JEE Main 2024 Apr 4 Shift 1 — Physics

The equation of stationary wave is :

$$y = 2a \sin\left(\frac{2\pi nt}{\lambda}\right) \cos\left(\frac{2\pi x}{\lambda}\right).$$

Which of the following is NOT correct :

The co-ordinates of a particle moving in $x$-$y$ plane are given by : $x = 2 + 4t$, $y = 3t + 8t^2$. The motion of the particle is :

A wooden block, initially at rest on the ground, is pushed by a force which increases linearly with time t. Which of the following curve best describes acceleration of the block with time :

A body travels 102.5 m in $n^{\text{th}}$ second and 115.0 m in $(n+2)^{\text{th}}$ second. The acceleration is :

If a rubber ball falls from a height h and rebounds upto the height of h/2. The percentage loss of total energy of the initial system as well as velocity ball before it strikes the ground, respectively, are :

A metal wire of uniform mass density having length L and mass M is bent to form a semicircular arc and a particle of mass m is placed at the centre of the arc. The gravitational force on the particle by the wire is :

Given below are two statements :

Statement I : When speed of liquid is zero everywhere, pressure difference at any two points depends on equation $\mathrm{P_1 - P_2} = \rho g(\mathrm{h_2 - h_1})$.

Statement II : In ventury tube shown $2gh = v_1^2 - v_2^2$

a venturi tube with a wide section (pressure $P_1$, area $A_1$, speed $v_1$) and a narrow section (pressure $P_2$, area $A_2$, speed $v_2$); two vertical tubes rise from the two sections with liquid level difference h

In the light of the above statements, choose the most appropriate answer from the options given below.

On celcius scale the temperature of body increases by 40°C. The increase in temperature on Fahrenheit scale is :

P-T diagram of an ideal gas having three different densities $\rho_1$, $\rho_2$, $\rho_3$ (in three different cases) is shown in the figure. Which of the following is correct :

P vs T graph with three straight lines from the origin, with slopes decreasing in the order $\rho_1$, $\rho_2$, $\rho_3$ (line $\rho_1$ steepest)

An infinitely long positively charged straight thread has a linear charge density $\lambda~\mathrm{Cm^{-1}}$. An electron revolves along a circular path having axis along the length of the wire. The graph that correctly represents the variation of the kinetic energy of electron as a function of radius of circular path from the wire is :

The resistances of the platinum wire of a platinum resistance thermometer at the ice point and steam point are $8~\Omega$ and $10~\Omega$ respectively. After inserting in a hot bath of temperature 400°C, the resistance of platinum wire is :

An electron is projected with uniform velocity along the axis inside a current carrying long solenoid. Then :

In an ac circuit, the instantaneous current is zero, when the instantaneous voltage is maximum. In this case, the source may be connected to :

A. pure inductor.

B. pure capacitor.

C. pure resistor.

D. combination of an inductor and capacitor.

Choose the correct answer from the options given below :

The electric field in an electromagnetic wave is given by $\vec{\mathrm{E}} = \hat{i}~40 \cos\omega\left(\mathrm{t} - \frac{z}{c}\right)~\mathrm{N\,C^{-1}}$. The magnetic field induction of this wave is (in SI unit) :

An effective power of a combination of 5 identical convex lenses which are kept in contact along the principal axis is 25 D. Focal length of each of the convex lens is :

Which figure shows the correct variation of applied potential difference (V) with photoelectric current (I) at two different intensities of light ($\mathrm{I_1} < \mathrm{I_2}$) of same wavelengths :

Which of the following nuclear fragments corresponding to nuclear fission between neutron $\left({}^{1}_{0}\mathrm{n}\right)$ and uranium isotope $\left({}^{235}_{92}\mathrm{U}\right)$ is correct :

The value of net resistance of the network as shown in the given figure is :

three parallel branches between terminals at $-6$ V and $-8$ V — top branch: 15 Ω resistor; middle branch: 10 Ω resistor in series with a diode pointing toward the $-8$ V terminal; bottom branch: 5 Ω resistor in series with a diode pointing toward the $-6$ V terminal

In an experiment to measure focal length ($f$) of convex lens, the least counts of the measuring scales for the position of object ($u$) and for the position of image ($v$) are $\Delta u$ and $\Delta v$, respectively. The error in the measurement of the focal length of the convex lens will be :

To measure the internal resistance of a battery, potentiometer is used. For R = 10 Ω, the balance point is observed at $l = 500$ cm and for R = 1 Ω the balance point is observed at $l = 400$ cm. The internal resistance of the battery is approximately :

Two forces $\vec{\mathrm{F}}_1$ and $\vec{\mathrm{F}}_2$ are acting on a body. One force has magnitude thrice that of the other force and the resultant of the two forces is equal to the force of larger magnitude. The angle between $\vec{\mathrm{F}}_1$ and $\vec{\mathrm{F}}_2$ is $\cos^{-1}\left(\frac{1}{n}\right)$. The value of $|n|$ is ________.

A solid sphere and a hollow cylinder roll up without slipping on same inclined plane with same initial speed $v$. The sphere and the cylinder reaches upto maximum heights $\mathrm{h_1}$ and $\mathrm{h_2}$, respectively, above the initial level. The ratio $\mathrm{h_1} : \mathrm{h_2}$ is $\frac{n}{10}$. The value of n is ________.

A soap bubble is blown to a diameter of 7 cm. 36960 erg of work is done in blowing it further. If surface tension of soap solution is 40 dyne/cm then the new radius is ________ cm. Take $\left(\pi = \frac{22}{7}\right)$.

An elastic spring under tension of 3 N has a length $a$. Its length is $b$ under tension 2 N. For its length $(3a - 2b)$, the value of tension will be ________ N.

An infinite plane sheet of charge having uniform surface charge density $+\sigma_s~\mathrm{C/m^2}$ is placed on $x$-$y$ plane. Another infinitely long line charge having uniform linear charge density $+\lambda_e~\mathrm{C/m}$ is placed at $z = 4$ m plane and parallel to $y$-axis. If the magnitude values $|\sigma_s| = 2|\lambda_e|$ then at point (0, 0, 2), the ratio of magnitudes of electric field values due to sheet charge to that of line charge is $\pi\sqrt{n} : 1$. The value of n is ________.

Twelve wires each having resistance 2 Ω are joined to form a cube. A battery of 6 V emf is joined across point a and c. The voltage difference between e and f is ________ V.

a cube with top face vertices a, b, c, d and bottom face vertices e, h, g, f (e below a, f below d, g below c, h below h-corner); a 6 V battery connected across the face diagonal between vertices a and c of the top face

The magnetic field existing in a region is given by $\vec{\mathrm{B}} = 0.2(1 + 2x)\hat{k}~\mathrm{T}$. A square loop of edge 50 cm carrying 0.5 A current is placed in $x$-$y$ plane with its edges parallel to the $x$-$y$ axes, as shown in figure. The magnitude of the net magnetic force experienced by the loop is ________ mN.

x-y coordinate axes with a square loop located at x = 2 m, y = 2 m, its sides parallel to the axes and current circulating around it as marked by arrows

A alternating current at any instant is given by $i = \left[6 + \sqrt{56}\,\sin\left(100\pi \mathrm{t} + \pi/3\right)\right]$ A. The rms value of the current is ________ A.

Two wavelengths $\lambda_1$ and $\lambda_2$ are used in Young's double slit experiment. $\lambda_1 = 450$ nm and $\lambda_2 = 650$ nm. The minimum order of fringe produced by $\lambda_2$ which overlaps with the fringe produced by $\lambda_1$ is n. The value of n is ________.

A hydrogen atom changes its state from $n = 3$ to $n = 2$. Due to recoil, the percentage change in the wave length of emitted light is approximately $1 \times 10^{-n}$. The value of n is ________.

[Given Rhc = 13.6 eV, hc = 1242 eV nm, h = $6.6 \times 10^{-34}$ J s mass of the hydrogenatom = $1.6 \times 10^{-27}$ kg]