List of top Questions asked in JEE Main

Atomic number of element with lowest first ionisation enthalpy is:
Consider the following sequence of reactions given below: $ \text{Br-C}_6\text{H}_5 \xrightarrow{\text{alc. KOH}} \text{C}_6\text{H}_4 \xrightarrow{\text{NaNH}_2} \text{C}_6\text{H}_3 \xrightarrow{Hg^{2+}} \text{C}_6\text{H}_2 \xrightarrow{Zn-Hg} P $ The product P is:
Which of the following has $ sp^3d^2 $ hybridization?
Consider the last electron of element having atomic number 9 and choose the correct option.

A cone made of conducting material is given a charge $ Q $. $ \sigma_1, \sigma_2, \sigma_3 $ and $ \sigma_4 $ are charge densities at four points $ P, Q, R $ and $ S $. $ P $ is at the vertex of the cone and $ Q, R, S $ are at the periphery of the base. Choose the correct option.

A cube of side 10 cm is suspended from one end of a fine string of length 27 cm, and a mass of 200 grams is connected to the other end of the string. When the cube is half immersed in water, the system remains in balance. Find the density of the cube.

A rod of linear mass density $ \lambda $ and length $ L $ is bent into the form of a ring of radius $ R $. The moment of inertia of the ring about any of its diameters is:
A force $ 6 \hat{k} $ is applied for $ \frac{5}{3} $ seconds on a body of mass 2 kg. If the initial velocity of the body was $ 3\hat{i} + 4\hat{j} $, then find the final velocity of the body.
Bulk modulus of a liquid is $ 2 \times 10^9 \, \text{Pa} $. Initially and final pressure are 1 atm and 5 atm respectively. Find the initial volume of the liquid if change in volume is 0.8 cm$^3$.
An electron is released in the field generated by a non-conductivity sheet of uniform surface charge density $ \sigma $. The rate of change of de-Broglie wavelength associated with the electron varies inversely as the $ n $th power of the distance travelled. Find the value of $ n $.
A uniform disc of radius $ r $ is rotating about an axis passing through its diameter with angular speed 800 rpm. A torque of magnitude $ 25\pi \, \text{Nm} $ is applied on the disc for 40 sec. If the final angular speed of the disc is 2100 rpm, find the diameter of the disc if its mass is 1 kg.
Two balls are projected with the same speed at different angles. If the maximum height of the 1st ball is 8 times the maximum height of the 2nd ball, find the ratio of their time of flight.
Given $ \lambda = 2 \, \text{nC/m} $ (linear charge density) for a wire passing through the body diagonal of a closed cube with side length $ \sqrt{3} \, \text{cm} $, find the flux through the cube.
For a nucleus of mass number $ A $ and radius $ R $, mass density is $ \rho $. Then choose the correct option.
A convex lens (f = 30 cm) is in contact with a concave lens (f = -20 cm). An object is placed on the left side at a distance of 20 cm. Find the image distance.
A fractional error in $ x $, $ y $, and $ z $ are 0.1, 0.2, and 0.5 respectively. Find the maximum fractional error in $ x^{-2} y^{3/2} z^{-2/5} $.

Find output voltage in the given circuit.

Two balls are projected with the same speed at different angles. If the maximum height of the first ball is 2 times the maximum height of the second ball, find the ratio of their time of flight.
Consider the following statements:
Statement I: $H_2Se$ is more acidic than $H_2Fe$
Statement II: $H_2Se$ has higher bond dissociation enthalpy
In light of the above statements, choose the correct option.
For a nucleus of mass number $A$ and radius $R$, mass density $\rho$. Then choose the correct option.
A fractional errors in $x$, $y$, and $z$ are $0.1$, $0.2$, and $0.5$ respectively. Find the maximum fractional error in $x^{-2} y^3 z^{-2}$.
Given the series
$\frac{1}{1^4} + \frac{1}{2^4} + \frac{1}{3^4} + \cdots = \frac{\pi^4}{90},$
$\frac{1}{1^4} + \frac{1}{3^4} + \frac{1}{5^4} + \cdots = \alpha,$
$\frac{1}{2^4} + \frac{1}{4^4} + \frac{1}{6^4} + \cdots = \beta.$
Then find $\frac{\alpha}{\beta}$
Atomic number of element with lowest first ionisation enthalpy is
Consider the last electron of an element having atomic number $9$ and choose the correct option.
If \( f(\theta) = \frac{\tan(\tan(\theta)) - \tan(\sin(\theta))}{\tan(\theta) - \sin(\theta)} \) is continuous at \( \theta = 0 \), then the value of \( f(\theta) \) at \( \theta = 0 \) is equal to.