List of top Questions asked in JEE Main

Given a charge $ q $, current $ I $ and permeability of vacuum $ \mu_0 $. Which of the following quantity has the dimension of momentum?
In the experiment for measurement of viscosity \( \eta \) of a given liquid with a ball having radius \( R \), consider following statements: A. Graph between terminal velocity \( V \) and \( R \) will be a parabola.
B. The terminal velocities of different diameter balls are constant for a given liquid.
C. Measurement of terminal velocity is dependent on the temperature.
D. This experiment can be utilized to assess the density of a given liquid.
E. If balls are dropped with some initial speed, the value of \( \eta \) will change.
A capillary tube of radius 0.1 mm is partly dipped in water (surface tension 70 dyn/cm and glass water contact angle $ \approx 0^\circ $) with $ 30^\circ $ inclined with vertical. The length of water risen in the capillary is ____ cm. (Take $ g = 9.8 $ m/s$^2 $)
A force \( \mathbf{F} = 2\hat{i} + 3\hat{j} + 5\hat{k} \) acts on a particle moving in the direction of \( \mathbf{r} = 2\hat{i} + 3\hat{j} + \beta \hat{k} \). Find the value of \( \beta \) when the work done is zero.
In the context of the photoelectric effect, what is the threshold frequency \( f_0 \) for a metal if the work function is \( \phi = 2 \, \text{eV} \)?

A coil of area  A  and N turns is rotating with angular velocity \( \omega\) in a uniform magnetic field \(\vec{B}\) about an axis perpendicular to \( \vec{B}\) Magnetic flux \(\varphi \text{ and induced emf } \varepsilon \text{ across it, at an instant when } \vec{B} \text{ is parallel to the plane of the coil, are:}\)

What is the solution to the differential equation \( \frac{dy}{dx} = \frac{y}{x} \) with the initial condition \( y(1) = 2 \)?
If the probability that the random variable X takes the value x is given by \( P(X = x) = k(x + 1)3^{-x} \), \( x = 0, 1, 2, 3, ... \), where k is a constant, then \( P(X \ge 3) \) is equal to
The line $ L_1 $ is parallel to the vector $ \mathbf{a} = -3\hat{i} + 2\hat{j} + 4\hat{k} $ and passes through the point $ (7, 6, 2) $, and the line $ L_2 $ is parallel to the vector $ \mathbf{b} = 2\hat{i} + \hat{j} + 3\hat{k} $ and passes through the point $ (5, 3, 4) $. The shortest distance between the lines $ L_1 $ and $ L_2 $ is:
In an arithmetic progression, if \( S_{40} = 1030 \) and \( S_{12} = 57 \), then \( S_{30} - S_{10} \) is equal to:
The maximum covalency of a non-metallic group 15 element 'E' with the weakest E-E bond is:
The metal ion whose electronic configuration is not affected by the nature of the ligand and which gives a violet color in non-luminous flame under hot condition in borax bead test is:
Let the points \( \left( \frac{11}{2}, \alpha \right) \) lie on or inside the triangle with sides \( x + y = 11 \), \( x + 2y = 16 \), and \( 2x + 3y = 29 \). Then the product of the smallest and the largest values of \( \alpha \) is equal to:
The system of equations \[ x + y + z = 6, \] \[ x + 2y + 5z = 9, \] \[ x + 5y + \lambda z = \mu, \] has no solution if:
The number of ways, 5 boys and 4 girls can sit in a row so that either all the boys sit together or no two boys sit together is:

Match List-I with List-II

Choose the correct answer from the options given below :

The successive 5 ionisation energies of an element are 800, 2427, 3658, 25024 and 32824 kJ/mol, respectively. By using the above values, predict the group in which the above element is present:

The correct stability order of the following species/molecules is:
 


 

Which one of the following reactions will not lead to the desired ether formation in major proportion?
(iso-Bu = isobutyl, sec-Bu = sec-butyl, nPr = n-propyl, tBu = tert-butyl, Et = ethyl)
Propane molecule on chlorination under photochemical condition gives two di-chloro products, "x" and "y". Amongst "x" and "y", "x" is an optically active molecule. How many tri-chloro products (consider only structural isomers) will be obtained from "x" when it is further treated with chlorine under the photochemical condition?
Let \( y = y(x) \) be the solution of the differential equation \( \frac{dy}{dx} + 3(\tan^2 x) y + 3y = \sec^2 x \), with \( y(0) = \frac{1}{3} + e^3 \). Then \( y\left(\frac{\pi}{4}\right) \) is equal to
If for the solution curve \( y = f(x) \) of the differential equation \[ \frac{dy}{dx} + (\tan x) y = 2 + \sec^2 x, \quad y(\frac{\pi}{3}) = \sqrt{3}, \] \(\text{then}\) \( y(\frac{\pi}{4}) \) is equal to:
A gas is kept in a container having walls which are thermally non-conducting. Initially the gas has a volume of 800 $ cm^3 $ and temperature 27°C. The change in temperature when the gas is adiabatically compressed to 200 $ cm^3 $ is: (Take $ \gamma $ = 1.5 : $ \gamma $ is the ratio of specific heats at constant pressure and at constant volume)
If the sum of the first 20 terms of the series $$ \frac{4.1}{4 + 3.1^2 + 1^4} + \frac{4.2}{4 + 3.2^2 + 2^4} + \frac{4.3}{4 + 3.3^2 + 3^4} + \frac{4.4}{4 + 3.4^2 + 4^4} + ... $$ is $ \frac{m}{n} $, where $ m $ and $ n $ are coprime, then $ m + n $ is equal to:
Visualize a vibrant street food festival set in an urban environment. Consider street food stalls, chefs preparing dishes, people standing in line and a variety of cuisines. Include street decorations and seating arrangements capturing the lively and diverse scene. Use suitable colours of your choice.