate in activities.


• Learning disabled children may benefit from specialized educational interventions to help them succeed academically.


• Therefore, the answer "All of the above" is correct as it includes exceptional children who are gifted, orthopedically handicapped, and learning disabled.

Key Points:
- The most useful text-book of mathematics should contain a good balance of solved examples and exercises.
- It should have sufficient solved illustrations to help students understand the concepts.
- It should also provide a variety of questions for practice to reinforce learning.
Detailed Explanation:
- Solved Examples: The textbook should include a variety of solved examples to help students understand how to solve different types of problems.
- Exercise Questions: The textbook should also have a good number of exercise questions for students to practice and apply the concepts they have learned.
- Solved Illustrations: Having sufficient solved illustrations can help students see step-by-step solutions to problems and improve their problem-solving skills.
- Comprehensive Coverage: A good textbook should cover all the important topics in the syllabus and provide detailed explanations for each concept.
- Engaging Content: The textbook should present the content in a clear and engaging manner to keep students interested and motivated to learn.
- Practice Questions: Practice questions are essential for students to test their understanding and apply the concepts in different scenarios.
In conclusion, a good mathematics textbook should have a balance of solved examples, exercise questions, and solved illustrations to help students grasp the concepts effectively. It should provide comprehensive coverage of the syllabus and engage students with clear explanations and practice questions.

Explanation:

• Complementary written work: The term "complementary written work" refers to any additional written assignments or tasks that complement the main written work assigned to students. This could include extra practice exercises, research assignments, or creative writing tasks.


• Options:
  
  
  
  • A. Written work: This option is too general and does not specify if it is complementary or not.
  
  
  • B. Homework: Homework is a common type of written work assigned to students to be completed outside of the classroom. While homework can include complementary written work, not all homework is necessarily complementary.
  
  
  • C. Oral work: Oral work refers to assignments or tasks that involve speaking or presenting information orally, rather than in written form. This option is not related to the concept of complementary written work.
  
  
  • D. None of these: This option suggests that none of the given options are correct, but based on the context of the question, option B (Homework) is the most appropriate choice.
  
  
  
  


• Correct Answer: The correct answer is B. Homework as it is the most relevant option that aligns with the concept of complementary written work.

Achievement Test Explanation:

• Definition: Achievement tests are designed to assess a person's knowledge or skills in a particular area.


• Purpose: These tests measure what a person has learned or achieved after instruction or training.


• Focus: Achievement tests focus on specific content areas and are used to determine a person's level of mastery in a subject.


• Types: Achievement tests can be in the form of standardized tests, classroom assessments, or performance tasks.


• Scoring: Achievement tests typically provide a score or grade based on the individual's performance compared to a predetermined standard.


• Use: Achievement tests are commonly used in education to assess student learning and inform instructional decisions.

Calculating Arjun's IQ:

• Mental Age: 15 years


• Chronological Age: 12 years

Formula to Calculate IQ:

• IQ = (Mental Age / Chronological Age) * 100

Substitute the Values:

• IQ = (15 / 12) * 100


• IQ = 1.25 * 100


• IQ = 125

Conclusion:

• Arjun's IQ is 125.

We have 

The vector form of component of 
Here, 

∴ Vector form of component of 

• Statement A: If we draw a line parallel to the y-axis, it can cut the graph of a function at a maximum of 2 points.




• This statement is not true. A line parallel to the y-axis will intersect the graph of a function at most once, as it will only touch the graph at a single point.




• Statement B: If we draw a line parallel to the y-axis, it can cut the graph of a function at a maximum of 1 point.




• This statement is true. A line parallel to the y-axis will intersect the graph of a function at most once, touching it at a single point.




• Statement C: If we draw a line parallel to the x-axis, it can cut the graph of a function at a maximum of 1 point.




• This statement is true. A line parallel to the x-axis will intersect the graph of a function at most once, touching it at a single point.

Therefore, the correct answer is B: If we draw a line parallel to the y-axis, then it can cut the graph of a function at a maximum of 1 point.

We have ax + b 
Putting this value in the second equation, we get

This quadratic equation will have equal roots if 

Now, for f (x) to be real, 

0(mb - mx) - a(o - m (b - x)) + x(o - m(b - x)) = o 
am(b - x) - mx(b - x) = o 
m(b - x)(a - x) = o 
x = a, x = b 

tan 54° can be written as tan(45º + 9º)

Since 

So f(x) is not contionous at x = 1
We have 

Therefore f(x) is continous at x = 1.
f(x) is not differentiable at x = 1, because LHD at x = 1 and RHD at x = 1 is 1.

Multiply the first equation by  2 and subtract the second equation from first
4x + 2y = 12
4x + 2y = 5
No solution.

Equilateral Triangle and its Vertices

• Given: Two vertices of an equilateral triangle are (x₁, y_{1>) and (x2, y2>).}


• To Find: Coordinates of the third vertex.

Solution

• Equilateral Triangle: In an equilateral triangle, all three sides are equal in length and all three angles are equal to 60 degrees.


• Distance between Two Points: The distance between two points (x₁, y_{1>) and (x2, y2>) is given by the formula:
  √[(x2 - x1)² + (y2 - y1)²]}


• Calculating Third Vertex: Since the triangle is equilateral, the third vertex will be at a distance equal to the side length from either of the given vertices along a line making a 60-degree angle with the line joining the given vertices.


• Using Distance Formula:
  - Calculate the distance between the two given vertices.
  - Use this distance to find the coordinates of the third vertex.


• Answer: The correct answer is option D, both (1) and (2).

Given points 
A(3,4,5); B(6,7,2); C(0,−5,2)
Centroid is given as

 is not true for n =1.
However, it is true for n =2.

We observe that P(1) = 2
Hence, P(n) = n(n + 1) + 2 is not true for n = 1
So, principle of induction is not applicable and nothing can be said about P(n) = n(n + 1) + 2 .

opposite sides of a parallelogram are equal.
∴ Distance AB = Distance DC
And distance BC = Distance AD

Since, a= i + 2j + 3k      ......(1)
and b = 3i -j +2k,          ........(2)
From (1) and (2) dot product of vector a and b 
3 - 2 + 6 = 14 cos θ
⇒ (1/2) = cos θ
Therefore, θ =60°
Hence angle between a and b = 60º.

We can measure the lengths of the diagonals by using the distance formula.
Since the length of diagonals are not equal therefore its a Parallelogram.

The order is the highest numbered derivative in the equation, While the degree is the highest power to which a derivatives is raised.
Hence the order of given equation is 11 and the degree is 22.