List of top Questions asked in JEE Main- 2022

Let K1 and K2 be the maximum kinetic energies of photo-electrons emitted when two monochromatic beams of wavelength λ1 and λ2, respectively are incident on a metallic surface. If λ1 = 3λ2 then:
If the shortest distance between the lines \(\frac{x-1}{2} = \frac{y-2}{3} = \frac{z-3}{λ}\; and\; \frac{x-2}{1 }= \frac{y-4}{4 }= \frac{z-5}{5 }\;is\; \frac{1}{\sqrt3}\), then the sum of all possible values of \(λ\) is :
The number of solutions of the equation \(cos \bigg(x+\frac{π}{3}\bigg)cos\bigg(\frac{π}{3-x}\bigg)=\frac{1}{4}cos^22x,x ∈ [-3π, 3π]\) is:
A person moved from A to B on a circular path as shown in figure. If the distance travelled by him is 60 m, then the magnitude of displacement would be
(Given cos135°= –0.7)
Which one of the following is an example of disproportionation reaction?
The most common oxidation state of Lanthanoid elements is +3. Which of the following is likely to deviate easily from +3 oxidation state?
Following statements related to radioactivity are given below:
(A) Radioactivity is a random and spontaneous process and is dependent on physical and chemical conditions.
(B) The number of un-decayed nuclei in the radioactive sample decays exponentially with time.
(C) Slope of the graph of loge (no. of undecayed nuclei) Vs. time represents the reciprocal of mean life time (τ).
(D) Product of decay constant (λ) and half-life time (T1/2) is not constant.
Choose the most appropriate answer from the options given below:

In the given circuit the input voltage Vin is shown in figure. The cut-in voltage of p–n junction diode
(D1 or D2) is 0.6 V. Which of the following output voltage (V0) waveform across the diode is correct?

A random variable \(X\) has the following probability distribution : 
x01234
P(x)k2k4k6k8k

The value of \(P(1 < X < 4 | x ≤ 2)\) is equal to

The number of distinct real roots of the equation \(x^7 – 7x – 2 = 0\) is
A charge particle moves along circular path in a uniform magnetic field in a cyclotron. The kinetic energy of the charge particle increases to 4 times its initial value. What will be the ratio of new radius to the original radius of circular path of the charge particle
\(lim _{ n → ∞}\bigg (\frac{n^2}{(n^2+1)(n+1)}+\frac{n^2}{(n^2+4)(n+2)}+\frac{n^2}{(n2+9)(n+3)}.....+ \frac{n^2}{(n^2+n^2)(n+n)}\bigg)\)is equal to
The major product of the following reaction is:
 Chemical Reaction With No2FI
Which of the following reactions will yield benzaldehyde as a product?
reactions will yield benzaldehyde as a product
A body of mass 0.5 kg travels on straight line path with velocity v = (3x2 + 4) m/s. The network done by the force during its displacement from x = 0 to x = 2 m is
Let the maximum area of the triangle that can be inscribed in the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{4} = 1, a>2\), 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 \(6\sqrt3\). Then the eccentricity of the ellipse is
The measured BOD values for four different water samples (A-D) are as follows:
A = 3 ppm; B = 18 ppm; C = 21 ppm; D = 4 ppm;. The water samples which can be called as highly polluted with organic wastes, are
A certain amount of gas of volume V at 27°C temperature and pressure 2 × 107 Nm–2 expands isothermally until its volume gets doubled. Later it expands adiabatically until its volume gets redoubled. The final pressure of the gas will be (Use, γ = 1.5)
A student in the laboratory measures thickness of a wire using screw gauge. The readings are 1.22 mm, 1.23 mm, 1.19 mm and 1.20 mm. The percentage error is \(\frac{x}{121}\)%. The value of x is _________.

A block of metal weighing 2 kg is resting on a frictionless plane (as shown in figure). It is struck by a jet releasing water at a rate of 1 kgs–1 and at a speed of 10 ms–1. Then, the initial acceleration of the block, in ms–2, will be:

A block of metal weighing 2 kg is resting on a frictionless plane

Following statements are given:
(A) The average kinetic energy of a gas molecule decreases when the temperature is reduced.
(B) The average kinetic energy of a gas molecule increases with increase in pressure at constant temperature.
(C) The average kinetic energy of a gas molecule decreases with increase in volume.
(D) Pressure of a gas increases with increase in temperature at constant pressure.
(E) The volume of gas decreases with increase in temperature.
Choose the correct answer from the options given below:

In van der Wall equation

\([P=\frac{a}{V^2}[v-b]=RT;\)

P is pressure, V is volume, R is universal gas constant and T is temperature. The ratio of constants a/b is dimensionally equal to:

Two vectors \(\overrightarrow{A}+\overrightarrow{B}\) have equal magnitudes. If magnitude of \(\overrightarrow{A}+\overrightarrow{B}\) is equal to two times the magnitude of \(\overrightarrow{A}-\overrightarrow{B}\) then the angle between vec A and \(\overrightarrow{B}\) will be

A zener of breakdown voltage VZ = 8 V and maximum Zener current, IZM = 10 mA is subjected to an input voltage Vi = 10 V with series resistance R = 100 Ω. In the given circuit RL represents the variable load resistance. The ratio of maximum and minimum value of RL is __________.
The escape velocity of a body on a planet ‘A’ is 12 kms–1. The escape velocity of the body on another planet ‘B’, whose density is four times and radius is half of the planet ‘A’, is