MPTET Varg 2 Math Mock Test - 8 - MPTET MCQ

Given:

Some triangles and quadrilaterals are given.

Find the line of symmetry.

Concept used:

The line of symmetry can be defined as the axis or imaginary line that passes through the center of the shapes and divide into two identical halves.

Calculation:

In isosceles triangle,

Only one line of symmetry.

In Kite,

Only one line of symmetry.

In rhombus,

Two lines of symmetry.

In rectangle, Two line of symmetry.

In scalene triangle,

No any line of symmetry.

In parallelogram,

No any line of symmetry.

∴ Option 4 both have no same line of symmetry.

∴ Option 4 is correct.

Given:

log10 (x - 9) + log10 x = 1

Concept Used:

log_b (M) + log_b (N) = log_b(MN)

Calculations:

log10 (x - 9) + log10 x = 1

⇒ log10 (x - 9)(x) = 1

⇒ log10 (x - 9)(x) = log₁₀10

⇒ x² - 9x - 10 = 0

⇒ x² - 10x + x - 10 = 0

⇒ x(x - 10) + 1(x - 10) = 0

⇒ (x + 1)(x - 10) = 0

⇒ x = -1 and x = 10

∴ option 4 is correct

Given:

The altitude drawn to the base of an isosceles triangle is 8 cm and the perimeter of the triangle is 32 cm.

Concept used:

Area of a triangle = 1/2 × base × altitude

Calculation:

Let the equal sides of the isosceles triangle be x

So, base = 32 - 2x

As we in an isosceles triangle the altitude drawn to the base bisects the base

So, according to that,

BD = DC = BC/2 = 16 - x

Now,

8² + (16 - x)² = x²

⇒ 64 + 256 + x² - 32x = x²

⇒ 32x = 320

⇒ x = 10

So, base is 32 - 20

⇒ 12 cm

Now,

Area = 1/2 × 8 × 12

⇒ 48 cm²

∴ The required answer is Option 4.

Concept:

Formula of Logarithms:

 here a ≠ 1 and a > 0 and x be any number.

Properties of Logarithms:

Calculation:

Given: log 2 = 0.301 and log 5 = 0.699.

As we know that, 

⇒ log (5 / 2) = log (5) - log (2)

By substituting the values of log 5 and log 2 in the above equation we get,

⇒ log (5 / 2) = 0.699 - 0.301 = 0.398

Hence, log (5 / 2) ≈ 0.4.

A mathematical game is an activity that engages children for amusement or fun. It should be a part of the mathematics classroom as it will be a child-centered and happy classroom where children get opportunities to observe, explore and share experiences.

Key Points

Characteristics of mathematical games-

• Mathematical games must not be confused with open-ended play and there is a set of rules that governs decision making. The rules should be based on mathematical ideas and the game should end when the goal is reached.
• Mathematical games provide non- didactic feedback to the children be the minimum amount of teacher intervention.
• Mathematical games promote processes of anticipation and planning in children which help them stimulate interest in a topic and develop mathematical skills.

Hence, we conclude that the correct statements are (b) and (c).

Given:

The angle of elevation of the top of a building at a distance of 70 m from its foot on a horizontal plane is found to be 60°.

Concept used:

tanθ = P/B

Here,

P = Perpendicular

B = Base

Calculation:

Let AB be the building and BC be the distance

Now,

In ΔABC

tan60° = AB/BC

⇒ √3 = AB/70

⇒ AB = 70√3

So, the height = 70√3 m

∴ The height of the building is 70√3 m.

Given:

47 + {7 + [61 − (21 ÷ 3)] ÷ 9}

Concept Used:

Follow the BODMAS rule according to the table given below:

Calculation:

47 + {7 + [61 − (21 ÷ 3)] ÷ 9}

= 47 + {7 + [61 − 7] ÷ 9}

= 47 + {7 + 54 ÷ 9}

= 47 + {7 + 6}

= 47 + 13

= 60

Hence, the required value is 60.

Given:

Ratio of radius = 2 : 5

Ratio of Heights = 5 : 7

Formula Used:

Volume of cylinder = πr²h

(where r = radius, h = height)

Calculation:

Let, the radii be 2x and 5x and the heights be 5y and 7y.

For 1st cylinder, radius = 2x, height = 5y

For 2nd cylinder, radius = 5x, height = 7y

According to question,

Ratio of their volume(1st : 2nd) = π × (2x)² × 5y : π × (5x)² × 7y

⇒ 4x² × 5y : 25x² × 7y

⇒ 4 : 35

∴ The ratio of their volume is 4 : 35.

Concept used:

If the speed of a man in still water is u km/hr. and the speed of the current is v km/hr., then we can formulate the below relations:
The speed with current = (u+v) km/hr. or downstream
Speed against current = (u-v) km/hr. or upstream

Calculations:
We have been given a man's speed with the current is 12 km/hr. and the speed of the current is 1.5 km/hr.
Therefore, we will substitute the known values from the question in relation as follows,
Man's speed (with current) = u+v = 12 km/hr. and v = 1.5 km/hr.

u = 12 - v = 12 - 1.5 = 10.5 km/hr

we actually need to find the speed of man against the current of water. We have both values u and v, so we can put these values in above stated formula for the speed of man against the current which is
Speed against the current of water = u-v
Now we know u = 10.5 km/hr and v = 1.5 km/hr
Putting these values in the formula u-v = 10.5 - 1.5 = 9 km/hr

Hence, the correct option is 1.

Given:

PT is a tangent to a circle, whose centre is O.

OP = 17 cm

OT = 8 cm

Formula used:

Pythagoras Theorem: In a right-angle triangle, the hypotenuse is equal to -

OP² = OT² + TP²

Calculation:

This, the length of the tangent TP is equal to:

TP2 = OP2 - OT2

TP2 = (17)2 - (8)2

TP2 = 289 - 64

TP2 = 225

TP = √225 = 15

∴ The length of the tangent segment PT is equal to 15 cm.

Given:

The circumference of the two circles is 110 cm and 330 cm respectively.

Concept used:

Circumference of a circle = 2πR (R = Radius)

Calculation:

Let the radii of the bigger and smaller circles be R and r respectively.

Difference between their radii = (R - r)

According to the concept,

2πR - 2πr = 330 - 110

⇒ 2π(R - r) = 220

⇒ 44/7 × (R - r) = 220

⇒ (R - r) = (220 × 7)/44

⇒ (R - r) = 35

∴ The difference between their radii is 35 cm.

Given:

LCM = 4104 , HCF = 9, one of the number = 171

Concept used:

LCM × HCF = Product of the numbers

Calculations:

LCM × HCF = Product of the numbers

⇒ 4104 × 9 = 171 × other number

⇒ other number = 4104 × 9/171 = 216

Hence, The Required value is 216.

Given:

The numbers are 12/5, 14/15 and 16/17

Concept used:

HCF = HCF of numerator/LCM of the denominator

Calculation:

LCM of 5, 15, 17 = 255

HCF of 12, 14, 16 = 2

So, HCF = 2/255

∴ The required answer is 2/255.

Given:

Base Area = 154 sq cm

CSA = 550 sq cm

Formula used:

CSA(cone) = π x r x l

r = radius of the base

l = slant height of the cone

Base area = 22/7 x r x r

Volume(Cone) = 22/7 x r x r x h

Calculation:

Base area = 22/7 x r x r = 154

r = 7 cm

CSA(cone) = 22/7 x r x l = 550

l = 25 cm

h² = 25² - 7²

h = 24 cm

Volume(Cone) = 1/3x 22/7 x r x r x h = 1/3 x 22/7 x 7 x 7 x 24

Volume = 1232 cm³

Hence, the correct answer is option 1).

Given:

Numbers are 32, 48 and 72

Calculation:

LCM of 32, 48, and 72

LCM=2 × 2 × 2 × 2 × 3 × 2 × 3 = 288.

The smallest number which on adding 17 means we have to subtract the number 17 from LCM then we get the required number,

∴ Required number = 288 - 17 = 271.

Given:

Calculation:

⇒ Squaring both the sides, we get

⇒ 529 + x = 576

⇒ x = 576 – 529 = 47

Therefore, the value of x is 47.

Given:

The summation of n terms for the given series =

Formula used:

Calculation:

According to the question,

The sum of two terms = 13

Therefore,

Average = 13/2 = 6.5

Therefore, '6.5' is the required answer.

Concept:

Physical quantity:

• The quantities which are measurable are known as a physical quantities.
• Types of quantity are:
  • Scalar
  • Vector

Explanation:

Momentum:

• Momentum is the quantity of motion of a moving body.
• It is also measured as the product of its mass, and velocity.
• Its SI unit is Kgms^-1.

Impulse:

• Impulse is a term that quantifies the overall effect of a force acting over time.
• Its SI unit is Ns or Kgms-1.

Thus, the correct answer is momentum, and impulse.

Additional Information

Velocity:

• Velocity is a vector quantity that refers to the rate at which an object changes its position.
• Its SI unit is ms^-1.

Acceleration:

• Acceleration is a vector quantity that refers to the rate at which an object changes its velocity.
• Its SI unit is ms-2.

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.

Given:

The exterior angle of regular octagon is x degrees.

Formula used:

Each exterior angle of the polygon = 360^o/n

Where, n = number of sides of a polygon

Calculation:

A regular octagon will have all its sides equal in length.

Total sides of octagon = 8.

So, the exterior angle (x) = 360/8 = 45°

∴ The answer is 45°

Calculation:

From the given diagram,

2x = 120°

x = 60°

2z = 60°

z = 30°

So, a = 180 - 60 - 30 = 90°

2t = 50°

t = 25°

So,

b = 180 - 30 - 25 = 125°

So, a + b = 215°

∴ Value of a + b is 215°

Given:

Dimensions = 12 cm × 6 cm × 4 cm

Concept used:

Diagonal of the cuboid =

Calculation:

The length of the longest rod that can be kept in a rectangular box = Diagonal of the cuboid

Diagonal of the cuboid =

∴ The correct answer is 14 cm.

Given:

Concept used:

1. secα = 1/cosα

2. cosecα = 1/sinα

3. sinα/cosα = tanα

Given:

sides = 10, 6.5 and a

Concept used:

The third side of the triangle is always, less than the sum of two other sides of the triangle.

Solution:

10 < a="" +="" />

a >= 4

The least value a can have is 4 as a whole number.

Hence, the correct option is 4.

Each number is perfect square except 181.

169 = 13²

121 = 11²

Given:

sin² 45° + cos2 45° - tan2 45°

Concept used:

Calculation:

sin² 45° + cos² 45° - tan² 45°

∴ sin² 45° + cos² 45° - tan² 45° is equal to 0.

Given:

The point P(2, 1) lies on the line segment joining points A(4, 2) and B(8, 4).

Concept Used:

Using the distance formula to calculate the length of each side of triangle.

Solution:

By Section formula let P divide AB externally in m: n

(m(8) - n(4))/ (m - n) = 2, (m(4) - n(2))/ (m - n) = 1

By solving above equation we get m/ n = 1/3

So, P divides the Line AB in 1: 3 externally.

We have,

A(4, 2) and B(8, 4) and P(2, 1)

Then, using distance formula

Now, similarly for AP

∴ Option 4 is correct.

Volume of pyramid

Given, area of base = 30 m² and volume = 500 m³

⇒ height of the pyramid = 50 m

Concept:

The distance 'd' between two points (x₁, y₁) and (x₂, y₂) is obtained by using the Pythagoras' Theorem: d² = (x₁ - x₂)² + (y₁ - y₂)².

Calculation:

Using the formula for the distance between two points:

AP² = (x - 4)2 + (y - 1)2

BP² = (x + 1)2 + (y - 4)2

Since the distances are equal, we have:

AP² = BP²

⇒ (x - 4)2 + (y - 1)2 = (x + 1)2 + (y - 4)2

⇒ x² - 8x + 16 + y² - 2y + 1 = x² + 2x + 1 + y² - 8y + 16

⇒ 10x = 6y

⇒ 5x = 3y.

Given:

The cost price of 10 articles equals the selling price of 12 articles.

Concept:

Solution:

As per the question,

The cost price of 10 articles equals the selling price of 12 articles.

10 CP = 12 SP

Loss % = 16.66 %

Hence, option 3 is correct.