List of top Questions asked in JEE Main

For the given cell :
\(\mathrm{Cu(s)\,|\,Cu^{2+}(C_1\,M)\,||\,Cu^{2+}(C_2\,M)\,|\,Cu(s)}\)
change in Gibbs energy (\(\Delta G\)) is negative, if :
Which one of the following statements is not true?
The value of \(K_C\) is 64 at 800 K for the reaction
\(\mathrm{N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)}\)
The value of \(K_C\) for the following reaction is :
\(\mathrm{NH_3(g) \rightleftharpoons \frac{1}{2}N_2(g) + \frac{3}{2}H_2(g)}\)
For a \(\mathrm{d^4}\) metal ion in an octahedral field, the correct electronic configuration is :
For a reaction,
\(4\mathrm{M(s)}+n\mathrm{O_2(g)}\rightarrow2\mathrm{M_2O_n(s)}\)
the free energy change is plotted as a function of temperature. The temperature below which the oxide is stable could be inferred from the plot as the point at which :
The output characteristics of a transistor is shown in the figure.

When VCE is 10 V and IC = 4.0 mA, then value of \(\beta_{ac}\) is __________.
The centre of mass of solid hemisphere of radius 8 cm is x from the centre of the flat surface. Then value of x is __________.
In a series LR circuit, power of 400 W is dissipated from a source of 250 V, 50 Hz. The power factor of the circuit is 0.8. In order to bring the power factor to unity, a capacitor of value C is added in series to the L and R. Taking the value of C as \(\left(\frac{n}{3\pi}\right)\mu\)F, then value of n is __________.
For a plane electromagnetic wave, the magnetic field at a point x and time t is
\(\vec{B}(x,t)=\left[1.2\times10^{-7}\sin\left(0.5\times10^{3}x+1.5\times10^{11}t\right)\hat{k}\right]\) T
The instantaneous electric field \(\vec{E}\) corresponding to \(\vec{B}\) is :
(speed of light c = \(3\times10^{8}\) ms\(^{-1}\))
A Young's double-slit experiment is performed using monochromatic light of wavelength \(\lambda\). The intensity of light at a point on the screen, where the path difference is \(\lambda\), is K units. The intensity of light at a point where the path difference is \(\frac{\lambda}{6}\) is given by \(\frac{nK}{12}\), where n is an integer. The value of n is __________.
In the figure shown, the current in the 10 V battery is close to :
A student measuring the diameter of a pencil of circular cross-section with the help of a vernier scale records the following four readings 5.50 mm, 5.55 mm, 5.45 mm, 5.65 mm. The average of these four readings is 5.5375 mm and the standard deviation of the data is 0.07395 mm. The average diameter of the pencil should therefore be recorded as :
A particle moving in the xy plane experiences a velocity dependent force \(\vec F=k\left(v_y\hat i+v_x\hat j\right)\), where \(v_x\) and \(v_y\) are the x and y components of its velocity \(\vec v\). If \(\vec a\) is the acceleration of the particle, then which of the following statements is true for the particle?
When a car is at rest, its driver sees rain drops falling on it vertically. When driving the car with speed \(v\), he sees that rain drops are coming at an angle \(60^\circ\) from the horizontal. On further increasing the speed of the car to \((1+\beta)v\), this angle changes to \(45^\circ\). The value of \(\beta\) is close to :
Consider the force \(F\) on a charge \(q\) due to a uniformly charged spherical shell of radius \(R\) carrying charge \(Q\) distributed uniformly over it. Which one of the following statements is true for \(F\), if \(q\) is placed at distance \(r\) from the centre of the shell?
A fluid is flowing through a horizontal pipe of varying cross-section, with speed \(v\ \mathrm{ms^{-1}}\) at a point where the pressure is \(P\) pascal. At another point where pressure is \(\dfrac{P}{2}\) Pascal its speed is \(V\ \mathrm{ms^{-1}}\). If the density of the fluid is \(\rho\ \mathrm{kg\,m^{-3}}\) and the flow is streamline, then \(V\) is equal to :
In a dilute gas at pressure \(P\) and temperature \(T\), the mean time between successive collisions of a molecule varies with \(T\) as :
When a particle of mass \(m\) is attached to a vertical spring of spring constant \(k\) and released, its motion is described by \(y(t)=y_0\sin^2\omega t\), where \(y\) is measured from the lower end of unstretched spring. Then \(\omega\) is :
Two identical electric point dipoles have dipole moments \(\vec{p}_1=p\hat{i}\) and \(\vec{p}_2=-p\hat{i}\) and are held on the x axis at distance \(a\) from each other. When released, they move along the x-axis with the direction of their dipole moments remaining unchanged. If the mass of each dipole is \(m\), their speed when they are infinitely far apart is :
The linear mass density of a thin rod AB of length \(L\) varies from A to B as \(\lambda(x)=\lambda_0\left(1+\dfrac{x}{L}\right)\), where \(x\) is the distance from A. If \(M\) is the mass of the rod then its moment of inertia about an axis passing through A and perpendicular to the rod is :
A circuit to verify Ohm's law uses ammeter and voltmeter in series or parallel connected correctly to the resistor. In the circuit :
Particle A of mass \(m_1\) moving with velocity \((\sqrt3\,\hat i+\hat j)\ \mathrm{ms^{-1}}\) collides with another particle B of mass \(m_2\) which is at rest initially. Let \(\vec V_1\) and \(\vec V_2\) be the velocities of particles A and B after collision respectively. If \(m_1=2m_2\) and after collision \(\vec V_1=(\hat i+\sqrt3\,\hat j)\), the angle between \(\vec V_1\) and \(\vec V_2\) is :
A double convex lens has power \(P\) and same radii of curvature \(R\) of both the surfaces. The radius of curvature of a surface of a plano-convex lens made of the same material with power \(1.5\,P\) is :
A square loop of side \(2a\) and carrying current I is kept in xz plane with its centre at origin. A long wire carrying the same current I is placed parallel to z-axis and passing through point \((0, b, 0)\), \((b \gt\gt a)\). The magnitude of torque on the loop about z-axis will be :
Three rods of identical cross-section and lengths are made of three different materials of thermal conductivity \(K_1\), \(K_2\) and \(K_3\), respectively. They are joined together at their ends to make a long rod (see figure). One end of the long rod is maintained at \(100^\circ\mathrm{C}\) and the other at \(0^\circ\mathrm{C}\) (see figure). If the joints of the rod are at \(70^\circ\mathrm{C}\) and \(20^\circ\mathrm{C}\) in steady state and there is no loss of energy from the surface of the rod, the correct relationship between \(K_1\), \(K_2\) and \(K_3\) is :