MPTET Varg 2 Math Mock Test - 8 - MPTET MCQ

'कितना नया है यह अनुभव मेरे लिए।' पंक्ति के माध्यम से कवि ने यह कहने का प्रयास किया है कि कवि को उम्मीद नहीं थी कि चिट्ठियाँ लौट आएँगी।

Key Points

• पद्यांश के अनुसार :-
• यह खत पहला नहीं, जो लौटा है कई और भी लौट चुके हैं पहले बस एक ही खबर लिए कोई नहीं मिला, ठिकाने पर ताला था।

Additional Information

• अनुभव का अर्थ -काम की जानकारी।
• अनुभव का विलोम -अनुभवहीन।
• अनुभव का पर्यायवाची -अनुभूति, आपबीती, संवेदनशीलता, इंद्रियबोध क्षमता, इंद्रियबोध, शक्ति, संवेदन, संवेदना आदि।

कविता में प्रकृति मेहनती व्यक्ति व्यक्ति से सदा हार जाती है। 

• पद्यांश के अनुसार:-
  • कवि का मानना है कि प्रकृति कभी भाग्य के बल से डरकर नहीं झुकती। वह सदा परिश्रम करने वालों से भयभीत रहती है।
  • जब एक मेहनती व्यक्ति अपना पसीना बहाता है तब उसके सम्मुख प्रकृति को भी अपनी हार स्वीकार करनी पड़ती है। 

Key Points

• मेहनती = मेहनत + ई 
  •  'मेहनत' मूल शब्द और 'ई' प्रत्यय ​
  • अर्थ: परिश्रमशील, कर्मठ, उद्यमी, उद्योगी, परिश्रमी, प्रयत्नशील।
  • विलोम शब्द- 'कामचोर, आलसी, अकर्मण्य'

Additional Information

भाग्यवान:- 

• भाग्य + वान = भाग्यवान
• 'भाग्य' मूल शब्द और ' वा
• न' प्रत्यय
• अर्थ: सौभाग्यशाली, भाग्यवान, खुशनसीब
• विलोम शब्द- 'भाग्यहीन, बदकिस्मत'

बलवान:-

• बल + वान = बलवान 
• 'बल' मूल शब्द और ' वान' प्रत्यय
• अर्थ: शक्तिशाली, बलशाली, ताकतवर, पुष्ट, मजबूत, दृढ़।
• विलोम शब्द- 'बलहीन'

पापी:-

• अर्थ: पाप में रत रहनेवाला, दुष्ट, नीच, दुर्जन।
• विलोम शब्द- 'निष्पाप'

The correct answer is 'cordial'.

Key Points

• The word "hospitable" means to be friendly, welcoming, and generous towards guests or strangers. In this sentence, the author is describing the local people as being hospitable to strangers, which means that they are friendly and welcoming to those who are not from the area.
• The most appropriate option that is nearest in meaning to "hospitable" is "cordial".
• Cordial means being warm and friendly, and therefore it accurately describes the local people's behavior towards strangers.
• The other options - "surly," "distant," and "frosty" - are all antonyms of "hospitable".
  • Surly means rude or bad-tempered, distant means cold or aloof, and frosty means unfriendly or unwelcoming.
  • None of these options accurately convey the idea of friendliness or warmth that is present in the word "hospitable", and are therefore not suitable alternatives for it.

Correct answer: Option 2: ​to do something that is too difficult

Key Points

• The most appropriate meaning of the underlined idiom is ​to do something that is too difficult.
• Bitten off more than she can chew: to take on or attempt more than one is capable of doing.
  • Example: The key to success lies in not biting off more than you can chew.
• Thus, the correct answer is to do something that is too difficult.

The correct answer is Protection and improvement of environment and safeguarding of forests and wild life.

Key Points

• 42nd Constitutional Amendment act of 1976 added four new directive principles to the original list.
  • Article 39F: To secure opportunities for the healthy development of children.
  • Article 39A: To provide free legal aid to the poor.
  • Article 43A: Participation of workers in the management of industries.
  • Article 48A: To protect and improve the environment and safeguarding of forests and wildlife.
• 44^th Constitutional Amendment act of 1978 added on more new directive principles to the original list.
  • State to minimise inequalities in income, status, facilities, and opportunities(Article 38).​
• 86^th Constitutional Amendment act of 2002 changed the subject matter of Article 45 and made elementary education a fundamental right under Article 21 A.
• 97th Constitutional Amendment act of 2011 added on more new directive principle relating to the co-operative societies(article 43B).

Additional Information

• Directive Principles of State Policy are part IV of the Indian constitution from Articles 36 to 51.
• Framers borrowed this idea from the Irish constitution.
• It resembles the 'Instrument of instructions' enumerated in the government of India act of 1935.
• They are non-justiciable in nature.

Jharokha-darshan was discontinued during the reign of Aurangzeb.

Key Points

• Jharokha-darshan was a daily practice of addressing the public audience (darshan) at the balcony (jharokha) at the forts and palaces of the emperor.
• Jharokha-darshan was introduced by Akbar with the objective of broadening the acceptance of the imperial authority as part of popular faith.
• The emperor began his day at sunrise with personal religious devotions or prayers, and then appeared on a small balcony, the jharoka, facing the east.
• Below, a crowd of people (soldiers, merchants, craftspersons, peasants, women with sick children) waited for a view, darshan, of the emperor.
• The practice of Jharokha-darshan was continued by Akbar's son and grandson ie Jahangir and Shah Jahan respectively.

• The practice of Jharokha-darshan was banned by Mughal Emperor Aurangzeb (son of Shah Jahan) during his 11th year of reign, as he considered it a non-Islamic practice, a form of idol worship.

Hence, the correct answer is - Aurangzeb.

The correct answer is South Africa, China, Australia, and India.

Key Points

• Manganese is a chemical element.
• It is found as the free element in nature and in many minerals.
• The correct descending order of manganese production countries are:
  • South Africa- 6,200,000
  • China- 3,000,000
  • Australia- 2,900,000
  • India- 950,000
• South Africa is the world's largest producer of manganese, accounting for 33.5% of global production.
• Its annual manganese production amounts to 6.2 million tonnes, with a majority of manganese mining concentrated in the Kalahari Desert, which is believed to hold more than 70% of global reserves.

Thus, we can say that the correct descending order of manganese production countries is South Africa, China, Australia and India.

The relationship between which is best illustrated by the Venn diagram is given below,

• Because All uncles are males, so uncles will come under the males circle.
• But all Farmers are not males, only some farmers are males and some are uncles too, hence they will share a part with males and uncles circle.

Hence, option 4) is the correct answer.

Assessment of personality refers to the measurement of the personal characteristics of an individual.

It involves information gathering through interviews etc. and administering the psychological test to understand the typical characteristics.

Key Points

Methods of personality assessment can be categorized under three headings:

• Personality Inventories - In this method statements about certain traits of personality are constructed and the testee is required to answer them as “ right/wrong” or “yes/no”.
• Projective Techniques - In this method, a person projects his or her own desires, needs, and feelings onto another person or object. Writing a story on a particular subject is a projective method.
• Observational methods - It involves the observation and recording of the activities of a person by the observer in a controlled or natural situation and then analyzing it.

Hence we conclude that story writing is a projective method of assessing personality.

Wolfgang Kohler, a German psychologist, proposed the ‘Insightful Theory of learning’.

Key PointsAccording to Kohler, insight doesn't take place with trial & error, rather than it is a sudden reorganization of experience.

‘Insight Theory of learning’ implies that:

• The solution to a problem arrives ‘all of a sudden’ flash of insight when a person is struggling.
• Insight enhances an individual's ability to perceive and understand something or someone instinctively.
• Insight doesn't rely on behavior or observation, it is the sudden realization of a problem's solution using intuition.

For this, Kohler demonstrated the following experiment:

• He kept chimpanzees in a closed room where food was kept out of their reach, and items like boxes, stick was there.
• The chimpanzee would roam inside the room to reach the food.
• They would ‘suddenly’ stand on a box and use the stick to bring food close to them.
• It should be noted that it was not the result of trial and error instead, the chimpanzee suddenly came up with the idea to use boxes and stick.

Hence, we conclude that the Insight Theory of Learning was given by Kohler.

Additional Information

• B. F. Skinner, an American psychologist, propounded the "Theory of Operant Conditioning" which is also known as "Instrumental Conditioning Theory".
• Clark Hull was one of the famous behaviorists. He gave drive-reduction theory.
• Carl Rogers, an American humanistic psychologist has proposed 'Experiential Learning Theory'.

Given:

Some triangles and quadrilaterals are given.

Find the line of symmetry.

Concept used:

The line of symmetry can be defined as the axis or imaginary line that passes through the center of the shapes and divide into two identical halves.

Calculation:

In isosceles triangle,

Only one line of symmetry.

In Kite,

Only one line of symmetry.

In rhombus,

Two lines of symmetry.

In rectangle, Two line of symmetry.

In scalene triangle,

No any line of symmetry.

In parallelogram,

No any line of symmetry.

∴ Option 4 both have no same line of symmetry.

∴ Option 4 is correct.

Given:

log10 (x - 9) + log10 x = 1

Concept Used:

log_b (M) + log_b (N) = log_b(MN)

Calculations:

log10 (x - 9) + log10 x = 1

⇒ log10 (x - 9)(x) = 1

⇒ log10 (x - 9)(x) = log₁₀10

⇒ x² - 9x - 10 = 0

⇒ x² - 10x + x - 10 = 0

⇒ x(x - 10) + 1(x - 10) = 0

⇒ (x + 1)(x - 10) = 0

⇒ x = -1 and x = 10

∴ option 4 is correct

A mathematical game is an activity that engages children for amusement or fun. It should be a part of the mathematics classroom as it will be a child-centered and happy classroom where children get opportunities to observe, explore and share experiences.

Key Points

Characteristics of mathematical games-

• Mathematical games must not be confused with open-ended play and there is a set of rules that governs decision making. The rules should be based on mathematical ideas and the game should end when the goal is reached.
• Mathematical games provide non- didactic feedback to the children be the minimum amount of teacher intervention.
• Mathematical games promote processes of anticipation and planning in children which help them stimulate interest in a topic and develop mathematical skills.

Hence, we conclude that the correct statements are (b) and (c).

Given:

47 + {7 + [61 − (21 ÷ 3)] ÷ 9}

Concept Used:

Follow the BODMAS rule according to the table given below:

Calculation:

47 + {7 + [61 − (21 ÷ 3)] ÷ 9}

= 47 + {7 + [61 − 7] ÷ 9}

= 47 + {7 + 54 ÷ 9}

= 47 + {7 + 6}

= 47 + 13

= 60

Hence, the required value is 60.

Given:

Ratio of radius = 2 : 5

Ratio of Heights = 5 : 7

Formula Used:

Volume of cylinder = πr²h

(where r = radius, h = height)

Calculation:

Let, the radii be 2x and 5x and the heights be 5y and 7y.

For 1st cylinder, radius = 2x, height = 5y

For 2nd cylinder, radius = 5x, height = 7y

According to question,

Ratio of their volume(1st : 2nd) = π × (2x)² × 5y : π × (5x)² × 7y

⇒ 4x² × 5y : 25x² × 7y

⇒ 4 : 35

∴ The ratio of their volume is 4 : 35.

Given:

The circumference of the two circles is 110 cm and 330 cm respectively.

Concept used:

Circumference of a circle = 2πR (R = Radius)

Calculation:

Let the radii of the bigger and smaller circles be R and r respectively.

Difference between their radii = (R - r)

According to the concept,

2πR - 2πr = 330 - 110

⇒ 2π(R - r) = 220

⇒ 44/7 × (R - r) = 220

⇒ (R - r) = (220 × 7)/44

⇒ (R - r) = 35

∴ The difference between their radii is 35 cm.

Given:

The numbers are 12/5, 14/15 and 16/17

Concept used:

HCF = HCF of numerator/LCM of the denominator

Calculation:

LCM of 5, 15, 17 = 255

HCF of 12, 14, 16 = 2

So, HCF = 2/255

∴ The required answer is 2/255.

Concept:

A.P having Common ratio d = a_n - a_{n -1}

The first term is a

a_n = a + (n - 1)d

Solution:

For the given A.P

a = 1/p d = ((1 - p)/p) -(1/p) = -1

4th term for the A.P = a + (4 -1) d = a + 3d = 1/p - 3

Hence, The correct option is 4

Given:

Distance = 35 km

Time in downstream = 2 h

Time in upstream = 7 h

Concept used:

Speed = D/t

Downstream = v + u

Upstream = v - u

D = Distance

t = time

v = speed of the boat

u = speed of stream of the river

Calculation:

Speed in downstream = 35/2 = 17.5 km/h

Speed in upstream = 35/7 = 5 km/h

v + u = 17.5 ----(1)

v - u = 5 ----(2)

⇒ 2v = 22.5 [From eq 1 and eq 2]

So, Speed of the boat = 22.5/2 = 11.25 km/h

∴ The speed (in km/h) of the boat in still water is 11.25.

Given:

Dimensions = 12 cm × 6 cm × 4 cm

Concept used:

Diagonal of the cuboid =

Calculation:

The length of the longest rod that can be kept in a rectangular box = Diagonal of the cuboid

Diagonal of the cuboid =

∴ The correct answer is 14 cm.

Given:

Numbers 24, 30 and 84.

Calculation:

To find the smallest number we have to find LCM of the given three numbers.

The prime factors of the numbers are

24 = 2 × 2 × 2 × 3

30 = 2 × 3 × 5

84 = 2 × 2 × 3 × 7

∴ The LCM of (24, 30, 84) = 2 × 2 × 2 × 3 × 5 × 7 = 840.

∴ The smallest number divisible by all the three numbers 24, 30, and 84 is 840.

Given:

rate = 10%

Principal = Rs. 400

time = 3/2 years

Concept used:

If compound is half yearly,

rate = 10/2 = 5%, time = (3/2 × 2) = 3 years

A = P(1 + r/100)^t

Where, A = Amount, P = Principal, r = rate of interest, t = time period

Calculation:

According to the above concept,

A = P(1 + r/100)^t

⇒ 400(1 + 5/100)³

⇒ (400 × 21/20 × 21/20 × 21/20)

⇒ Rs. (9261/20) = Rs. 463.05

∴ The required amount is Rs. 463.05

Given:

Base is 19.8 cm and height is 5.4 cm

Formula used:

Area of parallelogram = base × height

Calculation:

Area = 19.8 × 5.4

= 106.92 sq.cm.

∴ The answer is 106.92 sq.cm

The correct answer is 100 N.

Key Points

• We know that force is the rate at which momentum changes with respect to time.
• It is mathematically represented as: F = dp/dt
• We know that momentum, p=mass(m)*velocity(v).
  • So, F = v x dm/dt → (I)
• According to question, v= 500ms^-1
  • Mass of one bullet= 20g⇒ 20/1000 kg
  • And as per the question, 10 bullets are fired per second so, the mass of 10 bullets = 10*20/1000 kg ⇒ 0.2 kg.
  • So, from equation (I)
  • F= 500*0.2 ⇒ 100 N.

Given:

The diameter of cone = 14 cm,

The radius of the cone = 7 cm

The curved surface area of the cone = 440 cm²

Formula used:

The curved surface area of the cone = πrl

Where, r = radius, and l = slant height

Calculation:

Let the slant height of the cone be l

Now, according to the above concept,

⇒ πrl = 440 cm²

⇒ (22/7 × 7 × l) = 440 cm²

⇒ 22 × l = 440

⇒ l = 20 cm

∴ The required slant height of the cone is 20 cm.

Given:

sin² 45° + cos2 45° - tan2 45°

Concept used:

Calculation:

sin² 45° + cos² 45° - tan² 45°

∴ sin² 45° + cos² 45° - tan² 45° is equal to 0.

Given:

Two numbers are in ratio 3 ∶ 7.

Their LCM is 189 and their HCF is 9

Concept used:

L.C.M × H.C.F = Multiplication of two numbers

Calculation:

Let the numbers be 3x and 7x

Now,

3x × 7x = 189 × 9

⇒ 21x² = 189 × 9

⇒ 7x2 = 189 × 3

⇒ x2 = 27× 3

⇒ x2 = 81

⇒ x = 9

So, the numbers ate 27, 63

∴ The required answer is 27, 63.

Given:

Selling price of TV = Rs. 16,756

Profit = 18%

Concept used:

Cost price = [100/(100 + Profit%) × SP]

Where, SP = Selling price, CP = Cost price

Calculation:

Let the cost price of the TV be Rs. x

According to the above concept,

⇒ x = [100/(100 + 18) × 16,756]

⇒ x = (100/118 × 16,756)

⇒ x = Rs. (100 × 142)

⇒ x = Rs. 14,200

∴ The cost price of the TV is Rs. 14200.

Given:

Selling Price of an article is Rs. 990

Loss % = 10%

Formula used:

S.P = C.P (100 - Loss)/100

Where,

C.P = Cost Price of an article

S.P = Selling Price of an article

Calculation:

S.P = C.P (100 - Loss)/100

⇒ 990 = C.P (100 - 10)/100

⇒ C.P = 990/0.90

⇒ C.P = 1,100

∴ The cost price of an article is Rs. 1,100

Mathematics is one of the few subjects that have practical, cultural, and disciplinary value. Mathematics has the potential to range across all three values, but due to the inappropriate teaching-learning process, its potential is not being utilized to its optimum level.

Values of Mathematics

• Practical values: Everybody uses mathematics in their daily life. Any person who is ignorant of mathematics can be easily cheated. He will always be at the mercy of others. We have to make purchases daily. We buy cloth, food items, fruit, vegetables, groceries, etc. We have to calculate how much we have to pay for everything.
• Disciplinary values: As mathematical knowledge is exact, logical, real and to that point, it creates discipline in a human mind and develops an ability to grasp a situation, to analyze the situation, and to perceive correctly the state of affairs.
  • Helps the students to imbibe qualities like Simplicity • Accuracy • Certainty of results • Originality • Similarity to reasoning in life • Verification of results • Concentration of mind.
• Cultural values: A country’s civilization and culture are reflected in the knowledge of mathematics it possesses. Mathematics helps in the preservation, promotion, and transmission of cultures. Various cultural arts like poetry, painting, drawing, and sculpture utilize mathematical knowledge.

Other's values of Mathematics

• Intellectual values: Develops intellectual powers: imagination, Memorization, Observation, Invention, Concentration, Originality, Creativity, reasoning.
• Social values: Social values can be acquired by Tolerance, Open-mindedness, Objectivity, Honesty, Truthfulness, Cooperation.
• Moral values: Develops moral qualities like honesty, truthfulness, justice, dutifulness, punctuality, self-confidence, power of distinguishing between right and wrong.

Hence, we can conclude that the characteristics of simplicity come under the disciplinary educational value of Mathematics.