MPTET Varg 2 Math Mock Test - 6 - MPTET MCQ

Given:

a = x³ - 3x²y + 3xy² - y³

b = x³ - y³ 

Concept Used:

The concept of subtraction is when you take one number away from another number

Calculations:

We have to subtract a number from a to get b 

⇒ a - p = b

⇒ x³ - 3x²y + 3xy² - y³ - p =  x³ - y³

⇒ p= x³ - 3x²y + 3xy² - y³ -  x³ + y³

⇒ p= - 3x²y + 3xy²

Hence, We have to subtract from x³ - 3x²y + 3xy² - y³ to get x³ - y³ is - 3x²y + 3xy²

Assessment plays a very important role in the teaching-learning process. It helps a learner to know his\her progress and the teacher to evaluate the progress of the students.

Key Points

'Mr. Sinha: I am going to conduct a Diagnostic Assessment to find out which concepts taught in the previous year have the students mastered' is a most appropriate statement about the use of Diagnostic Assessment as:

• A diagnostic assessment is a pre-assessment where the teacher determines a student's strengths, weaknesses, and knowledge before giving an instruction.
• Diagnostic assessments are designed to help teachers identify what students know and can do in different domains to support their students' learning.
• This assessment is used only for specific purposes. For example, if a general achievement test indicates that there are weaknesses among the students in the learning of basic skills, the teacher may use a diagnostic test with those students having a learning difficulty. 

Thus, it is concluded that 'Mr. Sinha: I am going to conduct a Diagnostic Assessment to find out which concepts taught in the previous year have the students mastered' is a most appropriate statement about the use of Diagnostic Assessment.

Concept used:

Linear equation is the equation that contains variables and constants in which, it can have 1 or more variables having their power equal to 1.

The linear equation in one variable will have only one variable of its power equal to 1.

According to the definition of Linear variable,

It will be of this form : ax + b = 0

Here, a and b are constants and x is a variable having power = 1

Linear equation in one variable has only one variable with power 1.

Hence, the correct option is 3.

Given:

x = -3, y =  is the solution of the equation -2x + 5y = k 

Calculation:

x = -3, y =  is the solution of the equation -2x + 5y = k then these value satisfy the equation,

⇒ -2x + 5y = k ⇒ -2(-3) + 5(1/5) 

⇒ 6 + 1 = 7

Given:

The equation is 2y = 5x - 2

Calculation:

The equation is 2y = 5x - 2

Put (0, -1) in given equation,

⇒ 2(-1) = 5(0) - 2 

⇒ -2 = -2 

LHS = RHS

Put (-4, -11) in equation,

⇒ 2(-11) = 5(-4) - 2

⇒ -22 = -20 -2 = -22

LHS = RHs

Put (-2,6) in equation,

⇒ 2(6) = 5(-2) - 2 = -12

LHS ≠ RHS

Put (2, 4) in equation,

⇒ 2(4) = 5(2) - 2 = 8

LLHS = RHS

∴ (−2, 6) does not lie on the line 2y = 5x − 2

Given:

5 years ago, ratio of ages of A, B and C = 4 : 5 : 7.

Sum of their present ages = 135 years.

Concept used:

Total = Average × Number of entities

Calculation:

Let the common ratio be Q.

So, 5 years ago, the ages of A, B, and C are 4Q, 5Q, and 7Q respectively.

Now, their present ages are (4Q + 5), (5Q + 5), and (7Q + 5) respectively.

According to the question,

(4Q + 5) + (5Q + 5) + (7Q + 5) = 135

⇒ 16Q + 15 = 135

⇒ 16Q = 135 - 15

⇒ 16Q = 120

⇒ Q = 7.5

The present age of B = (5 × 7.5 + 5) = 42.5 years

The present age of C = (7 × 7.5 + 5) = 57.5 years

Now, 3 years from now, the sum of the ages of B and C

⇒ (42.5 + 3) + (57.5 + 3)

⇒ 106 years

∴ After 3 years from now, the sum of the ages of B and C will be 106 years.

Given:

The average of 40 observations is 32.

The average of the first 15 observations is 16

The average of the next 16 observations is 20

Let the Remaining 9 observation average is X

Calculation:

Average =

40 × 32 = 15 × 16 + 16 × 20 + 9 × X

⇒ 1280 = 240 + 320 + 9X

⇒ 720 = 9X

⇒ X = 80

∴  The average of the remaining observations is 80.

Shortcut Trick 

Objective-type Test: Objective type tests have been in existence since 1920 onwards. These are very popular means of devices to test the students' knowledge. These made their appearance in an effort to overcome the difficulties/weaknesses which are faced in essay type tests. These are widely used in nursing education. Objective type tests include a large number of questions and statements (items). Answers are indicated by marking the correct response in a specified method. 

Key Points

Objective Type Test-

• An objective type test item is characterized by its total objectivity and unambiguity in scoring. 
• It has one and only one correct response.
• Full marks are given for the correct response, which is unique, and no mark is given for an incorrect response.
• Another characteristic of an objective type test item is that it is completely strummed.
• Complete structuring of task limits student to the type of response called for.
• It prevents bluffing and avoids the influence of writing skills.
• The scoring of an objective type test item is not the only objective but also quick, easy, and consistent, which is its greatest advantage. 
• Objective-type tests include multiple-choice, true-false, completion, matching, analogical test, recall type test and short answer test items. 

Thus from the above-mentioned points, it is clear that the Prognostic test is not an objective type of test. 

Mistake Points 

Prognostic test- It is used to predict future behavior on the basis of present abilities. 

Formula:

SI = 

where-

P = Principal

SI = Simple Interest

R = Rate

T = Time

Calculation:

Time in years =  =  years

According to the question-

⇒ SI = 

⇒ SI = 186 × 5 = ₹930

The SI on the above sum is ₹930.

Given:

A train runs at a speed of 28 kmph for 4 hours and at 30 kmph for 5 hours and the remaining 48 kms in 1 hour.

Concept:

Average speed = 

Solution:

Distance D₁ covered at a speed of 28 kmph for 4 hours,

D1 = 28 x 4 = 112 km

Distance D2 covered at a speed of 30 kmph for 5 hours,

D2 = 30 x 5 = 150 km

Distance D3 [ 48 km ] in 1 hour.

Total distance covered = 112 + 150 + 48 = 310 km

Total time taken to cover the distance = 4 + 5 + 1 = 10 hours

 Average speed = 

Average speed = 31 km/hr

Hence, option 4 is correct.

Let, the original fraction be x/y

The sum of the numerator and denominator is 24.

⇒ x + y = 24      ----(1)

Now, the numerator is decreased by 5, and the denominator is increased by 8, the ratio becomes 5 : 4.

Therefore,

(x - 5)/(y + 8) = 5/4

⇒ 4x - 20 = 5y + 40

⇒ 4x - 5y = 40 + 20

⇒ 4x - 5y = 60      ----(2)

By solving equations (1) and (2), we get,

x = 20 and y = 4

Therefore, the ratio  x/y = 20/4 

Therefore, the original fraction is 20/4.

Given:

The line joining the points (–3, 7) and (9, –1) internally in the ratio 3 : 1

Concept used:

Calculation:

Let P(x, y) be the point that divides the line segment internally. 

Here, m₁ = 3, m₂ = 1

(x₁, y₁) = (-3, 7) and (x₂, y₂) = (9, -1)

Putting the above values in the above formula, we get

∴ (6, 1) is the point that divides the line segment 

Concept:

• cos(180 - x) = - cosx.......(equation 1)
• cos(180 + x) = - cosx..........(equation 2)
• cos(270 + x) = sinx.........(equation 3)

Explanation:

We are given, cos24° + cos55° + cos125° + cos204° + cos300° 

⇒ cos24° + cos55° + cos(180-55)° + cos(180+24)° + cos(270+30)° 

⇒ cos24° + cos55° - cos55° - cos24° + sin30° (Using equation 1, 2 and 3)

⇒ sin30°

⇒ 

Given :

Total number of coins shiya had = 270

Ratio of 5 rupee, 1 rupee and 2 rupee coins = 4 : 3 : 2

Calculation :

Number of 5 rupee coins = 

Number of 1 rupee coins =  

Number of 2 rupee coins = 270 - (90 + 120) = 60

Total amount shiya had = 120 x 5 + 90 x 1 + 60 x 2 = Rs. 810

∴ The answer is Rs. 810 .

Given:

(m + n + s)/3 = 40

m = 19

(19 + n + s)/3 = 40

19 + n + s = 40 x 3

n + s = 120 - 19 = 101

here, m < n < s

so, here, m = 19 then the second lowest value would be 20 i.e. n = 20 

The second lowest possible is 20

101 - 20 = 81

The highest possible is 81

Hence, the correct option is 1.

Given :

Data of the number of 5 types of cars (A, B, C, D, E) manufactured (in thousand) by company X over the years.

Calculation :

The Production of 'E' type cars in 2016 = 115

The Production of 'B' type cars in 2019 = 215

Percentage of E-type cars in 2016 according to B-type cars in 2019 =  

⇒ 53.5%

∴ The answer is 53.5%.

Given:

The ratio of two numbers is given as 5: 9.

If 25 is subtracted from each, the ratio becomes 25 ∶ 49

Calculations:

Consider two numbers 5x and 9x, where x is a common multiple of two numbers.

Also, the ratio of two numbers is given as 25: 49 when 25 is subtracted from each of the numbers 5x and 9x.

(5x - 25)/(9x - 25) = 25/49

⇒ 49(5x - 25) = 25(9x - 25)

⇒ 245x - 1225 = 225x - 625

⇒ 245x - 225x = 1225 - 625

⇒ 20x = 600

⇒ x = 600/20 = 30

Substituting the value of x in two numbers:

⇒ 5x = 5 × 30 = 150

⇒ 9x = 9 × 30 = 270

∴ The two numbers are 150 and 270.

Given:

The angle of Quadrilateral are in the ratio 2: 5 : 3 : 8

Concept:

Sum of supplementary angles = 180∘ 

Complementary angles: When the sum of two angles is 90°, then the angles are known as complementary angles.

The Sum of angles of Quadrilateral is 360°

Key Points

The angle of Quadrilateral are in the ratio 2: 5 : 3 : 8

∴  2x + 5x + 3x + 8x = 360° 

⇒ 18x = 360°

⇒ x = 20°

∴ the angles of Quadrilateral are 40°, 100°, 60°, 160°  

Now,

Let Supplement of Largest angle = ∠b and The Complement of the Smallest angle = ∠d 

∴ ∠b + 160° = 180° 

⇒ ∠b = 20° 

and ∠d + 40° = 90° 

⇒ ∠d = 50° 

The sum of Supplement of largest angle and Complement of the smallest angle 

∴ ∠b + ∠d = 20° + 50° = 70°        

∴The sum of Supplement of largest angle and Complement of the smallest angle  = 70° 

Given:

Remainder = 3

The number is divisible by 17

Calculation:

LCM of 8, 12, 18, and 25 = 1800

Let the number be (1800k + 3) and k is a natural number

Now,

(1800k + 3) must be divisible by 17 also (1800k + 3) is a 5-digit number

1800 × 6 + 3 = 10803 is not divisible by 17

1800 × 7 + 3 = 12603 is not divisible by 17

1800 × 8 + 3 = 14403 is not divisible by 17

1800 × 9 + 3 = 16203 is not divisible by 17

1800 × 10 + 3 = 18003 is divisible by 17

So, the number is 18003

Now, sum of the digits = 1 + 8 + 0 + 0 + 3 = 12

∴ The required answer is 12.

Concept:

Calculation:

Given: Height of lighthouse AB = 70 m.

Now, in ΔABC

As we know that,

Given:

If AD is median of triangle ABC and P is a point on AC such that area (Δ ADP) : area (Δ ABD) = 2 : 3

Calculation:

Let area (Δ ABD) = x

D is the mid point of BC.

Area (Δ ADP) = 2/3 area(Δ ABD)

Area (Δ ADP) = 2/3x

ar(Δ PDC) = ar(Δ ADC) - ar(Δ ADP) = x - 2/3x = x/3

∴ ar(ABC) = 2(ar(ABD) = 2x

∴  area (Δ PDC): area (Δ ABC) = x/3 : 2x = 1 : 6  

x² - 16x + 63

Calculation:

x² - 16x + 63 

⇒ x² - 9x - 7x + 63

⇒ x(x - 9) - 7(x - 9) 

⇒ (x - 9)(x - 7) ÷ (x - 9)

⇒ (x - 7)

Given:

Number of products sold by 5 companies during 5 months

Calculation:

Number of products sold by P, S and T in February are 155, 110 and 90 respectively

Average number of products sold by company P, S and T in February =  ~ 118

∴ The answer is 118. 

Given :

Number of products sold by 5 companies in 5 different months

Calculation :

Number of products sold by S in january = 85

Number of products sold by S in april = 140

Percentage of increase =  

∴ The answer is 64.71 %  .

The correct answer is Steaming.

Key Points​

• Cooking with steam is referred to as steaming.
• Steaming is the cooking method by which Idli is cooked.
• Food can also be steamed in a wok, though this is frequently done with a food steamer, kitchen equipment designed expressly to cook food with steam.
• Using steam to cook a variety of items is seen to be a healthy cooking method.
• Because steaming requires less energy to produce and has superior thermodynamic heat transfer characteristics compared to boiling water, steaming can be just as quick, if not quicker, than boiling water cooking.

Additional Information

• Pressure cooking is the method of preparing food in a sealed pressure cooker while using high-pressure steam, water, or a water-based cooking liquid.
• In the cooking process known as poaching, food is heated while submerged in a liquid such as water, milk, stock, or wine.
• A combination of cooking techniques known as stewing involves submerging small, homogeneous chunks of meat completely in liquid and simmering them slowly.

Given:

Length of the arc = 15 cm 

Angle subtended by the arc at the centre = 24°

Formula used:

Length of the arc =  × 2πr

Where, 2πr = circumference and θ = angle subtended by the arc at the centre.

Calculations:

According to the question, 

⇒  × 2πr = Length of the arc

⇒  × 2πr = 15

⇒ 2πr = 15 × 15

⇒ 2πr = 225 cm

∴ The circumference is of length 225 cm.

Given:

3, 9, 11, 16, 19, 12, 18, 30, 19, 25

Concept:

Mode = Most repeated term of a data

The range of the data is the difference between the largest value and the smallest value.

If the total number of observation(n) is an odd number,

Median = ((n + 1)/2)^th term

If the total number of observations(n) is an even number,

Median = ((n/2)^th term + ((n/2) + 1)^th term)/2

Mean = (Mode+ Range + Median)/3

Calculations:

Arranging the given terms in Ascending order,

3, 9, 11, 12, 16, 18, 19, 19, 25, 30

Most repeated term = 19 (2 times)

⇒ Mode = 19

Number of terms = 10

Median = ((10/2)^th term + ((10/2) + 1)^th term)/2

⇒ Median = (5^th term + 6^th term)/2

⇒ Median = (16 + 18)/2 = 17

⇒ Range = (30 - 3) = 27

⇒ Mean of the mode, median and range = ( 19 + 17 + 27)/3 = 63/3 = 21

Mean of the mode, median and range = 21

Given:

Percentage of various brands of LED TVs sold in the year 2020.

Calculations:

Total LED TVs sold = 1.5 lakh units.

Percentage of TVs sold by Bb brand = 23%

Number of TVs sold = 23% of 1.5 lakh units

⇒ 150000 ×

⇒ (1500 × 23) = 34500

∴ The answer is 34500.

–5)^x+1 × (–5)⁵ = (–5)⁷

(–5)^x+1+5 = (–5)⁷ {a^m × aⁿ = a^m+n}

(–5)^x+6 = (–5)⁷

On both sides, powers have the same base, so their exponents must be equal.

Therefore, x + 6 = 7

                  x = 7 – 6 = 1

                  x = 1 

Given

16x⁴ + 25y² – 40x²y at x = 5 and y = 2 

Formula used

(a - b)² = a² + b² - 2ab

Calculation

16x⁴ + 25y² – 40x²y 

⇒(4x²)² + (5y)² - 2 × 4x² × 5y

⇒ (4x² - 5y)²

Put x = 5 and y = 2

(4 × 5² - 5 × 2)²

⇒ (4 × 25 - 10)²

⇒ (100 - 10)²

⇒ 90²

⇒ 8100

∴ The value of 16x⁴ + 25y² – 40x²y is 8100.