List of top Questions asked in JEE Advanced

Let \[ f(x) = \begin{cases} \frac{7}{2}, & x = 0 \\ \frac{6x + \sin x}{2x + \sin x}, & x \neq 0 \end{cases} \] Then, which of the following statements are correct?

Calculate the sum of magnetic moments (in Bohr Magnetons, B.M.) of the complexes: \[ [\mathrm{MnCl}_6]^{3-} \quad \text{and} \quad [\mathrm{Mn(CN)}_6]^{3-} \]

A mass \(2m\) collides elastically with a stationary mass \(m\). After collision, the angle \(\theta\) is formed between their velocities. Find the maximum possible value of \(\theta\).

Let \[ \left(1 + \frac{2}{5}x\right)^{23} = \sum_{i=0}^{23} a_i x^i \] If the maximum value of \(a_i\) occurs at \(i = r\), find the value of \(r\).

If \[ \alpha = \frac{1}{\sin 60^\circ \sin 61^\circ} + \frac{1}{\sin 62^\circ \sin 63^\circ} + \dots + \frac{1}{\sin 118^\circ \sin 119^\circ} \] Then find the value of \(\dfrac{\csc^2 1^\circ}{\alpha^2}\)

Let a complex number \(z\) satisfy the equation \[ |z - z_1| = 2 |z - z_2|,\quad \text{where } z_1 = 1 + 2i,\ z_2 = 3i \] Then choose the correct options:

Find the dimensional formula of the quantity \(\alpha\), given: \[ \alpha = \frac{S^2 \cdot \sigma}{k}, \quad S = \frac{\text{EMF}}{\text{time}},\quad \sigma = \text{electric conductivity},\quad k = \text{thermal conductivity} \]

Evaluate the limit: \[ \lim_{x \to 0} \frac{\frac{\alpha}{2} \int_0^x \frac{dt}{1 - t^2} + \beta x \cos x}{x^3} = \gamma \]

Given the differential equation: \[ x^2 \frac{dy}{dx} + xy = x^2 + y^2, \quad \text{with } y(1) = 0 \] Find the value of \(\frac{y^2(e)}{y(e^2)}\).

Among \([Co(CN)_4]^{4-}\), \([Co(CO)_3(NO)]\), \(XeF_4\), \([PCl_4]^+\), \([PdCl_4]^{2-}\), \([ICl_4]^-\), \([Cu(CN)_4]^{3-}\), and \(P_4\), the total number of species with tetrahedral geometry is:

Consider the developed surface in Figure K. Lines of cut and fold are indicated. Draw the 3D view of the solid in a manner that the faces A, B, and C are visible.

A thin stiff insulated metal wire is bent into a circular loop with its two ends extending tangentially from the same point of the loop. The wire loop has mass \( m \) and radius \( r \) and is in a uniform vertical magnetic field \( B_0 \). When a current \( I \) is passed through the loop, the loop turns about the line PQ by an angle \( \theta \). The angle \( \theta \) is given by: 

Considering the operation given in Figure E, what is the result of the operation in Figure F?

Four circular cutouts have been made in the text in Figure B. Identify the option with the group of those four cutouts.

Five identical pillars, having equal height of 10 units and equal cross section, are inserted into the ground. Figure C shows only the portions of the pillars visible above ground. Which of the options given below indicates the ratio of the total volume of the pillars above and below the ground?

A table lamp designed with simple geometrical forms is shown below in plan, and elevations from S1 and S2. Draw the elevation of the same lamp from the direction P, as indicated in the plan.

A charge is kept at the central point \( P \) of a cylindrical region. The two edges subtend a half-angle \(\theta\) at \( P \), as shown in the figure. When \(\theta = 30^\circ\), then the electric flux through the curved surface of the cylinder is \(\Phi\). If \(\theta = 60^\circ\), then the electric flux through the curved surface becomes \(\frac{\Phi}{\sqrt{n}}\), where the value of \(n\) is \_\_\_\_. \includegraphics[width=0.3\linewidth]{ph8.png}

Among [Co(CN)₄]⁴⁻, [Co(CO)₃(NO)], XeF₄, [PCl₄ ]⁺, [PdCl₄ ]²⁻ , [ICl₄ ]⁻ , [Cu(CN)₄]³⁻ and P₄ the total number of species with tetrahedral geometry is _____.

Let \(a=3\sqrt2\) and \(b=\frac{1}{5^{1/6}\sqrt5}\). If x, y ∈ R are such that
\(3x+2y=\log_a(18)^{\frac{5}{4}}\) and
\(2x-y=\log_b(\sqrt{1080})\), 
then 4x + 5y is equal to _______.