List of top Questions asked in CBSE CLASS XII

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\((i)(k,0),(4,0),(0,2)(ii)(−2,0),(0,4),(0,k)\)

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

Find \(\frac{1}{2}(A+A')\)and \(\frac{1}{2}(A-A'),\)when \(A=\begin{bmatrix}0&a&b\\ -a&0&c\\ -b&-c&0\end{bmatrix}\)

If \(A=\begin{bmatrix}0& -tanα/2\\ tanα/2& 0\end{bmatrix}\) and I is the identity matrix of order 2,show that \(I+A=(I-A)\begin{bmatrix}cosα& -sinα\\ sinα& cosα\end{bmatrix}\)

Given \(3\begin{bmatrix}x&y\\z&w\end{bmatrix}\)\(=\begin{bmatrix}x&6\\-1&2w\end{bmatrix}+\begin{bmatrix}4& x+y\\ z+w& 3\end{bmatrix}\),find the values of x,y,z and w

Find X,if \(Y=\begin{bmatrix}3&2\\1&4\end{bmatrix}\)and \(2X+Y=\begin{bmatrix}1&0\\-3&2\end{bmatrix}\)

Find X and Y,if \((i)X+Y=\begin{bmatrix}7&0\\2&5\end{bmatrix}\) and \(X-Y=\begin{bmatrix}3&0\\0&3\end{bmatrix}\)\((ii)2X+3Y=\begin{bmatrix}2&3\\4&0\end{bmatrix}\)and \(3X+2Y=\begin{bmatrix}2&-2\\-1&5\end{bmatrix}\)

If \(A=\begin{bmatrix}1&2&-3\\ 5&0&2\\ 1&-1&1\end{bmatrix}\)\(,B=\begin{bmatrix}3&-1&2\\ 4&2&5\\ 2&0&3\end{bmatrix}\)\(,and\space C=\begin{bmatrix}4&1&2\\ 0&3&2\\ 1&-2&3\end{bmatrix}\), then compute(A+B)and(B-C). Also, verify that A+(B-C)=(A+B)-C.

Compute the indicated products \((i)\begin{bmatrix}a&b\\-b&a\end{bmatrix}\begin{bmatrix}a&-b\\b&a\end{bmatrix}\)\((ii)\begin{bmatrix}1\\2\\3\end{bmatrix}\begin{bmatrix}2&3&4\end{bmatrix}\)\((iii)\begin{bmatrix}1&-2\\2&3\end{bmatrix}\begin{bmatrix}1&2&3\\2&3&1\end{bmatrix}\)\((iv)\begin{bmatrix}2&3&4\\ 3&4&5\\ 4&5&6\end{bmatrix}\begin{bmatrix}1&-3&5\\ 0&2&4\\ 3&0&5\end{bmatrix}\)
\((v)\begin{bmatrix}2&1\\3&2\\-1&1\end{bmatrix}\begin{bmatrix}2&-3\\1&0\\3&1\end{bmatrix}\)\((vi)\begin{bmatrix}3&-1&3\\-1&0&2\end{bmatrix}\begin{bmatrix}2&-3\\1&0\\3&1\end{bmatrix}\)

Find the equation of a curve passing through the origin given that the slope of the tangent to the curve at any point (x,y) is equal to the sum of coordinates of the point.

Which of the following differential equations has y= c₁e^x+c₂e^-x as the general solution?

Let \(f: R→ R\) be defined as \(f(x)=x^4\). Choose the correct answer.

Let \(A=R−\{3\}\) and \(B=R−\{1\}\). Consider the function \(f: A→B\) defined by \(f(x)=\bigg(\frac{x-2}{x-3}\bigg)\). Is f one-one and onto? Justify your answer.

Let \(f: N → N\) be defined by \(f(n) = \begin{cases} \frac{n+1}{2} & \quad \text{if } n \text{ is odd}\\ \frac{n}{2} & \quad \text{if } n \text{ is even} \end{cases}\) for all \(n∈N\).
State whether the function f is bijective. Justify your answer.

Find general solution: \(y dx+(x-y^2)dy=0\)

Prove that\(\begin{vmatrix} a^2&bc &ac+c^2 \\ a^2+ab&b^2 &ac\\ ab&b^2+bc &c^2 \end{vmatrix}=4a^2b^2c^2\)

Solve the equation \(\begin{vmatrix} x+a &x &x \\ x &x+a &x \\ x&x &x+a \end{vmatrix}=0\) , a≠0