List of top Questions asked in JEE Main

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 block of mass \( m \) is moving with velocity \( v \) on a smooth horizontal surface. If a constant force \( F \) is applied to the block, what is the work done by this force after 5 seconds?
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 time period of a simple pendulum of length \( L \) and acceleration due to gravity \( g \)?
In a sound wave, the displacement of the air particles follows the equation \( y = A \cos(kx - \omega t) \). What is the wave velocity?
What is the solution to the differential equation \( \frac{dy}{dx} = \frac{y}{x} \) with the initial condition \( y(1) = 2 \)?
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?
For the function \( f(x) = \ln(x^2 + 1) \), what is the second derivative of \( f(x) \)?
Find the value of the integral \( \int_0^{\frac{\pi}{2}} \sin^2(x) \, dx \).
Let \( D = \{a, b, c\} \). How many distinct ways can \( D \) be partitioned into non-empty subsets, representing equivalence relations?
Which of the following has the maximum size?
In \( I(m, n) = \int_0^1 x^{m-1} (1-x)^{n-1} \, dx \), where \( m, n > 0 \), then \( I(9, 14) + I(10, 13) \) is:
Consider a parallel plate capacitor of area \( A \) (of each plate) and separation \( d \) between the plates. If \( E \) is the electric field and \( \epsilon_0 \) is the permittivity of free space between the plates, then the potential energy stored in the capacitor is:
A thin plano-convex lens made of glass of refractive index 1.5 is immersed in a liquid of refractive index 1.2. When the plane side of the lens is silver coated for complete reflection, the lens immersed in the liquid behaves like a concave mirror of focal length 0.2 m. The radius of curvature of the curved surface of the lens is:
An electron of mass \( m \) with an initial velocity \( \vec{v} = v_0 \hat{i} (v_0>0) \) enters an electric field \( \vec{E} = -E_0 \hat{k} \). If the initial de Broglie wavelength is \( \lambda_0 \), the value after time \( t \) would be:
One mole of the octahedral complex compound \( \text{Co(NH}_3)_5\text{Cl}_3 \) gives 3 moles of ions on dissolution in water. One mole of the same complex reacts with excess of \( \text{AgNO}_3 \) solution to yield two moles of \( \text{AgCl}(s) \). The structure of the complex is:

Which of the following linear combinations of atomic orbitals will lead to the formation of molecular orbitals in homonuclear diatomic molecules (internuclear axis in z-direction)?
(1) \( 2p_z \) and \( 2p_x \) 
(2) \( 2s \) and \( 2p_x \) 
(3) \( 3d_{xy} \) and \( 3d_{x^2-y^2} \) 
(4) \( 2s \) and \( 2p_z \) 
(5) \( 2p_z \) and \( 3d_{x^2-y^2} \) 
 

Ksp for \( \text{Cr(OH)}_3 \) is \( 1.6 \times 10^{-30} \). What is the molar solubility of this salt in water?
Let \[ f(x) = \lim_{n \to \infty} \sum_{r=0}^{n} \left( \frac{\tan \left( \frac{x}{2^{r+1}} \right) + \tan^3 \left( \frac{x}{2^{r+1}} \right)}{1 - \tan^2 \left( \frac{x}{2^{r+1}} \right)} \right) \] Then, \( \lim_{x \to 0} \frac{e^x - e^{f(x)}}{x - f(x)} \) is equal to:
A circle C of radius 2 lies in the second quadrant and touches both the coordinate axes. Let \( r \) be the radius of a circle that has centre at the point \( (2, 5) \) and intersects the circle C at exactly two points. If the set of all possible values of \( r \) is the interval \( (\alpha, \beta) \), then \( 3\beta - 2\alpha \) is equal to:
Let \( f(x) \) be a real differentiable function such that \( f(0) = 1 \) and \( f(x + y) = f(x)f'(y) + f'(x)f(y) \) for all \( x, y \in \mathbb{R} \). Then \( \sum_{n=1}^{100} \log_e f(n) \) is equal to :
Let the foci of a hyperbola be \( (1, 14) \) and \( (1, -12) \). If it passes through the point \( (1, 6) \), then the length of its latus-rectum is:

Sliding contact of a potentiometer is in the middle of the potentiometer wire having resistance \( R_p = 1 \, \Omega \) as shown in the figure. An external resistance of \( R_e = 2 \, \Omega \) is connected via the sliding contact.
The current \( i \) is : 

 

An electron in the ground state of the hydrogen atom has the orbital radius of \( 5.3 \times 10^{-11} \, \text{m} \) while that for the electron in the third excited state is \( 8.48 \times 10^{-10} \, \text{m} \). The ratio of the de Broglie wavelengths of the electron in the ground state to that in the excited state is: