List of top Questions asked in JEE Main

Consider the following data.

$$\begin{array}{|c|c|} \hline \text{Electrolyte} & \Lambda_m^\circ (\text{S cm}^2 \text{ mol}^{-1}) \\ \hline \text{BaCl}_2 & x_1 \\ \hline \text{H}_2\text{SO}_4 & x_2 \\ \hline \text{HCl} & x_3 \\ \hline \end{array}$$

$\text{BaSO}_4$ is sparingly soluble in water. If the conductivity of the saturated $\text{BaSO}_4$ solution is $x$ S cm$^{-1}$ then the solubility product of $\text{BaSO}_4$ can be given as
(Here $\Lambda_m = \Lambda_m^\circ$)

Given below are two statements:

Statement I: Aluminium is more electropositive than thallium as the standard electrode potential value of $E^\circ_{Al^{3+}/Al}$ is negative and $E^\circ_{Tl^{3+}/Tl}$ is positive.
Statement II: The sum of first three ionization enthalpies of boron is very high when compared to that of aluminium. Due to this reason boron forms covalent compounds only and aluminium forms $Al^{3+}$ ion.

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

The correct statements among the following are.

A. Basic vanadium oxide is used in the manufacture of $H_2SO_4$.
B. The spin-only magnetic moment value of the transition metal halide employed in Ziegler-Natta polymerization is 2.84 BM.
C. The p-block metal compound employed in Ziegler-Natta polymerization has the metal in +3 oxidation state.
D. The number of electrons present in the outer most 'd' orbital of metal halide employed in Wacker process is 8.

Choose the correct answer from the options given below:

Match the LIST-I with LIST-II

Choose the correct answer from the options given below:

One mole each of He and $A(g)$ are taken in a 10 L closed flask and heated to 400 K to establish the following equilibrium.
$$A(g) \rightleftharpoons B(g)$$
$K_c$ for this reaction at 400 K is 4.0. The partial pressures (in atm) of He and $B(g)$ are respectively (at equilibrium)
(Assume He, $A(g)$ and $B(g)$ behave as ideal gases)
(Given : $R = 0.082 \text{ L atm K}^{-1} \text{ mol}^{-1}$)

When 0.25 moles of a non-volatile, non-ionizable solute was dissolved in 1 mole of a solvent the vapor pressure of solution was $x \%$ of vapor pressure of pure solvent. What is $x \%$?

If shortest wavelength of hydrogen atom in Lyman series is $x$, then longest wavelength in Balmer series of $He^{+}$ is:

An oxide of iron contains $69.9\%$ iron, its empirical formula, is:
(Given : Molar mass of $Fe$ and $O$ are $56$ and $16\ g\ mol^{-1}$ respectively.)

Match the LIST-I with LIST-II

Choose the correct answer from the options given below:

Arrange the following isothermal processes in order of the magnitude of the work (p - V) involved between states 1 and 2.

A. Expansion in single stage $w_A$
B. Expansion in multi stages $w_B$
C. Compression in single stage $w_C$
D. Compression in multi stages $w_D$

Choose the correct option.

The ratio of momentum of the photons of the $1^{\text{st}}$ and $2^{\text{nd}}$ line of Balmer series of Hydrogen atoms is $\alpha/\beta$. The possible values of $\alpha$ and $\beta$ are:-

An unpolarized light of intensity $I_0$ passes through polarizer and then through a certain optically active solution and finally it goes to analyser. If the angle between analyser and polariser is $0^\circ$ and intensity of light emerged from analyser is $\frac{3}{8} I_0$, the angle of rotation of the light by the solution with respect to analyser is ________ degrees.

A certain gas is isothermally compressed to $(\frac{1}{3})^{rd}$ of its initial volume ($V_0 = 3$ litre) by applying required pressure. If the bulk modulus of the gas is $3 \times 10^5 \text{ N/m}^2$, the magnitude of work done on the gas is ____ J.

A three coulomb charge moves from the point $(0, -2, -5)$ to the point $(5, 1, 2)$ in an electric field expressed as $\vec{E} = 2x\hat{i} + 3y^2\hat{j} + 4\hat{k} \text{ N/C}$. The work done in moving the charge is ____ J.

A LCR series circuit driven with $E_{\text{rms}} = 90 \text{ V}$ at frequency $f_d = 30 \text{ Hz}$ has resistance $R = 80 \text{ } \Omega$, an inductance with inductive reactance $X_L = 20.0 \text{ } \Omega$ and capacitance with capacitive reactance $X_C = 80.0 \text{ } \Omega$. The power factor of the circuit is ________.

A small cube of side $1$ mm is placed at the centre of a circular loop of radius $10$ cm carrying a current of $2$ A. The magnetic energy stored inside the cube is $\alpha \times 10^{-14}$ J. The value of $\alpha$ is ————. $(\mu_0 = 4\pi \times 10^{-7} \text{ Tm/A}, \pi = 3.14)$

A spherical interface lens of radius $R$ separates two media of refractive indices $1$ and $1.4$ respectively as shown in the figure below. A point source is placed at a distance of $4R$ in front of spherical interface. The magnitude of the magnification of point source image is ————.

The two wires $A$ and $B$ of equal cross-section but of different materials are joined together. The ratio of Young's modulus of wire $A$ and wire $B$ is $20/11$. When the joined wire is kept under certain tension the elongations in the wires $A$ and $B$ are equal. If the length of wire $A$ is $2.2\text{ m}$, then the length of wire $B$ is _______ $\text{m}$.

Two closed vessels of same volume are joined through a narrow tube and both vessels are filled with air of pressure $90\text{ kPa}$ and temperature $400\text{ K}$. Keeping the temperature of one vessel constant at $400\text{ K}$ the second vessel temperature is raised to $500\text{ K}$. The final pressure in the vessels is _______ $\text{kPa}$.

A solid sphere of radius $4\text{ cm}$ and mass $5\text{ kg}$ is rotating (rotation axis is passing through the centre of the sphere) with an angular velocity of $1200\text{ rpm}$. It is brought to rest in $10\text{ s}$ by applying a constant torque. The torque applied and the number of rotations it made before it comes to rest are ______ and ______ respectively.

The position of center of mass of three masses 2 kg, 3 kg and 15 kg placed with respect to mid point ($p$) of normal bisector, as shown in the figure is _________

In interference experiment the path difference between two interfering waves at a point $A$ on the screen is $\lambda/3$, where $\lambda$ is the wavelength of these waves, and at another point $B$ the path difference is $\lambda/6$. The ratio of intensities at points $A$ and $B$ is _______.

A smooth inclined plane ends in a vertical circular loop, as shown in the figure. A small body is released from height $h$ as shown. If the body exerts a force of three times its weight on the plane at the highest point of circle then the height $h = \alpha R$. The value of $\alpha$ is _________.

The potential energy of a particle changes with distance $x$ from a fixed origin as $V = \frac{A\sqrt{x}}{x + B}$, where $A$ and $B$ are constant with appropriate dimensions. The dimensions of $AB$ are

A lift of mass $1600\text{ kg}$ is supported by thick iron wire. If the maximum stress which the wire can withstand is $4 \times 10^8\text{ N/m}^2$ and its radius is $4\text{ mm}$, then maximum acceleration the lift can take is ______ $\text{m/s}^2$. (take $g = 10\text{ m/s}^2$ and $\pi = 3.14$)