For NAT type question, enter only one right answer, even if you get multiple answers for that particular question.

Notations:

$R$ = Set of real numbers $Q$ = Set of rational numbers
$Z$ = Set of integers
$N$ = Set of natural numbers

The set of natural numbers includes 0.

1 point

Find the y – coordinate of the point of intersection of straight lines represented by (1) and (2), given the following equations:

ax + by + c = E —- (1)

b x + cy + d^{2}

= F —- (2)

Given that

$E = F = 0$

Arithmetic mean of a and b is c.

Geometric mean of a and b is d.

Choose the correct option.

Note:

Arithmetic mean of m and n is $2 m + n$

Geometric mean of m and n is $mn$

Yes, the answer is correct.
Score: 1

Accepted Answers:

$(2 b ^{2} - a ^{2} - ab 2 a ^{2} b - ab - b ^{2}$

Answer question no. 2 and 3 based on the information mentioned below.

A mobile company wants to launch its new model in collaboration with a network provider named Astron to attract more customers.

The following are two options the mobile company gives to buy the mobile.

Option 1 – Mobile and 1-year Astron Network costs 34000 rupees (Network offers unlimited calls for one year)

Option 2 – Only Mobile costs 22000 rupees

Now Lalith wants to buy this new model mobile. Lalith needs only 200 minutes per month.

There are two network providers in the country.

1 point

2. What is the best option for Lalith to buy the mobile?

Choose the correct option.

Buy only a mobile and take 1 year Astron.

Buy mobile along with 1-year Astron network offered by the mobile company

Buy only mobile and take 1 year Proton network

Buy only mobile and use Astron network for 6 months and Proton network for 6 months.

Yes, the answer is correct.
Score: 1

Accepted Answers:

Buy only mobile and take 1 year Proton network

3. How much will he save per year if he chooses the best option to buy the mobile compared to the collaborated offer given by the company?

Yes, the answer is correct.
Score: 1

Accepted Answers:

(Type: Numeric) 8400

1 point

Answer question no. 4 and 5 based on the information mentioned below.

State Government wants to connect the state road to the national highway from a town. There are 3 possible locations in the town A,B and C to connect to the National Highway whose locations are given by coordinates

(3, 8)

(5, 7)

(6, 9)

. The National Highway connects the 2 points

(2, 1)

(10, 7)

and You, being the contractor, have the freedom to select any one of the 3 possible locations in the town.

Hint Always select the shortest path to construct the road.

Note: 1 unit = 100 meter

1 point

4. What point will you select to build the road?

None

Yes, the answer is correct.
Score: 1

Accepted Answers:

What is the minimum length of road in meter required to construct to connect to the National Highway?

No, the answer is incorrect.
Score: 0

Accepted Answers:

(Type: Numeric) 300

1 point

6. The total expenses of mess consists of fixed cost and the variable cost, Variable cost is proportional to the number of inmates of the mess, The total expenses are 16000 rupees when 12 members in the mess,and 20000 rupees when 20 members in the mess, find the Fixed cost of the mess.

Yes, the answer is correct.
Score: 1

Accepted Answers:

(Type: Numeric) 10000

1 point

7. A line perpendicular to the line segment joining A $(1, 0)$ and B $(2, 3)$ , divides it at C in the ratio of 1:5 internally. Then the equation of line is

$3 x + 9 y - 8 = 0$

$3 x + 9 y + 8 = 0$

$x + 3 y - 8 = 0$

$3 x + 9 y - 16 = 0$

Yes, the answer is correct.
Score: 1

Accepted Answers:

$3 x + 9 y - 8 = 0$

8. A bird is flying along the straight line $2 y - 6 x = 44$ . In the same plane, an aeroplane starts to fly in a straight line and passes through the point $(4, 12)$ . Consider the point where aeroplane starts to fly as origin. If the bird and plane collides then enter the answer as 1 and if not then 0. Note: Bird and aeroplane can be considered to be of negligible size.

Yes, the answer is correct.
Score: 1

Accepted Answers:

(Type: Numeric) 0

1 point

9. A surveyor needs to determine the area of a land show in Fig below. The coordinates of the four vertices of the land are as follows: A $(8, 13)$ , B $(3, 10)$ , C $(4, 4)$ , D $(16, 5)$

Fig:Survey Area

Yes, the answer is correct.
Score: 1

Accepted Answers:

(Type: Numeric) 68.5

1 point

Answer question no. 10 and 11 based on the information mentioned below.

A fitness trainer is analyzing the weight loss progress of his best client over a period of 6 months, to use it as for marketing. He recorded the weight of the client at the beginning and end of each month. Using straight line fitting, he came up with an equation

W = - 8 t + 98

, where W = Weight in Kg, t= time in months.

Now you want to check weather this equation is correct or not so you collected the data from the gym, the data is given in table below.

1 point

11. Equation that fitness trainer came up with $W = - 8 t + 98$ is well fitted to data. (Equation is said to be well fitted to data if the SSE is less than 5)

True

False

Yes, the answer is correct.
Score: 1

Accepted Answers:

True

12.2

You were impressed by the performance of the fitness trainer, so you want to get trained under him, you assumed that the rate of weight loss (weight loss per month) will be same as the case of the best client mentioned in the question. Considering your assumption is true, how many days are required for you to loss weight from 100 kg to 72 kg.

Note: 1 month has 30 days

Yes, the answer is correct.
Score: 1

Accepted Answers:

(Type: Numeric) 105

1 point

The equation used to measure the $C_{d}$ (discharge coefficient) of the venturimeter value in the lab is:

$Q = 1 - β ^{4} c _{d} 2 g Δ h$

$c_{d} - discharge coefficient$

$β - D d$

A1– Pipe section

A2– Restriction area

$Δ h - head losses$

Q– flow rate

Ramesh plotted the graph between Q on the y-axis and $Δ h$ on the x-axis and claimed that $1 - β ^{4} c _{d} 2 g$ is the slope of the obtained straight line.

Suresh plotted the graph between $Δ h$ on the y-axis and Q on the x-axis and claimed that $c _{d} 2 g 1 - β ^{4}$ is the slope of the straight line.

Who is/are actually correct?

Only Ramesh

Only Suresh

Both Ramesh and Suresh

None of them are correct

Yes, the answer is correct.
Score: 1

Accepted Answers:

Both Ramesh and Suresh

A rock is thrown in a pond, and creates circular ripples whose radius increases at a rate of 0.2 meter per second. What will be the value of $π A$ , where $A$ is the area (in square meter) of the circle after 5 seconds?
Hint: The area of a circle = $π r^{2}$ , where $r$ is the radius of the circle.

Yes, the answer is correct.
Score: 1

Accepted Answers:

(Type: Numeric) 1.0

given the following equations: – Students Community

Maths Week 2 Graded Assignments IIT Madras

Yes, the answer is correct.
Score: 1

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Yes, the answer is correct.
Score: 1

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Yes, the answer is correct.
Score: 1

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Yes, the answer is correct.
Score: 1

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No, the answer is incorrect.
Score: 0

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Yes, the answer is correct.
Score: 1

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Yes, the answer is correct.
Score: 1

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Yes, the answer is correct.
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Yes, the answer is correct.
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Yes, the answer is correct.
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Yes, the answer is correct.
Score: 1

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Yes, the answer is correct.
Score: 1

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Yes, the answer is correct.
Score: 1

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given the following equations: – Students Community

Maths Week 2 Graded Assignments IIT Madras

Yes, the answer is correct.Score: 1

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Yes, the answer is correct.Score: 1

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Yes, the answer is correct.Score: 1

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Yes, the answer is correct.Score: 1

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No, the answer is incorrect.Score: 0

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Yes, the answer is correct.Score: 1

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Yes, the answer is correct.Score: 1

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Yes, the answer is correct.Score: 1

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Yes, the answer is correct.Score: 1

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Yes, the answer is correct.Score: 1

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Yes, the answer is correct.Score: 1

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Yes, the answer is correct.Score: 1

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Yes, the answer is correct.Score: 1

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Yes, the answer is correct.
Score: 1

Yes, the answer is correct.
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Yes, the answer is correct.
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Yes, the answer is correct.
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No, the answer is incorrect.
Score: 0

Yes, the answer is correct.
Score: 1

Yes, the answer is correct.
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Yes, the answer is correct.
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Yes, the answer is correct.
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Yes, the answer is correct.
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Yes, the answer is correct.
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Yes, the answer is correct.
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Yes, the answer is correct.
Score: 1