MPTET Varg 2 Math Mock Test - 6 - MPTET MCQ

The correct answer is "The experiment is being conducted by the team"

Key Points

• Option 4) "The experiment is being conducted by the team" is expressed in passive voice.
• In passive voice, the subject of the sentence is acted upon by the verb, rather than performing the action.
• In this case, the subject "the experiment" is being acted upon by the verb "being conducted", the team is the agent performing the action.
• On the other hand, in active voice, the subject of the sentence performs the action of the verb.
• The sentences in options 1, 2, and 3 are in active voice since the subject (engineers, researchers, and scientist) is performing the action (problem solving, solution discovering, data studying)

Thus, option 4 is the correct answer.

The correct answer is 'Because'.

Key Points         

• Because  is used for the reason that; since. 
• • ​For example: I was absent from school because I had a cold.
• Though means despite the fact that; although.
• Yet means but at the same time; but nevertheless.
• If means (introducing a conditional clause) on the condition or supposition that; in the event that.
• By referring to the above explanation and the context of the given sentence, it can be concluded that Because is the appropriate option to be chosen for filling the blank.

Hence, the correct answer is option 3.

Hinglish 

• "Because" का उपयोग 'क्योंकि' या ' जिसके कारण' के लिए किया जाता है। 
• "Though" का अर्थ होता है 'हालांकि' या 'फिर भी'।
• "Yet" का अर्थ होता है 'लेकिन फिर भी' या 'तथापि'।
• "If" का उपयोग शर्तीय वाक्यांश को परिचयित करने के लिए किया जाता है, जिसका अर्थ होता है 'यदि' या 'अगर'।

The correct answer is Vidisha.

In News

• Vidisha, an aspirational district of Madhya Pradesh became the first-ever district in India for on-ground deployment of innovative 5G use cases offered by startups.

Key Points

• It is a joint initiative by Vidisha District Administration and the Centre for Development of Telematics (C-DOT), Department of Telecommunications (DoT) under the guidance of Additional Secretary (Telecom) and Administrator USOF.

Additional Information

• Madhya Pradesh:
  • Chief Minister - Mohan Yadav.
  • Governor - Mangubhai Chhaganbhai Patel.
  • State Animal - Barasingha.
  • State Bird - Indian paradise flycatcher.
  • National Parks - Bandhavgarh National Park, Fossil National Park, Kanha National Park, Madhav National Park, Panna National Park, Pench (Priyadarshini) National Park, Sanjay National Park, Satpura National Park.
  • Dams - Bansagar Dam (Sone river), Bheemgarh dam (Wainganga river), Gandhi Sagar Dam (Chambal River), Indira Sagar Dam (Narmada River) and Omkareshwar Dam (Narmada River).
  • Registered GI - Chanderi Fabric, Leather Toys of Indore, Bell Metal Ware of Datia and Tikamgarh, Ratlami Sev.

"Raymond Cattell" is a British psychologist.  Cattell (1971) on the basis of factor analysis, has divided the general factor of intelligence (G) into two parts- fluid intelligence (GF) and crystallized intelligence (GC). The former is innate, biologically, or genetically determined and the latter is acquired based on cultural educational experience.

Key Points"Fluid intelligence" refers to the ability for abstract and logical thinking and does not require any previous knowledge. It is the ability to think and reason abstractly, as well as solve any new problem or task without any prior knowledge or experience.

• It helps one to examine a novel problem, perceive the relationships and patterns that underlie the problem and solve it using logic.
• The fluid intelligence of an individual increases rapidly during childhood, but declines in later adulthood.
• It can be measured by tests of puzzle-solving, and spatial visualization. and block designs.
• The measures of fluid intelligence(Gf) are- The Cattell Culture Fair IQ tests and The Raven’s Progressive Matrices.

Hence, from the above-mentioned points, we can conclude that fluid intelligence depends on neurological development. 

Additional Information"Crystallized intelligence" refers to an individual's ability to use acquired knowledge comes a combination of previous learning, past experiences, and the ability to apply that knowledge. 

• An individual's intellectual achievement over the course of their life becomes better with age.
• Crystallized intelligence can be measured through tests of general knowledge, use of language (vocabulary), and a wide variety of acquired skills (Horn & Cattell,1967).
• Crystallized intelligence grows throughout the life span.

Given:

5 years ago, ratio of ages of A, B and C = 4 : 5 : 7.

Sum of their present ages = 135 years.

Concept used:

Total = Average × Number of entities

Calculation:

Let the common ratio be Q.

So, 5 years ago, the ages of A, B, and C are 4Q, 5Q, and 7Q respectively.

Now, their present ages are (4Q + 5), (5Q + 5), and (7Q + 5) respectively.

According to the question,

(4Q + 5) + (5Q + 5) + (7Q + 5) = 135

⇒ 16Q + 15 = 135

⇒ 16Q = 135 - 15

⇒ 16Q = 120

⇒ Q = 7.5

The present age of B = (5 × 7.5 + 5) = 42.5 years

The present age of C = (7 × 7.5 + 5) = 57.5 years

Now, 3 years from now, the sum of the ages of B and C

⇒ (42.5 + 3) + (57.5 + 3)

⇒ 106 years

∴ After 3 years from now, the sum of the ages of B and C will be 106 years.

Given:

The average of 40 observations is 32.

The average of the first 15 observations is 16

The average of the next 16 observations is 20

Let the Remaining 9 observation average is X

Calculation:

Average =

40 × 32 = 15 × 16 + 16 × 20 + 9 × X

⇒ 1280 = 240 + 320 + 9X

⇒ 720 = 9X

⇒ X = 80

∴  The average of the remaining observations is 80.

Shortcut Trick 

Objective-type Test: Objective type tests have been in existence since 1920 onwards. These are very popular means of devices to test the students' knowledge. These made their appearance in an effort to overcome the difficulties/weaknesses which are faced in essay type tests. These are widely used in nursing education. Objective type tests include a large number of questions and statements (items). Answers are indicated by marking the correct response in a specified method. 

Key Points

Objective Type Test-

• An objective type test item is characterized by its total objectivity and unambiguity in scoring. 
• It has one and only one correct response.
• Full marks are given for the correct response, which is unique, and no mark is given for an incorrect response.
• Another characteristic of an objective type test item is that it is completely strummed.
• Complete structuring of task limits student to the type of response called for.
• It prevents bluffing and avoids the influence of writing skills.
• The scoring of an objective type test item is not the only objective but also quick, easy, and consistent, which is its greatest advantage. 
• Objective-type tests include multiple-choice, true-false, completion, matching, analogical test, recall type test and short answer test items. 

Thus from the above-mentioned points, it is clear that the Prognostic test is not an objective type of test. 

Mistake Points 

Prognostic test- It is used to predict future behavior on the basis of present abilities. 

Formula:

SI = 

where-

P = Principal

SI = Simple Interest

R = Rate

T = Time

Calculation:

Time in years =  =  years

According to the question-

⇒ SI = 

⇒ SI = 186 × 5 = ₹930

The SI on the above sum is ₹930.

Given:

A train runs at a speed of 28 kmph for 4 hours and at 30 kmph for 5 hours and the remaining 48 kms in 1 hour.

Concept:

Average speed = 

Solution:

Distance D₁ covered at a speed of 28 kmph for 4 hours,

D1 = 28 x 4 = 112 km

Distance D2 covered at a speed of 30 kmph for 5 hours,

D2 = 30 x 5 = 150 km

Distance D3 [ 48 km ] in 1 hour.

Total distance covered = 112 + 150 + 48 = 310 km

Total time taken to cover the distance = 4 + 5 + 1 = 10 hours

 Average speed = 

Average speed = 31 km/hr

Hence, option 4 is correct.

The basic structure of mathematics includes arithmetic, algebra, geometry, and trigonometry that helps in learning the techniques to handle abstractions and structures.

• The teaching of mathematics must develop attitudes to think, reason, analyze, and articulate logically.
• The nature of mathematics highly influences the nature of the teaching-learning process in mathematics.

Key Points

• Mathematics education aims to make mathematics an important part of children's life experiences.
• To connect the real-life concrete experiences with mathematical knowledge and skills is the main purpose of mathematics education so that the students can co-relate their theoretical knowledge with its practical base.
• And, like all the human knowledge, mathematics grows out of our concrete experiences. Such as we see the different kinds of shapes around us i.e., round, sphere, oval, and square which gives birth to the concept of shapes and figures in mathematics.
• The mathematical concepts are hierarchical in nature as one mathematical concept is dependent on another or the understanding of one mathematical concept is a pre-requisite for another.
• For example, to understand the concept of area and volume, first, it is required to know the concept of shapes and perimeter.
• Every mathematical concept gives rise to more mathematical concepts as when we study the concepts of shapes or patterns as per the curiosity of learners, they wanted to learn more about the shapes in-depth which give rise to the concepts of area and volume, etc.

Hint

• It is not necessary that a person who is good in history is also good in mathematics and vice-versa. As the subject of history mainly focuses on the study of our past and how our present evolved from our past whereas, on the other side, mathematics deals with real-life problems and finding their solutions.

Hence, it is concluded that "a person good in history is also good in mathematics and vice-versa" is not a correct statement.

Given:

For the quadratic equation x2 - 20x + 100 = 0,

α and β are the two roots for the equation,

Concept used:

(1) For the quadratic equation ax2 + bx + c = 0,

If α and β are the roots for the equation, 

Therefore, 

α + β = 

α × β = 

(a + b)² = a² + b² + 2ab

Calculation:

For the quadratic equation x2 - 20x + 100 = 0,

The sum of roots, α + β =  = 20

The product of roots, α × β =  = 100

Now, 

⇒ (α + β)2 = α2 + β2 + 2αβ

⇒ (20)2 = α2 + β2 + 2(100)

⇒ 400 = α2 + β2 + 200

⇒ α2 + β2 = 200

∴ The required answer is 200.

Given:

BD = 7.5 cm

DC = 10 cm

Concept used:

In right ΔABC, ∠A = 90°

AD is perpendicular to BC

Then,

AD² = BD × CD

Calculation:

Using the above concept

⇒ AD2 = BD × CD

⇒ AD² = (7.5 × 10)

⇒ AD² = 75 cm²

⇒ AD = 5√3 cm

∴ The required value of AD is 5√3 cm.

Given:

α and β are the zeroes of the polynomial x2 − 5x + k, where α − β = 1,

Concept used:

In quadratic equation ax² + bx + c = 0

Sum of roots = -b/a 

Product of roots = c/a

Calculation:

Here,  x2 − 5x + k

Sum of roots (α + β) = -(-5)/1 = 5 --(i)

α − β = 1 (given)--(ii)

From (i) and (ii), we get

α = 3, β = 2

∴ product of roots (αβ) = k = 3 × 2 = 6

Given :

Total number of coins shiya had = 270

Ratio of 5 rupee, 1 rupee and 2 rupee coins = 4 : 3 : 2

Calculation :

Number of 5 rupee coins = 

Number of 1 rupee coins =  

Number of 2 rupee coins = 270 - (90 + 120) = 60

Total amount shiya had = 120 x 5 + 90 x 1 + 60 x 2 = Rs. 810

∴ The answer is Rs. 810 .

Given:

The ratio of the amount of imports to the amount of exports of a company over the years given.

Calculations:

In the year 2001, the respective ratio is 0.6, that is,

Let import be 6x and export be 10x as, import: export = 6 : 10

In the year 2002, the respective ratio is 0.8, that is,

Let import be 8x and export be 10x as, import: export = 8 : 10

In the year 2003, the respective ratio is 0.3, that is,

Let import be 3x and export be 10x as, import: export = 3 : 10

In the year 2004, the respective ratio is 1.2, that is,

Let import be 12x and export be 10x as, import: export = 12 : 10

In the year 2005, the respective ratio is 1.5, that is,

Let import be 15x and export be 10x as, import: export = 15 : 10

In the year 2006, the respective ratio is 0.9, that is,

Let import be 9x and export be 10x as, import: export = 9 : 10

In the year 2007, the respective ratio is 1.6, that is,

Let import be 16x and export be 10x as, import: export = 16 : 10

From the above information, we can conclude that in the years 2001, 2002, 2003 and 2006 export is more than that imports.

∴ The answer is 4.

Given:

The angle of Quadrilateral are in the ratio 2: 5 : 3 : 8

Concept:

Sum of supplementary angles = 180∘ 

Complementary angles: When the sum of two angles is 90°, then the angles are known as complementary angles.

The Sum of angles of Quadrilateral is 360°

Solution:

The angle of Quadrilateral are in the ratio 2: 5 : 3 : 8

∴  2x + 5x + 3x + 8x = 360° 

⇒ 18x = 360°

⇒ x = 20°

∴ the angles of Quadrilateral are 40°, 100°, 60°, 160°  

Now,

Let Supplement of Largest angle = ∠b and The Complement of the Smallest angle = ∠d 

∴ ∠b + 160° = 180° 

⇒ ∠b = 20° 

and ∠d + 40° = 90° 

⇒ ∠d = 50° 

The sum of Supplement of largest angle and Complement of the smallest angle 

∴ ∠b + ∠d = 20° + 50° = 70°        

∴The sum of Supplement of largest angle and Complement of the smallest angle  = 70° 

Given:

The curved surface area of the cylinder = 264 cm2

Height = 14 cm

Formula Used:

The curved surface area of the cylinder = 2πrh

Volume of cylinder = πr²h

Calculation:

Curved surface area = 264 cm2

⇒ 2πrh = 264

⇒ 2×  × r × 14 = 264

⇒ r =   =

⇒ r = 3 cm

Using above formula

⇒ Volume of cylinder = πr²h

⇒ Volume =  × 3² × 14 = 396 cm³

∴ The correct answer is 396 cm³.

Motivation, activity, and adjustment in mathematics teaching are related to the cognitive aspect.

 Key Points

• The cognitive aspect of mathematics teaching focuses on the mental processes and understanding involved in learning and problem-solving.
• Motivation plays a crucial role in engaging students and encouraging their active participation in the learning process.
• Activity refers to the active involvement of students in hands-on and interactive learning experiences.
• Adjustment involves adapting teaching strategies and approaches to accommodate individual student needs and promote effective learning.
• These aspects collectively contribute to the cognitive development and understanding of mathematics concepts.

Therefore, the correct answer is option 1) Cognitive aspect.

Concept:

Calculation:

Given: Height of lighthouse AB = 70 m.

Now, in ΔABC

As we know that,

Given:

The number is divisible by 15, 24, and 40

Concept Used:

The concept of LCM is the multiple of Least Common Multiple

Calculations:

⇒ LCM of 15, 24, and 40 = 120

⇒ Highest 4-digit number = 9999

On dividing 9999 by 120, we get

⇒ Remainder = 39

⇒ The highest 4-digit number divisible be 15, 24, and 40 = Highest 4-digit number - Remainder = 9999 - 39 = 9960

⇒ Hence, The highest 4-digit number exactly divisible by 15, 24, and 40 is 9960.

Formula:

sec²θ - tan²θ = 1

(a + b)(a - b) = a² - b²

Calculation:

secθ + tanθ = √3 (Equation 1)

Rearranging the (sec2θ - tan2θ ) identity-

⇒ (secθ + tanθ)(secθ - tanθ) = 1

Substituting the value, we get-

⇒ secθ - tanθ =  (Equation 2)

Subtracting Equation 2 from Equation 1

⇒ 2 tanθ = √3 - 

∴ tanθ = 

⇒ θ = 30° 

∴ tan3θ = 3 × 30° = 90° 

⇒ tan 90° = undefined 

∴ The answer to the identity is undefined.

Calculation:

Given that,

x2 = 4x - 1 

⇒ x2 - 4x + 1 = 0   ----(1)

Hence, require value

= x3 - 7x2 + 13x - 12

We can write it as,

⇒ x³ - 4x² - 3x² + 12x + x -12

⇒ x³ - 4x² + x - 3x² +12x - 12

= x(x2 - 4x + 1) - 3x² + 12x - 12 

⇒ x(x2 - 4x + 1) - 3(x2 - 4x + 1) - 9

From equation (1),

= x(0) - 3(0) - 9

⇒ x3 - 7x2 + 13x - 12 = -9

Given:

Distance = 11 km

Down Stream Time = 5hr

Upstream Time = 7hr

Formula used:

Down Stream (X + Y) = 

UP stream ( X - Y) = 

Where X = Boat speed, Y = Stream speed  

Calculation:

X + Y = 11/5      ....(1)

X - Y = 11/7       ....(2)

From equation 1 & 2

X = 66/35;  Y = 11/35

∴ The speed of the stream is 11/35 km/h

Given:

1729p465  is divisible by 9

Calculation:

If any number is divisible by 9 it means the sum of that number is also divisible by 9.

here, 1729p465  is divisible by 9

so, (1 + 7 + 2 + 9 + p + 4 + 6 + 5)/9 = (34 + p)/9

If we take p = 2 

then, (34 + 2)/9 = 4

So, the value of p is 2

Comprehension is the ability to understand. Comprehension is an exercise that tests how well an individual understands a concept.

Key Points

• The ability to count accurately - first forward is called number comprehension.
• Number comprehension gives meaning to numbers.
• Number comprehension means knowing how numbers are related to each other and what are their relative magnitudes.
• It is also based on the effect of mathematical operations on numbers,
• Number comprehension is very important to understand numerical aspects.

Hence, we can conclude that the ability to count accurately - first forward is called number comprehension.

Given:

Number of products sold by 5 companies during 5 months

Calculation:

Number of products sold by P, S and T in February are 155, 110 and 90 respectively

Average number of products sold by company P, S and T in February =  ~ 118

∴ The answer is 118. 

The correct answer is Steaming.

Key Points​

• Cooking with steam is referred to as steaming.
• Steaming is the cooking method by which Idli is cooked.
• Food can also be steamed in a wok, though this is frequently done with a food steamer, kitchen equipment designed expressly to cook food with steam.
• Using steam to cook a variety of items is seen to be a healthy cooking method.
• Because steaming requires less energy to produce and has superior thermodynamic heat transfer characteristics compared to boiling water, steaming can be just as quick, if not quicker, than boiling water cooking.

Additional Information

• Pressure cooking is the method of preparing food in a sealed pressure cooker while using high-pressure steam, water, or a water-based cooking liquid.
• In the cooking process known as poaching, food is heated while submerged in a liquid such as water, milk, stock, or wine.
• A combination of cooking techniques known as stewing involves submerging small, homogeneous chunks of meat completely in liquid and simmering them slowly.

Given:

Length of the arc = 15 cm 

Angle subtended by the arc at the centre = 24°

Formula used:

Length of the arc =  × 2πr

Where, 2πr = circumference and θ = angle subtended by the arc at the centre.

Calculations:

According to the question, 

⇒  × 2πr = Length of the arc

⇒  × 2πr = 15

⇒ 2πr = 15 × 15

⇒ 2πr = 225 cm

∴ The circumference is of length 225 cm.

Given: 

Exterior angle of triangle ABC = x, y , z 

Concept Used:

•  The Sum of an Exterior angel and Interior angle is 180° 
• An exterior angle of a triangle is equal to the sum of two opposite side interior angles.

Solution: 

Exterior angle + Interior angle = 180° 

⇒  

⇒   

⇒ 

⇒ x + y + z =  540°  - ( 

⇒ x + y + z = 540°  - 180°                 (we know interior angles sum = 180°) 

⇒ x + y + z = 360°  

CONCEPT:

• In the world, all objects emit radiation if they have a temperature greater than absolute zero ( 0K ).
• And this radiation energy (Q) is proportional to fourth the power of Temperature (T) in Kelvin.

i.e. Q α T4 or mathematically  Q = σAT4

where σ is Stefan-Boltzmann constant and A is the area from which radiation is emitted. 

EXPLANATION:

• All objects in this world which have a temperature greater than 0 K, emit radiation.
• This radiation energy is proportional to fourth the power of Temperature (T) in Kelvin.

Q α T4

• So, the correct answer is option 4.

Important Point

• An object that absorbs and emits all possible radiation with 100% is called a blackbody.