JEE Main 2024 April 06, Shift 1 Question Paper with Solutions

To find the spring constant $(k)$ of a spring experimentally, a student commits 2% positive error in the measurement of time and 1% negative error in measurement of mass. The percentage error in determining value of $k$ is :

Match List I with List II

A train starting from rest first accelerates uniformly up to a speed of 80 km/h for time $t$, then it moves with a constant speed for time $3t$. The average speed of the train for this duration of journey will be (in km/h ) :

A light string passing over a smooth light pulley connects two blocks of masses $m_1$ and $m_2$ (where $m_2>m_1$). If the acceleration of the system is $\frac{g}{\sqrt{2}}$, then the ratio of the masses $\frac{m_1}{m_2}$ is:

A bullet of mass 50 g is fired with a speed 100 m/s on a plywood and emerges with 40 m/s. The percentage loss of kinetic energy is :

Four particles A, B, C, D of mass $\frac{m}{2},m,2m,4m$, have same momentum, respectively. The particle with maximum kinetic energy is :

To project a body of mass m from earth's surface to infinity, the required kinetic energy is (assume, the radius of earth is $R_E,g=$ acceleration due to gravity on the surface of earth):

A small ball of mass m and density $\rho$ is dropped in a viscous liquid of density ${\rho }_0$. After sometime, the ball falls with constant velocity. The viscous force on the ball is :

A sample contains mixture of helium and oxygen gas. The ratio of root mean square speed of helium and oxygen in the sample, is:

The specific heat at constant pressure of a real gas obeying $P{V}^2=RT$ equation is:

Ques: $\sigma$ is the uniform surface charge density of a thin spherical shell of radius R. The electric field at any point on the surface of the spherical shell is :

The value of unknown resistance $(x)$ for which the potential difference between $B$ and $D$ will be zero in the arrangement shown, is :

An element $\Delta l=\Delta x\hat{i}$ is placed at the origin and carries a large current $I=10$ A. The magnetic field on the y-axis at a distance of 0.5 m from the elements $\Delta x$ of 1 cm length is:

Given below are two statements: Statement I: In an LCR series circuit, current is maximum at resonance. Statement II: Current in a purely resistive circuit can never be less than that in a series LCR circuit when connected to same voltage source. In the light of the above statements, choose the correct from the options given below:

Electromagnetic waves travel in a medium with speed of $1.5\times 10^8$ m $s^{-1}$. The relative permeability of the medium is 2.0 . The relative permittivity will be:

In photoelectric experiment energy of 2.48eV irradiates a photo sensitive material. The stopping potential was measured to be 0.5 V. Work function of the photo sensitive material is :

Which of the following phenomena does not explain by wave nature of light. A. reflection B. diffraction C. photoelectric effect D. interference E. polarization Choose the most appropriate answer from the options given below:

The ratio of the shortest wavelength of Balmer series to the shortest wavelength of Lyman series for hydrogen atom is :

The correct truth table for the following logic circuit is :

While measuring diameter of wire using screw gauge the following readings were noted. Main scale reading is 1 mm and circular scale reading is equal to 42 divisions. Pitch of screw gauge is 1 mm and it has 100 divisions on circular scale. The diameter of the wire is $\frac{x}{50}$ mm. The value of x is :

For three vectors $\vec{A}=(-x\hat{i}-6\hat{j}-2\hat{k})$, $\vec{B}=(-\hat{i}+4\hat{j}+3\hat{k})$ and $\vec{C}=(-8\hat{i}-\hat{j}+3\hat{k})$, if $\vec{A}\cdot (\vec{B}\times \vec{C})=0$, then value of x is _______

If the radius of earth is reduced to three fourth of its present value without change in its mass then value of duration of the day of earth will be _______ hours 30 minutes.

A big drop is formed by coalescing 1000 small droplets of water. The ratio of surface energy of 1000 droplets to that of energy of big drop is $\frac{10}{x}$. The value of x is _______

A particle is doing simple harmonic motion of amplitude 0.06 m and time period 3.14 s. The maximum velocity of the particle is _______ cm/s.

Three infinitely long charged thin sheets are placed as shown in figure. The magnitude of electric field at the point P is $\frac{x\sigma }{{ϵ}_0}$. The value of x is _______ (all quantities are measured in SI units).

A wire of resistance R and radius r is stretched till its radius become $r/2$. If new resistance of the stretched wire is xR, then value of x is _______

A circular coil having 200 turns, $2.5\times 10^{-4}$ $m^2$ area and carrying $100\mu$A current is placed in a uniform magnetic field of 1T. Initially the magnetic dipole moment ($\vec{M}$) was directed along $\vec{B}$. Amount of work, required to rotate the coil through $90^{\circ }$ from its initial orientation such that $\vec{M}$ becomes perpendicular to $\vec{B}$, is _______ $\mu$J.

When a dc voltage of 100 V is applied to an inductor, a dc current of 5 A flows through it. When an ac voltage of 200 V peak value is connected to inductor, its inductive reactance is found to be $20\sqrt{3}\Omega$. The power dissipated in the circuit is _______ W.

The refractive index of prism is $\mu =\sqrt{3}$ and the ratio of the angle of minimum deviation to the angle of prism is one. The value of angle of prism is _______

Radius of a certain orbit of hydrogen atom is 8.48 $\mathring{\text{A}}$. If energy of electron in this orbit is $E/x$, then $x=$ _______ (Given $a_0=0.529\mathring{\text{A}}$, $E=$ energy of electron in ground state).

The density of ' x ' M solution (' X ' molar) of NaOH is 1.12 g m$L^{-1}$, while in molality, the concentration of the solution is 3 m (3molal). Then x is (Given : Molar mass of NaOH is 40 g/mol )

The electron affinity value are negative for A. $\text{Be}\to {\text{Be}}^{-}$ B. $\text{N}\to {\text{N}}^{-}$ C. $\text{O}\to {\text{O}}^{2-}$ D. $\text{Na}\to {\text{Na}}^{-}$ E. $\text{Al}\to {\text{Al}}^{-}$ Choose the most appropriate answer from the options given below :

Which of the following material is not a semiconductor.

Match List I with List II

Match List I with List II

Match List I with List II

At $-20^{\circ }$C and 1 atm pressure, a cylinder is filled with equal number of ${\text{H}}_2$, ${\text{I}}_2$ and HI molecules for the reaction ${\text{H}}_2(g)+{\text{I}}_2(g)\rightleftharpoons 2\text{HI}(g)$, the $K_p$ for the process is $x\times 10^{-1}$. x = ____ [Given : R = 0.082 L atm $K^{-1}$ mo$l^{-1}$]

Functional group present in sulphonic acids is :

Which of the following statements are correct? A. Glycerol is purified by vacuum distillation because it decomposes at its normal boiling point. B. Aniline can be purified by steam distillation as aniline is miscible in water. C. Ethanol can be separated from ethanol water mixture by azeotropic distillation because it forms azeotrope. D. An organic compound is pure, if mixed M.P. is remained same. Choose the most appropriate answer from the options given below :

Which of the following is metamer of the given compound (X) ?

Given below are two statements: Statement I : Gallium is used in the manufacturing of thermometers.
Statement II : A thermometer containing gallium is useful for measuring the freezing point (256 K) of brine solution. In the light of the above statements, choose the correct answer from the options given below :

A conductivity cell with two electrodes (dark side) are half filled with infinitely dilute aqueous solution of a weak electrolyte. If volume is doubled by adding more water at constant temperature, the molar conductivity of the cell will -

The number of element from the following that do not belong to lanthanoids is $\text{Eu, Cm, Er, Tb, Yb}$ and $\text{Lu}$

Match List I with List II

he following complexes $[{\text{CoCl(NH}}_3{)}_5{]}^{2+}$, $[{\text{Co(CN)}}_6{]}^{3-}$, $[{\text{Co(NH}}_3{)}_5({\text{H}}_2\text{O}){]}^{3+}$, $[{\text{Cu(H}}_2\text{O}{)}_4{]}^{2+}$ The correct order of A, B, C and D in terms of wavenumber of light absorbed is :

Given below are two statements : Statement I : Piciric acid is 2,4,6 - trinitrotoluene. Statement II : Phenol - 2,4 - disulphonic acid is treated with Conc. ${\text{HNO}}_3$ to get picric acid. In the light of the above statements, choose the most appropriate answer from the options given below :

In Reimer - Tiemann reaction, phenol is converted into salicylaldehyde through an intermediate. The structure of intermediate is _____

Which among the following aldehydes is most reactive towards nucleophilic addition reactions?

Match List I with List II

DNA molecule contains 4 bases whose structure are shown below. One of the structures is not correct, identify the incorrect base structure.

Frequency of the de-Broglie wave of electron in Bohr's first orbit of hydrogen atom is _______ $\times 10^{13}$ Hz (nearest integer). [Given : ${\text{R}}_{\text{H}}$ ( Rydberg constant ) $=2.18\times 10^{-18}$ J, h (Plank's constant ) $=6.6\times 10^{-34}$ J.s.]

Number of molecules from the following which can exhibit hydrogen bonding is _______ (nearest integer)

An ideal gas, ${\bar{\text{C}}}_{\text{v}}=\frac{5}{2}\text{R}$, is expanded adiabatically against a constant pressure of 1 atm untill it doubles in volume. If the initial temperature and pressure is 298 K and 5 atm, respectively then the final temperature is _______ K (nearest integer). [${\bar{\text{C}}}_{\text{v}}$ is the molar heat capacity at constant volume]