List of top Mathematics Questions asked in CBSE CLASS XII

A function $ f : \mathbb{R}_+ \to \mathbb{R} $ (where $ \mathbb{R}_+ $ is the set of all non-negative real numbers) defined by $ f(x) = 4x + 3 $ is:

Find: \[ \int \frac{x^2}{(x^2 + 4)(x^2 + 9)} \, dx. \]

If $ P(A | B) = P(A' | B) $, then which of the following statements is true?

Find the integrals of the function: $cos\, 2x\, cos\, 4x\, cos\, 6x$

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.