List of top Mathematics Questions

When a current changes at the rate of $30\ \text{A s}^{-1}$, the induced emf is $12\ \text{V}$. The self-inductance of the coil is:

If an inductor coil of self-inductance 2 H stores 25 J of magnetic energy, then the current I passing through it is:

Which one is not a ferromagnetic material?

Two charged particles of same mass but charges in ratio 1:4 enter a uniform perpendicular magnetic field. The ratio of their time periods is:

A coil having 100 turns and area $0.02\ \text{m}^{2}$ is placed perpendicular to a magnetic field of $1\ \text{Wb m}^{-2}$. The magnetic flux linked with the coil is:

A wire of $25\ \Omega$ resistance is cut into n pieces of equal length. If these pieces are connected in parallel, the equivalent resistance is $1\ \Omega$, then n is:

The resistance of a wire at $30^{\circ}\text{C}$ and $40^{\circ}\text{C}$ are respectively $5\ \Omega$ and $6\ \Omega$. The temperature coefficient of resistance is:

The value of R in the given circuit is:

The equivalent capacitance of n capacitors of equal capacitance when connected in series and parallel are respectively $0.4\ \mu F$ and $10\ \mu F$. The capacitance of each capacitor is:

A charge of 5 C is moved from a point P to another point Q by doing a work of 10 J. If the potential at P is 0.5 V, then the potential at Q is:

The maximum value of the objective function $z=2x+3y$, when the corner points of the feasible region are (0, 0), (5, 0), (4, 1) and (0, 2), is:

The elimination of arbitrary constants $c_{1}, c_{2}, c_{3}, c_{4}$ from $y=(c_{1}+c_{2})\sin(x+c_{3})-c_{4}e^{x}$ gives a differential equation of order:

If $\frac{dy}{dx} = \frac{1}{8\left(\sqrt{16+\sqrt{25+\sqrt{x}}}\right)\left(\sqrt{25+\sqrt{x}}\right)\sqrt{x}}$, then $y =$

$\int_{-2}^{2}|x+3|\,dx =$

$\int_{0}^{\frac{\pi}{2}}\frac{1}{1+\sin x}\,dx =$

Given that $\int_{0}^{1}\tan^{-1}(t)\,dt = \frac{\pi}{4} - \frac{1}{2}\log 2$, then $\int_{0}^{1}\tan^{-1}(1-t)\,dt =$

The area bounded by $y=x-1$, $1\le x\le 2$, $y=0$ (in sq.units) is

$\int e^{\left(x+\frac{1}{x}\right)}\left(\frac{x^{2}-1}{x^{2}}\right)dx =$

$\int e^{2\theta}(2\cos^{2}\theta-\sin 2\theta)\, d\theta =$

$\int \frac{9e^{x}+4e^{-x}}{9e^{x}-4e^{-x}}dx =$

$\int \frac{\sec x}{(\sec x+\tan x)^{9}}dx =$

If $\int \frac{1}{x^{7}\left(\frac{1}{x^{8}}+1\right)^{p}}dx = -\frac{1}{2}\left(\frac{1}{\frac{1}{x^{8}}+1}\right)^{2} + c$, then $p =$

If $a+b=10$ and $ab$ is maximum, then the value of a is

The distance travelled by a moving particle is given by $s=\frac{t^{2}}{2}-6t+8$, where $t$ denotes the time in seconds. The velocity becomes zero when $t$ is equal to:

Let $f(x)=10-|x-3|,\; x\in\mathbb{R}$. The maximum of $f(x)$ occurs at: