List of top Questions asked in JEE Main- 2022

Suppose y = y(x) be the solution curve to the differential equation 
\(\frac{dy}{dx}−y=2−e^{−x}\) such that \(\lim_{{x \to \infty}}y(x)\)
 is finite. If a and bare respectively the x – and y – intercepts of the tangent to the curve at x = 0, then the value of a – 4b is equal to _____.

Different A.P.’s are constructed with the first term 100, the last term 199, and integral common differences. The sum of the common differences of all such A.P.’s having at least 3 terms and at most 33 terms is ______.

The number of matrices
\(A=\begin{pmatrix}   a & b \\   c & d \\ \end{pmatrix}\), where a,b,c,d ∈−1,0,1,2,3,…..,10
such that A = A-1, is ______.

On complete combustion of 0.492 g of an organic compound containing C, H and O, 0.7938 g of CO2 and 0.4428 g of H2O was produced. The % composition of oxygen in the compound is _______.
A microscope was initially placed in air (refractive index 1). It is then immersed in oil (refractive index 2). For a light whose wavelength in air is λ, calculate the change of microscope’s resolving power due to oil and choose the correct option.
Which of the following methods are not used to refine any metal?
  1. Liquation
  2. Calcination
  3. Electrolysis
  4. Leaching
  5. Distillation
Choose the correct answer from the options given below :
In base vs acid titration, at the endpoint methyl orange is present as
Which oxoacid of phosphorous has the highest number of oxygen atoms present in its chemical formula?
An element M crystallises in a body centred cubic unit cell with a cell edge of 300 pm. The density of the element is 6.0 g cm–3. The number of atoms present in 180 g of the element is ______× 1023. (Nearest integer)

A logic gate circuit has two inputs A and B and output Y. The voltage waveforms of A, B and Y are shown below.
 

Fig. Logic gate circuit


The logic gate circuit is :

At a particular station, the TV transmission tower has a height of 100 m. To triple its coverage range, height of the tower should be increased to

In a meter bridge experiment, for measuring unknown resistance ‘S’, the null point is obtained at a distance 30 cm from the left side as shown at point D. If R is 5.6 kΩ, then the value of unknown resistance ‘S’ will be ___Ω.

Fig. Meter Bridge
The one division of main scale of Vernier callipers reads 1mm and 10 divisions of Vernier scale is equal to the 9 division on main scale. When the two jaws of the instrument touch each other, the zero of the Vernier lies to the right of zero of the main scale and its fourth division coincides with a main scale division. When a spherical bob is tightly placed between the two jaws, the zero of the Vernier scale lies in between 4.1 cm and 4.2 cm and 6th Vernier division coincides with a main scale division. The diameter of the bob will be ___ × 10–2 cm.
Two beams of light having intensities I and 4I interfere to produce a fringe pattern on a screen. The phase difference between the two beams are π/2 and π/3 at points A and B, respectively. The difference between the resultant intensities at the two points is xI. The value of x will be ___.
While performing a thermodynamics experiment, a student made the following observations.
HCl + NaOH \(\rightarrow\) NaCl + H2O; ΔH = – 57.3 kJ mol–1
CH3COOH + NaOH \(\rightarrow\) CH3COONa + H2O; ΔH = –55.3 kJ mol–1
The enthalpy of ionization of CH3COOH, as calculated by the student, is ______ kJ mol–1. [nearest integer]
A long cylindrical volume contains a uniformly distributed charge of density ρ cm–3.
 The electric field inside the cylindrical volume at a distance \(x=\frac{2ε_0}{ρ} m\) from its axis is _______ Vm–1
Fig.
A mass 0.9 kg, attached a horizontal spring, executes SHM with an amplitude A1. When this mass passes through its mean position, then a smaller mass of 124 g is placed over it and both masses move together with amplitude A2. If the ratio A1/A2 is α/(α – 1), then the value of α will be _____.

For the decomposition of azomethane, CH3N2CH3(g) → 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 ______ × 10–5s. [Nearest integer]

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]
\(\lim_{x\rightarrow \frac{\pi}{4}}\) 8\(\sqrt2\)−(cosx+sinx)\(^{\frac{7}{\sqrt2}}\)−\(\sqrt2\)sin2x is equal to
A square aluminium (shear modulus is 25 × 109 Nm–2) slab of side 60 cm and thickness 15 cm is subjected to a shearing force (on its narrow face) of 18.0 × 104 N. The lower edge is riveted to the floor. The displacement of the upper edge is ______μm.
A pulley of radius 1.5 m is rotated about its axis by a force F = (12t – 3t2) N applied tangentially (while t is measured in seconds). If moment of inertia of the pulley about its axis of rotation is 4.5 kg m2, the number of rotations made by the pulley before its direction of motion is reversed, will be K/π. The value of K is ________.
A ball of mass m is thrown vertically upward. Another ball of mass 2 m is thrown at an angle θ with the vertical. Both the balls stay in air for the same period of time. The ratio of the heights attained by the two balls respectively is 1/x. The value of x is _______.

Velocity (v) and acceleration (a) in two systems of units 1 and 2 are related as
\(v_2=\frac{n}{m^2}v_1\) and \(a_2=\frac{a_1}{mn}\)
respectively. Here m and n are constants. The relations for distance and time in two systems respectively are :

A ball is spun with angular acceleration α = 6t2 – 2t, where t is in second and α is in rads–2. At t = 0, the ball has angular velocity of 10 rads–1 and angular position of 4 rad. The most appropriate expression for the angular position of the ball is :