MPTET Varg 2 Math Mock Test - 5 - MPTET MCQ

अनुच्छेद के अनुसार, कोकून के अंदर तितली स्वयं को सप्रयास मरोड़ती है ताकि तरल पदार्थ उसके शरीर से पंखों तक पहुंच जाए।

Key Points

• गद्यांश के अनुसार:-
  • ​कोकून से तितली बनने की प्रक्रिया में, यह जरूरी हैं कि उस छोटे से छेद में से ही निकले,
  • ताकि उसके पंखों को आवश्यक तरलता मिल सके और वो मजबूत बन सके और यह प्रक्रिया पूरी होने के बाद ऊँची उड़ान भर सकें।
• शरीर - देह, काया, गात्र, अंग, गात, तनु, कलेवर, वपु।
• पंख - डैना, पक्ष, पर, पखौटा, पाँख।

Additional Information
विस्तारित:-

• अर्थ: जिसका विस्तार हुआ हो या किया गया हो।

सशक्त:-

• अर्थ: जिसमें शक्ति हो, मज़बूत, शक्तिशाली, बलवान।

सहारा:-

• अर्थ: व्यक्ति या वस्तु जिससे किसी कार्य को करने में सहायता मिले।

जब उसे कोकून मिला तो 'आदमी ने तितली को अकेले छोड़ने का फैसला नहीं किया।'Key Points

• गद्यांश के अनुसार:-
  • एक आदमी को तितली का एक कोकून मिला। एक दिन इसमें एक छोटा सा छिद्र दिखाई दिया।
  • वह कई घंटों तक बैठकर तितली को देखता रहा क्योंकि यह छोटे छेद के माध्यम से अपने शरीर से बाहर निकलने के लिए संघर्ष कर रही थी।
  • फिर यह बंद हो गया, क्योंकि यह आगे नहीं निकल सकी। तो आदमी ने तितली की मदद करने का फैसला किया।
  • उसने कैंची ली और कोकून के शेष बिट्स को काट दिया। तितली आसानी से बड़ी हुई किंतु इसका शरीर फूला हुआ और पंख मुरझाये हुए थे।
  • आदमी को अपनी जल्दबाजी और दया के आगे कुछ समझ नहीं आया।
• तितली - रंग-बिरंगे पंखवाला एक छोटा कीड़ा जो प्रायः फूलों का रस चूसता है।

Additional Information
कोकून:-

• अर्थ: प्यूपा के रूप में संरक्षण के लिए कई कीड़ों के लार्वा द्वारा एक रेशमी मामला घूमता है।

कैंची:-

• अर्थ: दो फलोंवाला एक प्रसिद्ध औजार जिसके बीच में वस्तु रखकर काटी जाती है।

जर्मनी के आत्म समर्पण का मुख्य आधार था- विल्सन के चौदह सूत्र

Key Points

• जर्मनी ने इस शर्त पर आत्म समर्पण किया था कि विल्सन के चौदह सूत्र तथा अन्य वक्तव्य शांति का आधार बनेंगे।

Additional Information

विल्सन के चौदह बिन्दु इस प्रकार थे-

• 1. भविष्य में शांति संधियां प्रकट रूप से की जायें और गुप्त कूटनीति का अवलम्बन न किया जाये।
• 2. शांति तथा युद्ध दोनों के समय में समुद्र-तट सबके लिये स्वतंत्रता रहे और वे सबके लिये खुले रहें।
• 3. अन्तर्राष्ट्रीय व्यापार के मार्ग में उपस्थित बाधायें हटा दी जायें।
• 4. शस्त्रास्त्रों में कमी हो।
• 5. अधीन लोगों के हित का समुचित ध्यान रखते हुये औपनिवेशिक दावों का निष्पक्ष निर्णय हो।
• 6. केन्द्रीय राष्ट्र रूस की भूमि छोड़ दें और रूस को विकास के लिये पूर्ण अवसर प्राप्त हो।
• 7. जर्मनी, बेल्जियम को खाली कर दे और अपनी पूर्व स्थिति में पहुंच जाये।
• 8. इसी प्रकार फ्रेंच भूमि भी खाली करके पूर्व स्थिति में पहुंचा दी जाये। अल्सास-लोरेन फ्रांस को वापिस मिल जाये।
• 9. राष्ट्रीयता के सिद्धांत के आधार पर इटली की सीमाओं का संशोधन किया जाये।
• 10. आस्ट्रिया के लोगों को स्वायत्त शासन का अधिकार प्राप्त हो।
• 11. सर्बिया, मोंटोनीग्रो तथा रूमानिया को केन्द्रीय राष्ट्र खाली करके अपनी पूर्व स्थिति में पहुंचा दें और सर्बिया को समुद्र तट पर निवास स्थान प्राप्त हो।
• 12. टर्की के साम्राज्य के विरूद्ध तुर्की प्रदेशों की संप्रभुता सुरक्षित रहे और शेष भागों को स्वायत्त शासन प्राप्त हो और डार्डेन्लीज तथा बास्फोरस के जलडमरूमध्यों में सभी राष्ट्र के जहाजों को यातायात की स्वतंत्रता हो।
• 13. स्वतंत्र पोलैंड का निर्माण हो और उसे समुद्र तक पहुंचने की सुविधा दी जाये।
• 14. छोटे बड़े सभी राष्ट्रों को समान रूप से राजनीतिक स्वतंत्रता तथा प्रादेशिक अखण्डता का आश्वासन देने के लिये एक राष्ट्र संघ की स्थापना की जाये।

The correct answer is 'hid'

Key Points

• The given sentence is in the past tense as we can see that the second verb is in the past tense. So the first verb should be in the past tense.
• The verb forms of the hide are- Hide(Present simple)- Hid (past simple)- Hidden (past participle)
  • Example- Feeling rather like a schoolboy, Masters hid behind the counter of the clothes store.

So the correct sentence is- The moon hid behind the clouds and was not visible

The correct answer is 'The lorry has been driven off the road by somebody.'

Key Points

• The given sentence is in Present Perfect Tense and Active Voice.
• The rule for changing a Present Perfect Tense from Active voice to Passive voice:
• Interchange the object and subject with each other, i.e. object of the active sentence become the subject of the passive sentence.​
• Subject is "Somebody" and object is "the lorry" in active voice.
• So, the subject is "The lorry" and object is "somebody" in passive voice.
• Structure:
  • Subject + has/have + V3 + Object (Active Voice)
  • Object + has/have + been + V3 + by + Subject (Passive Voice)
• Example:
  • Disha has arranged the things. (Active Voice)
  • The things have been arranged by Disha. (Passive Voice)
• Therefore, the​ correct answer is Option 3.

​​Correct sentence: The lorry has been driven off the road by somebody.

The correct answer is " are losing their jobs as the employers are outsourcing their jobs to overseas employees in cheaper countries."

Key Points

• In the third sentence of the given passage, it is mentioned that employees who said they were happy working from home because it makes financial sense failed to consider their employer's perspective.
• In the fifth sentence of the passage, it is mentioned that this is a huge shift in the marketplace because companies haven't yet internationally outsourced many jobs that require higher education, says Anna Stansbury.
• In the fourth sentence of the given passage, the narrator states, "the employers are making another financial decision by outsourcing their jobs to overseas employees who are happy to make less than 20% of what they make."

​Hence, the correct sentence is option 3.

Logic:

Check all the options:

1) COMIC → There is the repetition of the letters 'C' in the given word

2) SHOES → There is the repetition of the letters 'S' in the given word.

3) TOUCH → There is no repetition of the letters in the given word.

4) MADAM → There is the repetition of the letters 'M' and 'A' in the given the word.

Here, Option (3) is different from all other options.

Hence, the correct answer is "Option (3)".

The logic followed here is:

Given the terms: Cricket players, Tennis fans, Students

Here,

Some Students can be Cricket players.

Some Cricket players can be Tennis fans.

Some Students can be Tennis fans.

Therefore, the Venn diagram is

Hence, "Option (3)" is the correct answer.

Teaching Learning Materials (TLMs):

• These are a set of tools that facilitate learning by providing the required input that meets the objectives.
• It consists of a variety of resources that are used by a teacher to teach the concepts outlined in the curriculum, and by the learner in learning and deriving knowledge out of the course.

Universal Design of Learning is an educational framework that implies providing teaching-learning materials in accessible formats to diverse learners.

It is a dynamic side of education which benefit the learners by:

• planning the class curriculum effectively.

• developing a flexible learning environment.

• improving accessibility to ample opportunities.

• providing a variety of strategies and resources.

Note: Universal Humanistic Approach of teaching allows students for social personal development and gives importance to learner's thoughts, feelings, and emotions in overall development.

Hence, providing teaching-learning materials in accessible formats to the diverse learners implies Universal Design of Learning.

Steinert disease is defined as a muscle disease characterized by myotonia and by multiorgan damage which combines various degrees of muscle weakness, arrhythmia and/or cardiac conduction disorders, cataract, endocrine damage, sleep disorders and baldness. It is also known as myotonic dystrophy.

Key Points

A system disorder characterized by a wide range of muscle-related manifestations (muscle weakness, myotonia, early onset cataracts (before age 50) and systemic manifestations (cerebral, endocrine, cardiac, gastrointestinal tract, uterus, skin and immunologic involvement) that vary depending on the age of onset.

• Myotonia that, is prominent especially in the early stages of the illness, which is aggravated by cold and stress. It is seen most consistently in the facial and hand intrinsic muscles.

Additional Information

• Duchenne muscular dystrophy (DMD) is a genetic disorder characterized by progressive muscle degeneration and weakness due to the alterations of a protein called dystrophin that helps keep muscle cells intact.
• Becker muscular dystrophy is caused by a genetic problem in producing dystrophin, a protein that protects muscle fibers from breaking down when exposed to enzymes.
• Limb-girdle muscular dystrophy is a term for a group of diseases that cause weakness and wasting of the muscles in the arms and legs.

Thus, we can conclude that Myotonic Muscular Dystrophy is also known as Steinert's Disease.

The National Institute of Open Schooling (NIOS) formerly known as National Open School (NOS) was established in November 1989 as an autonomous organization in pursuance of National Policy on Education 1986 by the Ministry of Education (MOE), Government of India.

• Recognizing the significant roles of NOS at the national and international level, the NOS was rechristened as the National Institute of Open Schooling (NIOS) by the Government of India Resolution dated 30th July 02.

Key Points

It was visualized that the NIOS will make its contribution to:

• universalisation of education
• greater equity and justice in society
• the evolution of a learning society

Additional Information

The objectives of NIOS, as approved by its governing body are to:

• develop and prescribe or offer a wide spectrum of courses of study, for purposes of general, vocational continuing education, either leading to certification at the-university level (including certificates/diplomas) or for life and job enrichment.
• plan and organize intensive training for capacity building in the area of open schooling at the national level.
• develop and prescribe or offer Vocational Education to its students.
• develop study materials, using print as well as non-print media.
• collaborate with institutions to provide learning assistance to the students through Study Centres and establish Regional Centres for the promotion of Open Schooling.
• serve as an agency for the effective dissemination of information related to Distance Education and Open Learning through the publication of newsletters, bulletins, or journals.
• Identify and promote standards of learning in Distance Education systems and Open Schools to maintain standards of equivalence with the formal system, while retaining its distinct character.

Hence, we can conclude that the full form of NIOS is the National Institute of Open Schooling.

Memory refers to the ability or power of the brain that helps an individual in obtaining, transforming, storing, retrieving, and using information when needed.

Key Points

In active memory, the content is retained for a long time as it is a kind of memory which:

• holds information for a longer period of time or for entire life.
• consists of information which is consciously stored and retrieved.
• forms by acquiring knowledge through our experiences or senses.

Hence, it could be concluded that 'active memory' is true in the context of the question.

There are different kinds of teaching approaches in fashion which facilitate learning in a meaningful way and 'Activity Centred Approach' is one of them.

Activity-centered approach refers to the involvement of learners in specially designed activities, in which they enjoy maximum autonomy.

Activity-centred approach is student-centred which emphasizes upon:

• allowing students to work at their own pace freely and willingly.
• giving primacy to students' experiences, understanding and needs.
• enabling students to develop naturally towards their fullest potential.
• providing opportunities to students to foster their own strategy of learning.
• developing self-learning skills among the learners and making learning meaningful for them.

Hence, it could be concluded that in Activity-centered approach, the learner enjoys maximum autonomy.

The correct answer is option 2.

Key Points

Concept:

Energy

• The capacity of doing work is called energy.
• SI unit of energy is the joule.
• Various forms of energy are heat energy, light energy, nuclear energy, electrical energy, mechanical energy, etc.
• Energy can be converted from one form to another.
• This happens through various processes or using certain appliances.
• For example, when a bulb glows by electricity, electrical energy is converted into light energy.

Explanation:

Windmill

• A windmill has large blades just as a fan.
• It wind rotates the blades attached to the turbine.
• The turbine rotates and electrical energy is produced.
• Energy to the motion is kinetic energy.
• So, the windmill converts the kinetic energy of blades into electrical energy.

Electric cell

• Chemical reactions take place in the cell.
• This makes a potential difference between the two terminals.
• When connected with the conductor, current flows.
• In this way, chemical energy is converted into electrical energy.

Electric bulb

• An electric bulb converts the electrical energy into light and heat energy.
• A filament present in the bulb burns and light energy is produced out of it.

Microphone

• A microphone receives the sound signal and converts it into electrical signals.
• In the microphone, there is a diaphragm.
• It vibrates and the diaphragm makes the coil attached to it vibrate.
• A permanent magnet near the coil induces a current in the coil by the process of electromagnetic induction.
• So, sound energy is converted into electrical energy.

Conclusion:

The correct sequence is hence a) - (ii), (b) - (iv), (c) - (i), (d) - (iii)

Mathematics improves children's thinking by providing clarity of thoughts, which helps them to convert assumptions to logical conclusions.

• The teaching of mathematics aims to develop many mathematical skills and processes among children such as handling abstractions, problem-solving, mathematical communication, conjecturing, and searching for proofs.

Key Points

Comparison addition:

• The fundamental "number operations" of mathematics such as addition, subtraction, multiplication, and division are taught by using real-life examples to make students familiar with them.
• This will help the students to achieve basic mathematical proficiency that will help them to learn complex abstractions of mathematics at a higher level.
• Suppose, we have to teach the children about comparison addition i.e., to compare the difference between two quantities to know how much one quantity is more than the other one.
• It helps the children to perform mathematical calculations in their minds without using paper.
• For example, I have 8 pens. Manisha has two more than me. How many pens does Manisha have?
• In this example, the students will compare his quantity of pens to the quantity or numbers of pens Manisha has i.e., 8 and 8 + 2 = 10 pens.

Hence, it is concluded that the type of the given word problem is comparison addition.

Given:

If the average of four consecutive numbers is 112.5.

Concept used:

Average = (Sum of all observations) ÷ (Number of observations)

When the second number and first number differ by 1, then the number are said to be consecutive numbers.

Calculation:

Let (a), (a + 1) , (a + 2) and (a + 3) are the four numbers.

The sum of the above four numbers = a + (a + 1) + (a + 2) + (a + 3) = 4a + 6

According to the question,

The sum of the above four numbers = 112.5 × 4 = 450

Now,

⇒ 4a + 6 = 450

⇒ 4a = 444

⇒ a = 111

The value of the first number = 111

The value of the second number = 111 + 1 = 112

The value of the third number = 111 + 2 = 113

The value of the fourth number = 111 + 3 = 114

Now,

The sum of second and third number = 112 + 113 = 225

∴ The sum of the second and third numbers is 225.

Given:

The diameter of a sphere made of copper = 3 cm

Length of the wire = 1/2 m = 0.5 m

Formula used:

Volume of the sphere = (4/3)πr³

Volume of the cylinder = πr²h

Calculation:

Volume of sphere = volume of the cylinder

⇒ (4/3)πR3 = πr²h

Since, R = D/2 & 1 m = 100 cm

⇒ (4/3) × (3/2)³ = r² × 0.5 × 100

⇒ (4/3) × (27/8) = 50 r²

⇒ 4.5 = 50 r²

⇒ r2 = 50/4.5

⇒ r2 = 0.09

⇒ r = 0.3 cm

The diameter of the wire

⇒ 2r = (2 × 0.3) cm = 0.6 cm

∴ The required diameter of the wire is 0.6 cm.

Given:

Area of trapezium is 48square cm

Sum of parallel sides is 48 cm

Formula used:

Area of trapezium = ½(sum of parallel sides) × height

Calculation:

According to the question:

∴ 48 = 1/2 × 48 × height

⇒ Height = 48/24 = 2

So, the height of the trapezium is 2 cm.

Concept:

cos (π + x) = - cos x

cos (π - x) = - cos x

Calculation:

Given,

Since,

⇒ x = y × (-1/2) = -y/2

⇒ y = -2x -----(i)

And

x = z × (-1/2) = -z/2

⇒ z = -2x -----(ii)

Now, We have to find the vlaue of xy + yz + zx

Now, From (i) and (ii), we get

⇒ xy + yz + zx = x(-2x) +(-2x)(-2x) + (-2x)x

⇒ xy + yz + zx = -2x² + 4x² - 2x² = 0

∴ The correct answer is option (2).

Given

Formula used

cosec(90 - θ) = secθ

tan(90 - θ) = cotθ

Solution

The correct option is 1.

Given:

Volume of cuboid = 864 cu. cm

Area of ​​the base is 108 sq. cm

Formula Used:
Volume of Cuboid = Length × Breadth × Height

Since, Length and Breadth makes the base of cuboid,

Area of Base = Length × Breadth

Volume of Cuboid = Area of Base × Height

Calculation:

Area of Base × Height = 864

⇒ 108 × Height = 864

⇒ Height = 864 ÷ 108 = 8 cm

Hence, Height of cuboid is 8 cm.

Mathematics education must be affordable to every child and at the same time, it needs to be enjoyable so that students can enjoy learning mathematics instead of fearing away from it.

• The teaching-learning resources in mathematics are used to bring concreteness into the teaching of abstract concepts in the classroom and also stimulates the interest of learners.
• They are specifically used by the students to explore, investigate, and internalize the concepts to enhance their mathematical competency.

Key Points

Desirable practice in teaching and learning of measurement of area and perimeter:

• Mensuration is an integral part of mathematics that deals with the quantification and estimation of different types of geometric figures and their attributes such as length, volume, shape, perimeter, area, etc.
• It includes the shapes and the depth study of their characteristics where they hold some complex abstractions which can only be comprehended learning by doing.
• The perimeter is the total length of the boundary of any object or shape. To calculate the perimeter of a shape, we just need to measure and add the length of all its sides. For example, the perimeter of a house will be the length of its outer boundary.
• The area of a shape or any object is the space enclosed by it on a plane surface. For example, the area of a house will be the space occupied by it over a piece of land.
• The teacher should use real-life objects to teach them the concept of "area" and "perimeter" as learning becomes more lively, purposeful, and interesting when real-life examples or objects are used in teaching.
• By using real-life objects or examples, the children can become aware of the application of mathematical concepts in the real world and also they get to know the relevancy of mathematical knowledge with respect to their implications in real life.

Hint

• Instead of focusing on precise calculation, the emphasis should be led on providing contextual understanding among learners.
• The teacher should not introduce the hit and trial method to calculate the area and perimeter of geometrical shapes as it can not make the learners capable of understanding the basics of mensuration. They will just keep trying different ways due to which the learners may lose interest in learning.
• Starting with writing the formula of area and perimeter will only encourage cramming among learners. First, the teacher should provide the students real-life examples to make them familiar with the concepts of area and perimeter, and then the formulas should be introduced to them.

Hence, it is concluded that encouraging children to find out the area & perimeter of daily life objects is considered a desirable practice in teaching and learning of measurement of area and perimeter.

Mathematics is a branch of science which deals with counting, calculating, and studying numbers, shapes, and structures. The following are the features of mathematics:

• It is symbolic, therefore it is seen generally that children find it difficult to understand math's.
• There are many branches of mathematics namely algebra, geometry, trigonometry, and arithmetic.
• At the higher level, it is classified in Pure Mathematics and Applied Mathematics.
• Mathematics is considered as an organised structure of knowledge because it gives insight into the power of the human mind
• It is abstract since the problems require imagination and the ability to perceive.
• The beauty of math's is that it is certain, accurate, and logical; each result in maths can be proved, and if not, they are obvious and self-evident (axioms).

Hence, we conclude that all the above-mentioned statements are true.

Concept:

Formula of Logarithms:

 here a ≠ 1 and a > 0 and x be any number.

Properties of Logarithms:

​​​​​​​

Calculation:

Given: log 2 = 0.301 and log 3 = 0.477.

As we know that,

⇒ log 6 = log (2 × 3) = log 2 + log 3

By substituting the value of log 2 and log 3, we get

⇒ log 6 = 0.301 + 0.477 = 0.778

Hence, log 6 ≈ 0.8.

Given:

The surface area of a sphere is 38.5 cm2

Concept used:

Surface area of a sphere = 4πr²

Here,

r = radius

Calculation:

Let the radius of the sphere be r

So, 4πr² = 38.5

⇒ r² = 38.5 × (7/22) × (1/4)

⇒ r² = 269.5/88

⇒ r2 = 3.0625

⇒ r2 = 30625/10000

⇒ r2 = (175/100)²

⇒ r = 175/100

⇒ r = 1.75

∴ The radius of the sphere is 1.75 cm.

Concept:

Work

• Work is said to be done by a force, when it moves, its point of application through a distance.
• In this case, W = m × h × t
• Where, m = mass of body, h = height, t = time required
• 1 litre of water = 1 kg of water

Calculation:

Given:

m = 200 kg, h = 300 m, t = 60 min

W = 200 × 300 × 60

W = 3600000 kg metres

The correct option is The length of the rubber band increases when it is pulled.

Key Points

• Under the influence of force, the body can change its size, shape, velocity, and direction.
• An item changes shape when force is applied.
• A push or pull that an object experiences as a result of interacting with another item are known as a force.

Example:

• The length of the rubber band increases when it is pulled.
• The seat cushion changes their shape when we sit on them.
• You press a balloon it changes its shape due to force.

Calculation:

Given number = 625361

Since, it is near to 800² = 640000

Checking for 790² = 624100

791² = 625681

625681 - 625361 = 320

Hence, 320 will be added to it

Sum of the digits of 320 = 5

∴ Required answer = 5

Given:

Difference between squares of two consecutive numbers = 23

Formula used:

(a + b)² = a² + b² + 2ab

Calculation:
Let both numbers be x and x + 1

According to the question,

(x + 1)² - x² = 23

⇒ x² + 1 + 2x - x² = 23

⇒ 2x = 22

⇒ x = 11; x + 1 = 12

∴ The numbers are 11 and 12.