List of top Mathematics Questions

\(\cot^{-1}(1) + \cot^{-1}(2) + \cot^{-1}(3) =\)

If \(\tan\left(\alpha - \frac{\pi}{12}\right) = \frac{1}{\sqrt{3}}\), where \(0 < \alpha < \frac{\pi}{2}\), then the value of \(\alpha\) is equal to

Let \(f(x) = \begin{cases} x + \alpha, & \text{if } x < 0 \\ \max(2\cos x, 2\sin x), & \text{if } x \geq 0 \end{cases}\). If \(f\) is continuous at \(x = 0\), then the value of \(\alpha\) is equal to

Let \(f(x) = \frac{\sqrt[3]{x^4}}{\sqrt[3]{x^2}},\ x \neq 0\). Then the value of \(f'(27)\) is equal to

Let \(f(x) = \begin{cases} 5x^2 + ax + 16, & \text{if } x < 2 \\ x^2, & \text{if } x \geq 2 \end{cases}\). If \(f\) is differentiable at \(x = 2\), then the value of \(a\) is equal to

If \(f(x) = \frac{\sqrt{2\sin x}}{\sqrt{1 + \cos 2x}}\), then \(f'\left(\frac{\pi}{6}\right) =\)

Let \(f(x) = \frac{1}{x^2}\) and let \(u = f(x)f''(x)\). Then \(\frac{du}{dx} =\)

If \(y = (x - 1)\log_{e}(x - 1)\), then \(\frac{d^{2}y}{dx^{2}}\) at \(x = 3\) is

\(\int \frac{1}{x(1 + x^{4})} \, dx\) is equal to

Let \(f(x) = e^{x(2x^{2} + ax + 2 - a)}\). If \(f\) has a local minimum at \(x = 2\), the value of \(a\) is equal to

\(\int \frac{\sec^2(\sqrt{2x+5})}{\sqrt{2x+5}} \, dx =\)

\(\int_{0}^{2} \frac{x^{4}}{x^{4} + (2 - x)^{4}} \, dx =\)

A die was thrown \( n \) times until the lowest number on the die appeared. If the mean is \( \frac{n}{g} \), then what is the value of \( n \)?

\(f(x) = \frac{1}{7 - \cos x},\ x \in \mathbb{R}\). Then the range of \(f\) is

Let \(A\) and \(B\) be two finite sets. If \(n(A) = 7\) and the number of relations from \(A\) into \(B\) is 128, then \(n(B) =\)

The domain of the function \(f(x) = \sqrt{7 - 11x}\) is

The value of \((1 + i)^{10}\) is equal to

\(a_{1}, a_{2}, \ldots , a_{10}\) are in G.P., and if \(a_{1} + a_{2} = 6, a_{9} + a_{10} = \frac{3}{128}\) then the common ratio of the G.P. is equal to

Let \(a_{n} = 2^{n - 1}, n = 1, 2, 3, \ldots\) . Then the value of the sum \(\sum_{n = 1}^{20} a_{n}\) is equal to

Let \(z_{1} = \frac{1}{2} +i\frac{\sqrt{3}}{2}\) and \(z_{2} = -\frac{1}{2} -i\frac{\sqrt{3}}{2}\) . If \(w = z_{1} + \bar{z}_{2}\) , then \(\overline{w} =\)

Imaginary parts of \(\left(\frac{3 - 2i}{2i}\right)^2\) is equal to

The value of \(i^{3} + i^{4} + i^{5} + \ldots i^{93}\) , where \(i = \sqrt{-1}\) , is equal to

If \(\cos\left(2\sin^{-1}\alpha\right) = \frac{47}{72}\), where \(0 < \alpha < 1\), then the value of \(\alpha\) is

If \(x \neq 11\) satisfies the inequality \(\frac{2x - 21}{x - 11} \geq 3\), then \(x\) lies in the interval

\(\frac{3\tan 15^{\circ} - \tan^3 15^{\circ}}{1 - 3\tan^2 15^{\circ}}\)