JEE Main 2024 April 08, Shift 1 Question Paper with Solutions

In an expression $a\times 10^b$:

Young's modulus is determined by the equation given by $Y=49000\frac{m}{l}\frac{dyne}{c{m}^2}$ where M is the mass and l is the extension of wire used in the experiment. Now error in Young modulus (Y) is estimated by taking data from $M-l$ plot in graph paper. The smallest scale divisions are 5 g and 0.02 cm along load axis and extension axis respectively. If the value of M and l are 500 g and 2 cm respectively then percentage error of Y is :

A clock has 75 cm, 60 cm long second hand and minute hand respectively. In 30 minutes duration the tip of second hand will travel x distance more than the tip of minute hand. The value of x in meter is nearly (Take $\pi =3.14$ ) :

A stationary particle breaks into two parts of masses $m_A$ and $m_B$ which move with velocities $v_A$ and $v_B$ respectively. The ratio of their kinetic energies $(K_B:K_A)$ is :

Three bodies A, B and C have equal kinetic energies and their masses are 400 g, 1.2 kg and 1.6 kg respectively. The ratio of their linear momenta is :

A player caught a cricket ball of mass 150 g moving at a speed of 20 m/s. If the catching process is completed in 0.1 s, the magnitude of force exerted by the ball on the hand of the player is:

Two planets A and B having masses $m_1$ and $m_2$ move around the sun in circular orbits of $r_1$ and $r_2$ radii respectively. If angular momentum of A is L and that of B is $3L$, the ratio of time period $\left(\frac{T_A}{T_B}\right)$ is:

Correct Bernoulli's equation is (symbols have their usual meaning) :

Two different adiabatic paths for the same gas intersect two isothermal curves as shown in P-V diagram. The relation between the ratio $\frac{V_a}{V_d}$ and the ratio $\frac{V_b}{V_c}$ is:

A mixture of one mole of monoatomic gas and one mole of a diatomic gas (rigid) are kept at room temperature ($27^{\circ }$C). The ratio of specific heat of gases at constant volume respectively is:

Two charged conducting spheres of radii $a$ and $b$ are connected to each other by a conducting wire. The ratio of charges of the two spheres respectively is:

In the given circuit, the terminal potential difference of the cell is:

Paramagnetic substances: A. align themselves along the directions of external magnetic field. B. attract strongly towards external magnetic field. C. has susceptibility little more than zero. D. move from a region of strong magnetic field to weak magnetic field. Choose the most appropriate answer from the options given below:

A LCR circuit is at resonance for a capacitor $C$, inductance $L$ and resistance $R$. Now the value of resistance is halved keeping all other parameters same. The current amplitude at resonance will be now:

Critical angle of incidence for a pair of optical media is $45^{\circ }$. The refractive indices of first and second media are in the ratio:

A proton and an electron are associated with same de-Broglie wavelength. The ratio of their kinetic energies is: (Assume h=$6.63\times 10^{-34}$ J s, $m_e=9.0\times 10^{-31}$ kg and $m_p=1836$ times $m_e$ )

Average force exerted on a non-reflecting surface at normal incidence is $2.4\times 10^{-4}$ N. If 360 W/c$m^2$ is the light energy flux during span of 1 hour 30 minutes, Then the area of the surface is:

Binding energy of a certain nucleus is $18\times 10^8$ J. How much is the difference between total mass of all the nucleons and nuclear mass of the given nucleus:

The output Y of following circuit for given inputs is :

The diameter of a sphere is measured using a vernier caliper whose 9 divisions of main scale are equal to 10 divisions of vernier scale. The shortest division on the main scale is equal to 1 mm. The main scale reading is 2 cm and second division of vernier scale coincides with a division on main scale. If mass of the sphere is 8.635 g, the density of the sphere is:

Three vectors $\overrightarrow{OP}$, $\overrightarrow{OQ}$ and $\overrightarrow{OR}$ each of magnitude A are acting as shown in figure. The resultant of the three vectors is A$\sqrt{x}$. The value of x is ________ .

A uniform thin metal plate of mass 10 kg with dimensions is shown. The ratio of x and y coordinates of center of mass of plate in $\frac{n}{9}$. The value of n is ________

A liquid column of height 0.04 cm balances excess pressure of a soap bubble of certain radius. If density of liquid is $8\times 10^3$ kg $m^{-3}$ and surface tension of soap solution is 0.28N$m^{-1}$, then diameter of the soap bubble is ________ cm. (if $g=10$ m $s^{-2}$ )

A closed and an open organ pipe have same lengths. If the ratio of frequencies of their seventh overtones is $\left(\frac{a-1}{a}\right)$ then the value of a is ________

An electric field, $\vec{E}=\frac{2\hat{i}+6\hat{j}+8\hat{k}}{\sqrt{6}}$ passes through the surface of 4 $m^2$ area having unit vector $\hat{n}=\left(\frac{2\hat{i}+\hat{j}+\hat{k}}{\sqrt{6}}\right)$. The electric flux for that surface is ________ Vm.

Resistance of a wire at $0^{\circ }$C, $100^{\circ }$C and $t^{\circ }$C is found to be $10\Omega$, $10.2\Omega$ and $10.95\Omega$ respectively. The temperature t in Kelvin scale is ________

An electron with kinetic energy 5eV enters a region of uniform magnetic field of 3 $\mu$T perpendicular to its direction. An electric field E is applied perpendicular to the direction of velocity and magnetic field. The value of E, so that electron moves along the same path, is ________ N$C^{-1}$. ( Given, mass of electron = $9\times 10^{-31}$ kg , electric charge = $1.6\times 10^{-19}$C)

A square loop PQRS having 10 turns, area $3.6\times 10^{-3}$ $m^2$ and resistance $100\Omega$ is slowly and uniformly being pulled out of a uniform magnetic field of magnitude B = 0.5 T as shown. Work done in pulling the loop out of the field in 1.0 s is ________ $\times 10^{-6}$ J.

A parallel beam of monochromatic light of wavelength 600 nm passes through single slit of 0.4 mm width. Angular divergence corresponding to second order minima would be ________ $\times 10^{-3}$rad.

In an alpha particle scattering experiment distance of closest approach for the $\alpha$ particle is $4.5\times 10^{-14}$ m. If target nucleus has atomic number 80 , then maximum velocity of $\alpha$ - particle is ________ $\times 10^5$ m/s approximately. ($\frac{1}{4\pi {ϵ}_0}=9\times 10^9$ SI unit, mass of $\alpha$ particle = $6.72\times 10^{-27}$ kg)

Combustion of glucose $({\text{C}}_6{\text{H}}_{12}{\text{O}}_6)$ produces ${\text{CO}}_2$ and water. The amount of oxygen (in g) required for the complete combustion of 900 g of glucose is : [Molar mass of glucose in gmo$l^{-1}$ = 180 ]

Match List I with List II

Match List I with List II

Match List I with List II

Given below are two statements: Statement I: ${\text{N(CH}}_3{)}_3$ and ${\text{P(CH}}_3{)}_3$ can act as ligands to form transition metal complexes. Statement II: As N and P are from same group, the nature of bonding of ${\text{N(CH}}_3{)}_3$ and ${\text{P(CH}}_3{)}_3$ is always same with transition metals. In the light of the above statements, choose the most appropriate answer from the options given below:

For the given hypothetical reactions, the equilibrium constants are as follows : $\text{Y}\rightleftharpoons {\text{Z; K}}_1=1.0$
$\text{Z}\rightleftharpoons {\text{W; K}}_2=2.0$
$\text{Z}\rightleftharpoons {\text{X; K}}_3=4.0$
equilibrium constant for the reaction $\text{X}\rightleftharpoons \text{W}$ is :

Among the following halogens ${\text{F}}_2,{\text{Cl}}_2,{\text{Br}}_2$ and ${\text{I}}_2$ Which can undergo disproportionation reactions?

Thiosulphate reacts differently with iodine and bromine in the reactions given below:
$2{\text{S}}_2{\text{O}}_3^{2-}+{\text{I}}_2\to {\text{S}}_4{\text{O}}_6^{2-}+2{\text{I}}^{-}$
${\text{S}}_2{\text{O}}_3^{2-}+5{\text{Br}}_2+5{\text{H}}_2\text{O}\to 2{\text{SO}}_4^{2-}+4{\text{Br}}^{-}+10{\text{H}}^{+}$
Which of the following statement justifies the above dual behaviour of thiosulphate?

Give below are two statements: One is labelled as Assertion $\mathbf{A}$ and the other is labelled as Reason $\mathbf{R}$: Assertion A: The stability order of +1 oxidation state of Ga, In and Tl is Ga < In < Tl. Reason R: The inert pair effect stabilizes the lower oxidation state down the group. In the light of the above statements, choose the most appropriate answer from the options given below:

Which of the following are aromatic?

Given below are two statements: Statements I:
Compound $A$
Given below are two statements: Statements I: IUPAC name of Compound $A$ is 4-chloro-1,3-dinitrobenzene. Statements II: IUPAC name of Compound B is 4-ethyl-2-methylaniline. In the light of the above statements, choose the most appropriate answer from the options given below:

In the given compound, the number of $2^{\circ }$ carbon atom /s is ______.

Iron (III) catalyses the reaction between iodide and persulphate ions, in which A. ${\text{Fe}}^{3+}$ oxidises the iodide ion B. ${\text{Fe}}^{3+}$ oxidises the persulphate ion C. ${\text{Fe}}^{2+}$ reduces the iodide ion D. ${\text{Fe}}^{2+}$ reduces the persulphate ion Choose the most appropriate answer from the options given below:

Number of Complexes with even number of electrons in $t_{2g}$ orbitals is - $[{\text{Fe(H}}_2\text{O}{)}_6{]}^{2+}$ , $[{\text{Co(H}}_2\text{O}{)}_6{]}^{2+}$ , $[{\text{Co(H}}_2\text{O}{)}_6{]}^{3+}$ , $[{\text{Cu(H}}_2\text{O}{)}_6{]}^{2+}$ , $[{\text{Cr(H}}_2\text{O}{)}_6{]}^{2+}$

An octahedral complex with the formula ${\text{CoCl}}_3\cdot {\text{nNH}}_3$ upon reaction with excess of ${\text{AgNO}}_3$ solution gives 2 moles of AgCl. Consider the oxidation state of Co in the complex is ' x '. The value of " $x+n$ " is ______