MPTET Varg 2 Math Mock Test - 4 - MPTET MCQ

काव्यांश की डोलती सुरभि राजा-घर कोने-कोने, से पता चलता है कि वसंत ऋतु में चारों ओर सुगंध व्याप्त है।

• काव्यांश के अनुसार:- ​
  • वसंत ऋतु में मेघ के बरसने पर चारों ओर सुगंध फैल जाता है।

Key Points

• सुरभि- सुगंधित, खुशबूदार, सुंदर, मनोरम।

  • विलोम शब्द- 'दुर्गंध'
• राजा- भूपति, भूप, नरेश, महीपति, अवनीश, नरपति, नरन्द्र, महिपाल।

• घर- गृह, गेह, आवास, धाम, निवास, बसेरा, डेरा, भवन।

Additional Information
रानी:-

• मालकिन, बेगम, राजपत्नी, महरानी, राज्ञी, महिषी।

विकल:-

• अर्थ: व्याकुल, विह्वल, बेचैन, अधीर।
• विकल का विलोम शब्द अविकल हैं।
• विशेषण शब्द

पानी:-

• अर्थ: जल, सलिल, उदक, तोय, जीवन, वारि।

दृग:-

• अर्थ: आँख, नेत्र, नयन, दृष्टि।

The correct answer is: Funny.

Key Points

• Hysterical: Something which causes unrestrained laughter; very funny. (हास्यजनक)
  • For example- Oh, that joke is hysterical!
• Let us look at the meaning of the given words in the options section.
  • Emotional: Having feelings that are easily excited and openly displayed. (भावनात्मक)
  • Dangerous: Able or likely to cause harm or injury. (खतरनाक)
  • Funny: Causing laughter or amusement; humorous. (मज़ेदार)
    • For example- I have found Charlie Chaplin to be very funny.
  • Scary: Frightening; causing fear. (भयानक)
• From the meaning of the given words, it is clear that the most appropriate synonym of 'Hysterical' is 'Funny'.
• Therefore, the correct answer is option 3.

The correct answer is "Germany".

Key Points

• We can find the following line in the 1st paragraph:
  • magine a country whose inhabitants work fewer hours than almost anyone else, whose workforce is not particularly productive, and whose children spend less time at school than most of its neighbors. Hardly a recipe for economic success, you might think.But the country described above is none other than Germany, Europe's industrial powerhouse and the world's second largest exporter; a country whose economy has single-handedly stopped the eurozone from falling back into recession and is the only nation rich enough to save the euro.

Hence, the correct answer is "option 1".

• The population of India is 1,210,193,422. This data is as per the consensus of India 2011.
• Nodal Ministry for the census is the Office of the Registrar General and Census Commissioner, Ministry of Home Affairs.

Importance of conducting census are as follows:

• It provides concrete data about the population’s characteristics.
• Analyse and make projections.
• For good governance.
• Demarcation of Constituencies.
• Giving grants.

Key Points

• Uttar Pradesh was the highest populated state in India.
• Sikkim is the least populated state in India.
• Delhi is the most populated Union territory in India.
• Lakshadweep is the least populated Union territory in India.

Position values of the letters, according to the English alphabet series is:

The logic for RED is coded as 19 is mentioned below-

RED → 18 + 5 - 4 = 19

Similarly, WED will be coded as-

WED → 23 + 5 - 4 = 24

Hence, 24 is correct answer.

According to the given Venn diagram:

The shaded area shows the interior decorators are there who are NEITHER architects NOR dancers.

So, there are '150' interior decorators are there who are NEITHER architects NOR dancers.

Hence, the correct answer is "150".

Forgetfulness is the failure to recall or retain information. It can be a normal part of aging. As people grow older, they start forgetting things.

Important PointsThere are various ways of minimizing forgetfulness:

• Follow a routine
• Note down all the things
• Focus on one thing at a time
• Repetition of a lesson or memorizing things twice
• ​With training, practice, and motivation memory can be improved.

Thus, it is concluded that repetition of lessons is a way of minimizing forgetfulness.

Key PointsThere are a few causes of forgetfulness:-

• Lack of sleep
• Overwork, stress, and anxiety
• Depression, Fatigue or lack of exercise

A child who is average in intelligence, higher in achievement motivation, low in creativity, and just averages in social development shows variations in abilities within an individual.

Key Points The differences in two or more abilities of an individual arise due to the presence of intra-individual differences.

• Intra Individual difference are present in a particular individual and is present in almost everyone as each individual cannot possess all the abilities to a similar extent.
• For example, a child possessing average intelligence but high motivation or low creativity shows intra-individual differences.

Hence we conclude that a child having average intelligence, higher achievement motivation, low creativity, and just average in social development, is an example of Intra Individual difference.

Additional Information

• Inter Individual differences - are the differences in abilities between two or more individuals.
• Measurable Individual difference - Differences between two individuals that can be measured using standardized or nonstandardized tests.
• Observably Individual differences - are the differences that can be easily observed such as voice, communication skills, etc.

Inclusive Education means education for all children in school as It refers to the inclusion of all children in the education system, regardless of their differences and disabilities.

Key Points

• It values the diversity, each child brings to the classroom and facilitates all with equal opportunities to learn and grow.
• Inclusive education improves the quality of and makes provisions for education for all. Inclusive education welcomes and celebrates diversity.
• It provides a provision to include disabled children along with normal children in a regular classroom environment.
• It refers to an education system that accommodates all children regardless of their physical, intellectual, social, emotional, linguistic, or other conditions.

Important Points

Benefits of Inclusive Education include:

• Developing moral and ethical principles.
• Increasing communication and social skills.
• Increasing acceptance and appreciation of diversity.
• Fostering the potential of every child to grow and bloom.
• Addressing the diverse learning needs of every student.
• Valuing all learners equally and encouraging them to learn.
• Removing discrimination and providing adequate resources.
• Making adequate seating arrangements as per the child's requirement.

Hence, it could be concluded that at present the emphasis is on inclusive education. The objective behind inclusive education is Emphasis on Education of all Categories of learners.

Additional Information

Basic Principles of Inclusive Education:

• Well-constructed educational plan.
• Use of multilingualism as a resource.
• Equity and equal opportunities for all.
• Use of specific pedagogical strategies.
• Sensitization towards individual differences.

Formula Used:

We know that tan²θ + 1 = sec²θ

and sec²θ = 1/cos²θ

Calculation:

Using the identity, 1 + tan²θ = sec²θ

⇒ cos²θ (1 + tan²θ) = cos²θ (sec²θ) = cos²θ / cos²θ = 1

Hence, the value of cos²θ (1 + tan²θ) is equal to 1.

Concept used:

Median = I +[(N/2 − C)/f] × h

Here, l = lower limit of the median class

C = C.F. of the class preceding the median class

h = higher limit - lower limit

f = frequency of median class

Calculation:

N = 50

⇒ N/2 = 50/2 = 25

As 29 is just greater than 25, therefore the median class is 145 - 150.

The lower limit of median class = 145

C = 11

h = 150 − 145 = 5

f = 18

Median = 145 + [(25 − 11)/18]5

⇒ 145 + 3.89

⇒ 148.89

∴ Median is 148.89

Given:

Formula used:

∑ f = N

By Direct Method:

Mean = ∑ fx/N

Calculation:

∑ f = N = 4 + 8 + 14 + 11 + 3 = 40

∑ fx = 20 + 48 + 98 + 88 + 27 = 281

∴ Mean = 281/40

⇒ 7.025

Given:

Principal = Rs 6,25,000

Amount = Principal + CI = Rs 8,31,875

r = 10% per annum

Formula used:

In compound interest,

Amount = Principal × (1 + r / 100)n

Calculation:

Let, n be the number of years.

According to the question,

⇒ 8,31,875 = 62500 × (1 + 10 / 100)ⁿ .

⇒ 8,31,875 / 62500 = (11 /10)ⁿ

​⇒ 1331 / 1000 = (11 /10)n

​⇒ (11 /10)³ = (11 /10)n .

⇒ n = 3 years

∴ The time will be 3 years.

Given:

The length of a rectangle is twice of its width.

Concept used:

Area of a rectangle = Length × Breadth

Calculation:

Let the width of the rectangle be B.

Length = 2B

According to the question,

2(2B + B) = 60

⇒ 6B = 60

⇒ B = 10

Length = 2 × 10 = 20 cm

Now, the area of the rectangle = 20 × 10 = 200 cm²

∴ The area of the rectangle is 200 cm².

Given:

r = 1 cm

R = 6 cm

Formula used:

Volume(Sphere) = 4/3 x 22/7 x r³

Solution:

Volume of 1 small ball = 88/21 x 1³ = 88/21 cm³

Volume of solid sphere of lead = 88/21 x 6³ cm³

Number of ball that can be made = (88/21 x 6³)/(88/21) = 216 balls

Hence, the correct option is 3.

Calculation:

⇒ 42 - 25 = 17

⇒ 72 - 55 = 17

⇒ 84 - 67 = 17

Now, LCM (42, 72, 84) = 504

Hence, required number = 504 - 17 = 487

∴ The correct answer is 487.

Given:

Side of the cube = 5 cm

Calculation:

Length of the cuboid = sum of sides of the two cubes

⇒ 5 + 5

⇒ 10 cm

∴ The length of the cuboid so formed is 10 cm.

Given:

0 is a number

Concept used:

A rational number is a number that can be expressed as the ratio of two integers.

Calculation:

A rational number is a number that can be expressed as the ratio of two integers. 0 satisfies this definition as it can be expressed as the ratio of 0 and any non-zero integer.

An even number is a number that is divisible by 2. 0 satisfies this definition as it is evenly divisible by 2.

A natural number is a positive integer greater than 0. 0 does not satisfy this definition as it is not a positive integer greater than 0.

⇒ 0 is a rational number, an even number but not a natural number.

∴ 0 is a Rational number.

The correct answer is 0 J

Key Points

• Work is when a body is displaced by a distance on applying force.
  • Where distance is denoted by s and Force by F.
  • The formula for Work done is given by W = F.s
• In the case of work done by a force acting at an angle, the Force acts in such a direction that it makes an angle θ with the direction.
  • The formula is given by W = F.s cosθ.
• For the satellite, the direction is perpendicular and the angle between the direction and gravitational force is, θ = 90º.
• So, W = F x 40,000 x cos 90º = 0 J. Hence option 4 is correct.

Additional Information

• The work done is maximum at θ = 0º and minimum at θ = 90º.
• Work done is also a force on an object that is equal to the magnitude of a force multiplied by the distance moved in the direction of a force.
• The universal gravitational constant, G is given by 6.673 x 10^-11 N m²/kg².

The correct answer is Density.

Key Points:

• The pressure in a static fluid is determined by the vertical depth from the surface and is unaffected by the form or size of the container.
• The pressure in a static fluid is also affected by the density of the fluid and gravity's acceleration.
• The pressure exerted by the liquid increases with increasing depth inside the liquid.
• The pressure due to the weight of a liquid of constant density is given by P = ρgh
  where p is the pressure, h is the depth of the liquid, ρ is the density of the liquid, and g is gravity's acceleration.

Additional Information:

• Both depth and weight density are directly related to pressure.
• At a certain depth, liquid pressure remains constant in all directions.
• A liquid seeks its own level.
• Liquid exerts pressure on sides of the container.

Concept:

Irrational number: An irrational number is a type of real number that cannot be represented as a simple fraction.

Rational number: Rational number, in arithmetic, is a number that can be represented as the quotient p/q of two integers such that q ≠ 0.

Explanation:

∴ is a rational number.

Mathematics is the study of numbers, shape, quantity, and patterns. The nature of mathematics is logical and it relies on logic and connects learning with learners' day-to-day life.

• Teaching methods of mathematics include problem-solving, lecture, inductive, deductive, analytic, synthetic, heuristic and discovery method. Teacher adopts any method according to the needs and interests of students.

Key Points

Anisha is using deductive logic.

Deductive Method: The deductive method is based on deduction. At first, the rules are given and then students are asked to apply these rules to solve more problems.

• It begins with general premises and through logical argument, comes to a specific conclusion.
• For example, while teaching mathematics, the teacher introduces a theory and explains the rules of the theory and the formula, and the students are asked to solve problems using the given formula.

• Deductive approach proceeds from-

  • General to specific
  • Unknown to know
  • Complex to simple
  • Formula to example

In the above example Anisha proves it by taking the case n i.e, she uses the method from unknown to known.

Thus it is clear that Anisha is using deductive logic.

Additional Information

Inductive Method: Inductive approach is based on the process of induction. It is a method of constructing a formula with the help of a sufficient number of concrete examples.

• Induction means to provide a universal truth by showing, that if it is true for a particular case.
• Inductive approach proceeds from-
  • Particular to general
  • Known to unknown
  • Simple to complex
  • Example to formula

Mathematics is the study of patterns, numbers, geometrical objects, data, and information. It deals with data analysis, integration of various fields of knowledge, involves proofs, deductive and inductive reasoning, and generalizations.

• The teaching of mathematics should be done in the way, in which a student learns the best i.e., following the child-centered approaches by engaging students actively in the learning process.
• The teacher should focus more on providing practical exercises and abstract knowledge to students to foster their individualized discovery-oriented learning.

​Key Points

• The primary class students need a solid foundation in geometry in order to be successful later in middle school and high school geometry.
• The geometry content appropriate to the primary classroom is informal in the organization and should be presented in a way that allows students to construct meaning.
• Classroom activities should encourage students to observe, compare observations, make hypotheses, and then prove or disprove their hypotheses.
• The geometry presented in elementary classrooms focuses mainly on the identification and concrete observation of basic shapes.
• At the primary level, the teacher mainly expects their students to observe and identify the different shapes such as square, rectangle, triangle, pentagon, hexagon, etc.
• For example, the students should be asked to observe the shapes of their bottle, lunch box, pencil box, table, desk, and all other objects that are present in their surroundings.
• When students are able to observe and identify the geometrical shapes only then they will be able to define and draw them.

Hint

• Showing charts with different shapes, drawing several shapes on the blackboard, and giving oral knowledge about shapes will not help that much in teaching shapes as the students will not get concrete experience.

Hence, it is concluded that using concrete materials is the best teaching method to teach about shapes at the primary level.

There are test items that allow a variety of correct responses and elicit a different kind of student thinking. Such types of items are known as open-ended items.

Key PointsThe use of different types of test items in mathematics is crucial to assess the child’s learning in different areas like knowledge, understanding, application, etc. Further, the use of open-ended items in mathematics enables the learner to think of a solution to a particular problem from different dimensions and enhance the conceptual understanding of the learner.

Characteristics of Open-Ended Questions:

• Offer students scope for their own decision-making and natural mathematical way of thinking. Each child can think according to his own experience.
• Solved in different ways and on different levels. Students of different abilities can be able to give at least one correct answer.
• Provide teachers with valuable information regarding individual students' way of thinking and way of solving mathematical problems.
• Open to students’ creativity and imagination when relates to the real-life context of their experience.
• Develop students’ reasoning and communication skills when those are discussed in the classroom.
• Develop students’ self-confidence for higher achievement. Since, such items have several possible correct responses, every student, even the poor performers; can provide at least one correct response. The better-performing students can give several correct responses. All categories of students can aspire to perform on subsequent occasions.

Thus, it is clear that Open-Ended Questions develop conceptual understanding.

The correct answer is An electric current.

Key Points:

• The movement of electrons through a whole circuit of conductors is known as electric current.
• Everything from our lights to our trains is powered by it.
• An electric circuit is a closed channel that allows electric current to flow through it.
• To build an electric circuit, different components, such as a battery, resistor, wire, key, light, etc, can be linked in many ways.

Additional Information

• An electric circuit is a conduit for moving current.
• A battery or generator is a device that provides energy to the charged particles that make up the current, a device that uses current, such as a lamp, an electric motor, or a computer, and the connecting wires or transmission lines make up an electric circuit.
• Several categories are used to categorize electric circuits.
• Only one direction of current can flow through a direct-current circuit.
• As in most residential circuits, an alternating-current circuit transports current that pulses back and forth repeatedly every second.

{(2 cosp) (1 + cosp)/ (1 + sinp + cosp)} × (1 + cosp - sinp)/(1 + cosp - sinp)

{(2 cosp) (1 + cosp) × (1 + cosp - sinp)}/ {(1 + cosp)² - sin²P}

{(2 cosp) (1 + cosp) × (1 + cosp - sinp)}/ 1 + 2cosp + cos²p - sin²p

{(2 cosp) (1 + cosp) × (1 + cosp - sinp)}/ sin²p + cos²p + 2 cosp + cos²p - sin²p

(1 + cosp - sinp)

Concept used:

Line of symmetry:

On placing the Line between the Figure, the Figure Appears the same on both sides of the line.

Calculations:

Trapezoid has No line of symmetry

⇒ Assertion is True.

Isosceles Trapezoid has 1 line of symmetry But not the Correct Reason for the given Assertion.

⇒ The Reason is False.

Hence, (A) is true, but (R) is false.

Given:

Pipe A can fill a tank = 10 hours

Pipe B can fill a tank = 15 hours

Concept used:

Work = Efficiency × Time

Calculation:

LCM of 10 and 15 is 30

Efficiency of A = (30/10) = 3 units/hour

Efficiency of B = (30/15) = 2 units/hour

Time taken by A and B to fill the tank = [30/(3 + 2)] hours

⇒ (30/5) = 6 hours

∴ The required time taken is 6 hours.

Given:

x₁ = -4, x₂ = 2

y₁ = 7, y₂ = -5

Formula Used:

Distance formula = √(x2 - x1)2 + (y2 - y1)2

Calculation:

Distance formula = √(x2 - x1)2 + (y2 - y1)2

⇒ Distance = √(-4 - 2)2 + (7 - {-5})2

⇒ Distance = √(-6)2 + (12)2

⇒ Distance = √36 + 144

∴ Distance = 6√5 units

There are various methods to teach mathematics that helps in the discussion and analysis of their solutions.

Key Points

• Gallery Walk, Math Congress and Bansho provide students with organized and facilitated time to talk about and listen actively to one another’s mathematical thinking, justify their thinking to others and reflect on what they are learning. In fact, this organized and safe discussion forum encourages students to share and challenge ideas.
• Importantly, students are reassured that their voices, ideas, and experiences are valued and contribute directly to the whole class's learning.
• During Gallery Walk, Math Congress, and Bansho, it becomes evident to the students and teacher that mathematical communication is not about “answering the question using words, numbers, pictures, and symbols.” Instead, they realize that these forms of communication are selected and applied in order to create a precise mathematical argument, where labeled diagrams and/or numeric expressions and equations are viewed as being more precise, concise, and persuasive forms than descriptive narratives.

Hence, remedial teaching is not one of the methods of coordinating student discussion and analyzing their solutions in Mathematics.

HintRemedial teaching refers to teaching which is intended to improve the ability of slow learners to learn something. It is an integral part of the teaching-learning program, also known as compensatory or corrective teaching.

Additional Information

• Gallery Walk is an interactive discussion technique that gets students out of their chairs and into a mode of focused and active engagement with other students’ mathematical ideas.
• Math Congress is a mathematics instructional strategy developed by Fosnot and Dolk. The purpose of the congress is to support the development of mathematicians in the classroom learning community, rather than fixing mistakes in the children’s work or getting agreement on answers.
• Bansho, in Japanese, literally means board writing. The purpose of Bansho is to organize and record mathematical thinking derived from and collectively produced by students on a large-size chalkboard or dry-erase board.