List of top Mathematics Questions

If the algebraic sum of the distances from the points $(2, 0)$, $(0, 2)$, and $(1, 1)$ to a variable straight line is zero, then the line passes through the fixed point.
Let $R$ and $S$ be two equivalence relations on a non-void set $A$. Then
Let $f(n) = 2n + 1$, $g(n) = 1 + (n + 1)^{2n}$ for all $n \in \mathbb{N}$. Then
Let $f(x) = a_0 + a_1|x| + a_2|x^2| + a_3|x^3|$, where $a_0, a_1, a_2, a_3$ are real constants. Then $f(x)$ is differentiable at $x = 0$
If $a$, $b$ are odd integers, then the roots of the equation $2ax^2 + (2a + b)x + b = 0$, where $a \neq 0$, are
The value of $a$ for which the sum of the squares of the roots of the equation $x^2 - (a - 2)x - (a - 1) = 0$ assumes the least value is
If the transformation $z = \log \tan \frac{x}{2}$ reduces the differential equation $\frac{d^2y}{dx^2} + \cot x \frac{dy}{dx} + 4y \csc^2 x = 0$ into the form $\frac{d^2y}{dz^2} + ky = 0$, then $k$ is equal to
The side $AB$ of $\triangle ABC$ is fixed and is of length $2a$ units. The vertex $C$ moves in the plane such that the vertical angle is always constant and is $\alpha$. Let the $x$-axis be along $AB$ and the origin be at $A$. Then the locus of the vertex is
If $x \frac{dy}{dx} + y = x \frac{f(xy)}{f'(xy)}$, then $|f(xy)|$ is equal to
A particle moving in a straight line starts from rest, and the acceleration at any time $t$ is $a - kt^2$, where $a$ and $k$ are positive constants. The maximum velocity attained by the particle is
For the mapping $f: \mathbb{R} \setminus \{1\} \to \mathbb{R} \setminus \{2\}$ given by $f(x) = \frac{2x}{x - 1}$, which of the following is correct?
If $a$, $b$, and $c$ are in GP, and $\log a - \log 2b$, $\log 2b - \log 3c$, $\log 3c - \log a$ are in A.P., then $a$, $b$, and $c$ are the lengths of the sides of a triangle which is
The line $x - 2y + 4z + 4 = 0$, $x + y + z - 8 = 0$ intersects the plane $x - y + 2z + 1 = 0$ at the point
Let $f(x) = (x - 2)^{17} (x + 5)^{24}$. Then
Let $p(x_0)$ be a polynomial with real coefficients, $p(0) = 1$ and $p'(x)>0$ for all $x \in \mathbb{R}$. Then
Let $S$, $T$, $U$ be three non-void sets, where $f: S \to T$, $g: T \to U$, and the composed mapping $g \circ f: S \to U$ is defined. If $g \circ f$ is an injective mapping, then
Consider the equation $y - y_1 = m(x - x_1)$. If $m$ and $x_1$ are fixed, and different lines are drawn for different values of $y_1$, then
$f: X \to \mathbb{R}, X = \{x | 0<x<1\}$ is defined as $f(x) = \frac{2x - 1}{1 - |2x - 1|}$. Then
The maximum value of $f(x) = e^{\sin x} + e^{\cos x}$, where $x \in \mathbb{R}$, is
A curve passes through the point $(3, 2)$ for which the segment of the tangent line contained between the coordinate axes is bisected at the point of contact. The equation of the curve is
$AB$ is a chord of a parabola $y^2 = 4ax$, $(a > 0)$ with vertex $A$, $BC$ is drawn perpendicular to $AB$ meeting the axis at $C$. The projection of $BC$ on the axis of the parabola is
The point of contact of the tangent to the parabola $y^2 = 9x$ which passes through the point $(4, 10)$ and makes an angle $\theta$ with the positive side of the axis of the parabola, where $\tan \theta>2$, is
If $P_1P_2$ and $P_3P_4$ are two focal chords of the parabola $y^2 = 4ax$, then the chords $P_1P_3$ and $P_2P_4$ intersect on the
Let the tangent and normal at any point $P(at^2, 2at), (a>0)$, on the parabola $y^2 = 4ax$ meet the axis of the parabola at $T$ and $G$ respectively. Then the radius of the circle through $P$, $T$, and $G$ is
From the point $(-1, -6)$, two tangents are drawn to $y^2 = 4x$. Then the angle between the two tangents is