MPTET Varg 2 Math Mock Test - 1 - MPTET MCQ

सही उत्तर '24 अक्टूबर 1945 को' हैं।

• संयुक्त राष्ट की स्थापना के 4 मुख्य प्रयोजन थे।
• गद्यांश की पंक्ति: "स्वतंत्रता प्राप्ति के लगभग दो वर्ष पहले अप्रैल-जून 1945 में सैन फ्रांसिस्को में संयुक्त राष्ट्र की स्थापना सभा में भारत के प्रतिनिधि उपस्थित थे। अधिकांश सदस्यों द्वारा घोषणा पत्र की पुष्टि हो जाने पर संयुक्त राष्ट्र 24 अक्टूबर 1945 को अस्तित्व में आया।"

Key Points

• संयुक्त का संधि विच्छेद सम् + युक्त होता है।
• प्रयोजन के समानार्थी शब्द: हेतु, लक्ष्य, उद्देश्य आदि हैं।

The correct answer is: What should I do with my hands when I speak in public?

Key Points 

• The given sentence is in the active form and in the present Simple tense and we need to change it into the passive form.
• The  Present Simple in the active voice has the following form: Question Word + modal verb+ Subject+ V1+Object+?
• The  Present Simple in the passive voice has the following form: Question Word+  modal verb + be + Object+ V3+ by subject +?
• The auxilliary verb 'be' is used with modals. (can)
• In the passive voice of Present Simple, we have to change the structure, so the subject in the active voice becomes the object in the active voice.

​Therefore, the correct answer is option 2.
Correct Active Voice: What should I do with my hands when I speak in public?

Given:

Quant = 38 %

All Subjects = 100 %

Calculation:

All others subjects = 100% - 38 %

⇒ 62 %

The ratio of Quant and all other students = 38% : 62%

⇒ 19 : 31

The ratio of Quant and all other students = 19 : 31

Child-centered education- Child-centered approach means planning and transacting curriculum in the classroom in a way that allows for flexibility in pace and style of learning to keep in mind that children in a classroom are widely different. 

• Child-centered education assessment: It involves the active engagement of the students in setting goals for their development, and learning, and monitoring the progress towards those goals.

Key Points​Child-centered education:- 

• The teacher is a facilitator, the role of the teacher is to guide the learner to take part actively in the classroom learning
• The classroom approach should be based on the learner's needs and schools should make the curriculum flexible.
• Assessment in child-centered education is considered an integral part of the process of learning as it facilitates the learner and instructor for better grasping of a particular topic. 
• Under inclusive education, child-centered education should be done according to the mental level of the child because in an Inclusive class the learner of diverse background comes together, and study with normal students in the same class in the same school and in the same environment.
• As diverse learners are present in the class, the teacher should follow the approach according to the mental ability of the students, so all students participate in learning actively. 

Hence, from the above statements we can conclude that in child centered education we can asess the child in terms of his\her growth and developments towards the particular goals. so the assessment in child centered education is considered as an important part of learning.

Additional Information

•  Importance of child centered education 
  • It focuses on all around development
  • Flexible curriculum
  • Varied methods of teaching
  • Varied tasks
  • Varied learning time.
• In child-centered classroom
  • Child is an active participant 
  • Environment must be joyful, cheerful
  • Safe and secure environment
  • Activities based classroom
  • All round development of child.

Erik Erikson’s theory of psychosocial development is one of the best-known theories of personality in psychology. 

• Erikson’s theory describes the impact of social experience across the whole lifespan.
• He felt the course of development is determined by the interaction of the body (genetic biological programming), mind (psychological), and cultural (ethos) influences. 
• the psychosocial theory basically asserts that people experience eight ‘psychosocial crisis stages’ which significantly affect each person’s development and personality. 
• Each crisis stage relates to a corresponding life stage and its inherent challenges.
• Erikson used the words ‘syntonic’ for the first listed ‘positive’ disposition in each crisis (example trust) and ‘dystonic’ for the second listed ‘negative’ disposition (example, Mistrust)

Important Points

Industry vs. Inferiority ( Latency 6-12 yrs)

• At this stage, If the child is encouraged and praised by parents and teachers then he/she develops a feeling of competence and belief in their skills.
• Feelings of inferiority are likely to develop and this might lead the child to become an underachiever.

Key Points

Erikson’s Eight Stages of development-

Thus from the above-mentioned points, it is clear that Erik Erikson’s theory of psychosocial development emphasizes on Industry versus Inferiority stage. 

Additional Information

• Stimuli and Response and Operant Conditioning are theories related to learning.
• Ophallic and Latency stages are the stages related to Psychosexual Stages of Development proposed by Freud.

Learning disability refers to the neurological disorder that causes cognitive impairment. Dyslexia, dysgraphia, dyscalculia, etc are the example of learning disability.

Dyslexia a learning difficulty that primarily affects the skills involved in accurate and fluent word reading and spelling which makes learners:

• confuse with the same shapes and sounds of the alphabet.
• unable to read, interpret, and understand letters and words.
• bewilder in identifying and relating speech sounds with letters and words.

Hence, it could be concluded that a learning difficulty that primarily affects the skills involved in accurate and fluent word reading and spelling is known as Dyslexia.

Additional Information

Other Disabilities in Brief:

Given:

Concept used:

Calculation:

⇒ 

⇒ 

⇒ 

⇒ - 1

∴ The required answer is - 1.

Given :

Time = 25/4 years

SI = 3/8 of Principle

Formula used :

SI =                  ..............   Eq 1.

Where, P = principle , R = Rate , T = Time

Solution :

Now according to the question :

SI = 3/8 P 

Putting the values of SI and Time in Eq 1 we get :

3/8 P = [P × R × 25/4] / 100

⇒ 3/8 × 100 = R × 25/4

⇒ R = 300/8 × 4/25

⇒ R = (12 × 4) / 8

⇒ R = 6%

Hence the correct answer is "6%".

Given:

The two angles of the triangle are 2x and 3x.

QM ⊥ PR
∠Q = 90^º

Concept

The sum of all the angles of the triangle = 180^º

A perpendicular makes a 90º angle with the line.

Calculation

∠Q + ∠2x + ∠3x = 180^º

90^º + 5x = 180^º

5x = 180 - 90

x = 90/5

x = 18^º

3x = 3 × 18

∠QRM = 54° 

in the △QMR,

∠QMR + ∠QRM + ∠MQR = 180

90º + 54º + ∠MQR = 180º

∠MQR = 180º - 144º

∠MQR = 36º

Important Points

QM is Perpendicular to PR, not MQ is Perpendicular Bisector of ∠PQR

Given:

(2x - 1) is a factor of 2x³ + ax² + 11x + a + 3

Calculations:

As 2x - 1 is one of the factor, then one of the roots will be, x =

Now, putting x = in the given equation and equating the same to zero.

=> 2 × ()³ + a × ()² + 11 × + a + 3 = 0

=> 2 × + a × + 11 × + a + 3 = 0

=> + + a + 3 = 0

=> + = 0

=> 5a + 35 = 0

=> 5a = - 35

=> a =

= - 7

∴ The answer is - 7

Problem-solving: It is an important life skill which suggests a shift from memorization to understanding of concepts and ability to apply those in both familiar and unfamiliar situations, whether in daily life problems or in problems given in the textbooks. The problem-solving skills include skills of

• observation
• experimentation
• estimation
• reasoning
• verification

Also note that abstraction, quantification, analogy, case analysis, reduction to simpler situations, even guesses and verification are useful in many problem contexts.

Hence, we conclude that the above statement is about problem-solving method. 

Concept used:

1 hr = (60 × 60) sec = 3600 sec

1 min = 60 sec

Calculation:

According to the above concept

3 hrs and 45 minutes = ____________ seconds 

⇒ (3 × 3600 + 45 × 60) sec

⇒ (10800 + 2700) sec

⇒ 13500 sec

∴ The required value is 13500 seconds.

The correct answer is option 3, i.e 100 J.

CONCEPT:

• Work performed by force is equivalent to the product of the magnitude of force(F) applied and the distance the body moves through(d).  
• Mathematically, the Formula for worked done will be given as
  • W = Fd  --------(1)
  • where, F= |F|

CALCULATION:

• Given, the mass of a bag, m= 5kg
• Displacement, d = 2m
• As we know,
• F = mg
  • where,
  • Force is measured in Newtons, N.
  • Mass is measured in kilograms, kg.
  • Acceleration is measured in meters per second square. (g = 10m/s)
• Force, F = m × g =  5 × 10= 50N
• Put the value of F in eq (1)
  • W = 50 X 2 = 100J
• Thus, the work done by the boy is 100J.

Formula used:

Remainder (ax ± 1)ⁿ/x = (±1)ⁿ

Calculation:-

For 17¹⁰⁰/8 = (2 × 8 + 1)¹⁰⁰/8 

⇒ Remainder = 1¹⁰⁰/8 = 1

For 9¹⁹/8 = (1 × 8 + 1)¹⁹/8

⇒ Remainder = 1¹⁹/8 = 1

For 7

⇒ Remainder = 7/8 = 7

Combining all,

⇒ Overall Remainder = (1 + 1 + 7)/8

⇒ 9/8

∴ Remainder = 1

∴ The required remainder is 1.

Given:

Tunnel length = 300m

Time taken to cross the tunnel = 40s

Time is taken to cross pole = 25s

Formula used:

Speed = Distance/time

Calculation:

Distance difference = 300

Time difference = 15

⇒ S = 300/15

⇒ S = 20 m/s

Train length = Distance travel to cross pole

⇒ D = S × T

⇒ D = 20 × 25

⇒ D = 500m

∴ The answer is option A.

Given:

In a triangle ABC if ∠CAB = 70°, and AB = AC

Concept used:

Concept used:

In isosceles triangle, two angles opposite to equal sides are equal.

Sum of all angle of triangle = 180°

Calculation:

In a triangle ABC if ∠CAB = 70°, and AB = AC

⇒ ∠B = ∠C = x (let) ( by isosceles triangle property)

⇒ ∠BAC + ∠ACB + ∠ABC = 180º

⇒ 70 + x + x = 180°

⇒ 2x = 110°

x = 55°

∴ ∠B and ∠C are 55°, 55°

Given :

A number N = 35 × 53 × 7² 

Concept used :

For N = A^a x B^b x C^c, Number of factors = (a+1) x (b+1) x (c+1)

Calculation :

N = 35 × 53 × 7² 

Number of factors = (5+1) x (3+1) x (2+1)

⇒ 6 × 4 × 3 = 72

∴ The answer is 72.

Concept used:

Divisibility of 6: The given number should be divisible by both 2 and 3.

Solution:

⇒ 867Y8, Since its unit place is even it is divisible by 2 and we have to check for the divisibility of 3.

Divisibility of 3: The sum of digits of a number should be divisible by 3.

⇒ 867Y8 = 8 + 6 + 7 + Y + 8 = 29 + y

In order to make it divisible by 3 the least possible value of Y is 1.

⇒ 29 + 1 = 30

Hence, 86718 is completely divisible by 6.

Given that 64 is divided in the ratio 2 ∶ 4 ∶ x.

Let the common multiple be k.

Therefore, the numbers are 2k, 4k and xk.

2k + 4k + xk = 64

k = 64/(6 + x).

Given that the smallest number is 32/3.

Therefore,

2k = 

2 ×  = 

 = 

Given:

Principal amount = Rs 8,000

Time = 1 year

Rate = 10% p.a. compounded semi-annually

Concept Used:

Compound Interest = P

Calculation:

⇒ For compounded semi-annually, n = 2.

= 10/100 = 0.1% p.a.

⇒ Compound Interest = 8000 × 

⇒ Compound Interest = 8000 × [(2.1 ÷ 2)² – 1]

⇒ Compound Interest = 8000 × [1.1025 – 1]

⇒ Compound Interest = 8000 × 0.1025 = Rs 820

Therefore, the compound interest for the period of one year is Rs 820.

Given:

Equation 2m2 - 8m = 0 . 

Concept Used:

General equation ax2 + bx + c = 0.

Sum of roots of the equation = - 

product of roots of the equation =  

Calculation:

Comparing the equation 2m2 - 8m = 0 to the standard for of equation ax² + bx + c = 0.

Here, a = 2, b = - 8 and c = 0

Sum of roots of the equation = -  =  = 4.

product of roots of the equation =  = 0 .

∴ Sum and Product of roots of the given equation is 4, 0 .

Formula:

tan θ = p / b

Where “p” and “b” are perpendicular and base of a right-angled triangle.

Calculation:

In ΔCBP-

⇒ tan 30º =  CP / BC

⇒   = 

∴ BC = 240√3 m or 415.7 m 

In ΔAPC-

⇒ tan 45º = CP / AC

Since tan 45 = 1, CP = AC = 240 m

From the figure, Distance between the objects = AC + BC

⇒ Distance between the objects = 240 + 415.7 = 656 m (to the nearest meter).

The distance between the objects is 656 m.

Given:

Percentage distribution of population of five states on the basis of poverty line and also on the basis of sex

Calculations:

In state C, percentage of population above the poverty line is (100 - 25)% = 75%

So, The total population above poverty line is 75% of 4000000

⇒ 4000000 × = 3000000

Number of females above poverty line is × 3000000

⇒ 3 × 600000 = 1800000 = 1.8 million

∴ The answer is 1.8 million

Given:

Rate = 20% per annum, Time = 2 years

CI = Rs 2288

Formula used:

CI = P(1 + )ⁿ - P

 Where, P = Principal amount, r = rate , n = Time

Calculation:

Putting the values of CI,  r and time in the above formula we get:

2288 = P(1 +  )² - P

⇒ 2288 = P()² - P

⇒ 2288 = P(36/25) - P

⇒ 2288 = (36P - 25P) / 25

⇒ 2288 × 25 = 11P

⇒ P = 57200 ÷ 11

⇒ P = Rs 5200

Hence the correct answer is "Rs 5200".

Mathematics involves the in-depth study of patterns, shapes, various numbers, geometrical objects, data, and information. It includes various fields of knowledge that consist of proofs, deductive and inductive reasoning, and generalizations.

• It involves the mathematization of thoughts that develops through mathematical reasoning, consisting of abstract statements and their proofs.
• Every mathematical theory or statement is definable in terms of some given undefined terms.

Key Points

• The axiom is a logical statement in mathematics that is assumed to be based on truth.
• They are accepted widely but without being proved as they are considered as self-consistent sets of unproven statements. 
• They are a kind of prepositions that are assumed to be true without being proven and unlike postulates they can be universal in many areas of study.
• An axiom is useful to prove and derive the complex theorems and abstract statements of mathematics. It is used as a base to solve or prove the other theories and properties in various domains of mathematics. 
• It includes the suggestion to accept the existence of some facts or truths. These are considered as the basic structures from which the various theorems are derived.
• For example,
  • God is present everywhere.
  • Any square object will have four sides and each of them must be equal.
  • Two parallel lines can be extended parallelly till infinity as they will not intersect each other.

Hence, it could be concluded that the axioms are prepositions that are assumed is a correct statement.

Confusion Points

Given:

The average of 5 observations x, x + 2, x + 4, x + 6, x + 8 is 11

Concept used:

Average = Sum of observation / Number of observations

Calculation:

Average = Sum of observation / Number of observations

⇒ (x + x + 2 + x + 4 + x + 6 + x + 8)/5 = 11

⇒ 5x + 20 = 55

⇒ 5x = 55 - 20 = 35

⇒ x =  = 7

Average of last three observations =

⇒  = 

⇒ x + 6

⇒ 7 + 6 = 13

∴ The average of the last three observations is 13.

The correct answer is Siemens.

Key Points

• Siemens is the SI unit for measuring electric conductance.
• Siemens per unit is the unit of electrical conductivity.
• Mho is also known as siemens.
• The reciprocal of ohm is siemens.
• The reciprocal of resistance is siemens.
• In the 14th general conference on weights and measures, the unit of conductance known as siemens was adopted.
• The unit was named after Earner won Siemens.
• The ratio of current density to the electric field strength gives the value of electrical conductivity.
• If the conductivity of a substance is higher, then the resistance of that substance will be lower and the flow of electric current will be smoother.
• The ability of electrons or charge carriers decides the value of electrical conductivity.

Additional Information

•  Henry is the SI-derived unit of electrical inductance.
•  Farad is the SI-derived unit of electrical capacitance.
• Tesla  is a unit of the magnetic induction.

The correct answer is 76 cm of Hg.Key Points

• Atmospheric pressure, also known as barometric pressure (after the barometer), is the pressure within the atmosphere of Earth.
• The standard atmosphere (symbol: atm) is a unit of pressure defined as 101,325 Pa (1,013.25 hPa), which is equivalent to 1013.25 millibars, 760 mm Hg, (or 76 cm Hg) 29.9212 inches Hg, or 14.696 psi.
• The atm unit is roughly equivalent to the mean sea-level atmospheric pressure on Earth; that is, the Earth's atmospheric pressure at sea level is approximately 1 atm.

Additional Information Temperature Conversion Formula Table

The correct answer is option 2) i.e. prevents the mercury level from falling on its own when taken out of our body

CONCEPT:​

• Thermometer: ​A device that measures the temperature is called a thermometer.
• Clinical thermometer: The thermometer that measures the body temperature is called a clinical thermometer.
  • The temperature of the human body is between 35∘C to 42∘C. Thus, the range of a clinical thermometer is 35∘C to 42∘C.
  • It consists of a thin glass tube and a bulb that contains mercury.
  • The kink is a constriction that prevents the movement of mercury in the tube. Due to this, the mercury takes time to reach a given temperature reading and also does not fall rapidly.

​

​EXPLANATION:

• The thermometer is generally placed inside the human body and taken out to see the reading.
• While reading, it is necessary that the mercury does not fall back to show the room temperature.
• This is taken care of by the kink which prevents the mercury level from falling on its own when taken out of our body.

Given:

Five coins were simultaneously tossed 1000 times, and at each toss, the number of heads was observed. The number of tosses during which 0, 1, 2, 3, 4, and 5 heads were obtained are shown in the table below.

Concept:

The mean of the frequency distribution data is as follows,

Solution:

The mean of the given frequency data is as follows,

Therefore, the mean number of heads per toss is 2.47