List of top Questions asked in JEE Advanced- 2026

List-I shows four configurations made of straight and semi-circular narrow tubes containing air. A sound wave of wavelength \[ \lambda=0.29\ \text{m} \] enters these structures at the point \(S\) and a sound detector is placed at \(D\). Between the points \(S\) and \(D\), the sound travels only through the tubes. List-II contains the possible smallest values of \(l\) (refer to the figures) for which the detector \(D\) records maximum amplitude. Ignore effects of sharp corners. \[ [\text{Given: }\cos15^\circ=0.97] \]

As shown in the figure, an insulated container is fitted with a thermally conducting but immovable partition \((P_1)\) and a freely movable but thermally insulated piston \((P_2)\). The partition \(P_1\) with thermal conductivity \(K\), cross sectional area \(A\) and width \(x\) divides the container into two sections, \(S_1\) and \(S_2\), each containing one mole of a monoatomic gas. The piston \(P_2\) moves freely such that the gas in \(S_2\) is always at the atmospheric pressure. Initially, the temperature difference of \(S_1\) and \(S_2\) is \[ \Delta T_0 \] The time it takes for the temperature difference to become \[ \frac{\Delta T_0}{2} \] is \[ \frac{nRx}{KA} \] where \(R\) is the universal gas constant. The value of \(n\) is _______. \[ [\text{Given: }\ln2\approx0.7] \]

A hollow, right circular cone of base radius \(R\) and height \(h\), with its tip at the origin is rotating about the \(Z\)-axis with an angular velocity \(\omega\), as shown in the figure. The cone carries a total charge \(Q\) uniformly distributed on its curved surface. The magnitude of magnetic field at a point \[ (0,0,z), \qquad z\gg R \text{ and } z\gg h \] is \[ \frac{n\mu_0QR^2\omega}{4\pi z^3} \] The value of \(n\) is _______.

A quasi-static cycle of a monoatomic ideal gas contains an isothermal process \((ab)\), followed by an isochoric process \((bc)\) and an adiabatic process \((ca)\) as shown in the figure. The volumes of the gas are \(V_1\) and \(V_2\) at \(a\) and \(b\), respectively. If the cycle has heat input \(Q_{\mathrm{in}}\) and output \(Q_{\mathrm{out}}\), then the efficiency of the cycle is defined as \[ \eta=\frac{Q_{\mathrm{in}}-Q_{\mathrm{out}}}{Q_{\mathrm{in}}} \] The correct statement(s) is/are: \[ [\text{Given: }\ln2\approx0.7] \]

The electric field associated with an electromagnetic wave travelling in vacuum is given by \[ \vec E = E_0\sin(3y+4z+\omega t)\,\hat i \] where \(\omega\) is the angular frequency. All quantities are in SI units. The correct statement(s) about this wave is/are: \[ [\text{Given: speed of light in vacuum }c=3\times10^8\ \text{m s}^{-1}] \]

A double convex lens made of glass of refractive index \(1.5\) and radii of curvature \(20\,\text{cm}\) each is immersed in a liquid of refractive index \(n_L\). The correct plot showing the variation of the power, in the units of diopter \((D)\), as a function of \(n_L\), is:

Consider a hydrogen atom with \(v_k,\ r_k,\) and \(K_k\) denoting the velocity, orbital radius and kinetic energy of the electron in \(k^{\text{th}}\) orbit, respectively. The electron undergoes a transition from the \(n^{\text{th}}\) orbit, emitting radiation corresponding to the Lyman series. Considering \(h\) to be the Planck's constant and \(\epsilon_0\) the permittivity of free space, the correct statement(s) is/are:

A tank contains two immiscible liquids of densities \[ 6\rho \quad \text{and} \quad 2\rho \] The higher density liquid is filled up to a height \[ \frac L2 \] from the bottom. A thin rod of density \(\rho\) and length \(L\) is fully immersed and hinged at the bottom so that it can oscillate freely, as shown in the figure. If the rod is slightly disturbed from its equilibrium position, the time period of small oscillations is \[ \frac{2\pi}{n}\sqrt{\frac Lg} \] where \(g\) is the acceleration due to gravity. The value of \(n\) is _______.

A particle is thrown with a speed \(v\) from a point \(O\) at an angle \(\theta\) with the horizontal plane such that it passes through the point \(P\) at a height of \(1\,\text{m}\) and horizontal distance of \(5\,\text{m}\) from \(O\), as shown in the figure. If acceleration due to gravity is \(g\,\text{m s}^{-2}\), then the correct statement(s) is/are:

Consider a circuit consisting of a capacitor of capacitance \(C\) and a coil with \(N\) turns per unit length, cross sectional area \(S\) and length \(d\), where \[ d^2\gg S \] There is another coil of length \[ \frac d2 \] cross sectional area \[ \frac S2 \] and \(2N\) turns per unit length completely inside the larger coil, as shown in the figure. The ends of this smaller coil are connected with each other by an insulated conducting wire. The self-inductance of the larger coil is \(L\). Neglecting edge effects and all the Ohmic resistances, the resonant frequency of the circuit is:

For real numbers \(\alpha,\beta,\gamma,\delta\) and \(\mu\), consider the matrix \[ M= \begin{bmatrix} \alpha & \frac1{\sqrt2} & -\frac1{\sqrt2} \frac1{\sqrt3} & \beta & \frac1{\sqrt3} \gamma & \delta & \mu \end{bmatrix} \] Suppose that \[ MM^T=I \] where \(M^T\) is the transpose of the matrix \(M\) and \(I\) is the \(3\times3\) identity matrix. Let \[ \vec u=\alpha\hat i+\frac1{\sqrt3}\hat j+\gamma\hat k \] \[ \vec v=\frac1{\sqrt2}\hat i+\beta\hat j+\delta\hat k \] \[ \vec w=-\frac1{\sqrt2}\hat i+\frac1{\sqrt3}\hat j+\mu\hat k \] Match each entry in List-I to the correct entry in List-II and choose the correct option.

A solid cylinder of radius \(R\) rolls without slipping with a center of mass speed \[ v_0=\sqrt{\frac{gR}{3}} \] on a horizontal surface with a vertical edge, as shown in the figure. Here, \(g\) is the acceleration due to gravity. At the moment when the cylinder loses contact with the surface due to rotation around the corner, the speed of its center of mass is:

Match each entry in List-I to the correct entry in List-II and choose the correct option.

Consider a large disk of radius \(R\) and two smaller disks, each of radius \[ r=\frac{R}{50} \] lying on its circumference, as shown in the figure. The smaller disks are initially in contact with each other, with an angular separation \(\Delta\theta\) between their centers. They are made to roll without slipping in opposite directions, with constant angular velocities \(\omega\) and \(2\omega\) while the large disk is held stationary. The time at which the smaller disks are again in contact is: \[ \text{[Use }\sin(\Delta\theta)=\Delta\theta\text{ and ignore gravity.]} \]

Let \[ \alpha= \left(1-2\cos\frac{\pi}{11}\right) \left(1-2\cos\frac{3\pi}{11}\right) \left(1-2\cos\frac{9\pi}{11}\right) \left(1-2\cos\frac{27\pi}{11}\right) \left(1-2\cos\frac{81\pi}{11}\right) \] Then the value of \[ 5-\alpha^2 \] is ________.

The number of ways to distribute \(10\) identical red pens and \(14\) identical blue pens among four persons such that each person gets \(6\) pens is ________.

Match each entry in List-I to the correct entry in List-II and choose the correct option.

Match each entry in List-I to the correct entry in List-II and choose the correct option.

Let \(\mathbb R\) denote the set of all real numbers. Let \[ f:\mathbb R\to\mathbb R \] be an arbitrary function and let \[ g:\mathbb R\to\mathbb R \] be the function defined by \[ g(x)=xf(x),\qquad \forall x\in\mathbb R \] Then which of the following statements is (are) TRUE?

Consider the function \[ f:\left(-\frac{\pi}{2},\frac{\pi}{2}\right)\to(-\infty,\infty) \] defined by \[ f(x)=\left(|x|+|x-1|\right)\sin x+[x\sin x] \] where \([x\sin x]\) denotes the greatest integer less than or equal to \(x\sin x\). Let \(\alpha\) be the total number of points in the interval \[ \left(-\frac{\pi}{2},\frac{\pi}{2}\right) \] at which \(f\) is NOT continuous, and let \(\beta\) be the total number of points in the interval \[ \left(-\frac{\pi}{2},\frac{\pi}{2}\right) \] at which \(f\) is NOT differentiable. Then the value of \[ \alpha+\beta \] is ________.

Let \(P\) be the plane such that it contains the straight line \[ \frac{x-1}{2}=\frac{y-3}{3}=\frac{z+2}{1} \] and is perpendicular to the plane \[ x+2y+3z=4 \] Let \(P_1\) be the plane which passes through the point \((4,2,2)\) and is parallel to \(P\). Then which of the following statements is (are) TRUE?

Suppose that Box I contains \(6\) red balls and \(9\) green balls, and Box II contains \(8\) red balls and \(12\) green balls. All the balls of Box I and Box II are mixed together and a ball is chosen at random from them. Let \(E_1\) be the event that the ball chosen belonged to Box I and let \(E_2\) be the event that the ball chosen belonged to Box II. Let \(F_1\) be the event that the ball chosen is red and let \(F_2\) be the event that the ball chosen is green. Then which of the following statements is (are) TRUE?

Let \(P\) be the point on the parabola \(y=x^2\) such that the slope of the tangent to the parabola at the point \(P\) is \(4\). Let \(Q\) be the point in the first quadrant lying on the circle \[ x^2+y^2=2 \] such that the slope of the tangent to the circle at the point \(Q\) is \(-1\). Let \(R\) be the point in the first quadrant lying on the ellipse \[ x^2+4y^2=8 \] such that the slope of the tangent to the ellipse at the point \(R\) is \(-\frac12\). Then the radius of the circle passing through the points \(P\), \(Q\) and \(R\) is:

Considering only the principal values of the inverse trigonometric functions, evaluate: \[ \cot^{-1}(\cot(-11)) +10\sin\left(2\cos^{-1}\left(\frac1{\sqrt2}\right)\right) +10\sin\left(2\tan^{-1}(2)\right) \]