The area of a regular polygon

 × perimeter × perpendicular distance from the center of the polygon to any side

 × 30 × 4.125

= 61.875cm²

Hence, (C).

Let the initial number of students be 2x, 3x & 4x

And the final number of students be 3y, 4y & 5y

Now, 2x + 30 = 3y;.... (1)

3x + 30 = 4y; ......(2)

4x + 30 = 5y ......(3)

Solve for x & y

y = 30 & x = 30

total number of students will be 12y = 12(30) = 360.

Let the total work be 36 units

1 day work of A will 36/12 = 3 units = a

1 day work of B will 36/18 = 2 units = b

In 3 days A & B will total do 3(2 + 3) = 15 units of work

Work left 36 - 15 = 21 units

4(a + b + c) = 21 => c = 0.25

Therefore, C alone can complete 50 % of the same work  = 72 days.

The highest marks scored is 85 and the lowest marks scored is 35.

CASE 1: Let all the other students score as much time as the highest marks scored by the student

35 + 85 + 85 + 85 + 85 + 85 + 857 = 77.85

CASE 2 : Let all the other students score as much time as the lowest marks scored by the student

35 + 35 + 35 + 35 + 35 + 35 + 857 = 42.14

So, the average score of these 7 students will lie between 42.14 & 77.85.

For every 500gm weighing machine shows 550gm

Therefore, to show 330gm packet he gives 300gm of rice because of faulty machine

The cost price of 300gm of rice will be  = Rs.84

The selling price of each packet of 330gm according to the faulty machine must be 84 × 1.5 = 126.

Since the perimeter is even then the total number of non-congruent triangles must be 

The closet integer is 7

Therefore, 7.

Total surface area is (14 × 2) + (2 × 12) + (14 × 12) = 220cm²

We need a sheet whose total surface area is greater than 220cm².

There are only two meeting points irrespective of their positions

So we can conclude that their speeds are in ratio 1:1

Therefore, time taken by Karan to complete the round will be equal to time taken by Arjun to complete the round therefore, time taken by Arjun will be 25secs.

8|y| = 48 - 16x

|y| =7 - 2x

Since, |y| will always be positive therefore, 7 - 2x should also be positive

7 - 2x ≥ 0

7 ≥ 2x

3.5 ≥ x

Range of x = (-∞,3.5]

Therefore, non –negative integral values of x will be 0, 1, 2, 3.

when in logab; a < 1 then 

n² + 36 < 15n + 10

n² - 15n + 26 < 0

(n - 13) (n - 2) < 0

n belongs to (2, 13)

therefore, number of values n can hold is 10.