JEE Main 2022 25th July Evening Shift Question Paper with Solutions

Sound travels in a mixture of two moles of helium and n moles of hydrogen. If rms speed of gas molecules in the mixture is $\sqrt2$ times the speed of sound, then the value of n will be :

A block of ice of mass 120 g at temperature 0$^\circ$C is put in 300 g of water at 25$^\circ$C. The x g of ice melts as the temperature of the water reaches 0$^\circ$C. The value of x is _____________.

[Use specific heat capacity of water = 4200 Jkg^$-$1K^$-$1, Latent heat of ice = 3.5 $\times$ 10⁵ Jkg^$-$1]

A current of 15 mA flows in the circuit as shown in figure. The value of potential difference between the points A and B will be:

In AM modulation, a signal is modulated on a carrier wave such that maximum and minimum amplitudes are found to be 6 V and 2 V respectively. The modulation index is :

In a potentiometer arrangement, a cell of emf 1.20 V gives a balance point at 36 cm length of wire. This cell is now replaced by another cell of emf 1.80 V. The difference in balancing length of potentiometer wire in above conditions will be ___________ cm.

An electron with energy 0.1 keV moves at right angle to the earth's magnetic field of 1 $\times$ 10^$-$4 Wbm^$-$2. The frequency of revolution of the electron will be :

(Take mass of electron = 9.0 $\times$ 10^$-$31 kg)

A drop of liquid of density $\rho$ is floating half immersed in a liquid of density ${\sigma}$ and surface tension $7.5 \times 10^{-4}$ Ncm^$-$1. The radius of drop in $\mathrm{cm}$ will be :

(g = 10 ms^$-$2)

A ball is projected from the ground with a speed 15 ms^$-$1 at an angle $\theta$ with horizontal so that its range and maximum height are equal,
then 'tan $\theta$' will be equal to :

The maximum error in the measurement of resistance, current and time for which current flows in an electrical circuit are $1 \%, 2 \%$ and $3 \%$ respectively. The maximum percentage error in the detection of the dissipated heat will be :

Capacitance of an isolated conducting sphere of radius R₁ becomes n times when it is enclosed by a concentric conducting sphere of radius R₂ connected to earth. The ratio of their radii $\left( {{{{R_2}} \over {{R_1}}}} \right)$ is :

Two waves executing simple harmonic motions travelling in the same direction with same amplitude and frequency are superimposed. The resultant amplitude is equal to the $\sqrt3$ times of amplitude of individual motions. The phase difference between the two motions is ___________ (degree).

A convex lens of focal length 20 cm is placed in front of a convex mirror with principal axis coinciding each other. The distance between the lens and mirror is 10 cm. A point object is placed on principal axis at a distance of 60 cm from the convex lens. The image formed by combination coincides the object itself. The focal length of the convex mirror is ____________ cm.

Light wave travelling in air along x-direction is given by ${E_y} = 540\sin \pi \times {10^4}(x - ct)\,V{m^{ - 1}}$. Then, the peak value of magnetic field of wave will be (Given c = 3 $\times$ 10⁸ ms^$-$1)

Hydrogen atom from excited state comes to the ground state by emitting a photon of wavelength $\lambda$. The value of principal quantum number '$n$' of the excited state will be : ($\mathrm{R}:$ Rydberg constant)

The length of a seconds pendulum at a height h = 2R from earth surface will be:

(Given R = Radius of earth and acceleration due to gravity at the surface of earth, g = $\pi$² ms^$-$2)

For an object placed at a distance 2.4 m from a lens, a sharp focused image is observed on a screen placed at a distance 12 cm from the lens. A glass plate of refractive index 1.5 and thickness 1 cm is introduced between lens and screen such that the glass plate plane faces parallel to the screen. By what distance should the object be shifted so that a sharp focused image is observed again on the screen?

An object is taken to a height above the surface of earth at a distance ${5 \over 4}$ R from the centre of the earth. Where radius of earth, R = 6400 km. The percentage decrease in the weight of the object will be :

A particle is moving in a straight line such that its velocity is increasing at 5 ms^$-$1 per meter. The acceleration of the particle is _____________ ms^$-$2 at a point where its velocity is 20 ms^$-$1.

Three identical spheres each of mass M are placed at the corners of a right angled triangle with mutually perpendicular sides equal to 3 m each. Taking point of intersection of mutually perpendicular sides as origin, the magnitude of position vector of centre of mass of the system will be $\sqrt x$ m. The value of x is ____________.

A bag of sand of mass 9.8 kg is suspended by a rope. A bullet of 200 g travelling with speed 10 ms^$-$1 gets embedded in it, then loss of kinetic energy will be :

Two parallel plate capacitors of capacity C and 3C are connected in parallel combination and charged to a potential difference 18 V. The battery is then disconnected and the space between the plates of the capacitor of capacity C is completely filled with a material of dielectric constant 9. The final potential difference across the combination of capacitors will be ___________ V.

Two ideal diodes are connected in the network as shown in figure. The equivalent resistance between A and B is __________ $\Omega$.

Let $\eta_{1}$ is the efficiency of an engine at $T_{1}=447^{\circ} \mathrm{C}$ and $\mathrm{T}_{2}=147^{\circ} \mathrm{C}$ while $\eta_{2}$ is the efficiency at $\mathrm{T}_{1}=947^{\circ} \mathrm{C}$ and $\mathrm{T}_{2}=47^{\circ} \mathrm{C}$ The ratio $\frac{\eta_{1}}{\eta_{2}}$ will be :

The electric current in a circular coil of 2 turns produces a magnetic induction B₁ at its centre. The coil is unwound and in rewound into a circular coil of 5 tuns and the same current produces a magnetic induction B₂ at its centre. The ratio of ${{{B_2}} \over {{B_1}}}$ is

Magnetic flux (in weber) in a closed circuit of resistance 20 $\Omega$ varies with time t(s) at $\phi$ = 8t² $-$ 9t + 5. The magnitude of the induced current at t = 0.25 s will be ____________ mA.

Two billiard balls of mass 0.05 kg each moving in opposite directions with 10 ms^$-$1 collide and rebound with the same speed. If the time duration of contact is t = 0.005 s, then what is the force exerted on the ball due to each other?

When you walk through a metal detector carrying a metal object in your pocket, it raises an alarm. This phenomenon works on :

${x \over {x + 4}}$ is the ratio of energies of photons produced due to transition of an electron of hydrogen atom from its

(i) third permitted energy level to the second level and

(ii) the highest permitted energy level to the second permitted level.

The value of x will be ____________.

The ratio of wavelengths of proton and deuteron accelerated by potential V_p and V_d is 1 : $\sqrt2$. Then the ratio of V_p to V_d will be :

For a free body diagram shown in the figure, the four forces are applied in the 'x' and 'y' directions. What additional force must be applied and at what angle with positive x-axis so that the net acceleration of body is zero?

The molar conductivity of a conductivity cell filled with 10 moles of 20 mL NaCl solution is ${\Lambda _{m1}}$ and that of 20 moles another identical cell heaving 80 mL NaCl solution is ${\Lambda _{m2}}$. The conductivities exhibited by these two cells are same. The relationship between ${\Lambda _{m2}}$ and ${\Lambda _{m1}}$ is

Glycosidic linkage between C₁ of $\alpha$-glucose and C₂ of $\beta$-fructose is found in

The total number of acidic oxides from the following list is

NO, N₂O, B₂O₃, N₂O₅, CO, SO₃, P₄O₁₀

The sum of number of lone pairs of electrons present on the central atoms of XeO₃, XeOF₄ and XeF₆, is ______________

Given below are two statements.

Statement I : Pig iron is obtained by heating cast iron with scrap iron.

Statement II : Pig iron has a relatively lower carbon content than that of cast iron.

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

A sample of 4.5 mg of an unknown monohydric alcohol, R-OH was added to methylmagnesium iodide. A gas is evolved and is collected and its volume measured to be 3.1 mL. The molecular weight of the unknown alcohol is __________ g/mol. [Nearest integer]

The correct order of energy of absorption for the following metal complexes is :

A : [Ni(en)₃]²⁺ , B : [Ni(NH₃)₆]²⁺ , C : [Ni(H₂O)₆]²⁺

Match List I with List II:

Choose the correct answer from the options given below :

${K_{{a_1}}}$, ${K_{{a_2}}}$ and ${K_{{a_3}}}$ are the respective ionization constants for the following reactions (a), (b) and (c).

(a) ${H_2}{C_2}{O_4} \mathbin{\lower.3ex\hbox{$\buildrel\textstyle\rightarrow\over {\smash{\leftarrow}\vphantom{_{\vbox to.5ex{\vss}}}}$}} {H^ + } + H{C_2}O_4^ -$

(b) $H{C_2}O_4^ - \mathbin{\lower.3ex\hbox{$\buildrel\textstyle\rightarrow\over {\smash{\leftarrow}\vphantom{_{\vbox to.5ex{\vss}}}}$}} {H^ + } + {C_2}O_4^{2 - }$

(c) ${H_2}{C_2}O_4^{} \mathbin{\lower.3ex\hbox{$\buildrel\textstyle\rightarrow\over {\smash{\leftarrow}\vphantom{_{\vbox to.5ex{\vss}}}}$}} 2{H^ + } + {C_2}O_4^{2 - }$

The relationship between ${K_{{a_1}}}$, ${K_{{a_2}}}$ and ${K_{{a_3}}}$ is given as :

What is the major product of the following reaction?

Arrange the following in decreasing acidic strength.

For the decomposition of azomethane.

CH₃N₂CH₃(g) $\to$ CH₃CH₃(g) + N₂(g), a first order reaction, the variation in partial pressure with time at 600 K is given as

The half life of the reaction is __________ $\times$ 10^$-$5 s. [Nearest integer]

For micelle formation, which of the following statements are correct?

A. Micelle formation is an exothermic process.

B. Micelle formation is an endothermic process.

C. The entropy change is positive.

D. The entropy change is negative.

56.0 L of nitrogen gas is mixed with excess hydrogen gas and it is found that 20 L of ammonia gas is produced. The volume of unused nitrogen gas is found to be _________ L.

Match List I with List II:

Choose the correct answer from the options given below:

High purity (> 99.95%) dihydrogen is obtained by :

The first ionization enthalpies of Be, B, N and O follow the order

A sealed flask with a capacity of 2 dm³ contains 11 g of propane gas. The flask is so weak that it will burst if the pressure becomes 2 MPa. The minimum temperature at which the flask will burst is ___________ $^\circ$C. [Nearest integer]

(Given : R = 8.3 J K^$-$1 mol^$-$1 , Atomic masses of C and H are 12u and 1u, respectively.) (Assume that propane behaves as an ideal gas.)