MPTET Varg 2 Math Mock Test - 2 - MPTET MCQ

जीवन में आने वाली कठिनाइयों की ओर संकेत वाला शब्द वीरानों नहीं है।

Key Points

• प्रलय, अँगारे, पद्यांश के अनुसार जीवन में आने वाली कठिनाइयों की ओर संकेत वाला शब्द है।
• यह कविता देश के पूर्व प्रधानमंत्री अटल बिहारी वाजपेयी जी द्वारा रचित है।
• उनकी काव्यात्मक रचनाओं में एक गम्भीर कवि की स्पष्ट झलक दिखाई देती है।

Additional Information

• जीवन में आने वाली कठिनाइयों की ओर संकेत वाला शब्द वीरानों नहीं है।
• प्रलय का विलोम है - सृष्टि।

The correct answer is 'about'.

Key Points

• The given sentence states that the officials were happy (by) something.
• “About” as a preposition indicates the subject of thought, feeling or action, as in, - Stop shouting about the problem and do something!
• Enthusiastic always takes the preposition 'about'.
  • ​I am enthusiastic about the colors you find in Tibetan temples.
• For the given sentence, the grammatically and contextually correct preposition will be 'about'.

Hence, the correct answer is Option 3.

Additional Information

• in: expressing the situation of something that is or appears to be enclosed or surrounded by something else.
• at: expressing location or arrival in a particular place or position.
• by: indicating the means of achieving something.

The correct answer is- '​Ambidexterity'
Key Points

• Let us see the meanings of the given options:
  • Ambivalence: the state of having two opposing feelings at the same time, or being uncertain about how you feel.
  • Ambidexterity: ability to use the right and left hands equally well; the quality of being ambidextrous.
    • Example: He displayed unprecedented ambidexterity while jumping off either foot during his competitive jumps.
  • Ambiparous: characterized by containing the rudiments of both flowers and leaves.
  • Sinistrality: the state or quality of having the left side or its parts or members different from and, usually, more efficient than the right side or its parts or members; left-handedness.
• Therefore, the ability to use both, right and left hands with equal expertise is "Ambidexterity."
• Thus, the correct answer is Option 2.

The logic followed here is:

(1st number)² ÷ 2 = 2nd number

As 64 ∶ 2048

64 → 64² → 4096 ⇒ 4096/2 → 2048

Similarly, 84 ∶ ?

84→ 842 → 7056 ⇒ 7056/2 → 3528

Therefore, 84 is related to 3528.

Hence, "Option (3)" is the correct answer.

Given:

The least common multiple of a and b is 42

Calculation:

According to the question,

LCM(a, b) = 42

LCM(5a, 11b) = LCM{LCM(5,11)(a,b)}

LCM(5a, 11b) = 5 × 11 × 42 = 2310

∴ The LCM of 5a and 11b is 2310.

The correct answer is Fuse.

Key Points

• Fuse is an electrical safety device used to protect an electrical or electronic device from over currents.
• The electric fuse is connected to the live wire.
• When the current above the rated value of the fuse flows through the fuse, the heat generated will cause the fuse wire to melt, thereby breaking the connection.
  • An electric fuse is a protective device that protects electrical equipment in the circuit by breaking the circuit when there is a short circuit.
  • It contains a fuse wire which has a low melting point, it allows normal current to pass through it safely but if there is any short circuit fuse wire can’t withstand the heat produced by that current (infinite current) so it melts and breaks the circuit
  • Hence fuse wire used to have a low melting point and high resistance to avoid overload or short circuit.
  • Whereas the fuse rating of electrical fuse is the maximum amount of current can pass through it without melting the fuse wire.

Additional Information

• The material used for fuse elements must be of:
  • Low melting point, low ohmic loss.
  • High resistivity.
  • Low cost and free from detraction.
  • The material used for making fuse element has a low melting point such as tin, lead, or zinc.
  • A low melting point is, however, available with a high specific resistance metal.
  • The material mainly used for fuse elements are tin, lead, silver, copper, zinc, aluminium, and an alloy of lead and tin.

Pedagogy is a ‘process of teaching’; we can say that it is the discipline concerned with theory as well as the practical aspects of education. It elaborates on how best teaching can occur in a classroom for the complete development of the learners. According to John Dewey “Pedagogy involves the organic relation between curriculum and teaching, and it entails study based, socially just and ethically sound practices resulting from negotiations among the teacher, learners, and others.”

Pedagogy of Mathematics: Mathematics is one of the few subjects that have practical, cultural, and disciplinary value. Mathematics has the potential to range across all the three values, but due to the inappropriate teaching-learning process, its potential is not being utilized to its optimum level. Note that:

• Optimization means utilization of available conditions and resources to the fullest extent which is never included in the school mathematics curriculum.
• Unfortunately, the current focus of Mathematics education is mostly on memorizing formulae to solve specific problems and applying them to examination questions.
• To make Mathematics an instrument of all the three values, it must be taught in an engaging, interesting, and interacting manner.
• According to National Curriculum Framework-2005, the main goal of Mathematics education in school is the mathematization of the child’s thought process.
• Mathematics relies on logic, reasoning, problem-solving, creativity, and a mathematical way of thinking. These skills can be useful in many other subjects.

Hence, we conclude that the above statement is about optimization.

Mathematics is interesting by using games, quizzes, riddles, tricks, etc. as learning activities. Every child deserves to be successful and confident in school life. Mathematical puzzles, riddles, and tricks develop many life skills in learners required to lead a successful and happy life. Children love games and puzzles, so learning through games makes the learning of Mathematics joyful and interesting.

Important Points

Benefits of recreational activities to develop following skills

• Encourage mathematical reasoning and logical thinking;
• Develop strategic thinking;
• Guide in concept development;
• Develop a positive attitude towards Mathematics;
• Help to develop the construction of ideas;
• Develop a variety of connections with the content that can form positive memories of learning;
• Improve fundamental operations of Mathematics;
• Help teachers to cater to the diverse needs of children;
• Help in the development of problem-solving, critical thinking skills, decision-making skills, etc.

Hence, we have concluded that mathematical puzzles, riddles and tricks develop all of the above skills.

Formula Used:

Distance = Speed × Time

Calculation:

Car travels 200 km in 8 hours

Using above formula -

⇒ Speed of Car = 200/8 = 25 kmph

⇒ Distance covered in 4.4 hours = 25 × 4.4 = 110 km

∴ The correct answer is 110 km

Concept used:

Calculation:

∴ The square root of 0.9 is equal to 0.9487.

Solution

Number of females patient in city A = 3/8 × 64 = 24

Number of females patient in city B = 4/9 × 54 = 24

Number of females patient in city C = 1/4 × 16 = 4

Number of females patient in city D = 5/12 × 48 = 20

Number of females patient in city E = 1/3 × 27 = 9

The total females = 24 + 24 + 4 + 20 + 9 = 81

Since the number given is in thousands = 81000

Average = 81000/5

⇒ 16200

Given:

The perimeter of a rectangular garden is 40 m whose length is 4 m more than its width.

Concept used:

Perimeter = 2(L + B)

Area = L x B

Calculation:

L = B + 4

Perimeter = 2(L + B)

⇒ 2(B + 4 + B) = 40

⇒ 2B + 4 = 20

⇒ B = 8 m

⇒ L = 12 m

Area = LB

⇒ 12 x 8

⇒ 96 m²

∴ The area of the rectangular garden is 96 m².

Given:

TR = TS

∠PTS = 115°

Concept used:

The alternate segment theorem is one of the circle theorems. The theorem states that “For any circle, the angle formed between the tangent and the chord through the point of contact of the tangent is equal to the angle formed by the chord in the alternate segment.

Calculation:

As TR = TS

So, ∠RST = ∠SRT

Let ∠RST, ∠SRT be θ

According to the concept,

∠PTR = ∠QTS = θ

Now,

∠QTS = 180° - ∠PTS

⇒ ∠QTS = 180° - 115°

⇒ ∠QTS = 65° i.e θ

So, ∠RST = 65°

∴ ∠RST is 65°

Given:

The image of the point (3, 4) in x - axis.

Concept used:

The reflection of point (x, y) along x axis is (x, -y)

The reflection of this point along y axis is (-x, y)

Calculations:

To find the reflection of the point along the x-axis, the abscissa remains constant.

So, the reflection of point (3, 4) along the x-axis is (3, -4).

∴ The answer is (3, -4)

Concept:

The n^th term of A.P., T_n = a + (n - 1)d

Sum of the n^th term of A.P.,

Here, a = first term, T_n = n^th term (last term)

Solution:

Odd numbers starting from 9 are 9,11,13...

Sum of first 'n' odd numbers, where a = 9 and d = 2 is.

∴ The correct option is (1)

Given:

The difference between two numbers is 4 and the difference between their squares is 56

Concept used:

(a + b)(a - b) = a² - b²

Calculation:

Let the numbers be x and y

According to the question,

x - y = 4 ----(i)

And x² - y² = 56

Now,

(x + y)(x - y) = 56

⇒ (x + y) = 56/4

⇒ x + y = 14 ---(ii)

From equations (i) and (ii) we get

2x = 18

⇒ x = 9

So, y = 5

So, x³ + y³ = 9³ + 5³

⇒ 729 + 125

⇒ 854

∴ The required answer is 854.

Given:

PQ ∥ RS

∠P = 85°

Concept used:

The sum of the interior angles on the same side of a transversal line is always 180 degrees.

The sum of opposite angles in a cyclic quadrilateral is 180°.

Calculation:

In a cyclic quadrilateral PQRS.

∠P = 85°

The sum of opposite angles in a cyclic quadrilateral is 180°.

∠P + ∠R = 180°

⇒ ∠R = 180° - ∠P

⇒ ∠R = 180° - 85°

⇒ ∠R = 95°

Now, ∠Q = 180° - ∠R

⇒ ∠Q = 180° - 95°

⇒ ∠Q = 85°

∴ The correct answer is 85°.

Given:

A cuboid having dimension:

Length = 4 cm, breadth = 6 cm, height = 6 cm

Formula used:

The radius of hemisphere = 1/2 × (√4h² + l² + b²)

Calculation:

2D image of the hemisphere:-

The radius of the hemisphere =

The radius of hemisphere = 1/2 × (√4h² + l² + b²)

⇒ 1/2 × √{4 × (6)²} + (4)² + (6)²

⇒ 1/2 × √144 + 16 + 36

⇒ 1/2 × √196 = 1/2 × 14 = 7 cm

∴ The radius of hemisphere = 7 cm

Given:

x = 2356 # 77 is divisible by 11

Concept used:

Divisibility rule of 11: If the difference of the sum of alternative digits of a number is divisible by 11, then that number is divisible by 11 completely.

Calculation:

According to the divisibility rule,

Sum of the odd place = (2 + 5 + # + 7) = 14 + #

Sum of the even place = (3 + 6 + 7) = 16

Difference = Sum of odd place - Sum of even place

⇒ 14 + # - 16

⇒ (# - 2)

For (# - 2) to be divisible by 11, # = 2

∴ The value of # is 2.

Given:

Adjacent sides = 11 cm, 13 cm

Diagonal = 16 cm

Concept:

The sum of squares of the diagonals of a parallelogram is equal to twice the sum of the square of the sides.

Calculation:

(d₁² + d₂²) = 2(a² + b²)

⇒ (16² + d₂²) = 2 (11² + 13²)

⇒ d₂ = √(242 + 338 - 256)

⇒ d2 = √ 324 = 18 cm

required difference = 18 - 16 = 2 cm

∴ The difference is 2 cm.

Mathematics is a diverse discipline that deals with data analysis, and integration of various fields of knowledge, involves proofs, deductive and inductive reasoning, and generalizations, and gives an explanation of natural phenomena and human behavior.

Key PointsMathematics is a conceptual subject, the emphasis should not be on rote learning, but rather on developing conceptual understanding in pupils so that they can apply those concepts to real-life scenarios.

• Students should be given ample opportunities to practice tasks/problems relating to the concepts they have learned so that their concept understanding might improve significantly.

Thus, mathematics books provide unit or lesson end assignments to increase learning opportunities, as well as a summary at the end to help revise all the taught concepts concisely.

Thus, it can be concluded that Each chapter of a Mathematics book ends with an exercise. What is the concept behind it is to extend learning opportunities.

Given:

ΔADE ∼ ΔACB

Concept used:

AA (or AAA) or Angle-Angle Similarity - If any two angles of a triangle are equal to any two angles of another triangle, then the two triangles are similar to each other.

Calculation:

ΔADE ∼ ΔACB

So, ∠ADE = ∠ACB, ∠AED = ∠ABC, ∠BAC = ∠EAD

So, ∠AED = 43°

So, ∠DEC = 180° - 43°

⇒ 137°

∴ The ∠DEC is 137°.

Given:

A certain number of two digits is three times the sum of its digits

45 is added to the number, the digits will be reversed.

Calculation:

Let the unit place digit be x and tens place digit be y.

So,

The number will be 10y + x.

According to the question

Two digits is three times the sum of its digits

⇒ 3(x + y) = 10y + x

⇒ 3x + 3y = 10y + x

⇒ 2x = 7y

⇒ x = (7/2)y .....(1)

Now,

45 is added to the number, the digits will be reversed.

⇒ 10y + x + 45 = 10x + y

⇒ 9y + 45 = 9x

Putting the value of x from the equation (1), we get

⇒ 9y + 45 = 9 × (7/2)y

⇒ 18y + 90 = 63y

⇒ 45y = 90

⇒ y = 2

Putting the value of y in equation (1), we get

⇒ x = (7/2 × 2)

⇒ x = 7

Now,

The sum of the squares of the two digit number is

⇒ (7)² + (2)²

⇒ (49 + 4)

⇒ 53

∴ The required value is 53.

Given

From 125 m high towers, the angle of depression of a car is 45°

Concept used

Tan 45° = 1

Calculation

AB is the height of the tower which is 125 m.

C is the point at which the car is standing.

In Δ ABC

Tan 45° = AB/BC

1 = AB/BC

AB = BC = 125 m

Distance between Tower and car is 125 m.

Given:

Cost Price = Rs. 800

Selling Price = Rs.900

Formula Used:

Profit = S.P. - C.P.

Calculation:

We have,

⇒ Profit = 900 - 800

⇒ Profit = 100

⇒ Profit% = 100/800 x 100

⇒ Profit% = 12.5%

∴ Ravi bought 1 shirt for Rs. 800 and sold for Rs. 900, His profit percentage is 12.5

The pattern recognition approach is used for the discovery, imaging, and interpretation of temporal patterns in seismic array recordings.

Key Points

Mathematics is a science that deals with logical reasoning, quantitative calculation, practices of counting describing shapes, abstraction of subject matter, etc. Mathematics plays a vital role in daily life.

• Pattern recognition requires the repetition of experience. All discoveries and inventions to date are a result of the pattern recognition skills of humans.
• The main goal of NCF 2005 is to mathematize the child's mind.

• The NCF focuses on conceptual understanding of any topic. It discourages rote memorization.
• Mathematics increases logical thinking.
• The teaching-learning process should not focus on robotic learning of steps of solving any question.
• The questions which only check the procedural learning, rote memorization, and drill do not initiate the mathematical thinking of students.

Hence, ‘Recognition of patterns and their completion’ is an essential part of the mathematics curriculum at the primary level as it Promotes creativity amongst students and helps them to understand the properties of numbers and operations.

Concept:

If a, b, c are in A.P. then 2b = a + c.

Calculation:

Given, a, b, c are in arithmetic progression,

⇒ 2b = a + c

So, the equation ax2 - 2bx + c = 0

⇒ ax2 - (a + c)x + c = 0

⇒ ax(x - 1) - c(x - 1) = 0

⇒ (ax - c)(x - 1) = 0

⇒ x = 1, c/a

∴ The correct answer is option (1).

Given:

Diagonal (D) of square = 18 cm

Formula used:

Perimeter (P) = 4a

Concept used:

The side of the square = a

Then diagonal = a√2

Calculation:

According to the question

D = a√2

⇒ 18 = a√2

⇒ a = 9√2

Now the perimeter,

P = 4 × a

⇒ 4 × 9√2

⇒ P = 36√2 cm.

∴ The perimeter of the square is 36√2 cm.

Let the larger number be x and the smaller number be 16 - x

According to the question:

2(x²) = (16 - x)² + 164

⇒ 2x² = 256 + x² - 32x + 164

⇒ x² + 32x - 420 = 0

⇒ x² + 42x - 10x - 420 = 0

⇒ x(x + 42) - 10 (x + 42)

⇒ (x - 10)(x + 42)

⇒ x = 10 or - 42

Neglecting the (-) value

x = 10

So the other number is 16 - x = 16 - 10 = 6

Hence the two numbers are 10 and 6.

Given:

Euclid stated that all right angles are equal to each other in the form of:

Calculations:

According to Euclid's fourth postulate, all the right angles are equal to each other.

∴ The answer is postulate.