List of top Mathematics Questions

The solution set of the system of inequalities \( 5-4x \leq -7 \) or \( 5-4x \geq 7,\ x \in R \) is

Find the value of \( \displaystyle \lim_{h \to 0} \frac{(a+h)^2 \sin(a+h) - a^2 \sin a}{h} \)

The order of the differential equation \( \frac{d}{dz}\left[\left(\frac{dy}{dz}\right)^3\right]=0 \) is

The solution of \( (x+\log y)dy+ydx=0 \) when \( y(0)=1 \) is

The total cost C(x) in Rupees associated with the production of x units of an item is given by C(x) = \(0.007x^3 - 0.003x^2 + 15x + 400\). The marginal cost when 10 items are produced is:

If $A = \begin{pmatrix} 1 & 2 & 3 \\ 2 & 1 & 1 \\ 1 & 3 & 1 \end{pmatrix}$ and $B = \begin{pmatrix} 2 & 3 & 4 \\ 3 & 2 & 2 \\ 2 & 4 & 2 \end{pmatrix}$, then $\sqrt{|\text{Adj}(AB)|} =$

Find the value of \( x \) in the equation \( 2x + 3 = 7x - 8 \).

Evaluate the following integrals: \[ \int \frac{(x^4 + 1)}{x(2x + 1)^2} \, dx \] and \[ \int \frac{1}{x^4 + 5x^2 + 6} \, dx \]

The domain of the function \( f(x) = \left(\sqrt{8x - x^2 - 7}\right)^{\frac{3}{2}} \) is:

If \(x = \frac{1 + \cos 2\theta}{\tan \theta - \sec \theta}\) and \(y = \frac{\tan \theta + \sec \theta}{\sec^2 \theta}\), then \(\frac{y}{x}\) is equal to:

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

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

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

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