List of top Mathematics Questions asked in CBSE CLASS XII

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?

A stone is dropped into a quiet lake and waves move in circles at the speed of \(5 cm/s\). At the instant when the radius of the circular wave is \(8 cm\), how fast is the enclosed area increasing?

The radius of a circle is increasing uniformly at the rate of \(3 cm/s\). Find the rate at which the area of the circle is increasing when the radius is \(10 cm\).

The volume of a cube is increasing at the rate of \(8 cm^3 /s\). How fast is the surface area increasing when the length of an edge is \(12 cm\)?

Find the rate of change of the area of a circle with respect to its radius r when (a) r=3 cm (b) r=4 cm

The total cost \(C (x)\) in Rupees associated with the production of \(x\) units of an item is given by \(c(x)=0.007x^3-0.003x^2+15x+4000\). 
Find the marginal cost when 17 units are produced.

For the matrix \(A=\begin{bmatrix}1&1&1\\ 1&2&-3\\ 2&-1&3\end{bmatrix}\)show that \(A^3−6A^2+5A+11I=O\).Hence,find A−1.

By using properties of determinants, show that:\((i)\begin{bmatrix}1&a&a^2\\ 1&b&b^2\\ 1&c&c^2\end{bmatrix}=(a-b)(b-c)(c-a)\)\((ii)\begin{bmatrix}1&1&1\\ a&b&c\\ a^3&b^3&c^3\end{bmatrix}=(a-b)(b-c)(c-a)(a+b+c)\)

Find the matrix X so that \(X\begin{bmatrix}1&2&3\\ 4&5&6\end{bmatrix}=\begin{bmatrix}-7&-8&-9\\ 2&4&6\end{bmatrix}\)

If \(A=\begin{bmatrix}3&-4\\1&-1\end{bmatrix}\),then prove \(A_n=\begin{bmatrix}1+2n& -4n\\ n& 1-2n\end{bmatrix}\)where n is any positive integer

If \(A=\begin{bmatrix}1&1&1\\ 1&1&1\\ 1&1&1\end{bmatrix}\),Prove that \(A^n=\begin{bmatrix}3^{n-1}& 3^{n-1}& 3^{n-1}\\ 3^{n-1}& 3^{n-1}& 3^{n-1}\\ 3^{n-1}& 3^{n-1}& 3^{n-1}\end{bmatrix},n∈N\)

Find the inverse of each of the matrices,if it exists.\(\begin{bmatrix}4&5\\3&4\end{bmatrix}\)

Find the inverse of each of the matrices, if it exists.\(\begin{bmatrix}2&5\\1&3\end{bmatrix}\)

Which of the following is a homogenous differential equation?

A homogenous differential equation of the form \(\frac{dy}{dx}=h(\frac{x}{y})\) can be solved by making the substitution

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

The volume of spherical balloon being inflated changes at a constant rate.If initially its radius is 3 units and after 3 seconds it is 6 units.Find the radius of balloon after \(t\) seconds.

Find the equation of a curve passing through the point \((0,0)\) and whose differential equations is \(y'=e^x sinx.\)

For the differential equation \(xy\frac{dy}{dx}=(x+2)(y+2)\),find the solution curve passing through the point\((1,-1)\).

Using Cofactors of elements of third column,evaluate\(△=\begin{bmatrix}1&x&yz\\ 1&y&zx\\ 1&z&xy\end{bmatrix}\)

Find values of k if area of triangle is 4 square units and vertices are\((i)(k,0),(4,0),(0,2)(ii)(−2,0),(0,4),(0,k)\)