PT is a tangent at the point R on a circle with centre O. SQ is a diameter, which when produced meets the tangent PT at P. If ∠SPT=32°, then what will be the measure of ∠QRP?

A man spends $$ {2\over3}rd$$ of his income. If his income increases by 14 % and the expenditure increases by 20%, then the percentage increase in his savings will be

The total number of students in sections A and B of a class is 72. The ratio of the number of students in A and B is 7 :5 . The average weight (in kg) of the students in section B is 20% more than that of the students in section A. If the average weight of all the students in the class is 52 kg, then what is the average weight (in kg) of the students in section B?

How many natural numbers less than 1000 are divisible by 5 or 7 but not by 35?

A train of length 212 meter is running at 45 km/h. In what time (in seconds) will it cross a platform of length 188 meter?

An article is sold Rs.680 after two successive discounts of 20% and x% on its marked price. The marked price of the article is Rs.1000. What is the value of x?

The volume of a solid right circular cone is 600 π cm³, and the diameter of its base is 30 cm. The total surface area (in cm²) of the cone is:

From a point 12 meter above the water level, the angle of elevation of the top of a hill is 60° and the angle of depression of the base of the hill 30°. What is the height ( in meter) of the hill?