List of top Questions asked in JEE Main

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.

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.)

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

Match the LIST-I with LIST-II

Choose the correct answer from the options given below:

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.

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:-

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.

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 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 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 ————.

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 ————. $(\mu_0 = 4\pi \times 10^{-7} \text{ Tm/A}, \pi = 3.14)$

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 _______ $\text{kPa}$.

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 _________

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.

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 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 _______ $\text{m}$.

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 _______.

The density $\rho$ of a uniform cylinder is determined by measuring its mass $m$, length $l$ and diameter $d$. The measured values of $m, l$ and $d$ are $97.42 \pm 0.02$ g, $8.35 \pm 0.05$ mm and $20.20 \pm 0.02$ mm, respectively. Calculated percentage fractional error in $\rho$ 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

Let $y = y(x)$ be the solution of the differential equation $(x^2 - x\sqrt{x^2 - 1}) dy + (y(x - \sqrt{x^2 - 1}) - x) dx = 0, x \geq 1$. If $y(1) = 1$, then the greatest integer less than $y(\sqrt{5})$ is ________.

The rain drop of mass $1$ g, starts with zero velocity from a height of $1$ km. It hits the ground with a speed of $5$ m/s. The work done by the unknown resistive force is —————— J.
(take $g = 10$ m/s$^2$)

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 $\pi = 3.14$)

The area of the region {(x, y) : 0 ≤ y ≤ 6 - x, y^2 ≥ 4x - 3, x ≥ 0} is:

For the functions $f(\theta) = \alpha \tan^{2}\theta + \beta \cot^{2}\theta$, and $g(\theta) = \alpha \sin^{2}\theta + \beta \cos^{2}\theta$, $\alpha>\beta>0$, let $\min_{0<\theta<\frac{\pi}{2}} f(\theta) = \max_{0<\theta<\pi} g(\theta)$. If the first term of a G.P. is $\left( \frac{\alpha}{2\beta} \right)$, its common ratio is $\left( \frac{2\beta}{\alpha} \right)$ and the sum of its first 10 terms is $\frac{m}{n}$, $\gcd(m, n) = 1$, then $m + n$ is equal to ________.

If $\vec{a} = \hat{i} + \hat{j} + \hat{k}$, $\vec{b} = \hat{j} - \hat{k}$ and $\vec{c}$ be three vectors such that $\vec{a} \times \vec{c} = \vec{b}$ and $\vec{a} \cdot \vec{c} = 3$, then $\vec{c} \cdot (\vec{a} - 2\vec{b})$ is equal to __________.