MPTET Varg 2 Math Mock Test - 10 - MPTET MCQ

The correct answer is "Urge."

Key Points

• Let us understand the meaning of the given and the marked words:
  • "Encourage" means to give hope, support or confidence to somebody.
    • Synonyms: Inspirit, embolden, hearten.
    • Example: Riya encouraged her brother to take the challenge and go ahead.
  • "Urge" means to advise or try hard to persuade somebody to do something.
    • Synonyms: Encourage, nudge, prompt.
    • Example: We would urge people to refrain from such activity.
• From the above explanation, it is clear that the word "urge" is same in meaning to the word "encourage."

Hence, the correct answer is option 3.

Additional Information

• "Constitute" means to be one of the parts that form something.
• "Condemn" means to say strongly that you think somebody/something is very bad or wrong.
• "Criticize" means to say what is bad or wrong with somebody/something.

The correct answer is 'He was operated on by the surgeons for nearly ten hours'.

Key Points

• The given sentence is in the active voice.
• To change the given sentence in the passive voice. We will do the following changes:
  • 'for nearly ten hours' will not be changed as it is an independent clause.
  • 'The surgeons operated on' will be changed into 'operated on by the surgeons'.
  • him will be changed into 'he'.
• Hence the correct sentence will be "He was operated on by the surgeons for nearly ten hours".

The correct answer will be Option 2.

The table shows the place value of the alphabet from A to Z.

The logic followed here is:

ZEBRA can be written as 2652181

Similarly, COBRA be written

Therefore, the COBRA is written as '3152181'.

Hence, the correct answer is "Option (2)".

As per the given Venn diagram:

Here, '8' males are managers but not Engineers.

Hence, the correct answer is "Option (4)".

Growth refers to the physical development of children from birth to adolescence. Development describes the growth of humans throughout their lifespan, from conception to death.

Key Points

• The development method is a comprehensive approach to studying how children grow and change over time across various domains including physical, cognitive, emotional, and social development.
• By systematically observing and documenting developmental changes over time, researchers gain valuable insights into the factors that shape children's development from infancy through adolescence and beyond.
• This methodological approach contributes significantly to our understanding of how children grow, learn, and adapt in various environments and contexts.

Hence, we can conclude that developmental method is the correct answer.

Development is an ongoing process. It starts from the birth of the child and goes up to death. While adults have a variety of emotional expressions, this is not so in the case of infants.

Key Points

• The newborn does not have dearly differentiated emotions. In the first year of life, the infant primarily shows two emotional states-delight and distress. They express delight by smiling or laughing. Talking to the baby, tickling, cuddling, and playing with the baby are likely to delight them.
• Have you ever tried approaching infants between five and twelve months of age who are not familiar with you? If you have, the chances are that most would have shown fear at your approach.
• The typical behavior of the infant in such situations is as follows: s/he studies the stranger's face for some time, then his/her face tightens and s/he begins to cry. If the stranger leaves, the child becomes quiet.
• The infant shows stranger anxiety. This is a direct result of his/her attachment to his/her parents. Once attached, infants become upset on seeing an unfamiliar adult.
• Such anxiety shows its beginning around six months and reaches its peak between eight and twelve months, gradually disappearing between fifteen and eighteen months.

Thus, it is concluded that infants develop stranger anxiety around the age of 5 to 6 months.

Creative children are those who exhibit creativity. Creativity is a cognitive ability to produce something original by offering a fresh perspective. It is the ability possesses by people who are creative, persistent, and imaginative.

Key Points

Characteristics of Creative child:

• Creativity is the ability to adopt an innovative approach to solving a problem, to cope with ideas that are both relevant and unusual, to go beyond the immediate situation to redefine the problem.
• Creativity can be referred to them as the unique or original production of ideas or products. Divergent thinking is associated with creativity.
• Curious, extrovert, and ambitious in nature. Think quickly and solve problems in a novel way.
• The creative thought process results in responses that are unexpected and may be regarded as novel or peculiar. Ideational fluency, the flexibility of thinking, originality, and elaboration are elements of creativity.
• Ideational fluency involves being able to generate a flow of ideas, while flexibility means the ability to modify the flow of information.
• Originality is the ability to come up with unique findings or new uses for products.
• Perceive the relation between impossible things.
• Convert imaginative and original ideas into reality.

Thus from the above-mentioned points, it is clear that creative children are those who adopt an innovative approach.

The word “personality” has been derived from the Latin word “persona” which means a mask worn by an actor while performing a character on the stage.

• Personality is an enduring organization of a person’s character, temperament, intellect, and physique that determine his unique adjustment to his environment.
• According to Allport (1961) personality is the “dynamic organization within the individual of those psycho-physical systems that determine his unique adjustment to his environment” It means that personality “resides” within the individual and these systems are woven into an organization.

Characteristics of Personality: These are some features that reflect the personality of an individual.

• Psychophysical systems: Personality is a system that has both psychological and physical aspects. This system is composed of interacting elements and the main elements of the system are traits, emotions, intellect, temperament, character, and motives.
• Dynamic organization: It signifies that different elements of the psychological system are independent but function in an interlocking manner and are subject to change. However, this change can take place over a period of time in a gradual manner.
• Unique adjustment to the environment: Every person is characterized by a dynamic organization of psychological traits that makes his adjustment. The reason for this is that experiences of every person are unique therefore their reaction to the environment is also unique.
• Development of personality structure: Personality development is the natural quality of a growing organism. The path is from simple to increasingly complex factors and situations an individual has to pass by.
• Consciousness: Personality is conscious in that it develops out of our interaction with the environment. This interaction results in the formation of the concept of self.

Hence, we can conclude that Personality is an organization of qualities that characterize an individual.

Given:

Δ ABC ~ ΔQRP

AB = 18 cm

BC = 15 cm

Concept used:

The ratio of the area of two similar triangles is equal to the square of the ratio of the corresponding side of the triangle

Calculations:

As we know,

The triangle is similar to each other,

Then the corresponding side of BC is PR

So,

⇒ PR = 10 cm

⇒ Hence, The length of PR is 10 cm

Given

A (k + 1, 1), B (4, -3) and C (7, -k)

Formula

The area of triangle = 1/2[(x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)]

Solution

Area of ΔABC,

⇒ 6 = 1/2[(k + 1)(−3 + k) + 4(−k − 1) + 7(1 + 3)]

⇒ 12 = [− 3k + k² − 3 + k − 4k − 4 + 28]

⇒12 = [k² − 6k + 21]

⇒ k² - 6k + 21 − 12 = 0

⇒ k² − 6k + 9 = 0

⇒(k − 3)² = 0

⇒ k − 3 = 0

⇒ k = 3

The correct option is 1.

Given:

Concept Used:

Similarity of triangles

If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.

Calculation:

⇒ In the given diagram

⇒ DE || BC

⇒ AC = AE + EC = 8 + 16 = 24 cm

Therefore, the value of AC is 24 cm.

Given:

Concept used:

Calculation:

cos (90° + θ) = – sin θ

sec (- θ) = sec θ

tan (180° – θ) = – tan θ

sec (360° – θ) = sec θ

sin (180° + θ) = – sin θ

cot (90° - θ) = tan θ

So,

⇒ -1

∴ The required answer is -1

Given:

First number = 3

Next two greater prime numbers = 5 and 7

Concept used:

LCM will be the smallest number divisible by all of them

Calculation:

3 = 3 × 1

5 = 5 × 1

7 = 7 × 1

LCM will be the uncommon factors = 3 × 5 × 7

⇒ 105

∴ The smallest whole number divisible by 3, 5 and 7 is 105

Given:

Rate = 4%

Time = 6 years

Amount = 5643

Concept used:

Annual installment = (100 × A)/[100 × T + {R × T( T – 1)}/2]

Where,

A → Amount

T → Time

R → Rate

Calculations:

Annual installment = (100 × A)/[100 × T + {R × T(T – 1)/2}]

⇒ (100 × 5643)/[100 × 6 + {4 × 6(6 – 1)/2}]

⇒ (100 × 5643)/{600 + (4 × 6 × 5/2)}

⇒ 564300/(600 + 60)

⇒ 564300/660

⇒ Rs. 855

∴ The annual installment is Rs. 855

Activity-oriented teaching is the process where the students learn by " learning by doing".The teacher just acts as a facilitator ensuring that more role is played by students, totally in contrast to the lecture method where students remain passive. Key Points

Characteristics of activity-oriented teaching

• Encourages "learning by doing" where the child participates actively.
• The approach will be interesting and meaningful.
• Provides an opportunity for a range of skills/abilities.
• Gives a lot of scope for thinking where children can participate and solve the problems in their ways.
• ​Avoids rote memorization as formulas in mathematics can be proved not to be just remembered.
• Helps the student in the application of his gained knowledge in a new way and finding the appropriate solution.

​Hence encouraging rote memorization is not true for activity-oriented teaching in a mathematics classroom.

Given:

A floor is 4 m long and 3 m wide

One-third of the floor is covered with yellow tiles of side 10 cm.

Another one-fourth of floor is covered with black tile of sides 15 cm.

The remaining area is covered with red tile of sides 20 cm.

Concept used:

Area = length × breadth

1m = 100 cm

Calculation:

Area of the floor = 4 x 3 = 12 m² = 120000 cm²

Total area covered by Yellow tiles = 1/3 x 120000 = 40000 cm²

Area of 1 Yellow tile = 10 x 10 = 100 cm²

⇒ Number of Yellow tiles = 40000/100 = 400 tiles

The portion of the area covered by red tiles = 1 - 1/3 - 1/4 = 5/12

Total area covered by red tiles = 5/12 x 120000 = 50000 cm²

Area of 1 red tile = 20 x 20 = 400 cm²

⇒ Number of Red tiles = 50000/400 = 125 tiles

∴ The number of yellow and red tiles used is 400 and 125 respectively.

The correct answer is option 1.

Given: The graph shows the import of a commodity X in crore rupees between 1993 and 1996.

Calculation:

⇒ Import Increases between 1993-94 and 1994-95 = 900 - 700 = 200

⇒ Import increases between 1994-95 and 1995-96 = 1200 -900 = 300

⇒ Import increases between 1995-96 and 1996-97 = 1200 - 1200 = 0

⇒ Import increases between 1996-97 and 1997-98 = 1300 - 1200 = 100

⇒ Import increases between 1997-98 and 1998-99 = 2000 - 1300 = 700

Total Increase in import = 200+300+0+100+700 = 1300

Given :

To find the Distance between the points A(4,-3) and B(-4,3).

Formula used :

Distance between two points (x,y) and (X,Y) =

Calculation :

Distance

∴ The answer is 10 .

Given :- 1st term of A.P. is p and common difference is q.

Concept used :- nth term of A.P. is

Solution :- We have a = p and d = q

then 

Hence 10th term is  p + 9q

Given:

A can do a work in 6 days. B takes 12 days. C takes as long as A and B would take working together.

Concept used:

Work done in 1 day = 1 / (Total number of days required to do work)

Calculation:

Work done by A in 1 day = 1/6

Work done by B in 1 day = 1/12

Work done by C in 1 day = 1/6 + 1/12  = 1/4

⇒ Work done by B and C in 1 day = 1/12 + 1/4 = 1/3

∴ B and C together will take 3 days to complete the work.

Given:

Ratio of Alcohol and water 23 : 17

Quantity = 240 L

Calculation:

According to question,

Since, 8 L of water is mixed

So,

⇒ 40 unit = 240

⇒ 1 unit = 6

⇒ 23 × 6 : 17 × 6

⇒ 138 : 102

⇒ 138 : (102 + 8)

⇒ 138 : 110

⇒ 69 : 55

∴ The correct answer is 69 : 55.

Given:

P = ₹4800

R = 5%

T = 2.5 years

∴ The amount of simple interest on ₹4800 at the rate 5% per annum in years will be ₹600.

Concept :

Additive identity: it does not alter the result even after the addition operation i.e. a + 0 = a where 'a' belongs to Integers

Multiplicative identity: it does not alter the result even after the multiplication operation i.e. a × 1 = a where 'a' belongs to Integers

commutative property with respect to addition: a + b = b + a where a, b belongs to integers.

Calculation:

option(2)

Additive identity: it does not alter the result even after the addition operation i.e. a + 0 = a where 'a' belongs to Integers

Example : 3 + 0 = 3 or -3 + 0 = -3

∴ option 2 is correct

option(3)

Multiplicative identity: it does not alter the result even after the multiplication operation i.e. a × 1 = a where 'a' belongs to Integers

Example: 4 × 1 = 4 and -5 × 1 = -5

∴ option 3 is correct

option(4)

commutative property with respect to addition: a + b = b + a where a, b belongs to integers.

Example : -3 + 1 = -2, 1 + (-3) = -2

∴ option 4 is correct

option (1)

subtraction is not commutative

a - b ≠ b - a where a and b are integers

Example : 3 - 1 = 2 ≠ 1 - 3 = -2

∴ option 1 is not true for integers

Given:

The sum of two numbers is 12.

The sum of their reciprocals is 4/9.

Calculation:

a + b = 12

⇒ ab = 27

Let the one number be x and the other number be 12 - x

Now there product is 27

⇒ x(12 - x) = 27

⇒ 12x - x² = 27

⇒ x² - 12x + 27 = 0

Given:

Downstream = 24 km

Upstream = 8 km

Time taken = 4 hours

Formula used:

Speed of current = 1/2 × (Downstream - Upstream)

Calculation:

According to Question

Rate of downstream = 24/4 = 6 km/hr

Rate of Upstream = 8/4 = 2 km/hr

Speed of current = 1/2 × (Downstream - Upstream)

⇒ 1/2 × (6 - 2)

⇒ 1/2 × (4)

⇒ 2 km/h

∴ The speed of the current is 2 km/h.

The correct answer is Option(2) i.e. Physical property.

The boiling point, melting point, and density are examples of the physical property of an element.

Physical Property:

• A physical property is a characteristic of matter that is not associated with a change in its chemical composition.
• Physical properties are characteristics that can be observed or measured without changing the makeup of a substance.
• Any characteristic of a material you can observe without changing the substances that make up the material.
• There are two types of physical properties: intensive and extensive.
• Intensive physical properties do not depend on how much of the object there is. For example, a small rock will be just as hard as a large rock. hardness, softness, and speed (quickness) are intensive physical properties.

Example:

• Examples of physical properties are color, smell, freezing point, boiling point, melting point, infra-red spectrum, attraction (paramagnetic) or repulsion (diamagnetic) to magnets, opacity, viscosity, and density of an element.

Chemical Property:

• A chemical property is a characteristic of a substance that may be observed when it participates in a chemical reaction.
• Chemical properties include things like reactivity to oxygen, flammability, and ability to hold on to electrons during a chemical reaction.
• The periodic table is a table that organizes elements based on their atomic number and properties.
• Chemical properties are properties that can be measured or observed only when matter undergoes a chance to become an entirely different kind of matter.
• Reactivity is the ability of matter to react chemically with other substances.

Example: Examples of chemical properties include flammability, toxicity, chemical stability, and heat of combustion, electronegativity, acidity & basicity, the degree of ionization, etc are classic example of chemical properties.

Additional Information

Characteristic property:

• A characteristic property is a chemical or physical property that helps identify and classify substances.
• These properties include colour, density, melting point, boiling point, and thermal and electrical conductivity.
• While some of these properties are due chiefly to the electronic structure of the element, others are more closely related to the properties of the nucleus, which is the mass number of an element.

Example:

• Examples of characteristic properties include freezing/melting point, boiling/condensing point, density, viscosity, and solubility of any object.
• Size, volume, and mass are characteristic properties of matter.

Concept used:

Mean = Sum of elements/Number of elements

Calculation:

The first nine odd prime numbers are 3, 5, 7, 11, 13, 17, 19, 23, 29

Total of numbers = (3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29)

⇒ 127

Mean = 127/9

⇒ 14.11

∴ The required answer is 14.11.

Given:

Mean = 8

Median = 11

Concept used:

Mode = 3 Median - 2 Mean

Calculation:

Mode = 3 × 11 - 2 × 8

⇒ Mode = 33 - 16

⇒ Mode = 17

∴ The mode is 17.

∴ Option 3 is the correct answer.

The correct answer is Volt.Key Points

• The SI unit of Electric Potential Difference is Volt.
• Electric potential Difference is an external work needed to bring a unit charge from one location to another under the influence of an electric field.
• The unit is named after the renowned scientist Alessandro Volta.
• The Volt is signified by the letter V in physics.
• The instrument used for measuring the potential difference between the 2 terminals is called a Voltmeter.

Additional Information

• Ampere is the SI unit of the Electric Current.
  • It is measured with an instrument named Ammeter.​
• Ohm is the SI unit of Electrical Resistance.
  • It is measured with an instrument named Ohmmeter.
• Joule is the SI unit of Work Done.
  • ​It is measured with the help of a formula that is a product of force and displacement.

Given:

Point = (-1, 5); line x = -3.

Concept Used:

In this type of question, reflection of the point in the line can be calculated by using below formula.

Formula Used:

If a point (x, y) is in the line x = c, then reflection point will be (2c - x, y); where c = constant

Calculation:

Using the above formulae, we get c = -3

Reflection point = (2c – x, y)

⇒ [2 × -3 – (-1), 5]

⇒ (-5, 5)

∴ The reflection of the point (-1, 5) in the line x = -3 is (-5, 5).