Mathematical Sk...

Find the value of \(\frac{\tan \mathrm{a}}{1-\cot \mathrm{a}}+\frac{\cot \mathrm{a}}{1-\tan \mathrm{a}}\)

Firstly the number 350 is increased by 20% and afterwards decreased by 20%. Ultimately the percentage increase or decrease is:

On a certain principal if the simple interest for two years is Rs. 1400 and compound interest for the two years is Rs. 1449, what is the rate of Interest?

The distance of the point (2, 3, 4) from the plane 3x - 6y + 2z + 11 = 0 is:

Tap A can fill a cistern in 12 hours and tap B can fill the same cistern in 8 hours while tap C can empty full cistern in 10 hours. Tap A started at 9 a.m. and tap B started at 11 a.m. At what time tap C should be started such that the cistern will be half full at 1 pm?

For two mutually exclusive events A and B, P(A) = 0.2 and P (A̅ ∩ B) = 0.3. What is P (A|(A ∪ B)) equal to?

If the lines \(\frac{x-3}{1}=\frac{y+2}{-4}=\frac{z}{5}\) and \(\frac{x-4}{1}=\frac{y-3}{-4}=\frac{z-a}{5}\) are coplanar then which of the following is correct?

The speed of two trains is in the ratio 6 : 7. If the second train runs 364 km in 4 hours, then the speed of first train is:

An amount of Rs. 735 was divided among A, B and C. If each of them had received Rs. 25 less, their shares would have been in the ratio 1:3:2. What was the amount received by C?

A certain sum becomes 4 times of itself in 6 years at simple interest. In how many years it will become 9 times of itself?