List of top Mathematics Questions asked in CBSE CLASS XII

The rate of change of the area of a circle with respect to its radius \(r\) at \(r = 6 cm\) is

A ladder \(5m\) long is leaning against a wall. The bottom of the ladder is pulled along the ground, away from the wall, at the rate of \(2 cm/s\). How fast is its height on the wall decreasing when the foot of the ladder is \(4 m\) away from the wall?

Find the second order derivatives of the function
\(sin(logx)\)

Find the second order derivatives of the function
\(log(logx)\)

Find the second order derivatives of the function
\(tan^{-1}x\)

Find the second order derivatives of the function
\(e^{6x}cos3x\)

Find the second order derivatives of the function
\(e^xsin5x\)

Find the second order derivatives of the function
\(x^3logx\)

Find the second order derivatives of the function
\(log\,x\)

Find the second order derivatives of the function
\(x.cosx\)

Find the second order derivatives of the function
\(x^{20}\)

If \(x\) and \(y\) are connected parametrically by the equation,without eliminating the parameter,find \(\frac{dy}{dx}\).
\(x=a(cosθ+θsinθ),y=a(sinθ-θcosθ)\)

If \(x\) and \(y\) are connected parametrically by the equation,without eliminating the parameter,find \(\frac{dy}{dx}\).
\(x=a\,secθ,y=b\,tanθ\)

If \(x\) and \(y\) are connected parametrically by the equation,without eliminating the parameter,find \(\frac{dy}{dx}\).
\(x=a(cos\,t+log\,tan\frac{t}{2}),y=a\,sint\)

If \(x\) and \(y\) are connected parametrically by the equation,without eliminating the parameter,find \(\frac{dy}{dx}\).
\(x=\frac{sin^3t}{\sqrt{cos\,2t}},y=\frac{cos^3t}{\sqrt{cos\,2t}}\)

If \(x\) and \(y\) are connected parametrically by the equation,without eliminating the parameter,find \(\frac{dy}{dx}\).
\(x=a(θ-sin\,θ),y=a(1+cos\,θ)\)

If \(x\) and \(y\) are connected parametrically by the equation,without eliminating the parameter,find \(\frac{dy}{dx}\).
\(x=cos\,θ-cos2θ,y=sin\,θ-sin2θ\)

If \(x\) and \(y\) are connected parametrically by the equation,without eliminating the parameter,find \(\frac{dy}{dx}\).
\(x=4t,y=\frac{4}{t}\)

If \(x\) and \(y\) are connected parametrically by the equation,without eliminating the parameter,find \(\frac{dy}{dx}\).
\(x=sin\,t,y=cos\,2t\)

If \(x\) and \(y\) are connected parametrically by the equation,without eliminating the parameter,find \(\frac{dy}{dx}\).
\(x= a\,cos\,θ,y=b\,cos\,θ\)

If \(x\) and \(y\) are connected parametrically by the equation,without eliminating the parameter,find \(\frac{dy}{dx}.\)
\(x=2at^2,y=at^4\)

If \(u,v\) and \(w\) are functions of \(x\),then show that
\(\frac{d}{dx}(u.v.w)=\frac{du}{dx}v.w+u.\frac{dv}{dx}+u.v\frac{dw}{dx}\) in two ways-first by repeated application of product rule,second by logarithmic differentiation.

Find the derivative of the function given by \(f(x)=(1+x)(1+x^2)(1+x^4)(1+x^8)\) and hence find \(f'(1)\)

Find \(\frac{dy}{dx}\) of function
\(xy=e^{(x-y)}\)

Find \(\frac{dy}{dx}\) of function
\((cosx)^y=(cosy)^x\)