The mean proportional of a and b is c. What is the mean proportional of a2 c and b2 c?
What is the value of
\[
\frac{\cos 20^\circ}{\sin 70^\circ} + \frac{\cos \theta}{\sin(90^\circ - \theta)}
\]
A boat racer can row \( 21 \frac{3}{2} \)km/hr in still water. If the speed of river is 12.5 km/hr, it takes him 40 minutes to row to a place and back, how far off is the place (consider up to two decimals)?
\( 5 \tfrac{5}{27} \, \text{km} \)
\( 5 \tfrac{2}{5} \, \text{km} \)
\( 4 \tfrac{5}{27} \, \text{km} \)
\( 3 \tfrac{5}{27} \, \text{km} \)
The number of mobile sim card owners in 4 states/UTs are given in the bar diagram. Study the diagram and answer the question. 
The average of sim card sold in the four State/UT in lakhs is:
A solid hemisphere has radius 21 cm. It is melted to form a cylinder such that the ratio of its curved surface area to total surface area is 2:5. What is the radius (in cm) of its base \( \text{(take } \pi = \frac{22}{7} \text{)} \)?
A, B and C can do a piece of work in 11 days, 20 days and 55 days respectively. If B works daily and is supported by A and C on alternate days beginning with A, then in how many days will the work be finished?
What will be the value of sin 10° - 4/3 sin³ 10°?
\( \frac{1}{3\sqrt{3}} \)
1/6
\( \frac{1}{2\sqrt{3}} \)
\( \frac{\sqrt{3}}{6} \)
Successive discounts of 18% and 22% are equal to a single discount of _______________