List of top Mathematics Questions

Evaluate \[ \int \frac{1}{1 + x^2} \, dx = ? \]
Let \( A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \), then \( A^2 - 5A + 6I = ? \)
If \( A = \begin{bmatrix} 1 & 2 & x \\ 4 & -1 & 7 \\ 2 & 4 & -6 \end{bmatrix} \) and the rank of \( A \) is 2, then the value of \( x \) is equal to:
If \( A = \begin{bmatrix} 1 & 2 & x \\ 4 & -1 & 7 \\ 2 & 4 & -6 \end{bmatrix} \) and the rank of \( A \) is 2, then the value of \( x \) is equal to:
If $x = 3 - 2\sqrt{3}i$, then evaluate $x^4 - 12x^3 + 54x^2 - 108x - 54 = $
If the number of diagonals of a regular polygon is 35, then the number of sides of the polygon is
The number of ways of forming the ordered pairs (p, q) such that p>q by choosing p and q from the first 50 natural numbers is:
The domain of the function $f(x) = \ln\left(\frac{1}{\sqrt{x^2-4x+4}}\right) + \sin^{-1}(x^2-2)$ is
Angle between a diagonal of a cube and a diagonal of its face which are coterminus is
Out of 8 students in a classroom, 4 of them are chosen and they are arranged around a table. If the remaining 4 are arranged in a row, then the total number of arrangements that can be made with those 8 students is
If \(f(x) = \sec^{-1} \left(\frac{1}{2x^2 -1}\right)\) and \(g(x) = \tan^{-1} \left(\frac{\sqrt{1 + x^2} - 1}{x}\right)\), then the derivative of \(f(x)\) with respect to \(g(x)\) is?
The differential equation of the family of circles passing through the origin and having centre on X-axis is
If \(y = \sqrt{\cosh x + \sqrt{\cosh x}}\), then \(\frac{dy}{dx} =\)
In \(\triangle ABC\), the sum of the lengths of two sides is \(x\) and the product of those lengths is \(y\). If \(c\) is the length of its third side and \(x^2 - c^2 = y\), then the circumradius of that triangle is:
The equation of chord AB of ellipse \(2x^2 + y^2 = 1\) is \(x - y + 1 = 0\). If O is the origin, then \(\angle AOB =\)
The mean of 10 numbers is 18. If one number is excluded, the mean becomes 17. What is the excluded number?
If \( \alpha \) is a repeated root of multiplicity 2 of the equation \( 18x^3 - 33x^2 + 20x - 4 = 0 \), then:
Evaluate \[ \lim_{x \to 0} \sqrt{\frac{x + 2 \sin x + 3 \tan x - \tan^3 x}{x^2 + 2 \sin x + \tan x + 3 - \sqrt{\sin^2 x - 2 \tan x - x + 3}}} = ? \]
\( \int x \cos^{-1}\left(\frac{1-x^2}{1+x^2}\right) \, dx \, (x>0) = \)
Tangents are drawn at three points P($t_1$), Q($t_2$), R($t_3$) on the parabola $y^2 = x$. Let these tangents intersect each other at the points L, M, N. If $t_1 = 2$, $t_2 = -4$, $t_3 = 6$, then the area of the triangle LMN is
If 3 squares are chosen at random from the 64 squares of a chessboard, then the probability that all of them lie along the same diagonal line is:
The circles $$ x^2 + y^2 - 2x - 4y - 4 = 0 $$ and $$ x^2 + y^2 + 2x + 4y - 11 = 0 $$ ...
Evaluate the limit: \[ \lim_{x \to 0} \frac{x^2 \sin^2(3x) + \sin^4(6x)}{(1 - \cos(3x))^2} \]
If the equation of the plane passing through the point (2, -1, 3) and perpendicular to each of the planes $3x - 2y + z = 8$ and $x + y + z = 6$ is $lx + my + nz = 1$, then $4m + 2n - 3l$ =
Identify the correct option from the following:
If \(O(0,0,0), A(1,2,1), B(2,1,3)\), and \(C(-1,1,2)\) are the vertices of a tetrahedron, then the acute angle between its face \(OAB\) and edge \(BC\) is