List of top Mathematics Questions asked in CBSE CLASS XII

Prove that \(y=\frac{ 4sinθ}{(2+cosθ)}-θ \)is an increasing function of \(θ\) in \([0,\frac π2]\).

Find \(\frac{dy}{dx}\), if y=sin-1x+sin-1\(\sqrt{1-x^2}\), -1≤x≤1

Find the values of x for which \(y=[x(x-2)]^2\) is an increasing function.

Find the general solution: \(\frac {dy}{dx}+2y=sin\ x\)

Show that \(y = log(1+x) - \frac {2x}{2+x}, \ x>-1\),is an increasing function of x throughout its domain.

The general solution of the differential equation \(e^{x}dy+(ye^{x}+2x)dx=0\) is

The general solution of a differential equation of the type \(\frac{dx}{dy}+p_{1}x=Q1\) is

Choose the correct answer.
If x,y,z are nonzero real numbers,then the inverse of matrix
A=\(\begin{bmatrix}x& 0& 0\\ 0& y& 0\\0&0& z\end{bmatrix}\)is

The general solution of the differential equation \(\frac{ydx-xdy}{y}=0 \) is
Verify Mean Value Theorem,if \(f(x)=x^3-5x^2-3x\) in the interval \([a,b]\),where \(a=1\) and \(b=3\).Find all \(c∈(1,3)\) for which \(f'(c)=0\)
Verify Mean Value Theorem,if \(f(x)=x^2-4x-3\) in the interval \([a,b]\),where \(a=1\) and \(b=4\)
If \(f:[-5,5]→R\) is a differentiable function and if \(f'(x)\)does not vanish anywhere, then prove that \(f(-5)≠f(5)\)

Choose the correct answer.
Let A=\(\begin{bmatrix}1&sin\theta&1\\-sin\theta&1&sin\theta\\-1&-sin\theta&1\end{bmatrix}\),\(where 0≤\theta≤2\pi,then\)

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
\(log(logx)\)