MPTET Varg 2 Math Mock Test - 7 - MPTET MCQ

कवि ने हार और जीत के माध्यम से यह बताने का प्रयास किया है कि जीवन के पथ पर हार-जीत जो भी मिले उसे सहर्ष स्वीकार कर लेना चाहिए|

Key Points

• पद्यांश के अनुसार:-
  • ​जीवन एक संग्राम है जिसमें हार और जीत दोनों होती हैं। इस कारण कवि को किसी प्रकार का डर नहीं है।
  • अर्थात कवि कहते है कि जीवन के पथ पर हार-जीत जो भी मिले उसे सहर्ष स्वीकार कर लेना चाहिए।
• पथ - मार्ग, रास्ता, सड़क, डगर, राह।
• सहर्ष - ख़ुशी के साथ, हर्ष के साथ, प्रसन्नतापूर्वक।

Additional Information
भयभीत:-

• अर्थ: डरा हुआ, आतंकित।

प्रसन्न:-

• अर्थ: ख़ुश, हर्षित, आनंदित, प्रफुल्लित, खिला हुआ।
  • विलोम शब्द - 'अप्रसन्न'

'क्षितिज-जंगलों से टोली' शब्द का भाव है- वह स्थान जहाँ पृथ्वी और आकाश मिलते दिखाई देते हैं।

• पृथ्वी- भू, भूमि, धरा, उर्वी, इला, अचला, अवनि, अवनी।
• आकाश- नभ, गगन, द्यौ, तारापथ, पुष्कर, अभ्र, अम्बर, व्योम, अनन्त।

Key Points
सागर:-

• अर्थ: समुद्र, पयोधि, उदधि, पारावार, नदीश, जलधि, वारिधि, नीरनिधि।

नदी:-

• अर्थ: सरिता, तटिनी, वाहिनी, तरंगिणी, निर्झरिणी, शैलजा, जलमाला।

बादल:-

• अर्थ: मेघ, जलद, पर्जन्य, जगजीवन, अंबुद, अंबुधर, अब्र, अभ्र, घटा।

पर्वत:-

• अर्थ: पहाड़, गिरी, अचल, नग, भूधर, महीधर, शैल, नगपति, शिखर।

वायु:-

• अर्थ: हवा, पवन, समीर, अनिल, वात, मारुत , प्रवात, प्रभंजन, बयार।

जंगल:-

• अर्थ: जंगल, अख्य, अरण्य, विपिन, कानन, गहन, विटप, कांतार, बीहड़।

The correct answer is: 'can'

Key Points

• In this context, it is said that with a single click, we can get access to any information on the internet.
• 'Can' is used to express "ability or capacity"
• In some cases 'can' is used to express permission.
  • Example- He can work this sum.
• ​Similarly, in this question, the 'can' should be used to highlight the ability of the internet to impart knowledge on any topic.

Therefore, the correct answer is: Internet can provide information on any topic with the click of a mouse.

Additional Information

• Ought to:- it expresses moral obligation or desirability or to express probability.
  • For example.- we ought to help him.
• May:- It is used to express permission in a formal way or express possibility in affirmative sentences or to express a wish.
  • For example.- may success attend you!
• Should:- It is used in all person to express duty or moral obligation or to express a supposition that may not be true.
  • For example.- We should obey the laws.

The correct answer is litterateur.

Key Points

• Bhawani Prasad Mishra was a Hindi poet and author.
• In 1972, he received the Sahitya Akademi Award for Buni Hui Rassi.
• Mishra, a Gandhian in both thought and deed, was much troubled by the alleged repercussions of colonization in the nation.

Additional Information

• Jangarh Singh Shyam is a famous painter from Madhya Pradesh.
• Akhilesh Sapre is a well known Indian classical Instrumentalist (Sitar) from Madhya Pradesh.
• Tansen and Baiju Bawra,singers, trace their roots to Gwalior in present-day MP.

Thinking is the mental process of manipulating information to draw a conclusion or to generate ideas. It is a higher cognitive function that allows beings to produce thought.

• Different kinds of thinking styles include divergent, convergent, creative, logical, concrete thinking, etc.

Key Points

Divergent thinking refers to a way of solving a problem by exploring many possible solutions. It emphasizes the idea that there is a limitless approach to any given problem.

• a way of solving problems by more than one approach.

• an act of working with open-ended questions using creativity and ingenuity.

• a process that includes brainstorming, imagination, and out of the box thinking.

• the ability possesses by people who are creative, persistent, and imaginative in nature.
• divergent thinking is seen in people having certain personality traits such as curiosity, willingness to take risks. A detective makes has the abilities to divergent thinking because he takes a risk and thinks from different angles and finds solutions to a problem. It is thinking outwards.

Thus from the above-mentioned points, it is clear that a detective tries to solve a case by putting various pieces of information together and then concludes, he uses divergent thinking.

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

Key Points

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

‘Insightful 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 Insightful Theory of Learning was given by Kohler.

Infants explore the world through sensory and motor activity. They experience, perceive, recognize, feel, and understand the environment through their senses.

• By the age of six months, infants are able to do the following, except 'Crawling'. Let's understand in brief by going through the language and physical development of infants.

Key Points

Language Development in infants:

• The language development of all children follows a certain sequence. This means that all children go through the same stages while acquiring language and they do so at approximately the same ages, irrespective of the language they speak.
• Stages in language acquisition
  • Crying: The earliest form of communication that a child uses is crying. From birth to one month of age, this is about the only sound the baby produces to communicate her distress and discomfort. Most mothers are able to make out what the baby's cry indicates-whether she is hungry, wet or just irritable.
  • Cooing: Around one month of age babies begin to make cooing sounds in addition to crying. This stage lasts till 4-5 months after birth. Cooing is a vowel-like sound, particularly like 'moo.....'. Babies make cooing sounds when they are content and satisfied.
  • Babbling: Between six and ten months, the infant begins to babble. She repeats syllables like 'ma', 'da', 'ki', and 'ne' over and over again so that we can hear sounds like "dadada ...", "kikikikiki...", "mamama....". As in the earlier stage, the infant continues to produce new sounds and experimenting with them.

Hence, we conclude that by the age of six months, infants are able to do the following, except crawling.

Hint

Physical development in infants:

• Eat solids: By 4 to 6 months, most infants start to eat solid foods.
• Sit up: By 5 to 6 months, most infants start to sit up with support.
• Crawling: By 7 to 8 months, most infants start crawling.

Given:

⇒ Sin3x × Sec2x = 1

Concept Used:

⇒ if, A + B = 90^°

⇒ then, Sinx = Cosx

and it's converse is also true.

Calculation:

⇒ Sin3x = 1/Sec2x

⇒ Sin3x = Cos2x

⇒ A = 3x and B = 2x

⇒ A + B = 90^°

⇒ 3x + 2x = 90^°

⇒ 5x = 90^°

∴ x = 18^°

⇒ [3tan²(5 × 18^°)/2 - 1]

⇒ [3tan²(90^°/2) - 1]

⇒ [3tan²45^° -1]

⇒ tan45^° = 1

∴ 3 × 1 - 1 = 3 - 1 = 2.

The correct answer is Force of friction.

Key Points

• A boat comes to rest if we stop rowing. The force responsible for changing the state of motion of objects is Force of friction.
  • ​Friction between water and the boat brings it to a stop once you stop rowing.
• Force of friction
  • It is the opposing force when two surfaces come in contact with each other to move either in the same direction or in opposite directions.​
  • The frictional forces are majorly affected by the texture of the surface of the objects that came in contact with each other and the amount of force exerted on them.
  • The formula for frictional force is given by F = μN
  • Frictional Forces are primarily classified into four different types-
    • rolling friction
    • sliding friction
    • static friction
    • kinetic friction

Important Points

• Force of Gravity
  • It is a force that attracts any objects with mass.
  • It is the force by which a planet or other body draws objects toward its center.
  • Objects with more mass have more gravity.
  • Gravity also gets weaker with distance. Hence, the closer objects are to each other, the stronger their gravitational pull is.
  • Gravitational Force = Gm¹m²/r² is the Gravitational force between two objects measured in Newton (N). G is the Universal Gravitational Constant with a value of 6.674 × 10^-11 Nm²kg^-2.
• Muscular force
  • It is any force applied by using our muscles like arms or legs.​
• Magnetic force
  • ​It is the attraction or repulsion that arises between electrically charged particles because of their motion.
  • The force is perpendicular to both the velocity v of the charge q and the magnetic field.
  • Magnetic Force F = qvB sinθ
    • F = magnetic force
    • q = charge of moving particle
    • v = particle velocity
    • B = magnetic field
    • θ = angle between velocity and magnetic field vectors

Calculations :

log 10 - log 5 + log 25

log 10 - log 5 + log 5² (log x2​ = 2logx)

⇒ log 10 - log 5 + 2 log 5

⇒ log 10 + log 5 [log a + log b = log (a.b)]

⇒ log 50

∴ Option 1 is the correct answer.

Given:

The number is 8x5215.

Concept used:

A number is divisible by 9 if the sum of all digit is divisible by 9.

Calculation:

Number = 8x5215

The sum of all digit = 8 + x + 5 + 2 + 1 + 5

⇒ 21 + x

Nearest multiple 9 = 27

To make the no. divisible by 9 then we have to replace the x by 6

∴ The least value of x is 6.

Given :

Index of year 1997 = 200

Index of year 1996 = 100

Calculation :

Required ratio :

⇒ 200 : 100

⇒ 2 : 1

Hence the correct answer is "2 : 1".

There are some strategies of teaching Mathematics like inductive – deductive, analysis-synthesis , problem solving, discovery, activity etc. which help the learner in constructing their knowledge. The purpose of these strategies is to make teaching- learning more interactive as well as effective.

Key Points

Deductive Approach:

• Deductive approach is based on deduction. It is just the opposite of inductive approach.
• It proceeds from abstract to concrete, from general rule to particular or specific instances, and from formula to examples, from unknown to known.
• This approach is relatively more teacher-centered. In this approach, rules are initially given by teachers and then learners are asked to apply these rules to solve more problems of similar nature.
• This approach is mainly used in Algebra, Geometry and Trigonometry because different relations, laws and formulae are used in these sub branches of Mathematics. It is more useful for teaching Mathematics in higher classes. This method is useful for revision and drill work.
• It enhances speed and efficiency.

Thus from above-mentioned points it is clear that deductive approach is mainly used in teaching of Algebra, Geometry and Trigonometry.

Additional Information

• Inductive approach is based on the process of induction i.e. reasoning from specific facts to general principles. Therefore, it proceeds from particular to general, from concrete to abstract.
• Synthesis refers to a combination of two or more entities that together form something new. In this method we move from known to unknown and from hypothesis to conclusion. It is just the opposite of analytic method.

The correct answer is Fractional distillation.

Key Points

• Fractional distillation is a process used to separate mixtures of liquids that have different boiling points. It is particularly effective for separating a mixture of alcohol and water.
• During fractional distillation, the mixture is heated to a temperature at which one of the components will vaporize. That vapor is then condensed back into a liquid and collected separately.
• The process takes advantage of the different boiling points of substances in the mixture, allowing for precise separation.

Additional Information

• Decantation:
  • A process for the separation of mixtures, by removing a layer of liquid, generally one from which a precipitate has settled. Not as effective for closely mixed liquids like alcohol and water.
• Evaporation:
  • A technique used to separate a solvent from a solution, which could be used but is not as efficient or precise for alcohol and water mixtures as fractional distillation.
• Sublimation:
  • A process where a solid changes directly into gas without passing through the liquid state, not applicable for liquid mixtures like alcohol and water.

The correct answer is Photosynthesis.

Key Points

• The dissolution of salt in water is a physical change.
• Because salt can be obtained again by making water vapor.
• As a result, no new substance is formed, called physical changes.
• Photosynthesis is the process by which green plants transform solar energy into chemical energy. During photosynthesis in green plants, light energy is captured and used to convert water, carbon dioxide, and minerals into oxygen and energy.
• In Photosynthesis, Solar energy is converted into chemical energy.
• Photosynthesis is not a physical process.

Additional Information

• ​Physical change -
  • Under this, there is no change in the chemical nature or chemical identity of the substance.
  • For example, after pouring water on a utensil and heating it from below, the water turns into vapor, if you keep a lid on that utensil, then that vapor again converts into the water, this is a kind of physical change.
• Chemical changes -
  • Under this, the structure of matter changes.
  • One or more substances combine or break down to form new substances.
  • Its properties and characteristics change
  • For example, when a candle is lit, wax changes from a solid state to a gaseous state, this is a chemical change.

Given fraction = 0.3555...

CONCEPT USED:

Suppose XY is a two-digit number after the decimal

Then, if there is a bar on the first digit i.e.  = (xy- x)/90

CALCULATION:

Fraction = 0.355... =

= (35 - 3)/90 = 32/90 = 16/45

Hence, option 1 is the correct answer.

Alternate Method

Let x = 0.3555...

then 10x = 3.5555...

⇒ 10x - x = 9x = (3.5555...) - (0.3555...)

⇒ 9x = 3.2

⇒ x = 3.2/9

⇒ x = 32/90

⇒ 0.355... = 32/90 = 16/45

Option 3 is the correct answer.

Given :

Index in 1998 = 200

Index in 1996 = 100

Calculation :

Required percentage :

⇒ 200 / 100 × 100

⇒ 200 %

Hence the correct answer is "200 %".

Explanation:

The closure property of integers under addition states that the sum of any two integers will always be an integer i.e. if p and q are any two integers, then (p + q) will also be an integer.

Example : 7 + 4 = 3, which is also an integer.

Hence, the option that says that the sum of the two integers is not an integer is not true.

Given:

Concept used:

Calculation:

⇒ tan A

∴ The required answer is tan A.

GIVEN:

A sum of non- zero number and its reciprocals is 2 .

FORMULA USED:

( a - b)² = a² + b² - 2ab

Where,

a = 1st term

b = 2nd term

CALCULATION:

Let us assume non-zero number be x

Reciprocal of the number = 1/x

So, according to the given question

⇒ x + 1/x = 2

⇒ x² + 1 = 2x

⇒ x² + 1 - 2x = 0

[As, x2 + 12 - 2 × 1 × x = ( x - 1)2 ]

⇒ ( x - 1 )² = 0

⇒ x = 1

Hence, the required number is 1 .

Given:

Ages (Sonu and Bulla) = 4 : 3

Sum = 49 years

Calculation:

Let the age of Sonu and Bulla be 4m and 3m.

According to the question,

⇒ 4m + 3m = 49

⇒ 7m = 49

⇒ m = 49/7 = 7

Ratio of ages after 4 years = (4m + 4) : (3m + 4)

⇒ (4 × 7 + 4) : (3 × 7 + 4)

⇒ 32 : 25

∴ The ratio of their ages after 4 years is 32 : 25.

Formula used :

Area of a trapezium = (1/2)(sum of parallel sides) × height

Calculations :

Let the height be H

48 = (1/2) × (16) × H

⇒ H = 96/16

⇒ H = 6

∴ Height of the trapezium is 6 cm

Given :

Quadratic equation = x² + 15x + 56 = 0

Formula used :

Calculation :

Let the two roots of equations be a and b

a = -7 , b = -8

∴ -7, -8 are roots of quadratic equation.

Given:

a + b = 10

ab = 9

Concept Used:

(a – b)² = a² + b² – 2ab

Calculation:

⇒ Squaring (a – b), we get

⇒ (a – b)2 = (a + b)² – 4ab

⇒ Putting the values in the formula,

⇒ (a – b)² = 10² – 4 × 9 = 100 – 36

⇒ (a – b)2 = 64

⇒ a – b = √64 = 8

Therefore, the value of a – b is 8.

Calculation:

Total expenditure = 48 cr

The total expenditure of the company Q, R & T together = (22 + 18 + 20)% = 60%

Now, according to the question

The total expenditure of the company Q, R & T together = 60% of total expenditure

⇒ (60% of 48) = (60/100 × 48)

⇒ 144/5 = 28.8

∴ The required expenditure is 28.8

Given :

10^th term of an A.P = 21

17^th term = 8 + 13^th term

Formula used :

A.P = a + (n - 1)d

Where, a = first term, d = difference and n = nth term

Calculation :

According to question,

10^th term = a + (10 - 1)d = a + 9d = 21 ----(1)

17^th term = a + 16d = 8 + a + 12d

⇒ 4d = 8

⇒ d = 2

So, from (1) we get

a = 21 - 9 x 2 = 3

A.P. series = 3, 5, 7, 9, 11, .......

∴ The answer is 3, 5, 7, 9 ..... .

Explanations:

Line of Symmetry: on placing a line on object it appears the same on both sides of line.

Hence, the Line of symmetry is 1

Calculation :

Required Average :

⇒ ( 50 + 75 + 100) / 3

⇒ 75

Hence the correct answer is "75".

Given:

Each edge of a cube is increased by 50 %

Formula used:

surface area of cub = 6 a² ( a = side )

Calculation:

Let side of cube is = a

According to statement

a + a x 50/100

⇒ 1.5 a

Area of cube = 6 a²

New area of cube = 6 ( 1.5 a) ( 1.5 a)

% increase in cube area = {( 13.5 a²) - ( 6 a²)} ÷ 6 a²

⇒ 125%

increased % of the surface area is 125%

The correct answer is Joule.

Key Points

• Heat
  • It is a form of energy that flows from one body to another due to the difference in temperature between the bodies.
  • It is simply the potential energy stored in the bonds that hold particles within the object together.
  • Heat or thermal energy is the form this energy possesses when it is transferred between systems and surroundings.
  • SI unit of energy is Joule (J) and from above it is clear that heat is a form of energy.
  • Therefore the SI unit of heat energy is Joule (J).

Additional Information

• SI unit of other quantities is as shown below