UPSC Prelims Questions

Q.10747Miscellaneous2015Easy

AB is a line segment of length 2a, with M as mid-point. Semicircles are drawn on one side with AM, MB and AB as diameter as shown in the above figure. A circle with centre O and radius r is drawn such that this circle touches all the three semicircles. The value of r is

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Q.10748Miscellaneous2015Easy

How many spherical bullets each of 4 cm in diameter can be made out of a cube of lead whose edge is 44 cm ?

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Q.10749Miscellaneous2015Easy

Let V be the volume of an inverted cone with vertex at origin and the axis of the cone is along positive y-axis. The cone is filled with water up to half of its height. The volume of water is

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Q.10750Miscellaneous2015Easy

The areas of three mutually perpendicular faces of a cuboid are x, y, z. If V is the volume, then xyz is equal to

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Q.10751Miscellaneous2015Easy

A water tank, open at the top, is hemispherical at the bottom and cylindrical above it. The radius is 12 m and the capacity is 3312π m³. The ratio of the surface areas of the spherical and cylindrical portions is

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Q.10752Miscellaneous2015Easy

ABCD is a square. If the sides AB and CD are increased by 30%, sides BC and AD are increased by 20%, then the area of the resulting rectangle exceeds the area of the square by

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Q.10753Miscellaneous2015Easy

From a rectangular sheet of sides 18 cm and 14 cm, a semicircular portion with smaller side as diameter is taken out. Then the area of the remaining sheet will be

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Q.10754Miscellaneous2015Easy

A square is inscribed in a right triangle with legs x and y and has common right angle with the triangle. The perimeter of the square is given by

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Q.10755Miscellaneous2015Easy

Let A denote the set of quadrilaterals having two diagonals equal and bisecting each other. Let B denote the set of quadrilaterals having diagonals bisecting each other at 90°. Then A ∩ B denotes

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Q.10756Miscellaneous2015Easy

A brick is thrown vertically from an aircraft flying two kilo metres above the earth. The brick will fall with a

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Q.10757Miscellaneous2015Easy

The two adjacent sides of a cyclic quadrilateral are 2 cm and 5 cm and the angle between them is 60°. If the third side is 3 cm, then the fourth side is of length

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Q.10758Miscellaneous2015Easy

If X is any point within a square ABCD and on AX a square AXYZ is described, which of the following is/are correct ? 1. BX² = DZ² or BZ² = DX² 2. ∠ABX = ∠ADZ or ∠ADX = ∠ABZ Select the correct answer using the code given below :

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Q.10759Miscellaneous2015Easy

The diameter of a wheel that makes 452 revolutions to move 2 km and 26 decametre is equal to

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Q.10760Miscellaneous2015Easy

30 metallic cylinders of same size are melted and cast in the form of cones having the same radius and height as those of the cylinders. Consider the following statements : Statement I: A maximum of 90 cones will be obtained. Statement II: The curved surface of the cylinder can be flattened in the shape of a rectangle but the curved surface of the cone when flattened has the shape of triangle. Which one of the following is correct in respect of the above ?

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Q.10761Miscellaneous2015Easy

Water is filled in a container in such a manner that its volume doubles every 5 minutes. If it takes 30 minutes for the container to be full, in how much time will it be one-fourth full ?

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Q.10762Miscellaneous2015Easy

From the solid gold in the form of a cube of side length 1 cm, spherical solid balls, each having the surface area πr² = 3 cm² are to be made. Assuming that there is no loss of the material in the process of making the balls, the maximum number of balls made will be

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Q.10763Miscellaneous2015Easy

The circumference of a circle is 100 cm. The side of the square inscribed in the circle is

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Q.10764Miscellaneous2015Easy

Consider the following statements: 1. If the height of a cylinder is doubled, the area of the curved surface is doubled. 2. If the radius of a hemispherical solid is doubled, its total surface area becomes fourfold. Which of the above statements is/are correct?

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UPSC Prelims Questions

AB is a line segment of length 2a, with M as mid-point. Semicircles are drawn on one side with AM, MB and AB as diameter as shown in the above figure. A circle with centre O and radius r is drawn such that this circle touches all the three semicircles. The value of r is

How many spherical bullets each of 4 cm in diameter can be made out of a cube of lead whose edge is 44 cm ?

Let V be the volume of an inverted cone with vertex at origin and the axis of the cone is along positive y-axis. The cone is filled with water up to half of its height. The volume of water is

The areas of three mutually perpendicular faces of a cuboid are x, y, z. If V is the volume, then xyz is equal to

A water tank, open at the top, is hemispherical at the bottom and cylindrical above it. The radius is 12 m and the capacity is 3312π m³. The ratio of the surface areas of the spherical and cylindrical portions is

ABCD is a square. If the sides AB and CD are increased by 30%, sides BC and AD are increased by 20%, then the area of the resulting rectangle exceeds the area of the square by

From a rectangular sheet of sides 18 cm and 14 cm, a semicircular portion with smaller side as diameter is taken out. Then the area of the remaining sheet will be

A square is inscribed in a right triangle with legs x and y and has common right angle with the triangle. The perimeter of the square is given by

Let A denote the set of quadrilaterals having two diagonals equal and bisecting each other. Let B denote the set of quadrilaterals having diagonals bisecting each other at 90°. Then A ∩ B denotes

A brick is thrown vertically from an aircraft flying two kilo metres above the earth. The brick will fall with a

The two adjacent sides of a cyclic quadrilateral are 2 cm and 5 cm and the angle between them is 60°. If the third side is 3 cm, then the fourth side is of length

If X is any point within a square ABCD and on AX a square AXYZ is described, which of the following is/are correct ? 1. BX² = DZ² or BZ² = DX² 2. ∠ABX = ∠ADZ or ∠ADX = ∠ABZ Select the correct answer using the code given below :

The diameter of a wheel that makes 452 revolutions to move 2 km and 26 decametre is equal to

Water is filled in a container in such a manner that its volume doubles every 5 minutes. If it takes 30 minutes for the container to be full, in how much time will it be one-fourth full ?

From the solid gold in the form of a cube of side length 1 cm, spherical solid balls, each having the surface area πr² = 3 cm² are to be made. Assuming that there is no loss of the material in the process of making the balls, the maximum number of balls made will be

The circumference of a circle is 100 cm. The side of the square inscribed in the circle is

Consider the following statements: 1. If the height of a cylinder is doubled, the area of the curved surface is doubled. 2. If the radius of a hemispherical solid is doubled, its total surface area becomes fourfold. Which of the above statements is/are correct?

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