List of top Questions asked in KEAM

The minimum of $f(x) = \dfrac{x^{100} - 1}{x^{100} + 1}, \; x \in \mathbb{R}$ is:

The geometry of a molecule of type $AB_3E_2$ with 3 bonding pairs and 2 lone pairs is

Which of the following statements are correct about the $PCl_5$ molecule? (i) It has trigonal bipyramidal geometry.
(ii) It has three equatorial and two axial bonds.
(iii) The equatorial bond pairs suffer more repulsive interaction from the axial bond pair.
(iv) The equatorial bonds are slightly weaker than axial bonds.
(v) The hybridization involved in the molecule is $sp^3d$.

Which of the following pair of elements have greater ability to form $p\pi - p\pi$ multiple bonds?

The rate of fall of the voltage across the capacitor in a filter used in a diode rectifier depends

The radius of innermost orbit of an electron in the hydrogen atom is $0.53\,\text{\AA}$. Then, the radius of the 3rd electron orbit is:

The minimum energy required to remove an electron from sodium atom is $3.313 \times 10^{-19}J$. What is the maximum wavelength of radiation that will eject photoelectron from sodium metal? ($h = 6.626 \times 10^{-34}Js$)

Which of the following statements are correct about the postulates of quantum mechanical model of an atom? (i) The energy of electron in atom is quantized.
(ii) The existence of quantized electronic energy level is a result of the particle property of electrons.
(iii) The path of the electron can be determined accurately.
(iv) In a multi electron atom, the electrons are filled in various orbitals in the order of increasing energy.
(v) The probability of finding an electron at a point within an atom is proportional to the square of the orbital wave function.

What is the volume of methanol needed for making $2\,L$ of $0.4\,M$ solution? (Density of methanol $= 0.64\,kg\,L^{-1}$ and molar mass $= 32\,g\,mol^{-1}$)

The energy released by $2.35\,g$ of $^{235}U$ by fission in a nuclear reactor (in $MeV$) is (Average energy released per fission is $200\,MeV$):

In a silicon crystal containing $N$ atoms, at absolute zero the $4N$ energy states of

A wire of certain length carrying current $I$, when bent into a circular coil of single turn produces a magnetic field $B$ at its centre. If the same wire is bent into a circular coil of 3 turns and it carries the same current, then the magnetic field at the centre of the coil is

The intensity of the transmitted light after passing through a first polaroid $P_1$ is $I_0$. If the second polaroid $P_2$ is rotated through an angle of $45^\circ$ with respect to $P_1$, then the change in the intensity of the transmitted light after passing through the second polaroid is

If the threshold wavelengths of two metals are in the ratio $1:3$, then the work functions of these metals are in the ratio

The order of the electric field required to pull out electrons from a metal by field emission (in $Vm^{-1}$) is

The magnifying power of a simple microscope can be increased by using

When a bar magnet placed parallel to the magnetic field is rotated by $45^\circ$, the amount of work done is $2.07J$. The amount of work to be done to rotate the magnet further by $45^\circ$ is

A real object is placed at distance $f$ in front of a convex mirror of focal length $f$. The image will be formed at a distance

The law that is a symmetrical counterpart of Faraday’s law of electromagnetic induction is

The r.m.s current of an alternating current given by $i = 4\sqrt{2}\sin \omega t + 3\sqrt{2}\cos \omega t$ is:

If an air core solenoid with self-inductance of $0.5\,mH$ is filled with soft iron of relative permeability of $1500$, its self-inductance becomes

For an electron of mass $m_e$ and charge $e$ revolving around the nucleus of an atom, the ratio of its angular momentum to magnetic moment is

Two charged particles $2q$ and $q$ having equal momentum enter a uniform magnetic field in a direction perpendicular to the magnetic field. Then their respective radii of circular paths $r_1$ and $r_2$ are in the ratio

Elimination of arbitrary constants $A$ and $B$ from $y = Ae^x + Be^{-2x}$ gives the differential equation:

Consider the Linear Programming Problem (LPP): Maximize $z = 30x + 60y$ subject to constraints $x + 2y \leq 12$, $2x + y \leq 12$, $4x + 5y \geq 20$, $x \geq 0$, $y \geq 0$. Then the number of corner points of the feasible region is