List of top Questions asked in JEE Main- 2019

A simple pendulum oscillating in air has period \(T\). The bob of the pendulum is completely immersed in a non-viscous liquid. The density of the liquid is 1/16 th of the material of the bob. If the bob is inside liquid all the time, its period of oscillation in this liquid is :

The total number of turns and cross-section area in a solenoid is fixed. However, its length \(L\) is varied by adjusting the separation between windings. The inductance of solenoid will be proportional to :

A stationary horizontal disc is free to rotate about its axis. When a torque is applied on it, its kinetic energy as a function of \(\theta\), where \(\theta\) is the angle by which it has rotated, is given as \(k\theta^2\). If its moment of inertia is \(I\) then the angular acceleration of the disc is :

The electric field of light wave is given as
\(\vec{E}=10^{-3}\cos\left(\frac{2\pi x}{5\times10^{-7}}-2\pi\times6\times10^{14}t\right)\hat{x}\ \frac{\mathrm{N}}{C}\)
This light falls on a metal plate of work function 2 eV. The stopping potential of the photoelectrons is :
Given, \(E\) (in eV) \(=12375/\lambda\) (in \(\mathrm{\AA}\))

The figure shows a Young's double slit experimental setup. It is observed that when a thin transparent sheet of thickness \(t\) and refractive index \(\mu\) is put in front of one of the slits, the central maximum gest shifted by a distance equal to \(n\) fringe widths. If the wavelength of light used is \(\lambda\), \(t\) will be :

The following bodies are made to roll up (without slipping) the same inclined plane from a horizontal plane. : (i) a ring of radius \(R\), (ii) a solid cylinder of radius \(R/2\) and (iii) a solid sphere of radius \(R/4\). If in each case, the speed of the centre of mass at the bottom of the incline is same, the ratio of the maximum heights they climb is :

In the density measurement of a cube, the mass and edge length are measured as \((10.00\pm0.10)\) kg and \((0.10\pm0.01)\) m, respectively. The error in the measurement of density is :

A moving coil galvanometer has resistance \(50\ \Omega\) and it indicates full deflection at 4 mA current. A voltmeter is made using this galvanometer and a \(5\ \mathrm{k\Omega}\) resistance. The maximum voltage, that can be measured using this voltmeter, will be close to :

A wire of resistance \(R\) is bent to form a square ABCD as shown in the figure. The effective resistance between E and C is : (E is mid-point of arm CD)

A system of three charges are placed as shown in the figure :

If \(D \gg d\), the potential energy of the system is best given by :

A concave mirror for face viewing has focal length of 0.4 m. The distance at which you hold the mirror from your face in order to see your image upright with a magnification of 5 is :

A rectangular coil (Dimension \(5\ \mathrm{cm} \times 2.5\ \mathrm{cm}\)) with 100 turns, carrying a current of 3 A in the clock-wise direction is kept centered at the origin and in the X-Z plane. A magnetic field of 1 T is applied along X-axis. If the coil is tilted through \(45^\circ\) about Z-axis, then the torque on the coil is :

Following figure shows two processes A and B for a gas. If \(\Delta Q_A\) and \(\Delta Q_B\) are the amount of heat absorbed by the system in two cases, and \(\Delta U_A\) and \(\Delta U_B\) are changes in internal energies, respectively, then :

Taking the wavelength of first Balmer line in hydrogen spectrum (n = 3 to n = 2) as 660 nm, the wavelength of the 2nd Balmer line (n = 4 to n = 2) will be :

A string is clamped at both the ends and it is vibrating in its 4th harmonic. The equation of the stationary wave is \(Y = 0.3\sin(0.157x)\cos(200\pi t)\). The length of the string is : (All quantities are in SI units.)

For a given gas at 1 atm pressure, rms speed of the molecule is 200 m/s at \(127^\circ\mathrm{C}\). At 2 atm pressure and at \(227^\circ\mathrm{C}\), the rms speed of the molecules will be :

The pressure wave, \(P = 0.01\sin[1000t - 3x]\ \mathrm{Nm^{-2}}\), corresponds to the sound produced by a vibrating blade on a day when atmospheric temperature is \(0^\circ\mathrm{C}\). On some other day, when temperature is T, the speed of sound produced by the same blade and at the same frequency is found to be \(336\ \mathrm{ms^{-1}}\). Approximate value of T is

A plane passing through the points \((0, -1, 0)\) and \((0, 0, 1)\) and making an angle \(\frac{\pi}{4}\) with the plane \(y - z + 5 = 0\), also passes through the point

If the line, \(\frac{x-1}{2} = \frac{y+1}{3} = \frac{z-2}{4}\) meets the plane, \(x + 2y + 3z = 15\) at a point P, then the distance of P from the origin is :

If the line \(y = mx + 7\sqrt{3}\) is normal to the hyperbola \(\frac{x^2}{24} - \frac{y^2}{18} = 1\), then a value of \(m\) is :

If the tangent to the curve, \(y = x^3 + ax - b\) at the point \((1, -5)\) is perpendicular to the line, \(-x + y + 4 = 0\), then which one of the following points lies on the curve ?

Let \(S = \{\theta \in [-2\pi, 2\pi] : 2\cos^2\theta + 3\sin\theta = 0\}\). Then the sum of the elements of S is

Let S be the set of all values of x for which the tangent to the curve \(y = f(x) = x^3 - x^2 - 2x\) at \((x, y)\) is parallel to the line segment joining the points \((1, f(1))\) and \((-1, f(-1))\), then S is equal to :

If the function \(f\) defined on \(\left(\frac{\pi}{6},\frac{\pi}{3}\right)\) by \(f(x)=\begin{cases}\dfrac{\sqrt2\cos x-1}{\cot x-1},&x\ne\dfrac{\pi}{4}\\ k,&x=\dfrac{\pi}{4}\end{cases}\) is continuous, then \(k\) is equal to

Let the sum of the first \(n\) terms of a non-constant A.P., \(a_1,a_2,a_3,\dots\) be \(50n+\frac{n(n-7)}{2}A\), where \(A\) is a constant. If \(d\) is the common difference of this A.P., then the ordered pair \((d,a_{50})\) is equal to