For the following questions answer them individually
If the speed of a boat in still water is a km/h and the speed of the water current is b km/h, then find the value of $$(a^2 + b^2)$$. It is given that the boat covers 3x km against the current in 0.5x hours and 2.4x km with the current in 0.3x hours, where x is a positive irrational quantity.
When two different dice are rolled together, what is the probability that the sum of the numbers coming up on the two dice is 9?
Which of the following is a function from A ® B, where A = {1, 2, 3} and B = {2, 3, 4, 5}?
Vessels A and B contain mixtures of milk and water. The ratios of milk and water in A and B are 4 : 5 and 3 : 1, respectively. In what ratio should the contents of A and B be drawn and mixed, to obtain a mixture having milk and water in the ratio 3 : 2?
Find the value of the expression $$(800 + 7n - n^2)$$ where n cm is the length of one diagonal of a quadrilateral whose opposite sides are parallel. The adjacent sides of the quadrilateral are 3 cm and 4 cm in length and the other diagonal is 1 cm in length.
The centres of three circles that touch each other externally form a triangle of sides 21 cm, 22 cm and 23 cm. Find the approximate area of the smallest circle?
If the second, third and first terms of a geometric progression (GP) form an arithmetic progression (AP), then find the first term of the GP, given that the sum to infinite terms of the GP is 36