List of top Questions asked in JEE Main

For the reaction:
\[ \text{A(g)} \rightleftharpoons \text{B(g)} + \text{C(g)} \] Initial moles of A(g) is \(a\). At equilibrium, \(x\) moles of A decompose at total pressure \(P\). Calculate \(K_P\) for the given reaction.
In 1 litre aqueous solution 20 g of Haemoglobin is present at 300 K. This solution has height difference of 80 mm, when separated from pure water through S.P.M. If density of solution is 1000 kg/m$^3$, then calculate molar mass of Haemoglobin in kg/mol. (Use : $g = 10$ m/s$^2$)
Find binding energy of \(^{12}_{6}C\). Given mass of proton \(m_p = 1.0078\,u\) and mass of neutron \(m_n = 1.0087\,u\).
A thin convex lens and a thin concave lens are kept coaxially in contact. Choose the correct option.

Figure shows a circuit consisting of cell of emf \(E\) and internal resistance \(r\) connected in series with external resistance \(R\). When \(R = 5\Omega\), current \(i = 1\,A\) and when \(R = 2\Omega\), current \(i = 2\,A\). Find \(r\) (in ohm). 

Assertion: EM radiation when falls on a surface exerts pressure. Reason: Radiation has no rest mass.

Find the voltage across the capacitor in steady state. 

Find ratio of potential energy of a body at point A to point B for the figure shown. 

8 small liquid drops combine to form a bigger drop. Surface tension of liquid is \(T\). Find change in surface potential energy.
Match the column : \[ \begin{array}{|c|c|} \hline \text{Column-I} & \text{Column-II} \\ \hline (A)\;\sin^2(\omega t) & (P)\; \text{Non-periodic} \\ (B)\;\cos(\omega t)+\cos(2\omega t) & (Q)\; \text{Periodic but not SHM} \\ (C)\;\sin^2(2\omega t) & (R)\; \text{SHM with time period } \frac{\pi}{2\omega} \\ (D)\;\cos(\pi+\omega t)+\cos(\omega t) & (S)\; \text{SHM with time period } \frac{\pi}{\omega} \\ \hline \end{array} \]
Escape velocity on earth is \(V_e=\sqrt{2gR}\). A planet has half the radius of earth and density equal to half that of earth. If escape speed from that planet is \(\dfrac{V_0}{N}\), find \(N\).
Match the column according to dimensions. \[ \begin{array}{c|c|c} \text{Column A} & & \text{Column B} \\ \hline (A) & \sqrt{\dfrac{GM}{C}} & (1)\; M^{-1}L^{2}T^{-3/2} \\ (B) & \sqrt{\dfrac{h^{2}}{GC}} & (2)\; M^{0}L^{2}T^{-3/2} \\ (C) & \sqrt{GMC} & (3)\; M^{3/2}L^{0}T^{0} \\ (D) & \sqrt{\dfrac{GC}{M}} & (4)\; LT^{-1/2} \\ \end{array} \]
A rod has volume \(V\) and Young's modulus \(Y\) and is subjected to stress \(\tau\). Find elastic energy stored in the rod.
In an RLC series circuit the value of \(R, L\) and \(C\) is given as \(R = 50\Omega\), \(L = 1.6\,H\) and \(C = 40\mu F\). Find the value inductive reactance \((X_L)\) at resonance.
In PN junction, if P side is highly doped and N side is lightly doped, then

Magnetic field at a distance \(x\) from point \(C\) as shown in the figure on rod is \(B = B_0 e^{-\lambda x}\), find induced emf between ends of metallic rod. 

If across a resistance, voltage applied is \((20 \pm 0.2)\,\text{V}\) and the current passing through it is \((10 \pm 0.1)\,\text{A}\). Find the maximum error in resistance.

If the rolling object reaches a maximum height \(\frac{7v_0^2}{10g}\), what may be the object? 

In a YDSE setup slit separation is \(d = 5\lambda\), where \(\lambda\) is wavelength of light and screen is placed at distance \(D = 10d\). If maximum intensity is \(I_0\), find intensity at a point directly in front of one of the slit.
An electron travelling with velocity \(v\) in free space enters a medium where its velocity is reduced by \(20\%\). The de-Broglie wavelength of the electron in the medium is \(\alpha \lambda_0\), where \(\lambda_0\) is the wavelength in free space. Find the value of \(\alpha\).
There is a metallic ring of radius \(20\,\text{cm}\) placed in a uniform unsteady magnetic field \( B = (2t^2 + 2t + 3)\,\text{T} \) perpendicular to the plane of the ring. If the resistance of the ring is \(2\,\Omega\), find the induced current at \(t = 2\,\text{s}\). \([\pi = 22/7]\)
A wheel initially at rest is subjected to a uniform angular acceleration about its axis. In the first \(2\) sec it rotates through an angle \(\theta_1\) and in the next \(2\) sec it rotates an angle \(\theta_2\). Find the ratio \(\theta_2/\theta_1\).

Friction is sufficient so that the block does not slide. Find the work done by friction in \(2\) sec. 

If \(x\) gm of water at \(50^\circ\text{C}\) cools to \(0^\circ\text{C}\), the heat released is \(H\). If \((100 - x)\) gm of water at \(50^\circ\text{C}\) is completely vapourised, the heat required is also \(H\). Find \(x\).
Consider the nuclear reaction: \[ {}^{2}_{1}H + {}^{2}_{1}H \rightarrow {}^{4}_{2}He \] Binding energy per nucleon of \( {}^{2}_{1}H \) and \( {}^{4}_{2}He \) are \(1.1\,\text{MeV}\) and \(7\,\text{MeV}\) respectively. Find the energy released in the nuclear reaction.