List of top Mathematics Questions asked in CBSE CLASS XII

Find the inverse of each of the matrices, if it exists. $\begin{bmatrix} 1 & 3\\ 2 & 7\end{bmatrix}$

For what values of x,$\begin{bmatrix} 1 & 2 & 1 \end{bmatrix}$$\begin{bmatrix} 1 & 2 & 0\\ 2 & 0 & 1 \\1&0&2 \end{bmatrix}$$\begin{bmatrix} 0 \\2\\x\end{bmatrix}$=O?

Find the inverse of each of the matrices,if it exists $\begin{bmatrix} 2 & 1 \\ 7 & 4 \end{bmatrix}$

Find the inverse of each of the matrices,if it exists. $\begin{bmatrix} 2 & 3\\ 5 & 7 \end{bmatrix}$

If A'= $\begin{bmatrix} 3 & 4 \\ -1 & 2 \\ 0 &1 \end{bmatrix}$$\begin{bmatrix} -1 & 2 & 1 \\ 1 &2 & 3\end{bmatrix}$ , then verify that
(i) $(A+B)'=A'+B' $
(ii) $(A-B)'=A'-B'$

If (i) A=$\begin{bmatrix} \cos\alpha & \sin\alpha\\ -\sin\alpha & \cos\alpha \end{bmatrix}$,then verify that A'A=I
(ii) A= $\begin{bmatrix} \sin\alpha & \cos\alpha\\ -\cos \alpha & \sin\alpha \end{bmatrix}$,then verify that A'A=I

Let A=$\begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix}$,show that(aI+bA)ⁿ=aⁿI+na^n-1bA,where I is the identity matrix of order 2 and n∈N

Evaluate $\begin{vmatrix} cos\alpha cos\beta &cos\alpha sin\beta &-sin\alpha \\ -sin\beta&cos\beta &0 \\ sin\alpha cos\beta&sin\alpha\sin\beta &cos\alpha \end{vmatrix}$

Find the vector and the cartesian equations of the lines that pass through the origin and(5,-2,3).

Let f: R→R be defined as f(x) = 3x. Choose the correct answer.

If A=$\begin{bmatrix}2&-1&1\\-1&2&-1\\1&-1&2\end{bmatrix}$verify that A³-6A²+9A-4 I=0 and hence find A^-1

The total revenue in Rupees received from the sale of $x$ units of a product is given by $R(x)=13x^2+26x+15$.The marginal revenue, when $x=7$ is

Find the following integral: $\int (ax^2+bx+c)dx$

Solve system of linear equations, using matrix method.
x-y+2z=7
3x+4y-5z=-5
2x-y+3z=12

By using the properties of definite integrals, evaluate the integral: $∫_0^π log(1+cosx)dx$

If $\frac{d}{dx}f(x) = 4x^3-\frac{3}{x^4}$ such that $f(2)=0$, then $f(x)$ is

2, b, c are in A.P. and the range of determinant $\begin{vmatrix}1&1&1\\ 2&b&c\\ 4&b^{2}&c^{2}\end{vmatrix}$ is [2, 16]. Then find range of c is

Show that the relation R in the set R of real numbers, defined as
R = {(a, b): a ≤ b²} is neither reflexive nor symmetric nor transitive.

If f (x) = 3x²+15x+5, then the approximate value of f (3.02) is

The cost of 4 kg onion,3 kg wheat and 2kg rice is Rs 60.The cost of 2 kg onion,4 kg wheat and 6 kg rice is Rs 90. The cost of 6 kg onion 2 kg wheat and 3 kg rice is Rs 70. Find cost of each item per kg by matrix method.

Evaluate$\begin{vmatrix} 1 & x & y\\ 1 & x+y & y\\1&x&x+y \end{vmatrix}$

A committee of 11 members is to be formed from 8 males and 5 females. Let m denotes the number of ways of selecting committee having atleast 6 males and n denotes the number of ways of selecting atleast 3 females then

Show that the relation R in R defined as R = {(a, b): a ≤ b}, is reflexive and transitive
but not symmetric.

For the differential equations , find a particular solution satisfying the given condition:$(x^3+x^2+x+1)\frac{dy}{dx}=2x^2+x;y=1$ when $x=0$

Show that the relation R in the set A = {1, 2, 3, 4, 5} given by R={(a,b) : Ia-bI is even}, is an equivalence relation. Show that all the elements of {1, 3, 5} are related to each other and all the elements of {2, 4} are related to each other. But no element of {1, 3, 5} is related to any element of 2, 4}.