List of top Questions asked in JEE Main

A solid sphere of mass \(M\) and radius \(R\) is split into two pieces of masses \( \frac{7M{8} \) and \( \frac{M}{8} \). The piece of mass \( \frac{7M}{8} \) is converted into a disc of radius \(2R\) and thickness \(t\) whose moment of inertia is \(I_1\). The other piece is made into a solid sphere with moment of inertia \(I_2\). Find \( \frac{I_1}{I_2} \).}
If $\int_{-2}^2 ([\sin x] + |x \sin x|) dx = 2 \sin 2 - 4 \cos 2 - \beta$, then the value of $|\beta|$ where $[\cdot]$ is GIF is
If Latus rectum of parabola $y^2 = 4kx$ and ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ coincide then the value of $e^2 + 2\sqrt{2}$ is, where $e$ is eccentricity of ellipse
An ideal gas has number of moles \(n=2\), initial volume \(V_0\) and pressure \[ P=P_0\left[1+\left(\frac{V_0}{V}\right)^2\right]^{-1}. \] The gas goes from state \(A\) (initial) to \(B\) (final) such that volume becomes \(3V_0\). Find \(T_A-T_B\).
Soluble in aqueous NaOH
Statement-1: Heat capacity at constant volume is always greater than heat capacity at constant pressure.
Statement-2: At constant volume as work done is zero, heat given to the chaotic motion is reflected by increase in temperature.
Let $y = \tan^{-1}\left( \frac{3\cos x - 4\sin x}{4\cos x + 3\sin x} \right) + \tan^{-1}\left( \frac{x}{1 + \sqrt{1 + x^2}} \right)$. Then the value of $\frac{dy}{dx}$ at $x = \frac{\sqrt{3}}{2}$ is :
Match the column-I with column-II:
Choose the correct match.
The domain of $f(x) = \cos^{-1} \left( \frac{4x + 2[x]}{3} \right)$ (where $[x]$ denotes greatest integer function) is
Consider the following reaction:
What is the colour of the final compound B?
If \( L_1 : x - y = 0 \), \( L_2 : y = -3x \), \( L_3 \) is the obtuse angle bisector of \( L_1 \) and \( L_2 \), and \( L_4 : x + 3 = 0 \). Let \( A \) be the point of intersection of \( L_4 \) and \( L_1 \), \( B \) be the point of intersection of \( L_4 \) and \( L_2 \), and \( C \) be the point of intersection of \( L_4 \) and \( L_3 \). Then the value of \( \dfrac{(BC)^2}{(AC)^2} \) is:
Statement-1: Maltose is a non-reducing sugar.
Statement-2: Lactose is a reducing sugar.
If $S = \{ A = \begin{bmatrix} a & b \\ c & d \end{bmatrix}, A^2 - 4A + 3I = \text{Null matrix}, a, b, c, d \in \{0, 1, 2, 3, 4\} \text{ and } \text{Tr}(A) = 4 \}$. Then the number of elements of set $S$ is/are
Anion \( X^- \) contains 45 neutrons and 36 electrons. The atomic mass, period number, and state in which "X" exists is:
Match the column:
} Match correct reagents with given reactions:
A slit of width \(a\) is illuminated by light of wavelength \(\lambda\). The linear separation between the 1st and 3rd minima in the diffraction pattern produced on a screen placed at a distance \(D\) from the slit is:
Calculate the number of molecules and moles of \( \text{SO_2 \) in its 1.479 liters at STP.}
Statement-1: Under certain conditions, the covalency of oxygen can be up to 4. In \( \text{SO}_2 \), the oxidation state of oxygen is \( -2 \) and in \( \text{OF}_2 \), the oxidation state of oxygen is \( +2 \). Statement-2: The anomalous behaviour of oxygen in the 16th group is due to its small size and high electronegativity.
Resolving power of a telescope is \(5\times10^{-7}\,\text{rad}\). If wavelength of incident light is \(500\,\text{nm}\), find the diameter of the aperture of the telescope.
If $f(x)$ is a non-constant polynomial satisfying $f(x) = f'(x)f''(x)$ and $f(0) = 0$. Then the value of $\int_0^2 f(x) dx + f'(2) + f''(2)$ is :
Let $A$ is a matrix of order 3 such that $|A| = -4$, then the value of $|\text{adj}(\text{adj}(2\text{adj} A)^{-1})|$ is
If $Z$ be a complex number such that $|Z + 2| = |Z - 2|$ and $\text{arg} \left( \frac{Z - 3}{Z + 1} \right) = \frac{\pi}{4}$, then the value of $|Z|^2$ is
If the right plate of a parallel plate capacitor is pulled with constant velocity as shown in the figure, find how the rate of change of energy stored in the capacitor depends on the separation \(x\).
If $f(x) = \min \{2x^2 + 3, 6x\} + |x-1| \cos(x^2 - \frac{1}{4})$, then the number of points of non derivability of $f(x)$ is/are
Let in a $\triangle ABC$, given that $A \equiv (1, 2)$, mid-point of $AB$ is $(-5, -1)$ and centroid is $(3, 4)$ then circumcentre is $(\alpha, \beta)$, then the value of $21(\alpha + \beta)$ is :