List of top Questions asked in JEE Main

Orbits of a particle moving in a circle are such that the perimeter of the orbit equals an integer number of de-Broglie wavelengths of the particle. For a charged particle moving in a plane perpendicular to a magnetic field, the radius of the \(n^{\mathrm{th}}\) orbital will therefore be proportional to :

This question has Statement-1 and Statement-2. Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement-1: In Young's double slit experiment, the number of fringes observed in the field of view is small with longer wavelength of light and is large with shorter wavelength of light.
Statement-2: In the double slit experiment the fringe width depends directly on the wavelength of light.

This question has Statement-1 and Statement-2. Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement-1: Short wave transmission is achieved due to the total internal reflection of the e-m wave from an appropriate height in the ionosphere.
Statement-2: Refractive index of a plasma is independent of the frequency of e-m waves.

An LCR circuit as shown in the figure is connected to a voltage source \(V_{ac}\) whose frequency can be varied.

(Circuit: inductor 24 H, capacitor 2 \(\mu\)F and resistor 15 \(\Omega\) in series with the source \(V_{ac} = V_0 \sin\omega t\); a voltmeter V is connected across the resistor.)
The frequency, at which the voltage across the resistor is maximum, is :

In a series L - C - R circuit, \(C = 10^{-11}\) Farad, \(L = 10^{-5}\) Henry and \(R = 100\) Ohm, when a constant D.C. voltage \(E\) is applied to the circuit, the capacitor acquires a charge \(10^{-9}\) C. The D.C. source is replaced by a sinusoidal voltage source in which the peak voltage \(E_0\) is equal to the constant D.C. voltage \(E\). At resonance the peak value of the charge acquired by the capacitor will be :

A dc source of emf \(E_1=100\) V and internal resistance \(r=0.5\ \Omega\), a storage battery of emf \(E_2=90\) V and an external resistance R are connected as shown in figure. For what value of R no current will pass through the battery?

To find the resistance of a galvanometer by the half deflection method the following circuit is used with resistances \(R_1=9970\ \Omega\), \(R_2=30\ \Omega\) and \(R_3=0\). The deflection in the galvanometer is d. With \(R_3=107\ \Omega\) the deflection changed to \(\frac d2\). The galvanometer resistance is approximately:

A and B are two sources generating sound waves. A listener is situated at C. The frequency of the source at A is 500 Hz. A, now, moves towards C with a speed 4 m/s. The number of beats heard at C is 6. When A moves away from C with speed 4 m/s, the number of beats heard at C is 18. The speed of sound is 340 m/s.

The frequency of the source at B is :

A mass \(m=1.0\) kg is put on a flat pan attached to a vertical spring fixed on the ground. The mass of the spring and the pan is negligible. When pressed slightly and released, the mass executes simple harmonic motion. The spring constant is 500 N/m. What is the amplitude A of the motion, so that the mass \(m\) tends to get detached from the pan ? (Take \(g=10\ \mathrm{m/s^2}\) ). The spring is stiff enough so that it does not get distorted during the motion.

A point charge of magnitude \(+1\,\mu\mathrm{C}\) is fixed at \((0,0,0)\). An isolated uncharged spherical conductor, is fixed with its center at \((4,0,0)\). The potential and the induced electric field at the centre of the sphere is :

A current \(i\) is flowing in a straight conductor of length \(L\). The magnetic induction at a point on its axis at a distance \(\frac{L}{4}\) from its centre will be :

A ball projected from ground at an angle of \(45^\circ\) just clears a wall in front. If point of projection is 4 m from the foot of wall and ball strikes the ground at a distance of 6 m on the other side of the wall, the height of the wall is :

Given two independent events, if the probability that exactly one of them occurs is \(\frac{26}{49}\) and the probability that none of them occurs is \(\frac{15}{49}\), then the probability of more probable of the two events is :

A body starts from rest on a long inclined plane of slope \(45^\circ\). The coefficient of friction between the body and the plane varies as \(\mu=0.3x\), where \(x\) is distance travelled down the plane. The body will have maximum speed (for \(g=10\ \mathrm{m/s^2}\)) when \(x=\)

The change in the value of acceleration of earth towards sun, when the moon comes from the position of solar eclipse to the position on the other side of earth in line with sun is: (mass of the moon \(=7.36\times10^{22}\) kg, radius of the moon's orbit \(=3.8\times10^{8}\) m ).

Given that 1 g of water in liquid phase has volume 1 cm\(^3\) and in vapour phase 1671 cm\(^3\) at atmospheric pressure and the latent heat of vaporization of water is 2256 J/g; the change in the internal energy in joules for 1 g of water at 373 K when it changes from liquid phase to vapour phase at the same temperature is :

A certain amount of gas is taken through a cyclic process (A B C D A) that has two isobars, one isochore and one isothermal. The cycle can be represented on a \(P-V\) indicator diagram as :

Let Q be the foot of perpendicular from the origin to the plane \(4x-3y+z+13=0\) and R be a point \((-1,-6)\) on the plane. Then length QR is :

If \(\hat a,\ \hat b\) and \(\hat c\) are unit vectors satisfying \(\hat a-\sqrt3\,\hat b+\hat c=\vec 0\), then the angle between the vectors \(\hat a\) and \(\hat c\) is :

The integral \(\int_{7\pi/4}^{7\pi/3}\sqrt{\tan^2x}\,dx\) is equal to :

The area of the region (in sq. units), in the first quadrant bounded by the parabola \(y=9x^2\) and the lines \(x=0,\ y=1\) and \(y=4\), is :

Consider the differential equation :
\(\frac{dy}{dx}=\frac{y^3}{2(xy^2-x^2)}\)
Statement-1: The substitution \(z=y^2\) transforms the above equation into a first order homogenous differential equation.
Statement-2: The solution of this differential equation is \(y^2e^{-y^2}/x=C\).

Statement-1: The function \(x^2(e^x+e^{-x})\) is increasing for all \(x \gt 0\).
Statement-2: The functions \(x^2e^x\) and \(x^2e^{-x}\) are increasing for all \(x \gt 0\) and the sum of two increasing functions in any interval \((a,b)\) is an increasing function in \((a,b)\).

For \(a \gt 0,\ t \in \left(0, \dfrac{\pi}{2}\right)\), let \(x = \sqrt{a^{\sin^{-1}t}}\) and \(y = \sqrt{a^{\cos^{-1}t}}\), Then, \(1 + \left(\dfrac{dy}{dx}\right)^2\) equals :

If the system of linear equations :
\(x_1 + 2x_2 + 3x_3 = 6\)
\(x_1 + 3x_2 + 5x_3 = 9\)
\(2x_1 + 5x_2 + ax_3 = b\)
is consistent and has infinite number of solutions, then :