JEE Main 2026 April 04, Shift 1 Question Paper with Solutions

In a screw gauge when the circular scale is given five complete rotations it moves linearly by $2.5$ mm. If the circular scale has 100 divisions, the least count of screw gauge is _____ mm.

The increase in the pressure required to decrease the volume $(\Delta V)$ of water is $6.3 \times 10^{7}\,\text{N/m}^{2}$. The percentage decrease in the volume is ____.
(Bulk modulus of water $= 2.1 \times 10^{9}\,\text{N/m}^{2}$)

The time taken by a block of mass m to slide down from the highest point to the lowest point on a rough inclined plane is $50$% more compared to the time taken by the same block on identical inclined smooth plane. Both inclined planes are at $45^{\circ}$ with the horizontal. The coefficient of kinetic friction between the rough inclined surface and block is ____.

Two nuclei of mass number 3 combine with another nucleus of mass number 4 to yield a nucleus of mass number 10. If the binding energy per nucleon for the mass numbers 3, 4 and 10 are $5.6$ MeV, $7.4$ MeV and $6.1$ MeV, respectively, then in the process, $\Delta Mc^{2} =$ ____ MeV.

A solid sphere of mass M and radius R is divided into two unequal parts. The smaller part having mass $\dfrac{M}{8}$ is converted into a sphere of radius r and the larger part is converted into a circular disc of thickness t and radius $2R$. If $I_{1}$ is moment of inertia of a sphere having radius r about an axis through its centre and $I_{2}$ is the moment of inertia of a disc about its diameter, the ratio of their moment of inertia $\dfrac{I_{2}}{I_{1}} =$ ____.

The two projectiles are projected with the same initial velocities at the $15^{\circ}$ and $30^{\circ}$ with respect to the horizontal. The ratio of their range is $1 : x$. The value of x is

The graph shows variation of stopping potential $V_{0}$ with the frequency $\nu$ of the incident radiation for three photosensitive metals $X_{1},\, X_{2}$ and $X_{3}$. Which metal will give out electrons with greater kinetic energy, for the same wavelength of incident radiation?

A slit of width a is illuminated by light of wavelength $\lambda$. The linear separation between $1^{\text{st}}$ and $3^{\text{rd}}$ minima in the diffraction pattern produced on a screen placed at a distance D from the slit system is ____.

A string A of length $0.314\,m$ and Young's modulus $2 \times 10^{10}\,N/m^2$ is connected to another string B of length and Young's modulus both twice of those of A. This series combination of strings is then suspended from a rigid support and its free end is fixed to a load of mass $0.8\,kg$. The net change in length of the combination is ____ mm.
(radius of both the strings is $0.2\,mm$ and acceleration due to gravity $= 10\,m/s^2$)
(Mass of both strings is to be neglected as compared to the mass of load)

One gas of $n_1$ mole of molecules at temperature $T_1$, volume $V_1$, and pressure $P_1$, and another gas of $n_2$ mole of molecules at temperature $T_2$, volume $V_2$, and pressure $P_2$, are mixed resulting in pressure P and volume V of the mixture. The temperature of the mixture is _____.

An ideal gas undergoes a process maintaining relation between pressure (P) and volume (V) as $P = P_0\left[1 + \left(\dfrac{V_0}{V}\right)^2\right]^{-1}$, where $P_0$ and $V_0$ are constants. If two samples A and B (two moles each) with initial volumes $V_0$ and $3V_0$ respectively undergo above mentioned process and attain same pressure, then the difference at the temperature of these samples, $T_B - T_A$ is _____. ($R =$ gas constant)

A voltmeter with internal resistance of $x\,\Omega$ can be used to measure upto $20\,V$. In order to increase its measuring range to $30\,V$, the required modification is to ____.

Two 4 bits binary numbers, $A = 1101$ and $B = 1010$ are given in the inputs of a logic circuit shown in figure below. The output $Y$ will be:

A rod of length $10\,cm$ lies along the principle axis of a concave mirror of focal length $10\,cm$ as shown in figure. The length of the image is ___ cm.

A parallel plate air capacitor is connected to a battery. The plates are pulled apart at uniform speed v. If x is the separation between the plates at any instant, then the time rate of change of electrostatic energy of the capacitor is proportional to $x^\alpha$, where $\alpha$ is ____.

An insulated wire is wound so that it forms a flat coil with $N = 200$ turns. The radius of the innermost turn is $r_1 = 3\,cm$, and of the outermost turn $r_2 = 6\,cm$. If $20\,mA$ current flows in it then the magnetic moment will be $\alpha \times 10^{-2}\,A\cdot m^2$. The value of $\alpha$ is _____.

Consider a circuit consisting of a capacitor $(20\,\mu F)$, resistor $100\,\Omega$ and two identical diodes as shown in figure. The resistance of diode under forward biasing condition is $10\,\Omega$. The time constant of the circuit is $\alpha \times 10^{-3}\,s$. The value of $\alpha$ is ______

The voltage and the current between A and B points shown in the circuit are _____.

A telescope with objective diameter R is used to observe a distant star emitting light of wavelength $500\,nm$, at a resolution of $5 \times 10^{-7}$ radian. The value of R is _____ cm.

A $1\,kg$ block subjected to two simultaneous forces $\left(2\hat{i}+3\hat{j}+4\hat{k}\right)\,N$ and $\left(3\hat{i}-\hat{j}-2\hat{k}\right)\,N$ is moved a distance of $25\,m$ along $\left(3\hat{i}-4\hat{j}\right)$ direction. The work done in this process is ____ J.

The surface tension of a soap solution is $3.5 \times 10^{-2}\,N/m$. The work required to increase the radius of a soap bubble from $1\,cm$ to $2\,cm$ is $\alpha \times 10^{-6}\,J$. The value of $\alpha$ is ____. $\left(\pi = \dfrac{22}{7}\right)$

The velocity of a particle executing simplee harmonic motion along x-axis is described as $v^2 = 50 - x^2$, where x represents displacement. If the time period of motion is $\dfrac{x}{7}\,s$, the value of x is ____.