Differentiation...

All possible number are formed using the digits $$1,1,2,2,2,2,3,4,4$$ taken all at a time. The number of such number in which the odd digits occupy even places is:

The derivative of $$\tan^{-1} \left (\dfrac {\sin x - \cos x}{\sin x + \cos x}\right )$$, with respect to $$\dfrac {x}{2}$$, where $$\left (x \epsilon \left (0, \dfrac {\pi}{2}\right )\right )$$ is

A group of students comprises of $$5$$ boys and $$n$$ girls. If the number of ways, in which a team of $$3$$ students can randomly be selected from this group such that there is at least one boy and at least one girl in each team, is $$1750$$, then $$n$$ is equal to

The value of $$(^{21}C_1-^{10}C_1)+(^{21}C_2-^{10}C_2)+(^{21}C_3-^{10}C_3)+(^{21}C_4+^{10}C_4)+......+(^{21}C_{10}-^{10}C_{10})$$ is:

The number of four -digit numbers strictly grater than $$4321$$ that can be formed using the digits $$0,1,2,3,4,5$$ (repetition of digits is allowed) is:

The value of '$$a$$' in order $$f(x)=\sqrt{3}\sin x-\cos x -2ax+b$$ decrease for all real values of $$x$$, is given by

Area of a triangle formed by the points A(5, 2), B(4, 7) and C(7, -4) is _____.

Value of 0! is always 1.

If $$y=2  \sin  x -3x^4 + 8$$, then $$\dfrac{dy}{dx}$$ is