DSSSB TGT Mathematics Mock Test - 2 - DSSSB TGT/PGT/PRT MCQ

• Knowledge of self: This is an essential professional skill for a teacher as it involves self-awareness, reflection, and understanding of one's own strengths and weaknesses in order to continuously improve as an educator.


• To experiment well: Teachers need to be open to trying new teaching methods, strategies, and approaches in order to cater to the diverse learning styles of their students and enhance their teaching effectiveness.


• Dedication: Dedication is crucial for a teacher as it involves a strong commitment to the profession, students, and their overall development, ensuring that they go above and beyond to support and inspire their students.


• Satisfactory knowledge of social matter: While having knowledge of social matters can be beneficial for a teacher in understanding the context in which their students live, it is not a core professional skill as compared to the other three points mentioned above. It is more of an additional knowledge area that can complement a teacher's effectiveness but is not a prerequisite for being a successful educator.

• Practicability: A successful teacher must be practical in their approach to teaching, using methods and strategies that are effective and applicable to the real world.



• Dedication: Dedication is crucial for a successful teacher as they need to be committed to their students' learning and development, putting in the time and effort required to help them succeed.



• Self Discipline: Self-discipline is important for a successful teacher to stay organized, manage their time effectively, and maintain a professional attitude in the classroom.



• Partial Behaviour: Partial behavior, favoritism, or bias towards certain students is not a characteristic of a successful teacher. A successful teacher treats all students equally, with fairness and respect.

In conclusion, the characteristic that is not a characteristic of a successful teacher is Partial Behaviour. A successful teacher should possess practicability, dedication, and self-discipline to effectively educate and support their students.

• Knowledge: Knowledge is a noun, not an action verb. It refers to information or understanding that someone has acquired through learning or experience.


• Understanding: Understanding is also a noun, not an action verb. It refers to the ability to comprehend or grasp the meaning of something.


• Application: Application can be an action verb when used in the context of applying something to a task or situation. However, in this case, it is used as a noun, not an action verb.


• All the above: This option includes all the choices given, which are all nouns and not action verbs. Therefore, the correct answer is d.

• Written Work: Written work can help in the development of alertness by requiring individuals to focus on reading and understanding information, which can improve cognitive skills and attention to detail.


• Homework: Homework can also aid in alertness development as it requires students to practice and apply what they have learned, reinforcing concepts and keeping their minds engaged.


• Oral Work: Oral work involves active participation and communication, which can enhance alertness by stimulating the brain and promoting quick thinking and responsiveness.


• All of the Above: Engaging in a variety of activities, including written work, homework, and oral work, can provide a holistic approach to developing alertness by challenging different cognitive functions and keeping the mind active.

• Simpson is related to Psychometor Domain: Psychometrics is a field of study concerned with the theory and technique of psychological measurement. The Simpson index, also known as the Simpson's Diversity Index, is a measure of diversity that takes into account the number of species present as well as the relative abundance of each species. It is commonly used in ecological studies to measure the biodiversity of a particular habitat.

• Utilitarian Values:




• Mathematics provides essential skills and knowledge that are applicable in various real-life situations, such as calculating finances, measuring distances, and understanding data analysis.


• It helps individuals in problem-solving, critical thinking, and decision-making, which are valuable skills in both personal and professional life.





• Disciplinary Values:




• Studying mathematics instills discipline, perseverance, and logical reasoning in individuals as they work through complex problems and concepts.


• It helps develop a systematic approach to learning and problem-solving, which can be applied to other subjects and areas of life.





• Cultural Values:




• Mathematics has a rich history and cultural significance, with contributions from various civilizations and cultures throughout the ages.


• It helps individuals appreciate the beauty and universality of mathematical concepts, fostering a sense of curiosity and wonder about the world around them.





• All of the Above:




• When combined, utilitarian, disciplinary, and cultural values of mathematics contribute to a well-rounded education that prepares individuals for success in academic, professional, and personal endeavors.


• By understanding and appreciating the diverse educational values of mathematics, students can develop a deeper understanding and appreciation for the subject, leading to lifelong learning and growth.

• Synthesis: Synthesis is the process of combining different elements or ideas to form a new whole. It involves creating something new from existing information.


• Deduction: Deduction is a method of reasoning from the general to the specific. It involves drawing logical conclusions based on given premises.


• Analysis: Analysis is the method of breaking down a complex problem or system into its individual parts to understand how they work together. It involves examining the components of a whole to understand how they contribute to the overall structure.


• Induction: Induction is the process of reasoning from specific observations to general principles. It involves drawing general conclusions based on specific instances.

• The method 'Unknown to Known' is advanced through the process of analysis.


• Analysis involves breaking down complex or unknown information into smaller parts to understand it better and make it known.


• By analyzing the components of a problem or concept, one can uncover patterns, relationships, and underlying principles that lead to a better understanding of the unknown.


• Therefore, when transitioning from 'Unknown to Known', the method of analysis is crucial in uncovering the underlying structure and meaning of the information.

• Visual Representation: Geometry involves shapes, angles, and spatial relationships that can be effectively illustrated using teaching aids such as geometric models, charts, and diagrams.


• Hands-on Manipulatives: Manipulatives like geometric solids, rulers, protractors, and compasses help students understand geometric concepts through tangible objects they can manipulate.


• Interactive Software: Tools like interactive geometry software allow students to explore geometric concepts in a dynamic and engaging way, enhancing their understanding of geometrical principles.


• Real-world Applications: Teaching aids in geometry can include real-world examples and applications, such as using maps, blueprints, and architectural designs to demonstrate practical uses of geometric concepts.


• Engagement and Motivation: By using a variety of teaching aids in geometry, educators can make the subject more interactive, engaging, and accessible to students with different learning styles.

• Focus on understanding: Continuous and Comprehensive Evaluation (CCE) encourages students to focus on understanding concepts rather than rote memorization. This helps in developing a deeper understanding of the subject matter.


• Regular assessments: CCE involves regular assessments in the form of formative and summative assessments. These assessments test the student's understanding of the concepts rather than their ability to memorize information.


• Varied assessment techniques: CCE utilizes a variety of assessment techniques such as projects, presentations, group discussions, etc., which require students to apply their understanding of the subject rather than just memorizing facts.


• Feedback mechanism: CCE provides continuous feedback to students on their performance, which helps them identify areas where they need to improve their understanding rather than just memorizing information.

• Encourages self-learning: CCE encourages students to take responsibility for their learning and engage in self-study to deepen their understanding of the concepts.


• Opportunities for self-assessment: CCE provides opportunities for self-assessment through projects, assignments, and other activities, which require students to study on their own to complete these tasks successfully.


• Personalized learning: CCE allows students to learn at their own pace and explore topics of interest through self-study, fostering a sense of independence and self-motivation in learning.

• Continuous evaluation: CCE involves continuous assessment throughout the academic year, which encourages students to study regularly to perform well in these assessments.


• Emphasis on learning outcomes: CCE focuses on achieving specific learning outcomes, which motivates students to study regularly to meet these objectives.


• Feedback loop: The feedback provided in CCE helps students identify areas where they need to study more and improve, promoting regular study habits to succeed academically.

• CCE plays a crucial role in eliminating memorization by focusing on understanding, utilizing varied assessment techniques, and providing regular feedback.


• While CCE does not eliminate self-study, it promotes self-learning, self-assessment, and personalized learning to enhance student's understanding of the subject matter.


• CCE also promotes regular study habits through continuous evaluation, emphasis on learning outcomes, and the feedback loop, ensuring students are consistently engaged in their academic pursuits.

• Gifted in nature: Some exceptional children may have exceptional abilities or talents that set them apart from their peers. These children may excel in areas such as academics, arts, or sports.



• Orthopedically handicapped: This category includes children who have physical disabilities that affect their mobility or physical functioning. These children may require special accommodations or assistive devices to help them participate in daily activities.



• Learning disabled: Children who have learning disabilities may struggle with academic skills such as reading, writing, or math. These children may require specialized instruction or support to help them succeed in school.



• All the above: Some exceptional children may fall into multiple categories, exhibiting a combination of giftedness, physical disabilities, or learning difficulties. It is important to recognize and support the unique needs of each exceptional child to help them reach their full potential.

L.H.S.

The word 'ERUASION' has 8 letters. It has 5 vowels and 3 consonants in it.
We can find required number of words by filling 8 places such that 1^st and 8^th places are occupied by consonant and remaining places are occupied by remaining letters as shown in figure:

So required number of words = 3 x 6 x 5 x 4 x 3 x 2 x 1 x 2 = 4320

If logx,logy and logz are in A.P.
then we can write
= 2 logy = log x + log z
= log y² = log xz
= y² = xz
Which means x,y and z are in G.P.

We have
(sinx + sinY + sinZ)(sinx + sinY - sinZ) = 3sinx sinY
= (sinx + sinY)² - sin²z = 3 sin X sinY
=sin²x + sin²Y -sin²z = sinX sinY
= Now using the formula
= sin²A - sin² B =sin A+ sin B
=Then
= sin²x + sin(Y+Z).sin (Y-Z) = sinx sinY
Now X+Y+Z = n
= sin(Y + Z) = sin(π -x) = sinx
So sin²x + sin(Y+ Z).sin (Y -Z) = sinx sinY
sin²x + sinx.sin (Y -Z) = sinx  sinY
= Sin X{ (sinx + sin (Y -Z)} = sinx sinY
= Sinx {(sin(Y+Z)+ sin (Y-Z)} = sinx sinY
= Sinx {(2 sinY.sinZ} = sin.x sinY
= Sin Z= 1/2
= z = 60°

D origin is the circumcentre of the triangle
⇒ Orthocentre of the triangle =

Hence distance between the circumcentre and the orthocentre of the triangle = 

xcos 2α + y sin2α =z
= x(cos²α -sim²α)+ y(2sin α cosα) = z
Divide both side by cos²α
x(1-tan²α)+ y(2 tanα) = z sec²α = z(1+ tan²α)
= x -x tan²α +2y tanα = z + z tan²α
= tan²α(x + Z)-2ytan α + (z -x) = 0
Clearly we can see that this is a quadratic equation with tanaa as a variable.
This has tanA and tan B as its roots
So sum of roots = tanA + tanB = 2y/(x+z)

we know that A square matrix is called lower triangular matrix if all its entries above the main diagonal are zero. So consider a lower triangular matrix of order 4.

So maximum number of distinct entries in lower triangular matrix of order 4 = 11
2nd method:
maximum number of distinct entries in lower triangular matrix of order n = 
here n = 4
So 

Let direction ratios of the line joining the points A (7,-8,-2) and B(3,-4,0) are a, b and c
a = x₂  – x₁ = 7 – 3 = 4
b = y₂ - Y₁ = -8+ 4 = -4
c = Z₂ - Z₁ = - 2 - 0 = - 2
So direction cosines of the line joining the points = (l,m,n)

If f(t) is increasing
f'(t) ≥ 0
= 2t + m ≥ 0
= t ≥ - (m/2)
Since 1 ≤ t ≤ 2
-(m/2) ≤ 1
m ≥ -2
Hence least value of m is -2.

Since the roots of the equation are of an opposite sign so we can say that the product of roots will be negative or less than zero.
Product of roots = 

Length of BC= p m
Length of BD = q m
A.T.Q.


= AB = p cot θ
= tan θ = P/AB ...(ii)
By equation (i) and (ii)

= The height of the hill is √pq

Let 
Square both sides
x² + y² + 2xyi = 3 - 4i 
Comparing imaginary parts both side
2xy = -4
⇒ xy = -2
Comparing real parts both side
x² - y² = 3

x⁴ - 3x² - 4 = 0
(x² - 4) ( x² + 1) = 0
(x² + 1) = 0 or (x² - 4) = 0
Now  ( x² + 1) = 0
There is no value that satisfy ( x² + 1) = 0
Also x² - 4 = 0 
x² = 4
x = 2
When  x= 2 , y = -1 
when x = -2 , y = 1
So 

Let x,y are two H.M. between 6 and 12/5
So 6,x, y, 12/5 are in H.P.

So First term(a) = 1/6


So x = 4 and y = 3.

Put l n x = t such that dx/x = dt

As y → ∞, we can clearly see that it is of the form ∞/∞
So 

Let y = 2e^-t 
Since 0 < 2e^-t ≤ 2 for all t ∈ 0,∞
Also 2e^-t = 0 , for t > In 2.

1x² + mx + n = 0 (0 < I < m < n)
Product of roots (z₁z₂) = (c/a) >1
Let z₁ = a+iB and z₂ = a-iB
= (a +iB) (a-iB)>1
= a² +B² >1
= |z₁| > 1, |z₂| > 1

Put sin x = t such that cosx dx = dt

tan(t)+c
tan(sinx)+c

a₁a₂ + b₁b₂ + c₁c₂ = 4 + 3 + 12 = 19 > 0
So that acute angle bisector is