MPTET Varg 2 Math Mock Test - 3 - MPTET MCQ

इस गद्यांश में लेखिका पाठकों को बतालाना चाहती है - टैगोर जैसे कलाकार की वृद्धावस्था में साधनहीनता पर दुःख।
Key Points

• गद्यांश के अनुसार -
  • जहाँ जीवन शिल्प की वर्णमाला भी अज्ञात है वहाँ वह साधनों का हिमालय खड़ा कर देता है और जिसकी उंगलियों में सृजन स्वयं उतरकर पुकारता है उसे साधन शून्य रेगिस्तान में निर्वासित कर जाता है। निर्माण की इससे बड़ी विडम्बना क्या हो सकती है कि शिल्पी और उपकरणों के बीच में आग्नेय रेखा खींचकर कहा कि कुछ नहीं बनता या सब कुछ बन चुका।

Additional Information

• विडम्बना- अपमान और उपहास का विषय; व्यंग्योक्ति
• शिल्प- किसी कथाकार या रचनाकार द्वारा अपनी रचनाओं में प्रयुक्त किया जाने वाला भावाभिव्यक्ति का विशिष्ट ढंग जो शैली से अधिक व्यापक माना जाता है।

गद्यांश का केंद्रीय भाव - 'भारत जैसे विशाल देश में भी शिल्प कार्य के लिए धन की कमी है।' कथन से है।
Key Points

• गद्यांश के अनुसार -
  • जीवन की संध्या बेला में 'शांति निकेतन' के लिए उन्हें अर्थ संग्रह में यत्नशील देखकर न कुतूहल हुआ न प्रसन्नता केवल एक गंभीर विषाद की अनुभूति से हृदय भर आया।
  • हिरण्यगर्भा धरती वाला हमारा देश भी कैसा विचित्र है! जहाँ जीवन शिल्प की वर्णमाला भी अज्ञात है वहाँ वह साधनों का हिमालय खड़ा कर देता है और जिसकी उंगलियों में सृजन स्वयं उतरकर पुकारता है उसे साधन शून्य रेगिस्तान में निर्वासित कर जाता है।

Additional Information

• हिरण्यगर्भा- हिरण्यगर्भ शब्द भारतीय विचारधारा में सृष्टि का आरंभिक स्रोत माना जाता है।
• शाब्दिक अर्थ है – प्रदीप्त गर्भ (या अंडा या उत्पत्ति-स्थान), प्राणात्मा, सूक्ष्म शरीर
• इस शब्द का प्रथमतः उल्लेख ऋग्वेद में हुआ है।

The correct answer is 'under'.

Key Points

• Under means 'affected by something'
  • For example : The wall collapsed under the strain.
• Off means moving away and often down from; situated or leading in a direction away from (a main route or intersection). (दूर)
• In means expressing the situation of something that is or appears to be enclosed or surrounded by something else. (के अंदर)
• From means indicating the point in space at which a journey, motion, or action starts. (से)
• By referring to the above explanation and the context of the given sentence, it can be concluded that under is the appropriate option to be chosen for filling the blank.

Hence, the correct answer is option 3.

The correct answer is 'Drugs and smoking​​.'

Key Points

• Let's have a look at the first sentence from 3rd paragraph in the passage:
  • “ Taking drugs and smoking are two of the deadly habits men have cultivated.”
• It is clear from the paragraph that two of the dangerous habits males have developed include using drugs and smoking.
• From the passage, it can be concluded that drugs and smoking are the two deadly habits that has man become a slave to.
• Therefore, the correct answer is Option 4.​

The correct answer is Rig Veda

Important Points

• The Vedic texts reflect two stages of development in terms of literature as well as social and cultural evolution.
• The Rigveda which is the oldest Vedic text reflects one stage of social and cultural development whereas the other three Vedas reflect another stage.
• The first stage is known as the Rigvedic period or Early Vedic period and the later stage is known as the Later Vedic period.
• Rig Veda is the only source of Early Vedic Civilization. Hence, option 2 is the correct answer.
• The age of the Early Vedic period corresponds with the date of the composition of the Rigvedic hymns.
• This date has been fixed between 1500 BC and 1000 BC.
• The later Vedic period is placed between 1000 BC and 600 BC.
• The Rigveda is a collection of 1,028 hymns divided into 10 mandalas.
• They are the earliest compositions and hence depict the life of the early Vedic people in India.
• Recently, the Rigveda has been included by the UNESCO in the list of literature signifying World Human Heritage.

The position of the English alphabet series is given below:

Option 1) MNG

Option 2) STM

Option 3) ABU

Option 4) HED

Hence, the correct answer is "HED".

Mental Retardation is also known as Intellectual disability which is the psychological Development stage compared to physical development remains lesser.

Key Points

• Mental Retardation or Intellectual Disability is a situation or condition where a child's Mental development occurs lesser according to his real or actual age.
• The 1973 and 1983 AAIDD definitions of intellectual disability divided the severity of disability into four categories (mild, moderate, severe, and profound intellectual disability), a classification system that continues to have widespread acceptance and use.
• Various tools such as PORTAGE, MDPS, BASIC-MR, BASAL-MR, GLAD, and FACP are used to assess the mental level of students.
• MR can be detected during the pregnancy time period through photoscopy while the genetic abnormality can be detected through Chorionic Villus sampling.
• Children with mental retardation should be treated with proper arrangements of oxygen the hospital at the time of delivery.

Hence, it can be concluded that MR is a situation.

The term growth is used for the positive changes in the physical appearance of an individual. It generally refers to an increase in size, length, height, and weight. Changes in the quantitative aspects that come into the domain of growth. It describes the changes that take place in particular aspects of the body of an individual.

Key Points

• Growth is one of the parts of the developmental process. Development in its quantitative aspect can be termed as growth.
• The growth of an individual generally refers to the progressive changes in one's weight, height, size, and length based on the genetic potentials of the individual. So, growth is a biological process.
• Growth does not continue throughout life. It stops when maturity has been attained. So, the growth of an individual is not continuous.
• The changes produced by the growth can be subject to measurement and can be quantified and are observable in nature.

Hence, it could be concluded that the growth of an individual is a biological process.

Confusion Points

Twins refer to two children produced by the same pregnancy. There are two types of twins including identical and fraternal twins.

Key Points

Let's understand it briefly:

Hence, we conclude that the twins who are produced from two different zygotes are fraternal twins while identical twins carry the same genes.

Key Points

Marfan Syndrome

• Marfan syndrome affects the heart, eyes, blood vessels, and bones.
• People with Marfan syndrome are tall and thin with long arms, legs, fingers, and toes.
• Marfan syndrome is an inherited disorder that affects connective tissue.
• The fibers that support and anchor your organs and other structures in your body.
• Marfan syndrome is caused by a mutation in a gene called FBN1.
• The mutation limits the body's ability to make proteins needed to build connective tissue.
• A person with Marfan syndrome has a 1 in 2 chance of passing it on to their child.

Therefore, Marfan Syndrome is a kind of Genetic disorder.
Additional Information

Genetic disorder

• A genetic disorder is a health problem caused by one or more abnormalities in the genome.
• It can be caused by a mutation in a single gene (monogenic) or multiple genes or by a chromosomal abnormality.
• The genetic abnormality can range from minuscule to major, from a discrete mutation in a single base in the DNA of a single gene to a gross chromosomal
• A genetic disorder is a disease caused in whole or in part by a change in the DNA sequence away from the normal sequence.

Viral Infection

• A viral infection is a proliferation of a harmful virus inside your body.
• Viruses cannot reproduce without the assistance of a host.
• Viruses infect a host by introducing their genetic material into the cells and hijacking the cell's internal machinery to make more virus particles.

Degenerative neuromuscular disease

• Affects the muscles and their direct nervous system control.
• There is a problem with central nervous control that can cause either spasticity or some degree of paralysis, from both lower and upper motor neuron disorders, depending on the location and the nature of the problem.
• Some examples of central disorders include cerebrovascular accident, Parkinson's disease, multiple sclerosis, Huntington's disease, and Creutzfeldt–Jakob disease.

Concept:

There are three methods of heat transfer between the two systems. They are conduction, convection, and radiation.

• Conduction is a method of heat transfer in solids and heat transfer takes place without the movement of particles.
• Convection is a method of heat transfer in fluids (gases and liquids) and heat transfer takes place due to the movement of particles.
• Radiation is a method of heat transfer where heat is transferred from one place to another without affecting the medium of heat transfer.

Explanation:

• Both are at the same temperature, the metal will feel colder than the wood because of the thermal conductivity of the metal, compared to the wood is more.

Metal will conduct the heat faster than wood to your hand.

The specific heat capacity of wood is much higher than iron. Hence it takes time to get cooler or hotter compared to metal.

Given:

Formula used:

Mean = (∑f_ix_i) / N

where f_i = frequency of i_th term

_Xi = i^th term

N = total observations

Calculations:

Mean = (∑f_ixi)/N

⇒ Mean = 661/27

⇒ Mean = 24.48

∴ The mean age of all patients is 24.48 years.

Concept:

Pressure:

• Pressure refers to the force applied perpendicular to the surface of an object per unit area over which that force is distributed.
• The SI unit is the pascal (pa).
• The formula for pressure is:
  • P = F / A
• The pressure is dependent on the area over which the force is acting.
• The pressure can be decreased or increased without any change in the force.
• The force applied is constant if the surface becomes smaller, the pressure increases, and vice versa.

Explanation:

• The weight of a bag is the force with which it is pulled towards the earth.
• The shoulder carries a bag that exerts a force that is equal to its weight.
• So, using a large and wide strap of bags ensures that the same weight (Force) is transferred to the shoulder through the large area of the strap.
• For the same force, pressure ∝ 1 / area. Hence, as the area increases the pressure produced is less.
• Therefore, since the broad and larger straps of the bag have greater area, the pressure on the shoulder becomes less, making it easier to carry the bag.

Thus, from the above discussion, the correct answer is the pressure exerted by the bag decreases.

Given:

Speed of the train = 60 kmph

Length of train = 500 meters

Formula Used:

Time taken by train to cross a pole = Length of train/Speed of train

Calculation:

Speed of train = 60kmph = 60 x 5/18 = 50/3 m/sec

Time taken by train to cross a pole = Length of train/Speed of train

⇒ 500/(50/3)

⇒ (500 x 3)/50

⇒ 10 x 3

⇒ 30 sec

∴ Time taken by the train to cross a pole is 30 seconds.

The correct answer is Muscular force.

Key Points

• The forces acting on a plastic bucket are:

1. Gravitational force
2. Muscular force

• Gravitational force is acting downwards, and muscular force is applied by the hands lifting the bucket upwards.
• Although these forces are acting on the bucket no change is found in its state of motion because the two forces are in the opposite direction & hence balancing each other. As a result net force is zero.
• This force is required whenever the movement of the body occurs. For example,

1. When we lie in a bucket of water, the force acting on the object is Muscular Force.
2. when you pick up a book on the table with your hands, you apply muscular force.

• The Muscular force is exerted by the Earth on every object, which is near or on its surface.

Additional Information

• Magnetic force is attraction, or repulsion that arises between electrically charged particles because of their motion.
• The frictional force is defined as the force generated by two surfaces that contact and slide against each other.
• The electrostatic force is defined as an attractive and repulsive force between particles are caused due to their electric charges.

Formula Used:

Perimeter of rectangle = 2[Length + Breadth]

Area of rectangle = Length × Breadth

Calculation:

Using above formula -

⇒ 2[L + B] = 76

⇒ L + B = 38 ...(1)

Area of rectangle is 360

⇒ L × B = 360 ...(2)

Using (1) & (2)

⇒ L(38 - L) = 360

⇒ 38L - L² = 360

⇒ L² - 38L + 360 = 0

⇒ L² - 18L - 20L + 360 = 0

⇒ L(L - 18) - 20(L - 18) = 0

⇒ (L - 18)(L - 20) = 0

⇒ L = 18 or 20 units

If L = 18 Units ,B = 38 - 18 = 20 Unit

If L = 20 Units ,B = 38 - 20 = 18 Unit

∴ The correct answer is 18 unit

Given:

The sum of the roots of an equation is 3

Concept:

For any given quadratic equation of the form ax² + bx + c = 0,

The relationship between the roots and the coefficient & constant of the quadratic equation is as follows,

The sum of the roots =

Solution:

From the given options,

–x2 + 3x – 3 = 0 has following values,

Coefficient of x = 3

Coefficient of x² = -1

The sum of the roots =

Hence, option 2 is correct.

Given:

10 bucket of 14 litres each is used

Formula used:

M₁D₁ = M₂D₂

Calculation:

According to the formula,

⇒ M₁D₁ = M₂D₂

⇒ 10 x 14 = 7 x D₂

⇒ D₂ = 20

⇒ Hence, Total 20 bucket of 7 l each required

Concept used:

Line of Symmetry :

On placing the line Vertically or Horizontally The figures appear the same on both sides of the line

Explanation:

From the above explaining diagrams, only ii option has no line of symmetry

Shortcut TrickA person invests Rs. P for two years in such a scheme that it will provide a% p.a. for the first year and b% p.a. for the second year.

The compound interest earned, C.I = P × (100% + a%) × (100% + b%) - P

According to the question,

The compound interest earned = 10000 × (100% + 10%) × (100% + 20%) - 10000

C.I = (10000 × 110% × 120%) - 10000

C.I = 10000 × 110/100 × 120/100 - 10000 = Rs. 3200

Therefore, 'Rs. 3200' is the required answer.

Alternate MethodGiven:

Principal = Rs. 10,000

Rate for first year = 10% p.a.

Rate for second year = 20% p.a.

Formula used:

(1.) Interest = Effective rate × Principal

(2.) Effective rate = R₁ + R₂ +

Calculation:

According to the question,

Effective rate = 10 + 20 +  = 32%

Interest = 10000 × 32% = Rs. 3200

Therefore, 'Rs. 3200' is the required answer.

Given:

The ratio of the son's age to the father's age is 1 ∶ 4.

The product of their ages is 196.

Calculation:

Let the son's age be x and the father's age be 4x,

According to the question,

⇒ x × 4x = 196

⇒ 4x² = 196

⇒ x2 = 49

⇒ x = 7

Son's age = x = 7 Years

Father's age = 4x = 4 × 7 = 28 Years

After 5 years,

Son's age = x + 5 = 7 + 5 = 12 Years

Father's age = 4x + 5 = 4 × 7 + 5 = 33 Years

∴ The ratio of their ages after 5 years will be 12 : 33 = 4 : 11.

Logarithms were invented by Scottish Mathematician John Napier. Logarithms refers to the quantity representing the power, to which a fixed number (the base) must be raised to produce a given number.

Given

The prices of a scooter and a moped are in the ratio = 9 ∶ 5.

Concept

Ratio:

Comparing two numbers or quantities by division is known as the Ratio.

Solution

Let the price of the scooter and mop be 9x and 5x.

As given, the difference between the two = 4200

⇒ 9x - 5x = 4200

⇒ 4x = 4200

⇒ x = 1050

∴ The price of a mop will be = 5x ⇒ 5 × 1050 = 5250

Given:

The numbers are 12, 15, 11, 13, 17, 11, 13, 12, 13

Concept used:

The following steps are helpful while applying the median formula for ungrouped data.

• Step 1: Arrange the data in ascending or descending order.
• Step 2: Secondly, count the total number of observations 'n'.
• Step 3: Check if the number of observations 'n' is even or odd.

When n is odd

Median = [(n + 1)/2]th term

When n is even

Median = [(n/2)th term + ((n/2) + 1)th term]/2

Mean = Sum of numbers/total numbers

Calculation:

Total of the numbers = 12 + 15 + 11 + 13 + 17 + 11 + 13 + 12 + 13

⇒ 117

So, mean = 117/9

⇒ 13

Now,

The numbers in ascending order = 11, 11, 12, 12, 13, 13, 13, 15, 17

Now, the median is (9 + 1)/2 = 5th term i.e 13

So, sum of mean and median = 13 + 13

⇒ 26

∴ The required answer is 26.

∴ Option 1 is the correct answer.

Concept:

Histogram: A histogram is a display of statistical information that

uses rectangles to show the frequency of data items in successive

numerical intervals of equal size.

Explanation:

This is the image of the histogram.

The height of the rectangle in the histogram represents the frequency

Mathematics: Mathematics is a systematized, organized, and exact branch of Science. It plays an important role in accelerating the social, economical, and technological growth of a nation. It helps in solving problems of life that need enumeration and calculation.

Key PointsMathematics is the gateway of all science. In school, those subject which is included in the curriculum must have certain aims and objectives based on which their nature is decided. The nature of Mathematics is enlisted in the following points:-

• Mathematics is based on understanding.
• Mathematics has its own language.
• Mathematics puts great emphasis on the child’s own methods of calculating and solving problems and rejects the previous practice of heavy emphasis on standard written algorithms.
• Mathematics is a science of discovery and logical reasoning.
• Mathematics is regarded as a powerful tool for interpreting the world and therefore should be rooted in real experience across the whole curriculum. Mathematics is brought out of the child’s everyday situations.
• Mathematics is an exact science.
• Mathematics with reason is rooted in action – learning through doing.
• Mathematics with reason puts less emphasis on representing numbers on paper as ‘sums’ and more emphasis on developing mental images in the child.

Important Points

The following are the characteristics of Mathematics:-

• Mathematics is an intellectual game.
• It deals with the art of concluding.
• It is a tool subject.
• It involves an intuitive method.
• It is the science of exactness, precision, and accuracy.
• It is the subject of a logical and specific sequence.
• It requires the application of rules and concepts to new situations.
• It is a logical study of structure and patterns.

Thus, it is concluded that Mathematics is changeable in the universe is incorrect about the nature of mathematics.

Given:

The frequency polygon displays the age groups of 100 patients getting treatment in a hospital.

Calculations:

The number of patients over less than 50 years of age = 0 + 10 + 15 + 20 + 25 = 70.

Total number of patients = 0 + 10 + 15 + 20 + 25 + 20 + 10 + 0 = 100.

The percentage of the patients who are less than 50 years of age = 70/100 × 100 = 70%.

∴ The answer is 70%.

The correct answer is 27.8 km.

Key Points

• Rotation is the movement of the earth on its axis.
• The movement of the earth around the sun in a fixed path is called revolution.
• The circumference of the Earth at the equator is 40,075 km.
• Earth completes one rotation in 24 hours.
  • One hour is equal to 60 min so 24 hours =24 × 60=1440min.
  • Speed of rotation
    • Time = 40075/1440 = 27.8 km per min.
• So, the Earth rotates approximately 27.8 kilometers in one minute at the equator.

Confusion Points

• The rotational speed of Earth at the equator is 27.8 km/min.
• As we move closer to the poles, its speed decreases because the earth's circumference is decreasing.

Given:

Hari weaves 66 baskets in 33 days.

Calculations:

66 baskets weaved in 33 days.

1 basket weaved in = 33/66 days

Required number of days to weave 374 baskets =

= 12342/66

= 187 days

∴ The answer is 187 days.