List of top Mathematics Questions asked in KEAM

If the numbers \( x, 6, y, 54, 162 \) are in geometric progression, then \( \dfrac{y}{x} \) is equal to

The sum of the geometric series \(\sqrt{3}+\sqrt{12}+\sqrt{48}+\dots\) up to \(10\) terms is

If \( z = \frac{3+i}{2-i} \), then \( z^{-1} \) is equal to

If \( z = 1 + i \tan \theta \), where \( \pi < \theta < \dfrac{3\pi}{2} \), then \( |z| \) is equal to

If \( f(x) = ax + bx^2 \), then the coefficient of \( x^3 \) in \( f(f(x)) \) is

If \(z\) is a complex number, then the minimum value of \(|z-2|+|z-4|\) is

If \(n(A) = 8\), then the number of subsets of \(A\) which contain \(2\) or \(6\) elements is

Let \( A = \{x : x \text{ is a positive multiple of } 2 \text{ less than } 36\},\)
\(B = \{x : x \text{ is a positive multiple of } 3 \text{ greater than } 16\}, \text{ and }\)
\(C = \{x : x \text{ is a positive multiple of } 4 \text{ less than } 42\}. \text{ Then } (A \cap B) \cap C =\)

If \(f(x) = [2x]\), where \([x]\) denotes the greatest integer function in \(x\), then the image of \(\{-2.3, 2.9\}\) is

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:

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:

Which one is not a ferromagnetic material?

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:

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:

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 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:

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:

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

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

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

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