If x+y+z=10, x²+y²+z²=30, then the value of x³+y³+z³-3xyz is _________.

A conical vessel, whose internal radius is 20 cm and height is 27 cm, is full of water. If this water is poured into a cylindrical vessel with internal radius 15cm, what will be the height to which the water rises in it?

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)

A dealer marks his goods at 40% above the cost price. He sells 60% of the goods at the marked price giving 10% discount and the rest by giving 50% discount on the marked price. What is his overall profit/loss per cent?

Out of the given responses, one of the factors of (a² – b² )3 + (b² – c²) 3 + (c² – a²) 3 is

A The cost of building a fence around a circular field is ₹7,425 at the rate of 13.50 per foot. What is the area of the circular field? [use $$π={22\over 7}$$]

Directions: Read the following data carefully and answer the questions given below:

There are 6300 students in Manipur University in the academic year 2020. The ratio of the boys to the girls in the University is 5 : 4. All the students are enrolled in different indoor activities (Chess, Carom, Debating, Painting, and Quiz) and one student is enrolled in only one indoor activity. The number of boys enrolled in the Painting is 621. The ratio of the number of boys who enrolled in Chess to the number of boys who enrolled in Carom is 5 : 3. 36% of the students are enrolled in Quiz. The number of boys enrolled in Debating is 25% of the total number of boys. The number of girls enrolled in Quiz is 640 which is 150 less than the number of girls enrolled in Carom. The number of girls enrolled in Chess is 186 more than the number of boys enrolled in the same activity. The total number of students enrolled in Painting is 816.

Find the ratio of the number of boys enrolled in Carom to the number of girls enrolled in the same

A certain sum amounts to ₹15,500 in 2 years at 12% p.a. simple interest. The same sum will amount to what in$$1{1\over 2}$$ years at 10% p.a., if the interest is compounded half yearly (nearest to ₹1)?