JEE Main 2024 April 05, Shift 1 Question Paper with Solutions

The angle between vector $\vec{Q}$ and the resultant of $(2\vec{Q}+2\vec{P})$ and $(2\vec{Q}-2\vec{P})$ is :

Time periods of oscillation of the same simple pendulum measured using four different measuring clocks were recorded as 4.62 s, 4.632 s, 4.6 s and 4.64 s. The arithmetic mean of these readings in correct significant figure is :

If G be the gravitational constant and u be the energy density then which of the following quantity have the dimensions as that of the $\sqrt{uG}$ :

A wooden block mass 5 kg rests on a soft horizontal floor. When an iron cylinder of mass 25 kg is placed on the top of the block, the floor yields and the block and the cylinder together go down with an acceleration of 0.1 m$s^{-2}$. The action force of the system on the floor is equal to:

A body of mass 50 kg is lifted to a height of 20 m from the ground in the two different ways as shown in the figures. The ratio of work done against the gravity in both the respective cases, will be :

Ratio of radius of gyration of a hollow sphere to that of a solid cylinder of equal mass, for moment of Inertia about their diameter axis AB as shown in figure is $\sqrt{8/x}$. The value of x is :

A simple pendulum doing small oscillations at a place R height above earth surface has time period of $T_1=4$ s. $T_2$ would be it's time period if it is brought to a point which is at a height 2R from earth surface. Choose the correct relation $[R=$ radius of earth$]$ :

In hydrogen like system the ratio of coulombian force and gravitational force between an electron and a proton is in the order of :

Match List I with List II :

Given below are two statements :
Statement I : When a capillary tube is dipped into a liquid, the liquid neither rises nor falls in the capillary. The contact angle may be $0^{\circ }$.
Statement II : The contact angle between a solid and a liquid is a property of the material of the solid and liquid as well.
In the light of the above statement, choose the correct answer from the options given below :

The heat absorbed by a system in going through the given cyclic process is :

If the collision frequency of hydrogen molecules in a closed chamber at $27^{\circ }$C is Z, then the collision frequency of the same system at $127^{\circ }$C is :

In the given figure $R_1=10\Omega ,R_2=8\Omega ,R_3=4\Omega$ and $R_4=8\Omega$. Battery is ideal with emf 12 V. Equivalent resistant of the circuit and current supplied by battery are respectively :

In a co-axial straight cable, the central conductor and the outer conductor carry equal currents in opposite directions. The magnetic field is zero :

Two conducting circular loops A and B are placed in the same plane with their centers coinciding as shown in figure. The mutual inductance between them is :

An alternating voltage of amplitude 40 V and frequency 4kHz is applied directly across the capacitor of 12$\mu$F. The maximum displacement current between the plates of the capacitor is nearly :

Light emerges out of a convex lens when a source of light kept at its focus. The shape of wavefront of the light is :

Given below are two statements :
Statement I : Figure shows the variation of stopping potential with frequency $(\nu )$ for the two photosensitive materials $M_1$ and $M_2$. The slope gives value of $\frac{h}{e}$, where h is Planck's constant, e is the charge of electron.
Statement II : $M_2$ will emit photoelectrons of greater kinetic energy for the incident radiation having same frequency.
In the light of the above statements, choose the most appropriate answer from the options given below.

An electron rotates in a circle around a nucleus having positive charge Ze. Correct relation between total energy (E) of electron to its potential energy (U) is :

Following gates section is connected in a complete suitable circuit. For which of the following combination, bulb will glow (ON) :

A body moves on a frictionless plane starting from rest. If $S_n$ is distance moved between $t=n-1$ and $t=n$ and $S_{n-1}$ is distance moved between $t=n-2$ and $t=n-1$, then the ratio $\frac{S_{n-1}}{S_n}$ is $\left(1-\frac{2}{x}\right)$ for $n=10$. The value of x is _______.

Three blocks $M_1,M_2,M_3$ having masses 4 kg, 6 kg and 10 kg respectively are hanging from a smooth pully using rope 1,2 and 3 as shown in figure. The tension in the rope 1, $T_1$ when they are moving upward with acceleration of 2 m$s^{-2}$ is _______N ( if g $=10$ m/$s^2$ ).

The density and breaking stress of a wire are $6\times 10^4$ kg/$m^3$ and $1.2\times 10^8$ N/$m^2$ respectively. The wire is suspended from a rigid support on a planet where acceleration due to gravity is ${\frac{1}{3}}^{\text{rd}}$ of the value on the surface of earth. The maximum length of the wire with breaking is _______ m (take, g $=10$ m/$s^2$ ).

Three capacitors of capacitances 25$\mu$F, 30$\mu$F and 45$\mu$F are connected in parallel to a supply of 100 V. Energy stored in the above combination is E. When these capacitors are connected in series to the same supply, the stored energy is $\frac{9}{x}$E. The value of x is _____.

In the experiment to determine the galvanometer resistance by half-deflection method, the plot of $\frac{1}{\theta }$ vs the resistance (R) of the resistance box is shown in the figure. The figure of merit of the galvanometer is _____ $\times 10^{-2}$ A / division. [The source has emf 2V]

A 2 A current carrying straight metal wire of resistance 1$\Omega$, resistivity $2\times 10^{-6}\Omega$m, area of cross-section 10 m$m^2$ and mass 500 g is suspended horizontally in mid air by applying a uniform magnetic field $\vec{B}$. The magnitude of B is _____ $\times 10^{-1}$ T (given, g $=10$ m/$s^2$ ).

An ac source is connected in given series LCR circuit. The rms potential difference across the capacitor of 20$\mu$F is _____V.

In Young's double slit experiment, carried out with light of wavelength 5000 Å, the distance between the slits is 0.3 mm and the screen is at 200 cm from the slits. The central maximum is at $x=0$ cm. The value of x for third maxima is _____mm.

If three helium nuclei combine to form a carbon nucleus then the energy released in this reaction is _____ $\times 10^{-2}$MeV. (Given 1u $=931$MeV/$c^2$, atomic mass of helium $=4.002603$u )

An organic compound has $42.1\%$ carbon, $6.4\%$ hydrogen and remainder is oxygen. If its molecular weight is 342, then its molecular formula is :

The incorrect postulates of the Dalton's atomic theory are : (A) Atoms of different elements differ in mass. (B) Matter consists of divisible atoms. (C) Compounds are formed when atoms of different element combine in a fixed ratio. (D) All the atoms of given element have different properties including mass. (E) Chemical reactions involve reorganisation of atoms. Choose the correct answer from the options given below :

Given below are two statements :
Statement I : In group 13, the stability of $+1$ oxidation state increases down the group.
Statement II : The atomic size of gallium is greater than that of aluminium.
In the light of the above statements, choose the most appropriate answer from the options given below :

The statement(s) that are correct about the species ${\text{O}}^{2-},{\text{F}}^{-},{\text{Na}}^{+}$ and ${\text{Mg}}^{2+}$. (A) All are isoelectronic (B) All have the same nuclear charge (C) ${\text{O}}^{2-}$ has the largest ionic radii (D) ${\text{Mg}}^{2+}$ has the smallest ionic radii Choose the most appropriate answer from the options given below :

Given below are two statements : One is labelled as Assertion (A) and the other is labelled as Reason (R)
Assertion (A) : Enthalpy of neutralisation of strong monobasic acid with strong monoacidic base is always $-57$ kJ mo$l^{-1}$. Reason (R) : Enthalpy of neutralisation is the amount of heat liberated when one mole of ${\text{H}}^{+}$ ions furnished by acid combine with one mole of ${\text{OH}}^{-}$ ions furnished by base to form one mole of water. In the light of the above statements, choose the correct answer from the options given below :

The following reaction occurs in the Blast furnance where iron ore is reduced to iron metal ${\text{Fe}}_2{\text{O}}_{3(s)}+3{\text{CO}}_{(g)}\rightleftharpoons {\text{Fe}}_{(l)}+3{\text{CO}}_{2(g)}$ Using the Le-chatelier's principle, predict which one of the following will not disturb the equilibrium.

The number of neutrons present in the more abundant isotope of boron is ' x '. Amorphous boron upon heating with air forms a product, in which the oxidation state of boron is ' y '. The value of $x+y$ is ________

Number of $\sigma$ and $\pi$ bonds present in ethylene molecule is respectively :

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Cis form of alkene is found to be more polar than the trans form. Reason (R): Dipole moment of trans isomer of 2-butene is zero. In the light of the above statements, choose the correct answer from the options given below :

For the Compounds : (A) ${\text{H}}_3\text{C}-{\text{CH}}_2-\text{O}-{\text{CH}}_2-{\text{CH}}_2-{\text{CH}}_3$ (B) ${\text{H}}_3\text{C}-{\text{CH}}_2-{\text{CH}}_2-{\text{CH}}_2-{\text{CH}}_3$ (C) (D)
The increasing order of boiling point is : Choose the correct answer from the options given below :

Given below are two statements:
Statement I : Nitration of benzene involves the following step -
Statement II : Use of Lewis base promotes the electrophilic substitution of benzene.
In the light of the above statements, choose the most appropriate answer from the options given below :

The reaction at cathode in the cells commonly used in clocks involves.

Molar ionic conductivities of divalent cation and anion are 57 S c$m^2$ mo$l^{-1}$ and 73 S c$m^2$ mo$l^{-1}$ respectively. The molar conductivity of solution of an electrolyte with the above cation and anion will be :

The metal that shows highest and maximum number of oxidation state is :

Which one of the following complexes will exhibit the least paramagnetic behaviour? [Atomic number, $\text{Cr}=24,\text{Mn}=25,\text{Fe}=26,\text{Co}=27$ ]

The correct order of ligands arranged in increasing field strength.