Two identical cylinders of the same height as a bigger hollow cylinder were put vertically into the latter to fit exactly into it. The volume of the bigger cylinder is V. The volume of each of the small cylinders is

• V/ 8

• V/ 4

• V/ 2

• V

What is the length of the longest rod that can be put in a hemispherical bowl of radius 10 cm such that no end of the rod is outside the bowl? (Assume that the rod has negligible thickness).

• 10$\sqrt{2}$ cm

• 10$\sqrt{3}$ cm

• 10$\sqrt{4}$ cm

• 10$\sqrt{5}$ cm

On a semi-circle of diameter, 10m drawn on a horizontal ground are standing 4 boys A, B, C and D with distances AB = BC = CD. The length of line-segment joining A and B is

• 5 m

• 6 m

• 7 m

• $\frac{5\mathrm{\pi }}{3}$ m

You get 20% returns on your investment annually, but also pay a 20% tax on the gain. At the end of 5 years, the net gain made by you (as percentage of the capital) is approximately

• 0

• 16

• 80

• 100

A cubic cavity of edge 20 μm is filled with a fluid with a cubic solid of edge 2 μm. What percent of the cavity volume is occupied by the fluid?

• 10.0

• 20.0

• 90.0

• 99.9

The following table shows the price of diamond crystals of a particular quality

What will be the price (in lakh Rs.) of 2.5 carat diamond crystal?

• 10

• 20

• 25

• 50

A man on the equator moves along 0° longitude up to 45° N. He then turns east and moves up to 90°E, and returns to the equator along 90°E. The distance covered in multiples of Earth's radius R is

• $\left(\frac{3}{4}\mathrm{\pi }\right)\mathrm{R}$

• $\left(\frac{\mathrm{\pi }}{2} + \frac{\mathrm{\pi }}{4\sqrt{2}}\right)\mathrm{R}$

• $\left(\frac{\mathrm{\pi }}{2} + \frac{\mathrm{\pi }}{2\sqrt{2}}\right)\mathrm{R}$

• $\left(\frac{\mathrm{\pi }}{2} + \frac{\mathrm{\pi }}{2\sqrt{2}}\right)\mathrm{R}$

Marks obtained by two students S1 and S2 in a four-semester course are plotted in the following graph

Which of the following statements is true?

• S2 got higher marks than S1 in all four semesters.

• Over four semesters, S1 improved by a higher percentage compared to S2.

• Total marks of S1 and S2 are equal.

• S1 and S2 did not get the same marks in any semester.

To go from the engine to the last coach of his train to another train moving on a parallel track in the opposite direction, waited till the last coach of his original train appeared and then jumped back. In how much time did he reach the last coach if the speed of each train was 60km/hr?

• 5 s

• 6 s

• 10 s

• 12 s

How many digits are there in

2¹⁷ × 3² × 5¹⁴ × 7 ?

• 14

• 15

• 16

• 17