List of top Mathematics Questions

\( \cos\theta (\csc\theta - \sec\theta) - \cot\theta = \)

Let ABC be an acute-angled triangle with area R. Then \( \sqrt{a^2b^2-4R^2} + \sqrt{b^2c^2-4R^2} + \sqrt{c^2a^2-4R^2} = \)

\( \frac{\sin x}{1+\cos x} + \frac{1+\cos x}{\sin x} = \)

The value of \( \sin(\frac{5\pi}{24}) \cdot \cos(\frac{\pi}{24}) \) is

The sum of all possible numbers that can be formed by using the digits 2,3,5,7 without repetition of digits is

If \( {}^n P_r = {}^{n-1}P_r + x \cdot {}^{n-1}P_{r-1} \quad \forall n,r \in N \text{ and } r \le n \), then x = .

\( \frac{x^3}{(x^2+1)(x^2+3)} = \)

If \(\alpha, \beta\) are the roots of \(ax^2+bx+c=0\), then the quadratic equation whose roots are \( \sqrt{5}\alpha, \sqrt{5}\beta \) is

The English alphabets have 5 vowels and 21 consonants. How many words with two different vowels and two different consonants can be formed from the alphabet?

\( \frac{(1+i)x-2i}{3+i} + \frac{(2-3i)y+i}{3-i} = i \implies x+y = \)

If \( A = \begin{bmatrix} 1 & -2 & 2 \\ -2 & -6 & 5 \\ 0 & 0 & 4 \end{bmatrix} \) then Adj A =

The rank of the matrix \( A = \begin{bmatrix} 2 & 1 & 2 \\ 1 & 0 & 1 \\ 4 & 1 & 4 \end{bmatrix} \) is

If 1, \(\omega, \omega^2\) denote the cube roots of unity, then, the value of \( (1-\omega+\omega^2)^5 + (1+\omega-\omega^2)^5 \) is

Let \( A = \begin{bmatrix} b^2+c^2 & a^2 & a^2 \\ b^2 & c^2+a^2 & b^2 \\ c^2 & c^2 & a^2+b^2 \end{bmatrix} \). If \(a = \sin \pi/6, b = \cos \pi/4\) and \(c = \cot \pi/2\) then A is

If a matrix A satisfies the equation \( A^3 - 6A^2 + 11A - 6I = 0 \), then \( A^{-1} \) can be

Let A and B be two non zero square matrices and AB and BA both are defined. It means

If $$ A = \begin{bmatrix} 1 & 0 \\ 2 & 1 \end{bmatrix}, \quad B = \begin{bmatrix} 1 & 3 \\ 0 & 1 \end{bmatrix} $$ then find: $$ \det(A^6 + B^6) $$

If $$ A = \begin{bmatrix} 3 & -3 & 4 \\ 2 & -3 & 4 \\ 0 & -1 & 1 \end{bmatrix} $$ then $ AA^T $ is:

If $$ f(x) = \log\left(\left(\frac{2x^2 - 3}{x}\right) + \sqrt{\frac{4x^4 - 11x^2 + 9}{|x|}}\right) $$ then $ f(x) $ is:

Let $ f : \mathbb{R} - \left\{-\frac{1}{2}\right\} \rightarrow \mathbb{R} $ be defined by $$ f(x) = \frac{x - 2}{2x + 1} $$ If $ \alpha, \beta $ satisfy the equation $$ f(f(x)) = -x $$ then evaluate: $$ 4(\alpha^2 + \beta^2) $$

The trigonometric function y = tan x in the II quadrant

The general solution of the differential equation: $$ \cos^2 x \cdot \frac{dy}{dx} + y = \tan x $$ is $$ y = \tan x - 1 + C e^{-\tan x} $$ If this solution satisfies $ y\left(\frac{\pi}{4}\right) = 1 $, then find $ C $.

Solve the differential equation: $$ \frac{dy}{dx} = \cos^2(3x + y) $$

Assertion (A): The order of the differential equation of a family of circles with constant radius is two.
Reason (R): An algebraic equation involving two arbitrary constants corresponds to the general solution of a second order differential equation.