List of top Questions asked in JEE Main

A capacitor is made of two square plates each of side $'a'$ making a very small angle a between them, as shown in figure. The capacitance will be close to :

A galvanometer of resistance $G$ is converted into a voltmeter of range $0-1 V$ by connecting a resistance $R _{1}$ in series with it. The additional resistance that should be connected in series with $R _{1}$ to increase the range of the voltmeter to $-2 V$ will be :

A particle is moving unidirectionally on a horizontal plane under the action of a constant power supplying energy source. The displacement (s) - time (t) graph that describes the motion of the particle is (graphs are drawn schematically and are not to scale) :

A 60 HP electric motor lifts an elevator having a maximum total load capacity of 2000 kg. If the frictional force on the elevator is 4000 N, the speed of the elevator at full load is close to : ($1 \,HP = 746 \,W, \,g = 10\, ms^{-2}$ )

Two particles of equal mass m have respective initial velocities $u\hat{i}$ and $u\left(\frac{\hat{i}+\hat{j}}{2}\right).$ They collide completely inelastically. The energy lost in the process is :

A sound source \(S\) is moving along a straight track with speed \(v ,\) and is emitting sound of frequency \(v_{0}\) (see figure). An observer is standing at a finite distance, at the point \(O ,\) from the track. The time variation of frequency heard by the observer is best represented by : 
\(\left( t _{0}\right.\) represents the instant when the distance between the source and observer is minimum)

A wire of length $L$ and mass per unit length $6.0 \times 10^{-3} \,kgm^{-1}$ is put under tension of $540\, N$. Two consecutive frequencies that it resonates at are: $420\, Hz$ and $490 \,Hz$. Then $L$ in meters is :

If $L=\sin ^{2}\left(\frac{\pi}{16}\right)-\sin ^{2}\left(\frac{\pi}{8}\right)$ and $M=\cos ^{2}\left(\frac{\pi}{16}\right)-\sin ^{2}\left(\frac{\pi}{8}\right),$ then :

$\displaystyle \lim_{x \to 1}$$\left\{log_{e}\left(e^{x\left(x-1\right)}-e^{x\left(1-x\right)}\right)-log_{e}\left(4x\left(x-1\right)\right)\right\}$ is equal to :

The length of a potentiometer wire is $1200\, cm$ and it carries a current of $60\, mA$. For a cell of emf $5\, V$ and internal resistance of $20 \, \Omega$, the null point on it is found to be at $1000\, cm$. The resistance of whole wire is :

A charge $Q$ is distributed over two concentric conducting thin spherical shells radii $r$ and $R$ $( R > r )$. If the surface charge densities on the two shells are equal, the electric potential at the common centre is :

For following reactions ${A ->[700\,K][] Product}$ ${A ->[500\,K][{\text{catalyst}}] Product}$ it was found that the $E_a$ is decreased by 30 k J/mol in the presence of catalyst. If the rate remains unchanged, the activation energy for catalysed reaction is (Assume pre exponential factor is same):

A particle of charge $q$ and mass $m$ is subjected to an electric field $E = E _{0}\left(1- ax ^{2}\right)$ in the $x$ -direction, where a and $E_{0}$ are constants. Initially the particle was at rest at $x=0$. Other than the initial position the kinetic energy of the particle becomes zero when the distance of the particle from the origin is :

The de Broglie wavelength of an electron in the $4^{th}$ Bohr orbit is :

Identify the correct output signal $Y$ in the given combination of gates (as shown) for the given inputs $A$ and $B$.

Complex X of composition $Cr(H_2O)_6Cl_n$ has a spin only magnetic moment of 3.83 BM. It reacts with $AgNO_3$ and shows geometrical isomerism. The IUPAC nomenclature of X is :

If the potential energy between two molecules is given by $U = - \frac{ A }{ r ^{6}}+\frac{ B }{ r ^{12}},$ then at equilibrium, separation between molecules, and the potential energy are :

A cube of metal is subjected to a hydrostatic pressure of $4 \,GPa$. The percentage change in the length of the side of the cube is close to (Given bulk modulus of metal, $\left. B =8 \times 10^{10} Pa \right)$

An electrical power line, having a total resistance of $2\Omega,$ delivers $1\, kW$ at $220\, V$. The efficiency of the transmission line is approximately:

A sample of red ink (a colloidal suspension) is prepared by mixing eosin dye, egg white, $HCHO $ and water. The component which ensures stability of the ink sample is :-

Let f(x) be a quadratic polynomial such that f(–1) + f(2) = 0. If one of the roots of f(x) = 0 is 3, then its other root lies in :

Let $f :(-1, \infty) \rightarrow R$ be defined by $f (0)=1$ and $f ( x )=\frac{1}{ x } \log _{ e }(1+ x ), x \neq 0 .$ Then the function $f$

Consider two ideal diatomic gases $A$ and $B$ at some temperature $T$. Molecules of the gas A are rigid , and have an mass $m$. Molecules of the gas $B$ have an additional vibrational mode, and have a mass $\frac{m}{4}.$ The ratio of the specific heats $(C^{A}_{V}$ and $C^{B}_{V})$ of gas $A$ and $B$, respectively is :

The coordinates of centre of mass of a uniform flag shaped lamina (thin flat plate) of mass $4\, kg$. (The coordinates of the same are shown in figure) are :

The electronic configurations of bivalent europium and trivalent cerium are : (atomic number: $Xe = 54, Ce =58, Eu ??63$)