MPTET Varg 2 Math Mock Test - 1 - MPTET MCQ

Given:

Concept used:

Calculation:

⇒ 

⇒ 

⇒ 

⇒ - 1

∴ The required answer is - 1.

Given:

The ratio of length and breadth of a rectangle = 4 ∶ 5

The perimeter of the rectangle is 18 cm 

Formula used:

Perimeter of rectangle = 2(l + b) 

Calculations:

Let the length and breadth of a rectangle be '4x' and 5x respectively

Perimeter of rectangle = 2 × (4x + 5x)

⇒ 18  = 2 × (9x)

⇒ 18 = 18x

⇒ x = 1

Hence, the length and breadth of a rectangle be 4 and 5 respectively

Diagonal of rectangle = 

⇒  = √41

∴ The diagonal of the rectangle is √41 

Given:

n = 2⁵ × 3⁴ × 7⁵ × 15⁴,

Concept:

To find the number of consecutive zeroes we need to separate out the number of 2’s and 5’s possible in the calculation. This is because equal numbers of 2’s and 5’s only lead to the formation of 10.

Calculation:

n = 25 × 34 × 75 × 15⁴

⇒ n = 25 × 34 × 75 × (3 × 5)⁴

⇒ n = 25 × 34 × 75 × 3⁴ × 5⁴

⇒ n = 2 × (2 × 5)⁴ × 3⁽4 + 4)  × 75 

⇒ n = 2 × (10)4 × 3⁸  × 75 

⇒ n = 2 × 38  × 75 × 10000

Hence, the number of consecutive zeroes in n is 4.

Concept:

Pressure:

• The force per unit area is called pressure. It is denoted by P.
• The SI unit of pressure is the pascal (Pa).
• It is a scalar quantity because the pressure acts in all directions at a point inside a gas.
• The basic formula for pressure is given by:

Explanation:

• More pressure signifies more stress. 
• If the same force is applied in a lesser area of contact, then more stress will be felt. 
• If the area of contact is increased, stress will be reduced. 
• Potters who carry heavy luggage keep cloth on the head to reduce the pressure by increasing the area of contact. 
• The correct option is to 'increase the area of contact of a load of luggage with their head.'

Given:

Production of company P in 2015 = 80 lakh tonnes

Production of company P in 2019 = 120 lakh tonnes

Calculation:

∴ The required percentage increase in 2019 = (120 - 80)/80 × 100

⇒ 40/80 × 100 = 50%

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

Given:

one face of a cube has an area 64 cm2

Formula Used:

Volume of cube = Side3

Calculation:

one face of a cube has an area 64 cm2

Let the side of the cube = L

L² = 64

L = 8 cm

∴ Volume of cube = Side³

Volume of cube = L³ 

Volume of cube = 8³

Volume of cube = 512 cm³

Given:

The principal amount Rs. 4,000 at 3% simple interest produce the same income as Rs. 5,000 in 5 years at 4% simple interest.

Concept:

Simple Interest, S.I. = 

Net amount  A = P + S.I

Key Points
Income produced from Rs. 5,000 in 5 years at 4% simple interest.

Interest = 

The net amount for a principal amount of Rs. 4,000 at 3% simple interest in T years = Income produced by principal amount of Rs. 5,000 in 5 years at 4% rate

The net amount for a principal amount of Rs. 4,000 at 3% simple interest in T years

S.I. =   

S.I. = 120T

According to the question,, 

⇒ 120T = 1000

⇒ 120T = 1000

T = 100/12

T = 8.33 Years

Hence, option 4 is correct.

Concept Used:-

The average of the group of numbers is the ratio of the sum of all the numbers given to the total number.

The formula to found the average is given below.

Explanation

Given numbers are,

80, 96, 89, 98, 55 & 38

There are total 6 number. Now we have to divide the sum of all these number by 6 to find the average of these numbers.

From the formula of average, we have,

So, the average of the provided numbers is 76.

Thus, the correct option is 4.

Given:

In 5 minutes, 4/11 of a bucket is filled.

Concept used:

1 minute = 60 seconds

Calculation:

Remaining bucket = 1 - 4/11 = 7/11

In 5 minutes, 4/11 of a bucket is filled.

Now, to fill 7/11 of the bucket, it will take = 

⇒ (5 × 7)/4 minutes

⇒ 8.75 minutes

⇒ 8 minutes 0.75 × 60 seconds

⇒ 8 minutes 45 seconds

∴ It will take 8 minutes 45 seconds to fill the remaining bucket.

Given:

Expenditure on food is 5000

Expenditure on Rent is 20000

Expenditure on Travel is 10000

Expenditure on Clothing is 3000

Expenditure on Miscellaneous is 15000

Expenditure on Savings is 7500

Formula used:

Savings percent =  (Savings/Monthly salary) × 100%

Calculation:

According to the question

Monthly salary = 5,000 + 20,000 + 10,000 + 3,000 + 15,000 + 7,500 = 60,500

Savings = 7500

According to the formula 

Savings percent =  (7500/60500) × 100%

⇒ 12.39 ~ 12.4

∴ 12.4 percent of her monthly salary is she able to save.

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 PQR. ∠P = 59°, ∠Q = 60° and ∠R = 61°.

Concept used:

The largest angle and side opposite to largest angle is the longest side

Calculation:

In a triangle PQR. ∠P = 59°, ∠Q = 60° and ∠R = 61°.

In these angles, ∠R = 61° is largest and side opposite to largest angle is the longest side.

∴ PQ is the longest side.

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.

Given:
Amount(A) = 36000
Interest (R) = 20%
Time (T) = 4 years

Concept Used:
Simple Interest, SI = (P × R × T)/100
Amount = P + SI
where
P = Principal amount
R = Rate of interest per year
T = time in years

Calculation:
Assume the principal amount is P
According to the question,
⇒ P + P× 20× 4/100 = 36000
⇒ 180P/100 = 36000, P = 20000

Shortcut TrickLet the total sum is 100% 
P + Interest = Amount
total interest 20× 4 = 80%      ....( R = 20%,T = 4 year)
180% = 36000, 100% = 20000

Given:

(x4 - y4) and (x6 - y6)

Concept used:

The Highest Common Factor (HCF) of two numbers is the highest possible number that divides both the numbers completely.

Calculation:

Let f(x) = (x4 - y4) and g(x) = (x6 - y6)

f(x) = (x²)² - (y²)² 

⇒ (x² + y²)(x² - y²) {∵ using a² - b² = (a+b)(a - b)}

⇒ (x2 + y2)(x + y)(x - y)

g(x) = (x6 - y6) = {(x³)² - (y³)²}

⇒ (x³ + y³)(x³ - y³)

⇒ (x + y) (x2 – xy + y2)(x – y) (x2 + xy + y²)

⇒ (x – y)(x + y)(x² – xy + y²)(x² + xy + y²)

∴ HCF of (x4 - y4) and (x6 - y6) = (x – y)(x + y) = x2 – y².

Given:

CD intersects the line AB at F

∠CFB = 50°

∠EFA = ∠AFD

Calculation:

Let ∠EFA = x.

Then ∠AFD = x.

It is given that CD intersects line AB at F.

Therefore, ∠CFB = ∠AFD (Vertically opposite angles) 

So, x = 50°

But ∠EFA = ∠AFD which gives ∠EFA = 50°

Now ∠CFB + ∠EFA + ∠EFC = 180° [As AB is a straight line].

or, 50° + 50° + ∠EFC = 180°

or, ∠EFC = 180° – 100°

Thus, ∠EFC = 80°.

Given:

(0.00032)^(3/5).

Calculation:

(0.00032)^(3/5)

⇒ (32/100000)^3/5

⇒ (2⁵/10⁵)^3/5

⇒ (2/10)^{(3/5)× 5} = (2/10)³

⇒ 8/1000 = 1/125

Concept-
Sum of the angles of a triangle is 180° 
If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite
angles.

Calculation
By linear angle property
∠ ACB + 110° = 180° 
∠ ACB = 70° 
Now in Δ ABC
∠ BAC + ∠ ABC + ∠ ACB = 180°
∠ BAC + 62° + 70° = 180° 
∠ BAC = 48°

Alternate Method
By exterior angle property in ΔABC
∠ BAC + 62° = 110° 
⇒ ∠ BAC = 48° 
∴ the measure of ∠ BAC is 48°.

Given:

Diagonal of rectangle = 17 cm

Perimeter of rectangle = 46 cm

Concept Used:

Diagonal² = Length² + Breadth²

Perimeter of Rectangle = 2(l + b)

Area of Rectangle = l × b

Calculation:

⇒ l² + b² = 17² = 289

⇒ 2(l + b) = 46

⇒ l + b = 23

Squaring both sides,

⇒ l² + b² + 2lb = 23²

Putting the values,

⇒ 289 + 2lb = 529

⇒ 2lb = 529 – 289 = 240

⇒ lb = 120 cm²

Therefore, the area of a rectangle is 120 cm².

Given:

Total amount of the Rs. 5, Rs. 2, and Rs. 1 coins = Rs. 220

Calculation:

Let the number of Rs. 5, Rs. 2, and Rs. 1 coins be 5x , 6x and 7x respectively.

According to question,

⇒ 5 × 5x + 2 × 6x + 1 × 7x = 220

⇒ 44x = 220

⇒ x = 5

Number of Rs. 2 coins = 6 × 5 = 30

∴The answer is 30 .

Given:

The ratio of two complementary angles = 1 : 5

Concept used: 

Sum of two complementary angle is 90° 

Calculation:

Let the ratio of two angles be 1x and 5x respectively

According to the above concept,

⇒ (1x + 5x) = 90° 

⇒ 6x = 90° 

⇒ x = 15° 

Required difference = (5x - x) = (75 - 15)° = 60° 

∴ The difference between the two angles is 60° 

A rectangle is a parallelogram with right angles.

• All sides in a rectangle are 90 degrees.
• Two pairs of opposite sides are equal and parallel to each other.
• Squares are a subset of rectangles.

Learning objectives are which skills and knowledge you want to acquire in the students at the end of the chapter, lesson, etc.

• Helps to capture the student's attention.
• It helps to improve the academic performance of students.
• Objectives describe what an instructor does to enhance learning.
• it is a student-centered approach.
• Objectives are those which help to achieve a particular target.

Key Points

Objectives of learning are classified into:-

Thus, it is concluded that "Child is able to Recall the definition of Rectangle." shows knowledge.

Formula Used:
The sum of the first n terms of any A.P. is given by

S_n = n/ 2[ 2a + (n - 1) × d] 

Where a is the first term and d is the common difference of the A.P,

Calculation:

For AP: 10,6,2,

a = 10 and d = 6 - 10 =  -4  
 ⇒ S₁₆ = 16/2 [2 × 10 + (16 - 1) × (-4)] 
 ⇒ S16 = 8 [2 × 10 + 15(-4)] 
 ⇒ S16 = 8 (20 - 60) 
 ⇒ S16 = 8 (-40) 
 ⇒ S16 = -320 .

Therefore, the Sum of the first 16 terms is -320.

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 × 75/100 = 3000000

Number of females above poverty line is 3/5 × 3000000

⇒ 3 × 600000 = 1800000 = 1.8 million

∴ The answer is 1.8 million

Calculation:

The general form of quadratic polynomial is

P(x) = ax² + bx + c

Where, x is a variable and a, b, and c are constants.

Hence, A polynomial of degree two is called a quadratic polynomial.

∴ The correct answer is Quadratic Polynomial.

The correct answer is option 4 i.e. does not become cold.

• Heat energy can transfer from one part of the body to another.
• This is known as heat energy transmission or simply heat transmission.
• There are three primary modes of heat transmission: conduction, convection, and radiation. 
• Conduction:
  • Conduction is the process by which heat is transferred from the hotter end of an object to the colder end.
  • Conduction is the process by which heat is transferred in solids.
  • The materials which allow heat to pass through them easily are conductors of heat. 
  • For examples, aluminum, iron and copper. 
  • Plastic and wood are poor heat conductors because they do not allow heat to easily pass through them.
  • Poor conductors are known as insulators.
  • A good heat conductor can transmit heat through any of these processes, whereas a bad heat conductor does not allow heat to transfer from one part of the body to another. 
  • A wooden spoon is a poor heat conductor.
  • Hence, when wooden spoon is dipped in a cup of ice cream it does not become cold.
• Convection:
  • Heat transfer occurs through the movement of fluid particles in this process (liquid or gas).
• Radiation:
  • In this process, heat transfer occurs in the form of electromagnetic waves.

The correct answer is Positive.

Key Points

• Positive work done means that force is parallel to displacement.
• When a horse pulls a cart, it gives force in the forwarding direction.
  • If the force is enough to displace the cart, the cart will displace in the same direction as the exerted force by the horse. 
  • So the work done is positive.

Additional Information

• Negative work done means that force is opposite to displacement.
  • Example: when a positive charge is moved towards another positive charge.
• If the force is perpendicular to the displacement and if either the force or the displacement is zero, work done will be zero.
  • Example: when a coolie travels on a platform with a load on his head.

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.