List of top Mathematics Questions

What is the probability of getting a sum of 9 when two dice are thrown?
Solve for $ x $ given: $$ 2 \cosh(2x) + 10 \sinh(2x) = 5 $$
In triangle $ ABC $, given: $$ a = 6,\quad b = 5,\quad c = 4,\quad \text{find } \cos 2A $$
Evaluate: $$ \sin^2\left(\frac{2\pi}{3}\right) + \cos^2\left(\frac{5\pi}{6}\right) - \tan^2\left(\frac{3\pi}{4}\right) $$
In triangle $ ABC $, if: $$ r_1 = 36,\quad r_2 = 18,\quad r_3 = 12 $$ then find the semi-perimeter $ s $.
Which of the following trigonometric values are negative?
  • I) $ \sin(-292^\circ) $
  • II) $ \tan(-193^\circ) $
  • III) $ \cos(-207^\circ) $
  • IV) $ \cot(-222^\circ) $
Evaluate: $$ \frac{1}{\sin 1^\circ \sin 2^\circ} + \frac{1}{\sin 2^\circ \sin 3^\circ} + \cdots + \frac{1}{\sin 89^\circ \sin 90^\circ} $$
If $$ S = \left\{ m \in \mathbb{R} : x^2 - 2(1 + 3m)x + 7(3 + 2m) = 0 \text{ has distinct roots} \right\} $$ then the number of elements in $ S $ is:
Solve: $$ 4^x - 3^{x - \frac{1}{2}} = 3^{x + \frac{1}{2}} - 2^{2x - 1} $$
If one root of the cubic equation: $$ x^3 + 36 = 7x^2 $$ is double of another, then the number of negative roots is:
Find the values of $ x $ for which the expressions $$ \sin x + i\cos 2x \quad \text{and} \quad \cos x - i\sin 2x $$ are conjugate to each other.
The locus of a point $ z $ satisfying: $$ |z|^2 = \text{Re}(z) $$ is a circle with centre:
Let $$ G(x) = \begin{bmatrix} \cos x & -\sin x & 0 \\ \sin x & \cos x & 0 \\ 0 & 0 & 1 \end{bmatrix} $$ If $ x + y = 0 $, then evaluate $ G(x)G(y) $
If $f(x) = \begin{cases} \dfrac{x^2 \log(\cos x)}{\log(1+x)}, & x \neq 0 \\ 0, & x = 0 \end{cases}$, then at $x=0$, $f(x)$ is
Evaluate: \[ \int_{\pi/4}^{5\pi/4} \left(\cos t |\sin t| + \sin t |\cos t|\right) dt = \]
Evaluate: \[ \int_{0}^{\pi/4} e^{\tan^2 \theta} \sin^2 \theta \tan \theta \, d\theta = \]
If \( 2x - y + c \log(|x - 2y - 4|) = k \) is the general solution of \[ \frac{dy}{dx} = \frac{2x - 4y - 5}{x - 2y + 2} \] then \( c = \):
If \( f(x) = \max(\sin x, \cos x) \) and \( g(x) = \min(\sin x, \cos x) \), then \[ \int_0^{\pi/2} f(x) dx + \int_0^{\pi/2} g(x) dx = \]
A closed cylinder of given volume will have least surface area when the ratio of its height and base radius is:
Two particles P and Q located at the points \( P(t, t^3 - 16t - 3) \), \( Q(t+1, t^3 - 6t - 6) \) are moving in a plane. The minimum distance between the points in their motion is:
If the straight line \( x\cos\alpha + y\sin\alpha = p \) touches the curve \( \left( \frac{x}{a} \right)^n + \left( \frac{y}{b} \right)^n = 2 \) at the point (a, b), and \( \frac{1}{a^2} + \frac{1}{b^2} = \frac{k}{p^2} \), then \( k = \):
If \( f(x) = \int_{x^2}^{\cos^2 x} (2x \tan^2 x - 2x - 6 \tan x) dx \), and \( f(0) = \pi \), then \( f(x) = \):
If $[\cdot]$ denotes greatest integer function, then $\lim_{x \to 3} \dfrac{[-x]}{x} =$
If $l, m$ $(l<m)$ are roots of $ax^2 + bx + c = 0$, then $\lim_{x \to a} \left| \dfrac{ax^2 + bx + c}{ax^2 + bx + c} \right|$ =
Calculate $\dfrac{d}{dx} \left(\lim_{y \to 2} \dfrac{1}{y-2} \left(\dfrac{1}{x} - \dfrac{1}{x+y-2}\right)\right)$