`Diatoms the chief producers in the oceans, are useful to us even after their death'. Evaluate the statement.

"Mountaineers on Everest have to use a pressure cooker to boil an egg". Jusity the statement.

Observe the following pattern of dots i) Find the number of dots in the n^(th) pattern. ii) Find the sum of number of dots upto n^(th) pattern and the mathematical statement using these facts. iii)Prove the statement obtained in question (ii) using principle of mathematical induction.

Using the given figure Find the equation of AB

Using the given figure find the area of the ellipse using integration

using the given figure find the area of the enclosed region

Using the first principle , find the derivative of cos x .