List of top Mathematics Questions

If the lines \( 3x - 4y + 4 = 0 \) and \( 6x - 8y - 7 = 0 \) are the tangents to the same circle, then the area of that circle (in sq. units) is
The tangent drawn at an extremity (in the first quadrant) of latus rectum of the hyperbola $$ \frac{x^2}{4} - \frac{y^2}{5} = 1 $$ meets the x-axis and y-axis at $ A $ and $ B $ respectively. If $ O $ is the origin, find $$ (OA)^2 - (OB)^2. $$
Let \( A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \), then \( A^2 - 5A + 6I = ? \)
If \((2, -1, 3)\) is the foot of the perpendicular drawn from the origin \((0, 0, 0)\) to a plane then the equation of that plane is
Evaluate: $$ \int_0^1 x \sin^{-1} x \, dx $$
The equation of the base of an equilateral triangle is \( x + y = 2 \) and its opposite vertex is \( (2,1) \). If \( m_1, m_2 \) are the slopes of the other two sides and the length of its side is \( a \), then \( |m_1 - m_2| + a\sqrt{2} = \):
The general solution of the differential equation \( \frac{dy}{dx} + \frac{\sec x}{\cos x + \sin x}y = \frac{\cos x}{1+\tan x} \) is
For all \( n \in \mathbb{N} \), which of the following is less than or equal to \( \frac{3^n - 1}{2} \)?
The variance of the ungrouped data \(2, 12, 3, 11, 5, 10, 6, 7\) is:
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 \(f(x) = \sec^{-1} \left(\frac{1}{2x^2 -1}\right)\) 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?
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 the number of diagonals of a regular polygon is 35, then the number of sides of the polygon is
If \( \alpha \) is a repeated root of multiplicity 2 of the equation \( 18x^3 - 33x^2 + 20x - 4 = 0 \), then:
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 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:
If $x = 3 - 2\sqrt{3}i$, then evaluate $x^4 - 12x^3 + 54x^2 - 108x - 54 = $
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
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
If \(y = \sqrt{\cosh x + \sqrt{\cosh x}}\), then \(\frac{dy}{dx} =\)
Evaluate the limit: \[ \lim_{x \to 0} \frac{x^2 \sin^2(3x) + \sin^4(6x)}{(1 - \cos(3x))^2} \]
P and Q are the ends of a diameter of the circle \( x^2+y^2=a^2(a>\frac{1}{\sqrt{2}}) \). \( s \) and \( t \) are the lengths of the perpendiculars drawn from P and Q onto the line \( x+y=1 \) respectively. When the product \( st \) is maximum, the greater value among \( s, t \) is:
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
\( \int x \cos^{-1}\left(\frac{1-x^2}{1+x^2}\right) \, dx \, (x>0) = \)