List of top Questions asked in CBSE CLASS XII

Verify Rolle’s Theorem for the function \(f(x)=x^2+2x-8,x∈[-4,2]\)

If \(y=(tan^{-1}x)^2\),show that \((x^2+1)^2y_2+2x(x^2+1)y_1=2\)

If \(y=500e^{7x}+600e^{-7x}\),show that \(\frac{d^2y}{dx^2}=49y\)

If \(y=Ae^{mx}+Be^{nx}\),show that \(\frac{d^2y}{dx^2}-(m+n)\frac{dy}{dx}+mny=0\)

If \(y=3cos(logx)+4sin(logx)\),show that \(x^2y_2+xy_1+y=0\)

If \(y=cos^{-1}x\),find \(\frac{d^2y}{dx^2}\) in terms of \(y\) alone.

If \(y=5cosx-3sinx\),prove that \(\frac{d^2y}{dx^2}+y=0\)

The total revenue in Rupees received from the sale of \(x\) units of a product is given by \(R(x)=3x^2+36x+5\).The marginal revenue, when \(x=15\) is

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 \(\frac{dy}{dx}\).
\(x=a(θ-sin\,θ),y=a(1+cos\,θ)\)