List of top Questions asked in JEE Main

A block kept on a rough inclined plane, as shown in the figure, remains at rest upto a maximum force $2 \,N$ down the inclined plane. The maximum external force up the inclined plane that does not move the block is $10\, N$. The coefficient of static friction between the block and the plane is : [Take $g = 10\, m/s^2$]

A block of mass $10\, kg$ is kept on a rough inclined plane as shown in the figure. A force of $3\, N$ is applied on the block. The coefficient of static friction between the plane and the block is $0.6$. What should be the minimum value of force $P$, such that the block doesnot move downward ? (take $g = 10 \; ms^{-2}$)

A copper wire is wound on a wooden frame, whose shape is that of an equilateral triangle. If the linear dimension of each side of the frame is increased by a factor of 3, keeping the number of turns of the coil per unit length of the frame the same, then the self inductance of the coil :

A $10\, m$ long horizontal wire extends from North East to South West. It is falling with a speed of $5.0\,ms^{-1}$, at right angles to the horizontal component of the earth's magnetic field, of $0.3 \times 10^{-4}\,Wb/m^2$. The value of the induced emf in wire is :

An insulating thin rod of length $\ell$ has a x linear charge density $p(x) = \rho_0 \frac{x}{\ell}$ on it . The rod is rotated about an axis passing through the origin $(x = 0)$ and perpendicular to the rod. If the rod makes n rotations per second, then the time averaged magnetic moment of the rod is :

The figure shows a square loop $L$ of side $5\, cm$ which is connected to a network of resistances. The whole setup is moving towards right with a constant speed of $1\, cms^{-1}$. At some instant, a part of $L$ is in a uniform magnetic field of $1T$, perpendicular to the plane of the loop. If the resistance of $L$ is $1.7\, \Omega$ , the current in the loop at that instant will be close to :

A parallel plate capacitor is of area $6 \; cm^2$ and a separation $3\, mm$. The gap is filled with three dielectric materials of equal thickness (see figure) with dielectric constants $K_1, = 10, K_2 = 12 $ and $K_3 = 14$. The dielectric constant of a material which when fully inserted in above capacitor, gives same capacitance would be :

A parallel plate capacitor with square plates is filled with four dielectrics of dielectric constants $K_1, K_2, K_3, K_4$ arranged as shown in the figure. The effective dielectric constant K will be :

A plane electromagnetic wave of frequency $50\, MHz$ travels in free space along the positive $x$-direction. At a particular point in space and time, $\vec{E} = 6.3 \hat{j} V/m$ . The corresponding magnetic field $\vec{B}$ , at that point will be:

In the circuit shown, find $C$ if the effective capacitance of the whole circuit is to be $0.5 \mu F$. All values in the circuit are in $\mu F$.

In the figure shown, after the switch $'S'$ is turned from position $'A'$ to position $'B'$, the energy dissipated in the circuit in terms of capacitance $'C'$ and total charge $'Q'$ is:

In the figure shown below, the charge on the left plate of the $10 \; \mu F$ capacitor is $-30 \; \mu C$ . The charge on the right plate of the $6 \; \mu F$ capacitor is :

A solid conducting sphere, having a charge $Q$, is surrounded by an uncharged conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface o f the hollow shell be $V$. If the shell is now given a charge of $-4\, Q$, the new potential difference between the same two surfaces is :

In a meter bridge, the wire of length $1\, m$ has a non-uniform cross-section such that, the variation $\frac{dR}{dl}$ of its resistance $R$ with length $l$ is $\frac{dR}{dl} \propto \frac{1}{\sqrt{l}}$. Two equal resistances are connected as shown in the figure. The galvanometer has zero deflection when the jockey is at point $P$. What is the length $AP$ ?

Drift speed of electrons, when $1.5\, A$ of current flows in a copper wire of cross section $5\, mm^2$, is $v$. If the electron density in copper is $9 \times 10^{28} /m^3$ the value of $v$ in mm/s is close to (Take charge of electron to be = $1.6 \times 10^{-19}C$)

An ideal battery of $4\, V$ and resistance $R$ are connected in series in the primary circuit of a potentiometer of length $1\, m$ and resistance $5\Omega$. The value of $R$, to give a potential difference of $5 \,mV$ across $10\, cm$ of potentiometer wire, is :

When the switch $S$, in the circuit shown, is closed, then the value of current $i$ will be :

In the experimental set up of metre bridge shown in the figure, the null point is obtained at a distance of $40\, cm$ from $A$. If a $10 \Omega$ resistor is connected in series with $R_1$, the null point shifts by $10\, cm$. The resistance that should be connected in parallel with $(R_1 + 10)\Omega$ such that the null point shifts back to its initial position is :

In the given circuit, an ideal voltmeter connected across the $10\, \Omega$ resistance reads $2V$. The internal resistance $r$, of each cell is :

In the given circuit diagram, the currents, $I_1 = 0.3\,A, I_4 = 0.8\, A$ and $I_5 = 0.4\, A$, are flowing as shown. The currents $I_2,I_3$ and $I_6$,respectively, are :

In the given circuit the cells have zero internal resistance. The currents (in Amperes) passing through resistance $R_1$, and $R_2$ respectively, are:

The Wheatstone bridge shown in Fig. here, gets balanced when the carbon resistor used as $R_1$ has the colour code ( Orange, Red, Brown). The resistors $R_2$ and $R_4$ are $80\Omega $ and $40 \Omega $ respectively. Assuming that the colour code for the carbon resistors gives their accurate values, the colour code for the carbon resistor, used as $R_3$, would be :

The resistance of the meter bridge $AB$ is given figure is $4\Omega$ . With a cell of emf $\varepsilon = 0.5 \;V $ and rheostat resistance $R_h = 2 \; \Omega$ the null point is obtained at some point $J$. When the cell is replaced by another one of emf $\varepsilon = \varepsilon_2$ the same null point $J$ is found for $R_h = 6 \; \Omega$. The emf $\varepsilon_2$ is;

In the circuit shown, a four-wire potentiometer is made of a $400\, cm$ long wire, which extends between $A$ and $B$. The resistance per unit length of the potentiometer wire is $r = 0.01 $ $\Omega/cm$. If an ideal voltmeter is connected as shown with jockey $J$ at $50\, cm$ from end $A$, the expected reading of the voltmeter will be :

A $2\, W$ carbon resistor is color coded with green, black, red and brown respectively. The maximum current which can be passed through this resistor is :