List of top Questions asked in JEE Main

The electric field in a region is given by $ \vec{E} = (2\hat{i} + 4\hat{j} + 6\hat{k}) \times 10^3 \, N/C $. The flux of the field through a rectangular surface parallel to x-z plane is $ 6.0 \, Nm^2C^{-1} $. The area of the surface is ____ $ cm^2 $.

Let $ [\cdot] $ denote the greatest integer function. If \[ \int_0^3 \left\lfloor \frac{1}{e^x - 1} \right\rfloor \, dx = \alpha - \log_e 2, \] then $ \alpha^3 $ is equal to:

A steel wire of length 2 m and Young's modulus $ 2.0 \times 10^{11} \, \text{N/m}^2 $ is stretched by a force. If Poisson's ratio and transverse strain for the wire are $ 0.2 $ and $ 10^{-3} $ respectively, then the elastic potential energy density of the wire is $ \times 10^6$, in SI units .

The number of ways, in which the letters A, B, C, D, E can be placed in the 8 boxes of the figure below so that no row remains empty and at most one letter can be placed in a box, is:

Two large plane parallel conducting plates are kept 10 cm apart as shown in figure. The potential difference between them is $ V $. The potential difference between the points A and B (shown in the figure) is:

Quantitative analysis of an organic compound (X) shows the following percentage composition.
C: 14.5%
Cl: 64.46%
H: 1.8%
Empirical formula mass of the compound (X) is:

Two biased dice are rolled. Out of which one die contains 1, 1, 2, 2, 3, 3, and another die contains 1, 2, 2, 3, 3, 4. Then the probability of getting a sum of 4 or 5 is:

A Carnot engine (E) is working between two temperatures 473K and 273K. In a new system two engines - engine $E_1$ works between 473K to 373K and engine $E_2$ works between 373K to 273K. If $\eta_{12}$, $\eta_1$ and $\eta_2$ are the efficiencies of the engines $E$, $E_1$ and $E_2$, respectively, then:

A proton of mass 'mp' has same energy as that of a photon of wavelength 'λ'. If the proton is moving at non-relativistic speed, then ratio of its de Broglie wavelength to the wavelength of photon is.

Let the ellipse $ E_1 : \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 $, $ a>b $ and $ E_2 : \frac{x^2}{A^2} + \frac{y^2}{B^2} = 1 $, $ A<B $, have the same eccentricity $ \frac{1}{\sqrt{3}} $. Let the product of their lengths of latus rectums be $ \frac{32}{\sqrt{3}} $ and the distance between the foci of $ E_1 $ be 4. If $ E_1 $ and $ E_2 $ meet at A, B, C, and D, then the area of the quadrilateral ABCD equals:

Two parabolas have the same focus $ (4, 3) $ and their directrices are the x-axis and the y-axis, respectively. If these parabolas intersect at points A and B, then $ (AB)^2 $ is equal to:

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Time period of a simple pendulum is longer at the top of a mountain than that at the base of the mountain.
Reason (R): Time period of a simple pendulum decreases with increasing value of acceleration due to gravity and vice-versa. In the light of the above statements, choose the most appropriate answer from the options given below:

The area of the region enclosed by the curves $ y = e^x $, $ y = |e^x - 1| $, and the y-axis is:

Let $ A = \left\{ x \in (0, \pi) \mid - \log\left(\frac{2}{\pi}\right)\sin x + \log\left(\frac{2}{\pi}\right)\cos x = 2 \right\} $ and

\[ B = \left\{ x \geq 0 : \sqrt{x}(\sqrt{x - 4}) - 3\sqrt{x - 2} + 6 = 0 \right\}. \]

Then $ n(A \cup B) $ is equal to:

If $ A $ and $ B $ are the points of intersection of the circle $ x^2 + y^2 - 8x = 0 $ and the hyperbola $ \frac{x^2}{9} - \frac{y^2}{4} = 1 $, and a point $ P $ moves on the line $ 2x - 3y + 4 = 0 $, then the centroid of $ \triangle PAB $ lies on the line:

For a short dipole placed at origin $ O $, the dipole moment $ P $ is along the $ x $-axis, as shown in the figure. If the electric potential and electric field at $ A $ are $ V_0 $ and $ E_0 $ respectively, then the correct combination of the electric potential and electric field, respectively, at point $ B $ on the $ y $-axis is given by:

An electron projected perpendicular to a uniform magnetic field $ B $ moves in a circle. If Bohr’s quantization is applicable, then the radius of the electronic orbit in the first excited state is:

Which one of the following is the correct dimensional formula for the capacitance in F? M, L, T, and C stand for unit of mass, length, time, and charge.

The compound with molecular formula C$_6$H$_6$, which gives only one monobromo derivative and takes up four moles of hydrogen per mole for complete hydrogenation has $\_\_\_\_\_$$ \pi $ electrons.

20 mL of 2 M NaOH solution is added to 400 mL of 0.5 M NaOH solution. The final concentration of the solution is $\_\_\_\_\_$ x $10^{-2}$M. (Nearest integer)

What is the shape of the $ \text{ClO}_2^- $ ion according to VSEPR theory?

In a resistive circuit, the power dissipated by a resistor $ R $ when a current $ I $ flows through it is given by $ P = I^2 R $. What happens to the power when the current is doubled?

What is the sum of the infinite series $ S = \sum_{n=0}^{\infty} \frac{1}{3^n} $?

If the equation of a circle is $ 4x^2 + 4y^2 - 12x + 8y = 0 $, what is the radius of the circle?

Given below are two statements:
Statement I: The conversion proceeds well in a less polar medium. \[ {CH}_3{CH}_2{CH}_2{CH}_2{Cl} \xrightarrow{{HO}^-} {CH}_3{CH}_2{CH}_2{CH}_2{OH} + {Cl}^- \] Statement II: The conversion proceeds well in a more polar medium. \[ {CH}_3{CH}_2{CH}_2{CH}_2{Cl} \xrightarrow{{R}_3{N}} {CH}_3{CH}_2{CH}_2{CH}_2{NH}_2 + {Cl}^- \] In the light of the above statements, choose the correct answer from the options given below: