MPTET Varg 2 Math Mock Test - 9 - MPTET MCQ

The Van Hiele's levels originated in 1957 given by Pierre Van Hiele and his wife from the Utrecht University in the Netherlands. It helped in shaping the curriculum throughout the world which especially influenced the learning of geometry at a large level.

• It provides insight to the teacher about how the students learn geometry at different levels. It describes how the students learn at each level and pass to another level.

Key Points

Van Hiele levels:

• In early schooling, the students began to learn about shapes and try to differentiate various shapes from each other.
• The students learn according to their individual differences, the age can be different in each stage as they learn at their own pace.
• The Van Hiele levels are described below:

So, it is concluded that according to Van Hiele's stages, the child at level 2, is able to perceive the relationship between properties and figures.

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,
nth term of AP = 0

The given AP = 45, 42, 39 …..

Formula:

T_n = a + (n – 1)d

a = first term

d = common term

Calculation:

a = 45

d = 42 – 45

d = (-3)

T_n = a + (n – 1) d

⇒ 0 = 45 + (n – 1) × (-3)

⇒ (n – 1) × (-3) = -45

⇒ n – 1 = 45/3

⇒ n – 1 = 15

⇒ n = 15 + 1

⇒ n = 16

Given:

A floor is 4 m long and 3 m wide

One-third of the floor is covered with blue tiles of side 10 cm.

Another one-fourth of floor is covered with green tile of sides 15 cm.

The remaining area is covered with red tile of sides 20 cm.

Concept used:

Area = length × breadth

1m = 100 cm

Calculation:

Area of the floor = 4 x 3 = 12 m = 120000 cm²

Total area covered by Blue tiles = 1/3 x 120000 = 40000 cm²

Area of 1 Blue tile = 10 x 10 = 100 cm²

⇒ Number of Blue tiles = 40000/100 = 400 tiles

The portion of the area covered by red tiles = 1 - 1/3 - 1/4 = 5/12

Total area covered by red tiles = 5/12 x 120000 = 50000 cm²

Area of 1 red tile = 20 x 20 = 400 cm²

⇒ Number of Red tiles = 50000/400 = 125 tiles

∴ The number of red tiles used is 125 respectively.

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.

Reason is correct.

perimeter of triangle = a + b + c ; a, b, c are the sides of triangle.

Assertion is also true.

sides are 9 cm, 13 cm and 14 cm.

perimeter = 9 + 13 + 14 = 36 cm.

∴ Option 1 is correct.

Given:

5^th and 9^th terms of an arithmetic progression are 24 and 38 respectively

Formula used:

In an arithmetic progression, nth term = a + (n – 1) d, where a = first term and d = common difference

Calculation:

5^th term = a + 4d = 24 ----(1)

9^th term = a + 8d = 38 ----(2)

[2 × equation (1)] – equation (2) gives

2a + 8d – a – 8d = 48 – 38

⇒ a = 10

∴ the first term = 10

Calculation:

International Number System

Indian Number System

⇒ Product = 100,000 × 10,000 = 1,000,000,000

∴ 9 zeroes in 1 billion.

The correct option is 1 i.e. 9

Given:

Akshita plays Badminton for 1 hr and Volleyball for 2 hr and Ridhima Plays badminton for 4: 30 hours

Calculation:

⇒ Akshita's total cost = 1(100) + 1(150) = Rs. 250

⇒ Ridhima's total cost = 4.5(100) = Rs. 450

∴ Akshita pays less.

Given:

Number of people = 55

Juice served to each person = 200 ml

Formula Used:

1 L = 1000 ml

Calculation:

Juice served to people = Number of people × Juice served to each person

⇒ Juice served to all people = 200 × 55 = 11000 ml

1 L = 1000 ml

⇒ 11000 ml = 11 L

∴ Juice served to all 200 people is 11 L.

Mathematical Communication refers to the Communication by which learners discuss, share, analyze, and make their sense of maths. It used to express mathematical thoughts and ideas.

Communication in Mathematics develops the ability to organize, consolidate, and express mathematical thinking among the students.

Aims of encouraging mathematical communication in the classroom:

• Enabling learners to reason logically.
• Enhancing mathematical understanding.
• Making learners able to assimilate mathematical terms.
• Enabling learners to express mathematical thoughts and ideas.
• Developing the ability to recognize the patterns of mathematical thought.
• Enabling learners to use precise language while talking about mathematical statements and using them.

Hence, it could be concluded that Communication in Mathematics class refers to developing an ability to organise, consolidate and express mathematical thinking.

Given:

The angle of elevation of the top of a tower from a point on the ground is 30°.

After walking 30 meters towards the tower, the angle of elevation of the top becomes 60°.

Calculations:

Let AB be tower and C and D be the point of observation.

=> h = 15√3

=> h = 15 × 1.73

=> h = 25.95~26

∴ The answer is 26 m.

Given:

Concept used:

1. (a - b)² = a² - 2ab + b²

2. (a + b)² = (a - b)² + 4ab

Calculation:

Given:

The perimeter of a regular pentagon = 320 cm

Concept used:

The perimeter of a regular pentagon = 5 × side

Calculation:

According to the question,

⇒ 5 × side = 320 cm

⇒ side = 320/5 = 64 cm

∴ The length of one side is 64 cm.

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 Used:-

AAS Theorem-According to the angle-angle-side theorem of congruence of triangle, when the two included angles and one side of any triangle are equal in measure to the 2 included angles and 1 side of any another triangle, then these triangles are known as the congruent triangles.

Explanation:-

Given that, l ∥ m and M is the mid-point of a line segment AB. Redraw the given figure with naming the angles as 1, 2, 3, and 4.

Since ray l and m are parallel to each other. So, the angle 1 and 3 will be alternate equal angles.

⇒ ∠1 = ∠3 ......(1)

Also, angle 2 and angle 4 are the vertical opposite angles. Thus,

⇒ ∠2 = ∠4 ......(2)

Since M is the midpoint of AB. So it will cut AB in equal parts. Thus,

⇒ AM = BM ......(3)

So, the △ AMC and △ BMD will be congruent by AAS rule of concurrency.

⇒△ AMC ≅ △ BMD

Now the corresponding parts of concurrent triangles are equal. Thus,

⇒ CM = DM

Thus, M is also the mid-point of any line segment CD, having its endpoints on l and m, respectively.

Hence, the correct option is 1.

Concept:

Theorem: Angles opposite to equal sides are equal.

∠A + ∠B = ∠D (Exterior angle property)

⇒ ∠A = ∠E (Alternate angles)

Calculation:

According to the above figure,

∠HDC = ∠DCF = 10a + 5 [alternate angles]

⇒ 10a + 5 = 40 + 6a - 5 [exterior angle of ΔECF]

⇒ 4a = 30

⇒ a = 7.5

∴ The required value of a is 7.5

Calculation:

As we can see clearly in the line graph that in tests 3 and 4 he got 45 and 48

∴ Required answer is 2

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.

Calculations:

According to the question,

Students obtained 135 marks = 2

Students obtained 140 marks = 8

Students obtained 145 marks = 5

Students obtained 150 marks = 4

Students obtained 155 marks = 1

Total students obtained marks more than 130 = 2 + 8 + 5 + 4 + 1 = 20

∴ 20 students obtained marks more than 130.

Concept:

• MKS system is a Meter kilogram and second system while the CGS system is a centimeter, gram, and second based system.
• The CGS system is developed for small-scale systems for convenience in small-scaled machines and equipment.
• The unit of force in the MKS system is newton while the unit of force in the CGS system is dyne.
• So, 1 newton = 1 kg m s^-2 and 1 dyne = 1 cm gm s^-2
• We know that 1 kg = 1000 gm and 1 m = 100 cm

Calculation:

The correct answer is Steel Rod.

Key Points

• For transferring heat, a steel rod would be an ideal material.
• Metals are always good conductors of heat and electricity.
• However, stainless steel is not a good conductor of heat.
• Woolen Thread, water, and wooden plank are all poor conductors of heat.
• These materials act as insulators.

Given:

Principal = Rs. 1000

Time = 2 years

Rate of interest = 10%

Formula:

C.I = P × [(1 + r/100)n – 1]

Here,

P = Principal Amount

r = Rate of interest

n = Time in years

Calculation:

We know that -

C.I = P × [(1 + r/100)n – 1]

According to the question,

C.I = 1000 × [(1 + 10/100)2 – 1]

⇒ C.I = 1000 × [(1 + 1/10)2 – 1]

⇒ C.I = 1000 × [(11/10)2 – 1]

⇒ C.I = 1000 × [121/100 – 1]

⇒ C.I = 1000 × [(121 – 100)/100]

⇒ C.I = 1000 × [21/100]

⇒ C.I = 210

∴ The Interest Amount will be Rs. 210.

Given:

Area of a circle is 616 cm2

Formula Used:

Area = πr²

Circumference = 2πr

Calculation:

Area = πr²

⇒ 616 = πr²

⇒ r = 14

Now,

Circumference = 2πr

Circumference = 2 x 22/7 x 14

Circumference = 88 cm

Therefore, the circumference of the circle is 88 cm.

Formula Used:

Perimeter of rectangle = 2[Length + Breadth]

Area of rectangle = Length × Breadth

Calculation:

Using above formula -

⇒ 2[L + B] = 76

⇒ L + B = 38 ...(1)

Area of rectangle is 360

⇒ L × B = 360 ...(2)

Using (1) & (2)

⇒ L(38 - L) = 360

⇒ 38L - L² = 360

⇒ L² - 38L + 360 = 0

⇒ L² - 18L - 20L + 360 = 0

⇒ L(L - 18) - 20(L - 18) = 0

⇒ (L - 18)(L - 20) = 0

⇒ L = 18 or 20 units

If L = 18 Units ,B = 38 - 18 = 20 Unit

If L = 20 Units ,B = 38 - 20 = 18 Unit

∴ The correct answer is 18 unit

Given:

The given number = 84705 ⊗ 2 is divisible by 9

Concept used:

Divisibility rule of 9: If the sum of digits of the number is divisible by 9, then the number itself is divisible by 9.

Calculation:

According to the above concept,

⇒ 84705⊗2 = 8 + 4 + 7 + 0 + 5 + ⊗ + 2

⇒ 26 + ⊗

Now, we replace ⊗ by 1, then it becomes 27, which is divisible by 9.

∴ The required value is 1.

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 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.