List of top Mathematics Questions

The length of the projection of the line segment joining the points $ (5, -1, 4)$ and $(4, -1, 3)$ on the plane, $x + y + z = 7$ is:

If sum of all the solutions of the equation $8 \cos x.\left(\cos \left(\frac{\pi}{6} + x\right). \cos\left(\frac{\pi}{6} - x\right) - \frac{1}{2}\right)= 1 $ in $\left[0, \pi\right]$ is $ k \pi $, then $k$ is equal to :

If $\tan \, A$ and $\tan \, B$ are the roots of the quadratic equation, $3x^2 - 10x - 25 = 0$, then the value of $3 \, \sin^2(A + B) -10 \, \sin ( A + B)?\cos(A + B)-25 \cos^2(A+B) $ is :

If A, B, C are the angles of $\Delta ABC$ then $\cot \, A. \cot \, B + \cot \, B. \cot \, C + \cot \, C. \cot \, A =$

If $f(x) = \begin{cases} x^2 + \alpha & \text{for } x \ge 0 \\[2ex] 2\sqrt{x^2 + 1} + \beta & \text{for} x < 0 \end{cases}$ is continuous at x = 0 and $f \left(\frac{1}{2} \right) = 2 $ then $\alpha^2+ \beta^2$ is

Letters in the word HULULULU are rearranged. The probability of all three L being together is

A coin is tossed three times. If X denotes the absolute difference between the number of heads and the number of tails then P(X = 1) =

If $\log_{10} \left(\frac{x^{3} - y^{3} }{x^{3} + y^3} \right) = 2$ then $ \frac{dy}{dx} = $

If $y = \left(\tan^{-1} x\right)^{2}$ then $ \left(x^{2} + 1\right)^{2} \frac{d^{2}y}{dx^{2} } + 2x \left(x^{2} + 1 \right) \frac{dy}{dx} = $

The sum of the first 10 terms of the series 9 + 99 + 999 + ?., is

If $f : R - \{2\} \to R$ is a function defined by $f(x) = \frac{x^2 - 4}{x - 2}$ , then its range is

The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0 $ then the value of k is

Is equal to $$ \left| \begin{matrix} b^2 + c^2 & c^2 + b^2 \\ c^2 & c^2 + a^2 \\ b^2 & a^2 + b^2 \end{matrix} \right| $$ 

Solve for $x \ (a \neq 0)$ $$ \sqrt{(a + x)^2 + 4\sqrt{(a - x)^2}} = 5\sqrt{a^2 - x^2} $$

The value of \( \int \frac{\sin^2 x \cos^2 x}{(\sin^3 x + \cos^3 x)^2} \, dx \) is

Evaluate the limit: \[ \lim_{x \to 0} \frac{1 - \cos 4x}{2 \sin^2 x + x \tan 7x} \]

Evaluate the limit: \[ \lim_{x \to a} \frac{\log{(x^{a-1})}}{x-a} \]

Find the limit \[ \lim_{x \to 0} \left( 1 + \tan^2 \sqrt{x} \right)^{3/x} \]