MPTET Varg 2 Math Mock Test - 9 - MPTET MCQ

एक से एक कतरा मिले तो दरिया बन जाता है।

• पद्यांश के अनुसार:-
  • 'एक से एक मिले तो कतरा बन जाता है दरिया'
  • भावार्थ- इन पंक्तियों में कवि कहते हैं कि पानी की बूँद-बूँद से समुद्र का निर्माण किया जा सकता है।

Key Points

• कतरा- किसी भी तरल अर्थात द्रव पदार्थ की बूँद।

Additional Information
पहाड़:-

• अर्थ: पर्वत, शैल, नग, भूधर, अंचल, महीधर, गिरि, भूमिधर, तुंग, अद्रि।

खतरा:-

• अर्थ: भय, डर, खौफ, आशंका, खटका, अंदेशा।

समुद्र:-

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

कवि ने शरीर के सीना और बाँहें अंगों को फौलादी कहा है।

• पद्यांश के अनुसार:-
  • 'फ़ौलादी हैं सीने अपने फ़ौलादी हैं बाँहें' ​
  • भावार्थ- मजबूत इच्छाशक्ति के लिए मजबूत सीना आवश्यक है और इन कार्यों को पूरा करने के लिए मजबूत हाथ आवश्यक है।
  • इसलिए कवि ने इस गीत में मजदूर के सीने और बाँह को फ़ौलादी कहा है।

Key Points

• सीना- छाती, उरोज, वक्षस्थल, स्तन।
• बाँह- बाहु, हाथ, भुज, भुजा।

Additional Information
नाक:-

• अर्थ: नासा, घ्राण, घ्राणेन्द्रिय, नासिका, नास्य, घ्राण अंग, नासिका अंग।

मुँह:-

• अर्थ: मुख, आनन, चेहरा, शक्ल।

आँख:-

• अर्थ: नेत्र, दृग, नयन, लोचन, चक्षु, अक्षि, अंबक, दृष्टि, विलोचन।

पैर:-

• अर्थ: चरण, पाँव, पद, चरण-चिह्न, कदम, पाद, पग, डग।

उपर्युक्त गद्यांश के अनुसार, यूरेनियम के केन्द्र के विखण्डन का अध्ययन विद्युत के सिद्धांतो के प्रयोग का विचार हो सकता है।

• गद्यांश के अनुसार :-
  • प्रौद्योगिकी में हम उन अनगिनत विधियों का उल्लेख करते हैं जिनसे विज्ञान को मानव सेवा के लिए प्रयुक्त किया जा सके।
  • दोनों में स्पष्ट अन्तर बताने के लिए आणविक विज्ञान और प्रौद्योगिकी के वर्तमान सर्वाधिक लोकप्रिय क्षेत्रों से उदाहरण दिए जा सकते हैं।
  • यह 'विज्ञान' है जिसमें भारी धात्विक तत्व यूरेनियम के नाभिक से अलग या विखण्डित हुए अंशो की प्रकृति और संख्या का मापन होता है।

Key Points

• विद्युत का अर्थ :-
  • विद्युत चल अथवा अचल इलेक्ट्रान या प्रोटान से सम्बद्ध एक भौतिक घटना है।

Additional Information

• नैतिक का अर्थ :-
  • नीति के अनुरूप होनेवाला।
• नैतिक में प्रत्यय :-
  • 'नीति' मूल शब्द है और 'इक' प्रत्यय।
• प्राचीन का अर्थ :-
  • पुराना
• प्राचीन के पर्यायवाची :-
  • पूर्वकालीन, पुराना, भूतकालीन, आदिम, कदीम आदि हैं।

Memory can be defined as a perceptually active mental system that receives, encodes, modifies, and retrieves information. Memory refers to the set of processes involved in storing information. This specific process is termed as retention, It can be studied indirectly by measuring retention.

• Three basic methods of measuring retention are Recall, Recognition, and Relearning.

Key PointsStages of Memory :

• Sensory memory, which is also known as ‘fleeting memory’ sometimes, is closely related to the process of perception. It is responsible for keeping a record of our percept for a very brief period of time.
• STM (Short Term Memory): This system also holds information for a short duration of time. Studies have suggested that it can hold information for up to 30 seconds. Tasks such as dialing a phone number manually or writing in a dictation.
• LTM (Long Term Memory): It has been considered a storehouse of all kinds of memories. You can remember things from last evening to your childhood due to this system of memory.

Hence, working memory is not a system of memory according to the stage model of memory.

Hint

• Working memory: Working memory can be defined as “a limited-capacity system for temporary storage and manipulation of inform
• ation for complex tasks such as comprehension, learning, and reasoning”

'Adolescence' comes from the Latin word 'Adolescere' which means 'to grow to become mature'. It a stage which lies between the age of '12 to 19 years'. Adolescence is a difficult journey of self-exploration and interaction with the world. It is characterized by contradictions, fantasies, surprises, uncertainties, etc. There are six immature characteristics of adolescent thought proposed by Elkind:

• Idealism and Criticalness: It is the situation in which they believe that they know better than other adults and consistently find faults in elders.
• Argumentativeness: It is the case in which they constantly look for situations to test their reasoning abilities.
• Indecisiveness: It is the case in which they are not able to make an effective strategy.
• Apparent Hypocrisy: They are not able to differentiate between situations in which they need to sacrifice something.
• Self Consciousness: The belief that they are being judged and observed constantly by people.
• Specialness and Invulnerability: The belief that someone/something is unique or special.

Hence, we conclude that assertiveness is not a form of immaturity of thinking during adolescence as proposed by Elkind.

Given:

Amount = Rs. 8800

Time = 4 years

Rate = 25%

Formula Used:

Amount = Principal + SI

P = principal

R = Rate of interest

T = Time

Calculation:

⇒ 8800 - P = P

⇒ 8800 = 2P

⇒ P = Rs. 4400.

Concept used:

A line of symmetry is an imaginary line, which divides any shape from the center, in such a way, that the divided parts are mirror images of each other.

Solution:

The given figure has 3 lines of symmetry.

Hence, the correct option is 3.

GIVEN:

First term = 25

Last term = -53

N = 14

FORMULAE USED:

Sum of first n terms = N × (first term + last term)/2

CALCULATION:

Sum = 14/2 (25 - 53) = 7 × (-28)

Given:

The equations 2x + ky + 4 = 0 and 3x + 15y + 7 = 0 will be inconsistent.

Concept Used:

Consider two equations a₁x + b₁y + c₁ =0 and a₂x + b₂y + c₂ =0 are inconsistent

Then they will have no solution i.e.

Calculation:

We know that, for inconsistent solution

⇒ 2/3 = k/15

⇒ k = 10

∴ k = 10

Given:

A and B together can do a piece of work in 4 days.

'A' alone can do it in 12 days

Concept used:

Total work = Efficiency × time

Ratio of time taken by the workers is equal to the ratio of their efficiency

Calculation:

Let the efficiency of A and B be a and b

According to the question,

12a = 4(a + b)

⇒ 12a = 4a + 4b

⇒ 8a = 4b

⇒ a/b = 4/8 = 1/2

So, ratio of efficiency of A and B = 1 : 2

So, time taken by B = 12/2

⇒ 6 days

∴ B alone can do the work in 6 days.

Given:

The ratio of three numbers is 2 ∶ 3 ∶ 6 and the sum of their square is 441.

Concept & Solution:

As per the question,

The ratio of three numbers is 2 ∶ 3 ∶ 6.

Let's say the numbers are 2x, 3x, and 6x

The sum of their square is 441.

(2x)² + (3x)² + (6x)² = 441

49x² = 441

x = 21/7 = 3

The value of the largest of the three numbers is 6x = 6 x 3 = 18

Hence, option 2 is correct.

Given:

Four figures data

Concept used:

Area of fully filled square = Area of more than half filled square = 1 square unit

Area of half-filled square = 0.5 square units

Area of less than half-filled square = 0 square units.

Calculation:

⇒ Area of Figure 1 = 5 + 7(0.5) + 4 + 9(0)= 12.5 square units.

⇒ Area of Figure 2 = 6 + 2 + 7(0) = 8 square units

⇒ Area of Figure 3 = 6 + 2(0.5) = 7 square units

⇒ Area of Figure 4 = 4 + 2(0.5) + 8 = 13 square units

∴ The figure with a larger area is Figure 4.

Given:

1024

Concept used:

m × m = m²

Calculation:

⇒ 1024 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

= 2¹⁰

∴ 1024 = 2¹⁰

Given:

a2 + b2 + c2 + 3 = 2 (a + b + c)

Concept used:

1. A2 + B2 + C2 = 0 then A = B = C = 0

2. (a - b)2 = a2 - 2ab + b2

3. (a + b)2 = a2 + 2ab + b2

Calculation:

a2 + b2 + c2 + 3 = 2 (a + b + c)

⇒ a2 + b2 + c2 + 3 - 2 (a + b + c) = 0

⇒ a2 + b2 + c2 + 3 - 2 (a + b + c) = 0

⇒ (a² - 2a + 1²) + (b2 - 2b + 12) + (c2 - 2c + 12) = 0

⇒ (a - 1)² + (b - 1)2 + (c - 1)2 = 0

According to the concept,

(a - 1)2 = 0

⇒ a = 1

Likewise, b = 1 and c = 1

Now, (a + b + c)

⇒ 1 + 1 + 1 = 3

∴ If a2 + b2 + c2 + 3 = 2 (a + b + c), then the value of (a + b + c) is 3.

Given :-

We have given that

Concept used :-

Ratio of area of two similar triangles is equal to the ratio of square of their corresponding sides.

Solution :- We have given that ΔABC ∼ △QRP

As we know, the ratio of the area of two similar triangles is equal to the ratio of squares of their corresponding sides.

Which means

Hence we deduce that​​​ RP = 10

Concept:

Median: Median is a statistical measure that determines the middle value of a dataset listed in ascending order

Mode: Mode is defined as the value that is repeatedly occurring in a given set.

Calculation:

Ascending order:

320, 320, 320, 330, 330, 340, 340, 360, 390

Median is the middle value. So, the median is 330.

Mode is the repeated value. 320 is repeated 3 times which is maximum. So, mode is 320.

⇒ Mean = 325

∴The mean of median and mode of the given data is 325.

GIVEN:

Number of children of age between( 8 -11) years

CALCULATION:

According to the given question,

Number of children below 11 years and above 8 years = Children of age group of 9 and 10 years

⇒ Number of children of age group of 9 and 10 years = ( 15 +42) = 57 years.

Hence, the number of children of age below 11 years and above 8 years = 57 years.

Concept:

• Work is said to be done by a force when the body is displaced actually through some distance in the direction of the applied force.
• Since the body is being displaced in the direction of F, therefore work done by the force in displacing the body through a distance s is given by:

Or, W = Fs cos θ

So, from this, we can conclude that

• Work done is positive when the direction of both force and displacement are the same
• Work done is negative when the direction of force and displacement are the opposite.
• Whereas work is done is zero when direction force (Centripetal force) and displacement are perpendiculars this case is true for an object moving in a circular motion

Explanation:

• Work done is not dependent on Time taken.
• It is dependent on Force and displacement.
• Since there is no change in any of them here.
• They displace the same upward displacement, so they do the same work.
• Hence Ram and Shyam have done an equal amount of work done.

Mistake Points

• In terms of power, they do different unit.
• As power equals = (Work done/Time)
• Shyam consumes more power than Ram or Shyam is more efficient.

Concept Used:

Diagonals of a rhombus bisect each other at a right angle.

Calculation:

For the following diagram,

AB = BC = CD = AD = 13 cm (all sides of a rhombus are equal.)

AC = 10 cm

⇒ AE = EC = 5 cm

and Let BE = DE = x cm

∠AEB = 90° (by the properties of the diagonal of the rhombus)

by Pythagoras' Theorem,

AB² = AE² + BE²

⇒ 13² = 5² + x²

⇒ 169 - 25 = x²

⇒ 144 = x²

⇒ x = ±12

But lengths can't be negative, thus x = 12

Hence, BD = BE + ED = 2x = 24 cm.

The correct answer is 3.

Concept:

Force

• Force is any push or pull that changes or tends to change the state of rest or motion, speed, direction of motion, or shape of the object.
• It is a vector quantity. That means both magnitude and direction are required to be calculated.
• Frictional force opposes the direction of motion. The frictional force between two surfaces up to a limit is equal to the applied force.

Calculation:

• Harish and Ashok are applying 2000 N each to move a box on the ground. The box will not move as frictional force is being applied.
• Total force applied = 2 × 2000 N = 4000 N
• If the force is equal to or more than f = 10000 N then the box may move.
• So, 6000 N (10000N - 4000 N) of more force is required.
• A person can provide a maximum of 2000 N
• So, the number of persons required to complete the rest of 6000 N is

6000 N / 3 = 2000 N

• So, 3 more people are required.

Additional Information

Types of Friction

• Sliding Friction: The frictional force acting between surfaces when one of them is sliding on another is sliding friction.
• Rolling Friction: When one body rolls over the surface of another body, the resistance to its motion is called rolling friction.
• Static Friction: The frictional force is acted when the object is kept stationary on the surface.

Important Points

• In the above case, when the box is not moving static friction is applied which keeps on increasing with applied force up to a certain limit. After that, as the box moves sliding friction is applied.
• Here people might get confused that at 5 people the force will just equal to frictional force so one extra person is required.
• But here we have to just slightly move the box which requires at least 10000N of force. This requirement can be fulfilled by at least 5 people.

Given:

The area of an equilateral triangle is 25√3 cm²

Concept used:

Inradius of an equilateral triangle (r) = a/2√3

Circumradius of an equilateral triangle (R) = a/√3

Here,

a = side of the triangle

Calculation:

Let the sides of the equilateral triangle be a

So, inradius = a/2√3

circumradius = a/√3

Now,

ratio = a/2√3 : a/√3

⇒ 1/2 : 1

⇒ 1 : 2

∴ The ratio of inradius and circumradius is 1 : 2.

Additional Information

Here, we do not need to operate on the area of the triangle.

Given:

Side of cube (a) = 7 cm

Concept used:

Total surface area of cube = 6a²

Calculation:

According to the above concept

Total surface area of cube = 6a²

⇒ [6 × (7)2] = (6 × 49) = 294 cm²

∴ The required total surface area is 294 cm².

Given:

Radius of the hemispherical container is 14 cm

Concept used:

Volume of a hemisphere = 2/3πr³

Calculation:

Volume of the container = 2/3πr³

⇒ 2/3 × 22/7 × 14³

⇒ 2/3 × 22/7 × 2744

⇒ 2/3 × 22 × 392

⇒ 17248/3

⇒ 5749.33 ≈ 5749 or 5.74 liters

∴ The required answer is 5.74 liters.

An error is a deviation from accuracy or correctness. A mistake is an error caused by a fault: the fault being misjudgement, carelessness, or forgetfulness.

A teacher may undergo the following steps for remediation of learning difficulties faced by the learners in your subject area:

• determining which students are having learning difficulty by analyzing their performance subject-wise and term wise
• determining the specific nature of learning difficulty through diagnosis
• determining the factors causing learning difficulty such as; attitude, interest, motivation and the like applying appropriate remedial procedures

Hence, we conclude that a teacher will take all the above steps for providing remedy in mathematical learning.

Given:

Radius of cone (r₁) = 3 cm.

Height of cone (h₁) = 7 cm.

Radius of sphere (r₂) = 10.5 cm.

Edge of cube (a) = 6 cm.

Formulae used:

Volume of cone = (1 / 3) × π × r₁² × h₁

where

r₁ = radius of cone

h₁ = height of cone

Volume of sphere = (4 / 3) × π × r₂³

where r₂ = radius of sphere.

Volume of cube = a³.

where

a = edge of cube.

Calculation:

Volume of cone (V1)

V₁ = (1 / 3) × π × r12 × h1

V₁ = 22 × 3

V₁ = 66 cm³.

Volume of sphere (V₂)

V₂ = (4 / 3) × π × r23

V₂ = 4 × 22 × 0.5 × 10.5 × 10.5

V₂ = 4851 cm³.

Volume of cube (V₃)

V₃ = a³

V₃ = 6³

V₃ = 216 cm³.

The ratio of volumes is,

V₁ : V₂ : V₃

66 : 4851 : 216

22 : 1617 : 72

∴ Ratio of volumes of cone, sphere and cube is 22 : 1617 : 72.

Given:

Ratio of radii of cones = 3 : 4.

heights of cones are equal = h = h'

Formula used:

Volume of cone = (1 / 3) × π × r² × h

where

r = radius of cone

h = height of cone

Calculation:

Ratio of volumes of cones

∴ Ratio of their volumes is 9 : 16.

Given:

The curved surface area of a cylinder = 594 cm²

Volume = 1336.5 cm³

Concept used:

Volume of cylinder = πr²h

Curved surface area of cylinder = 2πrh

Calculation:

According to the question

The curved surface area of a cylinder = 594 cm²

⇒ 2πrh = 594

⇒ 2 × 22/7 × r × h = 594

⇒ rh = (594 × 7/44) = 94.5

Now, Volume = 1336.5 cm³

⇒ 22/7×r²h = 1336.5

⇒ r²h = 425.25

∴ The required height is 21 cm.

Given:

The ratio of copper and zinc in brass = 11 : 6

Formula Used:

Amount of Copper : Amount of zinc = 11 : 6

Calculation:

According to the question,

⇒ 11x + 6x = 850

⇒ 17x = 850

⇒ x = 50

Amount of zink = 6x = 300kg

∴ The amount of zink is 300 kg.

Given:

The given number = 8, 9, 12, 15

Concept used:

LCM: The smallest number which is divisible by two or more given numbers.

Calculation:

LCM of 8, 9, 12 and 15 is 360

Now, according to the question

Adding the remainder in LCM, we get

⇒ (360 + 1) = 361

∴ The required least number is 361.

Calculation:

The smallest 4 digit number = 1000

The largest 2 digit number = 99

Difference = 1000 - 99 = 901