List of top Mathematics Questions asked in CBSE CLASS XII

Differentiate the function with respect to \(x\):
\(x^{sin\,x}+(sin\,x)^{cos\,x}\)

Differentiate the function with respect to \(x\):
\((sin\,x)^x+sin^{-1}\sqrt{x}\)

Differentiate the function with respect to \(x\)
\((log\,x)^x+x^{log\,x}\)

Differentiate the function with respect to \(x\). 
\((x+\frac{1}{x})^x+x^{(1+\frac{1}{x})}\)

Differentiate the function with respect to \(x\). 
\((x+3)^2.(x+4)^3.(x+5)^4\)

Differentiate the function with respect to \(x\). 
\(x^x-2^{sinx}\)

Differentiate the following w.r.t. \(x\):\((log\,x)^{cos\,x}\)

Differentiate the following w.r.t. \(x\):
\(\sqrt{\frac{(x-1)(x-2)}{(x-3)(x-4)(x-5)}}\)

Differentiate the following w.r.t. \(x\):
\(cosx.cos2x.cos3x\)

Differentiate the following w.r.t. \(x\):
\(cos(log\,x+e^x),x>0\)

Differentiate the following w.r.t. \(x\):
\(\frac{cos\,x}{log\,x},x>0\)

Differentiate the following w.r.t. \(x\):
\(log(log\,x),x>1\)

Differentiate the following w.r.t. \(x\):
\(\sqrt{e^{\sqrt{x}}},x>0\)

Differentiate the following w.r.t. \(x\):
\(e^x+e^{x^2}+....+e^{x^5}\)

Differentiate the following w.r.t. \(x\):
\(log(cos\,e^x)\)

Differentiate the following w.r.t. \(x\):
\(sin(tan^{-1}e^{-x})\)

Find the intervals in which the function \(f\) given by \(f(x) = 2x^2 − 3x\) is (a) strictly increasing (b) strictly decreasing

Show that the function given by \(f(x) = sin x\) is (a) strictly increasing in \((0,\frac{π}{2})\) (b) strictly decreasing in \((\frac{π}{2},π)\) (c) neither increasing nor decreasing in \((0, π)\)

Show that the function given by \(f(x) = e^{2x}\) is strictly increasing on \(R\).

A balloon, which always remains spherical, has a variable diameter \(\frac{3}{2}(2x+1)\) Find the rate of change of its volume with respect to \(x\)

The radius of an air bubble is increasing at the rate of \(\frac{1}{2} cm/s\). At what rate is the volume of the bubble increasing when the radius is \(1 cm\)?

A particle moves along the curve \(6y=x^3+2\).Find the points on the curve at which the y coordinate is changing 8 times as fast as the \(x\) coordinate

A balloon, which always remains spherical on inflation, is being inflated by pumping in 900 cubic centimetres of gas per second. Find the rate at which the radius of the balloon increases when the radius is 15 cm

The length \(x\) of a rectangle is decreasing at the rate of \(5 cm/minute\) and the width \(y\) is increasing at the rate of \(4 cm/minute\). When \(x = 8 cm\) and \(y = 6 cm\), find the rates of change of \((a)\) the perimeter, and \((b)\) the area of the rectangle.

The radius of a circle is increasing at the rate of \(0.7 cm/s.\) What is the rate of increase of its circumference?