Mathematical Sk...

A six faced die is a biased one. It is thrice more likely to show an odd number than to show an even number. It is thrown twice. The probability that the sum of the numbers in the two throws is even is:

Evaluate, \(\frac{\cos 7 \mathrm{x}+\cos 6 \mathrm{x}+\cos 5 \mathrm{x}}{\sin 7 \mathrm{x}+\sin 6 \mathrm{x}+\sin 5 \mathrm{x}}\).

A dishonest shopkeeper sells his items using 20% less than the true weight and earns 30% profit. Find his total profit percent.

In a drawer there are 5 white (W) socks, 4 red (R) socks and 3 green (G) socks. Two socks are picked randomly. What is the possibility that both the socks are of same color?

How many diagonals are there in a polygon of 12 sides?

Pipe A and pipe B can fill up a tank in 40 min and 80 min respectively. Both the pipes are opened simultaneously for some time and pipe B is closed. If the total time to fill up the tank is 30 minutes, then how long the pipe B was open for?

Find the radius and intercept of the circle x² + y² + 2x + 2y - 14 = 0 on x and y-axis

In what time would a cistern be filled by three pipes whose diameters are 2 cm, \(1 \frac{1}{3}\) cm and 3 cm, running together, when the largest alone can fill it in 133 minutes, the amount of water flowing in by each pipe is proportional to the square of their diameter?

A trader sells products at 25% less on cost price but weighs 600 gram instead of 1000 gram. What is his profit or loss percent?

The monthly income of Arun was Rs. 50,000 and his monthly expenditure was Rs. 25,000. His salary is increased by 20% and his expenditure is increased by 10%. Find the percentage of increase in his savings.