In △ABC, D and E are the mid points of sides BC and AC, respectively. If AD = 10.8 cm, BE = 14.4 cm and AD and BE intersect at G at a right angle, then the area (in cm²) of △ABC is:

A train of length 287 m, running at 80 km/h, crosses another train moving in the opposite direction at 37 km/h in 18 seconds. What is the length of the other train?

A takes 2 hours more than B to cover a distance of 40 km. If A doubles his speed, he takes $$1{1\over 2} $$ hours more than B to cover 80 km. To cover a distance of 90 km, how much time will B take travelling at his same speed?

A certain sum is lent at 4% p.a. for 3 years, 8% p.a. for the next 4 years, and 12% p.a. beyond 7 years. If for a period of 11 years, the simple interest obtained is ₹27,600, then the sum is (in ₹):

The curved surface area of a right cylinder is 3696 cm². Its height is three times its radius. What is the capacity (in litres) of the cylinder? (Take π =22/7)

The numerator of a fraction is 3 more than the denominator. When 5 is added to the numerator and 2 is subtracted from the denominator, the fraction becomes $$8\over 3$$ . When the original fraction is divided by$$5{1\over 2}$$, the fraction so obtained is:

A solid metallic sphere of radius 15 cm is melted and recast into spherical balls of radius 3 cm each. What is the ratio of the surface area of the original sphere and the sum of the surface areas of all the balls?

As observed from the top of a light house, 120 √3 m above the sea level, the angle of depression of a ship sailing towards it changes from 30° to 60°. The distance travelled by the ship during the period of observation is: