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A hollow sphere of radius 20cm has a cylinder of height 20cm inside it. What is the maximum possible radius of the cylinder?

  1. A 10 cm 20%
  2. B 10√3 cm 61%
  3. C 20 cm 11%
  4. D 10√2 cm 9%
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46 Attempts 1 Comment
DASARI POOJA SIVA SAI KIRAN 1 year ago
B

A right circular cone of radius 4 cm and slant height 5 cm is carved out from a cylindrical piece of wood of same radius and height 5cm the surface area of remaining wood is

4 Thanks 5 Comments
Udit 1 year ago
76pi
Divya Mani Tripathi 1 year ago
2(l + b) = p => p = (l+b)/2 ---(1)

l^2 = b*p (G.P.) => p = (l^2)/b ---(2)

from (1) and (2)

l^2 = 2lb + 2b, dividing by lb

(l/b) - (2b/l) = 2 => (l/b) - 2/(l/b) = 2

Put values for (l/b) from options and check.

there are two rectangular field of same area the length of first rectangular field is x % less than that of length of second field and bredth of first is 5x % greater then breadth of second field . find x ?

2 Thanks 3 Comments
Divya Mani Tripathi 1 year ago
[L - (x/100)L]*[B + (5x/100)B] = LB


[(100-x)/100]L * [(100+5x)/100]B = LB


Solve for x.

What is the area of a square whose vertices lie on the sides of an equilateral triangle of side 1 cm?

  1. A 4 - 2root3 9%
  2. B 7 - 4root3 14%
  3. C 21 - 12root3 18%
  4. D 21 - 4root3 5%
  5. E None 55%
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22 Attempts 2 Comments
Aakash Jaiswal 1 year ago
21 - 12root3

Struck with this Geometry Problem :)

The sides of a regular decagon are extended to form a star. Find the measure of the internal angle at each point of the star.

  1. A 72 15%
  2. B 108 60%
  3. C 144 25%
  4. D 145 0%
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20 Attempts 2 Comments
Aakash Jaiswal 1 year ago
interior + external angle in a polygon = 180 degrees

each external angle = 360/n = 36

each triangle so formed is isosceles. So interior angles of the triangle at each side of the decadon = 36 + 36 + x =180

x = 108

Ajay and Amar inherited a rectangular field of area 1000 sq.m. If they decide to split the land into / two halves by dividing it with a single straight line, then find the approximate minimum cost that Ajay would have to incur to fence his half of the land at the rate of Re.1 per metre. Assume that Ajay bears the complete cost of fencing the common boundary.

  1. A 67 Rs 26%
  2. B 90 37%
  3. C 95 22%
  4. D 112 15%
  5. E 81 0%
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1 Thanks 27 Attempts 1 Comment
Aakash Jaiswal 1 year ago
Let length of field be a and breadth be b.

The area is 1000 m^2.

so a x b = 1000.

So each half area - 500 m^2

If we factorise 500 = 2 x 5 x 5 x 5 x 2

Mimimum combination such that the perimeter is minimum would be 'a' = 25 and 'b' = 20

so perimeter = 2 (25 + 20) = 90 = Rs 90 Ans

A solid cube is cut into three solids such that two of them are cuboids with two dimensions exactly half of the bigger cube and the third dimension same as the original cube. The third solid has two dimensions same as the original cube. Find the ratio of total surface area of the smaller cuboids and the other solid.

  1. A 5:8 32%
  2. B 3:5 26%
  3. C 5:12 26%
  4. D 6:5 16%
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19 Attempts 1 Comment
Vishnu 1 year ago
Hi Harish,
There seems to be an error in this question. I'll explain how it works and perhaps then the error will become clear.
Consider the solid cube to be a unit cube. This means the surface area is 6 sqcm. For the two cuboids, the total surface area for each would be 2.5 sqcm and in total 5 sqcm. The third solid is such that two dimensions are same, the third dimension has to be half of the original cube. Draw this figure and check if it's not clear. For this solid, the TSA will be 4 sqcm. Now the question is asking the ratio of TSA of the smaller cubes (must be cuboids) and other solid. This has to be 5/4. Can't find this in the options.

Two identical circles intersect so that their centres, and the points at which they intersect, form a
square of side 1 cm. The area in sq. cm of the portion that is common to the two circles is

  1. A pi/4 25%
  2. B pi/2 -1 75%
  3. C pi/5 0%
  4. D root2 - 1 0%
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12 Attempts 2 Comments
Pooja Samanta 1 year ago
option B
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