List of top Questions asked in JEE Main

(A) Bond angle Cr–O–Cr in \( \text{CrO}_7^{2-} \) is 126° (B) \( \text{Na}_2\text{Cr}_2\text{O}_7 \) is used as primary standard solution in titration. (C) \( \text{K}_2\text{Cr}_2\text{O}_7 \) oxidises \( \text{Fe}^{2+} \) into \( \text{Fe}^{3+} \) in acidic medium. (D) \( \text{CrO}_4^{2-} \) and \( \text{Cr}_2\text{O}_7^{2-} \) are interconvertible by changing pH.
Find the length of image of rod \(AB\). The rod is placed in front of a concave mirror of focal length \(f = 10\,\text{cm}\). End \(A\) is \(20\,\text{cm}\) from the mirror and the length \(AB = 10\,\text{cm}\).
Choose the correct match.
Match the column:
} Match correct reagents with given reactions:
Arrange the following groups according to their decreasing order of electron withdrawing nature – \( \text{COOH} \), \( \text{CN} \), \( I \), and \( \text{NO}_2 \).
Soluble in aqueous NaOH
Statement-1: Maltose is a non-reducing sugar.
Statement-2: Lactose is a reducing sugar.
Match the column-I with column-II:
Choose the correct match.
IUPAC Name of the formed compound:
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
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 :
If $A = \frac{\sin 3^\circ}{\cos 9^\circ} + \frac{\sin 9^\circ}{\cos 27^\circ} + \frac{\sin 27^\circ}{\cos 81^\circ}$ and $B = \tan 81^\circ - \tan 3^\circ$, find $\frac{B}{A}$
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
Two projectiles \(A\) and \(B\) are launched with the same speed at angles \(15^\circ\) and \(30^\circ\) respectively. Find the ratio of range \(A\) to range \(B\).
Length of rods are \( \ell \) and \(2\ell\) respectively and their Young's modulus are \( \gamma \) and \(2\gamma\) respectively. Given: \[ \ell = 0.314\,\text{m}, \quad R = 0.2\,\text{mm} \,(\text{same}), \quad \gamma = 2\times10^9 \]
Find the total extension \( \Delta \ell \).
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
For the reaction
\[ \text{A} + \text{B} \rightleftharpoons \text{C}, \quad K_p = 2.7 \times 10^{-5} \] Calculate \( K_p \) for the reaction
\[ \frac{1}{3} \text{A} + \frac{1}{3} \text{B} \rightleftharpoons \frac{1}{3} \text{C} \]
The graph shows stopping potential \(V_s\) versus frequency \(f\) of incident light for three different metals \(X_1, X_2,\) and \(X_3\). Choose the metal which will eject photoelectrons with maximum kinetic energy for a given frequency.
Angular momentum of the electron in a hydrogen atom is $\frac{3h}{2\pi}$, then find the energy of the electron in the orbit :-

Velocity versus time graph is given. Find the magnitude of acceleration of the particle at t = 5 s.

Escape velocity on Earth is ve = √(2gR). A planet of half the radius of Earth has the same density as Earth. The escape speed on that planet is ve / N. Find the value of N.
For process \( X \to Y \), work done by the gas is 10 J and heat absorbed in the process is 2 J. For the reverse process, heat evolved is 6 J. Find the work done for the reverse process.
How many of the following are paramagnetic:
Lu\(^{3+}\), Yb\(^{2+}\), Gd\(^{2+}\), Ce\(^{4+}\), La\(^{3+}\), Zn\(^{2+}\), Cu\(^{2+}\), Mn\(^{2+}\), Sc\(^{3+}\), and Ti\(^{4+}\)
A bag contains 4 red balls, 6 yellow balls and 5 blue balls. In how many ways we can select 8 balls such that we get at least two balls of each colour?
The value of the sum of r / (4 + r⁴) for r = 1 to 10 is: