Differentiation...

Find the differential equations of all parabolas each having latus rectum $$4a$$ and whose axes are parallel to the x-axis.

$$\displaystyle \frac{d}{dx}(\tan ^{-1}\frac{\cos x-\sin x}{\cos x+\sin x})$$

$$\displaystyle \frac{d}{dx}(\tan^{-1}\sqrt{\left ( \frac{1-\cos x}{1+\cos x} \right )})$$

CE, GI, KM, OQ, ....

How many combinations of two-digit numbers having 8 can be made from the following numbers?
8, 5, 2, 1, 7, 6

Which letter will be the fifth from the right if the first and second, the third and fourth and so on are interchanged among each other in the word "COMPANIONATE"?

There are $$5$$ roads leading to a town from a village. The number of different ways in which a villager can go to the town and return back, is

BDF, CFI, DHL, ....

The spread sheet on the right contains 20 cells. A cell In a spread sheet can be identified fIrst by the column letter and then by the row number. For example,. the number 10 is found in cell C4. If the number in cell A3 =B4-3(E2 +D4) then which of the following must be the number in cell E2?

JE, LH, OL, SQ, ....