List of top Questions asked in JEE Main

A moving coil galvanometer of resistance $100\,\Omega$ shows a full scale deflection for a current of $1\,\text{mA}$. The value of resistance required to convert this galvanometer into an ammeter, showing full scale deflection for a current of $5\,\text{mA}$, is ________ $\Omega$.

A 1 m long metal rod AB completes the circuit as shown in figure. The area of circuit is perpendicular to the magnetic field of 0.10 T. If the resistance of the total circuit is 2 $\Omega$ then the force needed to move the rod towards right with constant speed (v) of 1.5 m/s is _____ N.

Identify the correct truth table of the given logic circuit.

The given circuit works as:

In a double slit experiment the distance between the slits is 0.1 cm and the screen is placed at 50 cm from the slits plane. When one slit is covered with a transparent sheet having thickness t and refractive index n(=1.5), the central fringe shifts by 0.2 cm. The value of t is_________ cm.

If an alpha particle with energy 7.7 MeV is bombarded on a thin gold foil, the closest distance from nucleus it can reach is_____ m.
(Atomic number of gold = 79 and $\frac{1}{4\pi\epsilon_0}=9\times10^{9}$ SI units)

A flexible chain of mass $m$ hangs between two fixed points at the same level. The inclination of the chain with the horizontal at the two points of support is $30^\circ$. Considering the equilibrium of each half of the chain, the tension of the chain at the lowest point is ________.

In a vernier callipers, 50 vernier scale divisions are equal to 48 main scale divisions. If one main scale division = 0.05 mm, then the least count of the vernier callipers is ________ mm.

Two identical thin rods of mass M kg and length L m are connected as shown in figure. Moment of inertia of the combined rod system about an axis passing through point P and perpendicular to the plane of the rods is $\frac{x}{12} ML^2$ kg m$^2$. The value of x is ______ .

A collimated beam of light of diameter 2 mm is propagating along the x-axis. The beam is required to be expanded into a collimated beam of diameter 14 mm using a system of two convex lenses. If the first lens has focal length 40 mm, then the focal length of the second lens is_____ mm.

10 mole of oxygen is heated at constant volume from 30 $^{\circ}$C to 40 $^{\circ}$C. The change in the internal energy of the gas is_____ cal.
(The molecular specific heat of oxygen at constant pressure, $C_p=7$ cal/mol $^{\circ}$C and $R=2$ cal/mol $^{\circ}$C.)

Consider the following reactions.
$PbCl_2 + K_2CrO_4 \rightarrow A + 2KCl$ (Hot solution)
$A + NaOH \rightarrow B + Na_2CrO_4$
$PbSO_4 + 4CH_3COONH_4 \rightarrow (NH_4)_2SO_4 + X$
In the above reactions, A, B and X are respectively:

Two identical circular loops $P$ and $Q$ each of radius $r$ are lying in parallel planes such that they have common axis. The current through $P$ and $Q$ are $I$ and $4I$ respectively in clockwise direction as seen from $O$. The net magnetic field at $O$ is:

If the mean and the variance of the data

are $\mu$ and 19 respectively, then the value of $\lambda + \mu$ is

An equilateral triangle OAB is inscribed in the parabola $y^2 = 4x$ with the vertex O at the vertex of the parabola. Then the minimum distance of the circle having AB as a diameter from the origin is

The fifth harmonic of a closed organ pipe is found to be in unison with the first harmonic of an open pipe. The ratio of lengths of closed pipe to that of the open pipe is $ \frac{5}{x} $. The value of $ x $ is ________.

In case of vertical circular motion of a particle by a thread of length $ r $, if the tension in the thread is zero at an angle $30^\circ$ as shown in the figure, the velocity at the bottom point (A) of the vertical circular path is ( $ g $ = gravitational acceleration ).

The least value of $(\cos^2 \theta - 6\sin \theta \cos \theta + 3\sin^2 \theta + 2)$ is

Distance between an object and three times magnified real image is 40 cm. The focal length of the mirror used is ________ cm.

The area of the region enclosed between the circles $x^2 + y^2 = 4$ and $x^2 + (y - 2)^2 = 4$ is:

Bag A contains 9 white and 8 black balls, while bag B contains 6 white and 4 black balls. One ball is picked from B and put in A. Then a ball is drawn from A. Probability it is white is $p/q$. Find $p+q$.

Points of intersection of ellipses $x^2 + 2y^2 - 6x - 12y + 23 = 0$ and $4x^2 + 2y^2 - 20x - 12y + 35 = 0$ lie on a circle. Value of $ab + 18r^2$ is

The velocity ($v$) – distance ($x$) graph is shown in the figure. Which graph represents acceleration ($a$) versus distance ($x$) variation of this system?

The binding energy for the following nuclear reactions are expressed in MeV.
\[ {}^{3}_{2}\text{He} + {}^{1}_{0}\text{n} \rightarrow {}^{4}_{2}\text{He} + 20 \text{ MeV} \] \[ {}^{4}_{2}\text{He} + {}^{1}_{0}\text{n} \rightarrow {}^{5}_{2}\text{He} - 0.9 \text{ MeV} \] If $ X_3, X_4, X_5 $ denote the stability of $ {}^{3}_{2}\text{He}, {}^{4}_{2}\text{He} $ and $ {}^{5}_{2}\text{He} $, respectively, then the correct order is:

Rhombus vertices A(1,2), C(-3,-6). Line AD parallel to $7x-y=14$. Find $|\alpha+\beta+\gamma+\delta|$.