JEE Main 2022 Question Paper with Solutions

Potential energy as a function of r is given by U = A r 10 − B r 5 , where r is the interatomic distance, A and B are positive constants. The equilibrium distance between the two atoms will be :

A fly wheel is accelerated uniformly from rest and rotates through 5 rad in the first second. The angle rotated by the fly wheel in the next second, will be :

A stone of mass m, tied to a string is being whirled in a vertical circle with a uniform speed. The tension in the string is

Identify the pair of physical quantities that have same dimensions:

Two massless springs with spring constants 2 k and 9 k, carry 50 g and 100 g masses at their free ends. These two masses oscillate vertically such that their maximum velocities are equal. Then, the ratio of their respective amplitudes will be :

At 25 $^\circ$ C and 1 atm pressure, the enthalpies of combustion are as given below : .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; overflow:hidden;padding:10px 5px;word-break:normal;} .tg th{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; font-weight:normal;overflow:hidden;padding:10px 5px;word-break:normal;} .tg .tg-baqh{text-align:center;vertical-align:top} Substance ${H_2}$ C (graphite) ${C_2}{H_6}(g)$ ${{{\Delta _c}{H^\Theta }} \over {kJ\,mo{l^{ - 1}}}}$ $- 286.0$ $- 394.0$ $- 1560.0$ The enthalpy of formation of ethane is

Which of the following reagents / reactions will convert 'A' to 'B' ?

Given below are two statements : Statement I : The presence of weaker π -bonds make alkenes less stable than alkanes. Statement II : The strength of the double bond is greater than that of carbon-carbon single bond. In the light of the above statements, choose the correct answer from the options given below :

In the industrial production of which of the following, molecular hydrogen is obtained as a byproduct?

The energy of one mole of photons of radiation of wavelength 300 nm is (Given : h = 6.63 $\times$ 10 $-$ 34 J s, N A = 6.02 $\times$ 10 23 mol $-$ 1 , c = 3 $\times$ 10 8 m s $-$ 1 )

A particle is moving in the xy-plane along a curve C passing through the point (3, 3). The tangent to the curve C at the point P meets the x-axis at Q. If the y-axis bisects the segment PQ, then C is a parabola with :

Let the maximum area of the triangle that can be inscribed in the ellipse ${{{x^2}} \over {{a^2}}} + {{{y^2}} \over 4} = 1,\,a > 2$ , having one of its vertices at one end of the major axis of the ellipse and one of its sides parallel to the y-axis, be $6\sqrt 3$ . Then the eccentricity of the ellipse is :

The number of solutions of the equation $\cos \left( {x + {\pi \over 3}} \right)\cos \left( {{\pi \over 3} - x} \right) = {1 \over 4}{\cos ^2}2x$ , $x \in [ - 3\pi ,3\pi ]$ is :

Consider the following statements: A : Rishi is a judge. B : Rishi is honest. C : Rishi is not arrogant. The negation of the statement "if Rishi is a judge and he is not arrogant, then he is honest" is

The number of distinct real roots of the equation x 7 − 7x − 2 = 0 is

Given below are two statements : Statement I : The reactance of an ac circuit is zero. It is possible that the circuit contains a capacitor and an inductor. Statement II : In ac circuit, the average power delivered by the source never becomes zero. In the light of the above statements, choose the correct answer from the options given below.

In Bohr's atomic model of hydrogen, let K, P and E are the kinetic energy, potential energy and total energy of the electron respectively. Choose the correct option when the electron undergoes transitions to a higher level :

What will be the most suitable combination of three resistors A = 2 Ω , B = 4 Ω , C = 6 Ω so that ( 22 3 ) Ω is equivalent resistance of combination?

A long cylindrical volume contains a uniformly distributed charge of density $\rho$ . The radius of cylindrical volume is R. A charge particle (q) revolves around the cylinder in a circular path. The kinetic energy of the particle is :

A proton, a deutron and an $\alpha$ -particle with same kinetic energy enter into a uniform magnetic field at right angle to magnetic field. The ratio of the radii of their respective circular paths is :

A random variable X has the following probability distribution : .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; overflow:hidden;padding:10px 5px;word-break:normal;} .tg th{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; font-weight:normal;overflow:hidden;padding:10px 5px;word-break:normal;} .tg .tg-c3ow{border-color:inherit;text-align:center;vertical-align:top} X 0 1 2 3 4 P(X) k 2k 4k 6k 8k The value of P(1 < X < 4 | X ≤ 2) is equal to :

If the shortest distance between the lines ${{x - 1} \over 2} = {{y - 2} \over 3} = {{z - 3} \over \lambda }$ and ${{x - 2} \over 1} = {{y - 4} \over 4} = {{z - 5} \over 5}$ is ${1 \over {\sqrt 3 }}$ , then the sum of all possible value of $\lambda$ is :

Let the system of linear equations x + y + α z = 2 3x + y + z = 4 x + 2z = 1 have a unique solution (x ∗ , y ∗ , z ∗ ). If ( α , x ∗ ), (y ∗ , α ) and (x ∗ , − y ∗ ) are collinear points, then the sum of absolute values of all possible values of α is

Let $x * y = {x^2} + {y^3}$ and $(x * 1) * 1 = x * (1 * 1)$ . Then a value of $2{\sin ^{ - 1}}\left( {{{{x^4} + {x^2} - 2} \over {{x^4} + {x^2} + 2}}} \right)$ is :

If $y = {\tan ^{ - 1}}\left( {\sec {x^3} - \tan {x^3}} \right),{\pi \over 2} < {x^3} < {{3\pi } \over 2}$ , then

The structure shown below is of which well-known drug molecule?

Which of the following chemical reactions represents Hall-Heroult Process?

Metals generally melt at very high temperature. Amongst the following, the metal with the highest melting point will be :

Which of the following is not an example of a condensation polymer?

Transition metal complex with highest value of crystal field splitting ( $\Delta$ 0 ) will be :