Mathematical Sk...

\(\frac{\sin 7 x+6 \sin 5 x+17 \sin 3 x+12 \sin x}{\sin 6 x+5 \sin 4 x+12 \sin 2 x}\) equals:

In a mixture of milk and water the proportion of water by weight was 70%. If in the 50 gm mixture, 10 gm water was added, what would be the percentage of water in the new mixture?

A, B, C entered a business by investing Rs. 10000 each. After 6 months, A and C withdraws Rs. 5000 of their investment. At the end of the year, the total profit is Rs. 100000. Find the Share of A and C in the profit.

If any leap year is selected at random, then the probability of containing \(53\) Fridays in that year will be:

50 employees in a company can complete a work in 23 days. They start work together and after every 5 days, 5 employees more join them. Then in how much time work will be completed?

Tap A can fill a tank in 12 hours and tap B can emptied it is 15 hours. Tap A starts filling and they opened for 1 hour each alternatively in what time will the tank be full?

Find the area of the quadilateral whose vertices are \(\mathrm{A}(0,0), \mathrm{B}(0,10), \mathrm{C}(8,2)\) and \(\mathrm{D}(8,7) ?\)

The value of \(\cos 20^{\circ}+\cos 100^{\circ}+\cos 140^{\circ}\) is:

Two pipes A and B can fill an empty tank in 8 hours and 12 hours respectively. They have opened alternately for 1 hour each, starting with pipe A first. In how many hours will the empty tank be filled?

It is given that $\angle \mathrm{DEG}=4\mathrm{a}°$ and $\angle \mathrm{GEF}={\left(\frac{11\mathrm{a}}{2}\right)}^{\circ }+9°$. If DEF is a straight line then find the value of $7\mathrm{a}°-15°$?