List of top Mathematics Questions asked in CBSE CLASS XII

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}.

Let $A=\begin{bmatrix}1&-2&1\\ -2&3&1\\ 1&1&5\end{bmatrix}$verify that -
$(i)[adjA]^{-1}=adj(A^{-1})$
$(ii)(A^{-1})^{-1}=A$

It is given that at x = 1, the function x⁴−62x²+ax+9 attains its maximum value, on the interval [0, 2]. Find the value of a.

Let R be the relation in the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}. Choose the correct answer.
A. R is reflexive and symmetric but not transitive.
B. R is reflexive and transitive but not symmetric.
C. R is symmetric and transitive but not reflexive.
D. R is an equivalence relation.

Find the maximum profit that a company can make, if the profit function is given by p(x) = 41−24x−18x²

The two equal sides of an isosceles triangle with fixed base $b$ are decreasing at the rate of 3 cm per second. How fast is the area decreasing when the two equal sides are equal to the base?

Show that the given differential equation is homogeneous and solve:$(x^2+xy)dy=(x^2+y^2)dx$

Find $|\vec{a}\times\vec{b}|$ if $\vec{a}=\hat{i}-7\hat{j}+7\hat{k}\space and\space \vec{b}=3\hat{i}-2\hat{j}+2\hat{k}.$

$\text {Find} \ \frac {dy}{dx}:$ $y=sin^{-1}(\frac {2x}{1+x^2})$

Without expanding the determinant, prove that
$\begin{vmatrix} a &a^2 &bc \\ b&b^2 &ca \\ c&c^2 &ab \end{vmatrix}=\begin{vmatrix} 1 &a^2 &a^3 \\ 1&b^2 &b^3 \\ 1&c^2 &c^3 \end{vmatrix}$

A company manufactures two types of novelty souvenirs made of polywood.Souvenirs of type A require 5 minutes each for cutting and 10 minutes each for assembling. Souvenirs of type B require 8 minutes each for cutting and building.3 hours 20 minutes are available for cutting and 4 hours of assembling. The profit is Rs 5 each for type A and Rs 6 each for type B souvenirs. How many types of souvenirs of each type should the company manufacture in order to maximize the profit?

Using the property of determinants and without expanding, prove that: $\begin{vmatrix}a-b&b-c&c-a\\b-c&c-a&a-b\\c-a&a-b&b-c\end{vmatrix}$=0

$∫\frac{dx}{e^x+e^{-x}}$ is equal to

An edge of a variable cube is increasing at the rate of $3 cm/s$. How fast is the volume of the cube increasing when the edge is $10 cm$ long?