List of top Questions asked in JEE Main- 2019

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 :

In a line of sight radio communication, a distance of about $50\, km$ is kept between the transmitting and receiving antennas. If the height of the receiving antenna is $70\,m$, then the minimum height of the transmitting antenna should be : (Radius of the Earth = $6.4 \times 10^6 m$).

A rod of mass $'M'$ and length $'2L'$ is suspended at its middle by a wire. It exhibits torsional oscillations; If two masses each of $'m'$ are attached at distance $'L/2'$ from its centre on both sides, it reduces the oscillation frequency by $20\%$. The value of ratio $m/M$ is close to :

In a hydrogen like atom, when an electron jumps from the $M$ - shell to the $L$ - shell, the wavelength of emitted radiation is $\lambda$. If an electron jumps from $N$-shell to the $L$-shell, the wavelength of emitted radiation will be :

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 :

A resonance tube is old and has jagged end. It is still used in the laboratory to determine velocity of sound in air. A tuning fork of frequency $512\, Hz$ produces first resonance when the tube is filled with water to a mark $11\, cm$ below a reference mark, near the open end of the tube. The experiment is repeated with another fork of frequency $256\, Hz$ which produces first resonance when water reaches a mark $27\, cm$ below the reference mark. The velocity of sound in air, obtained in the experiment, is close to:

Two vectors $\vec{A}$ and $\vec{B}$ have equal magnitudes. The magnitude of $(\vec{A} + \vec{B})$ is 'n' times the magnitude of $(\vec{A} - \vec{B})$ . The angle between $\vec{A}$ and $\vec{B}$ is :

Determine the electric dipole moment of the system of three charges, placed on the vertices of an equilateral triangle, as shown in the figure:

A sample of an ideal gas is taken through the cyclic process abca as shown in the figure. The change in the internal energy of the gas along the path ca is $-180\,J$. The gas absorbs $250\, J$ of heat along the path ab and $60\, J$ along the path $bc$. The work done by the gas along the path $abc$ is :

A $15\, g$ mass of nitrogen gas is enclosed in a vessel at a temperature $27^{\circ}C$. Amount of heat transferred to the gas, so that rms velocity of molecules is doubled, is about : [Take R = 8.3 J/ K mole]

A solid sphere and solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both roll without slipping all throughout. The two climb maximum heights $h_{sph}$ and $h_{cyl}$ on the incline. The ratio $\frac{h_{sph}}{h_{cyl}}$ is given by :

A concave mirror has radius of curvature of $40\, cm$. It is at the bottom of a glass that has water filled up to $5\, cm$ (see figure). If a small particle is floating on the surface of water, its image as seen, from directly above the glass, is at a distance d from the surface of water. The value of d is close to : (Refractive index of water $= 1.33$)

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 :

A metal coin of mass $5\,g$ and radius $1\, cm$ is fixed to a thin stick $AB$ of negligible mass as shown in the figure. The system is initially at rest. The constant torque, that will make the system rotate about $AB$ at $25$ rotations per second in $5\, s$, is close to :

A magnetic compass needle oscillates $30$ times per minute at a place where the dip is $45^{\circ}$, and $40$ times per minute where the dip is $30^{\circ}$. If $B_1$ and $B_2$ are respectively the total magnetic field due to the earth at the two places, then the ratio $B_1/B_2$ is best given by :

A block of mass $m$, lying on a smooth horizontal surface, is attached to a spring (of negligible mass) of spring constant $k$. The other end of the spring is fixed, as shown in the figure. The block is initally at rest in its equilibrium position. If now the block is pulled with a constant force $F$, the maximum speed of the block is :

Determine the charge on the capacitor in the following circuit :

Water flows into a large tank with flat bottom at the rate of $10^{-4} \; m^3 s^{-1}$. Water is also leaking out of a hole of area $1\, cm^2$ at its bottom. If the height of the water in the tank remains steady, then this height is :

What is the position and nature of image formed by lens combination shown in figure? $(f_1, f_2$ are focal lengths)

A satellite of mass $M$ is in a circular orbit of radius $R$ about the centre of the earth. A meteorite of the same mass, falling towards the earth, collides with the satellite completely inelastically. The speeds of the satellite and the meteorite are the same, just before the collision. The subsequent motion of the combined body will be :

Two wires $A$ & $B$ are carrying currents $I_1$ & $I_2$ as shown in the figure. The separation between them is $d$. A third wire $C$ carrying a current $I$ is to be kept parallel to them at a distance $x$ from A such that the net force acting on it is zero. The possible values of $x$ are :

Consider an electron in a hydrogen atom, revolving in its second excited state (having radius $4.65\,?$). The de-Broglie wavelength of this electron is :

In the cube of side $'a'$ shown in the figure, the vector from the central point of the face $ABOD$ to the central point of the face $BEFO$ will be:

The elastic limit of brass is $379\, MPa$. What should be the minimum diameter of a brass rod if it is to support a $400 \,N$ load without exceeding its elastic limit ?

Two radioactive materials $A$ and $B$ have decay constants $10 \lambda$ and $\lambda$, respectively. It initially they have the same number of nuclei, then the ratio of the number of nuclei of $A$ to that of $B$ will be $1/e$ after a time :