List of top Questions asked in JEE Main

Match List I with List II :

	List I		List II
A	3 Translational degrees of freedom	I	Monoatomic gases
B	3 Translational, 2 rotational degrees of freedoms	II	Polyatomic gases
C	3 Translational, 2 rotational and 1 vibrational degrees of freedom	III	Rigid diatomic gases
D	3 Translational, 3 rotational and more than one vibrational degrees of freedom	IV	Nonrigid diatomic gases

Choose the correct answer from the options given below:

' $A$' and ' $B$ ' formed in the following set of reactions are:

Given below are two statements: one is labeled as Assertion (A) and the other is labeled as Reason (R).
Assertion (A): Acidic nature follows the order:

Reason (R): F is a better electron-withdrawing group than Cl
In the light of the above statements, write the detailed answer:

The number of bijective functions $f :\{1,3,5$, $7, \ldots \ldots 99\} \rightarrow\{2,4,6,8, \ldots \ldots , 100\}$, such that $f (3) \geq f (9) \geq f (15) \geq f (21) \geq \ldots f (99), $ is _____

The d-electronic configuration of $\left[ CoCl _4\right]^{2-}$ in tetrahedral crystal field is $e ^{ m } t _2 ^n$ Sum of "$m$" and "number of unpaired electrons" is

A wire of resistance 160 Ω is melted and drawn in wire of one-fourth of its length. The new resistance of the wire will be

Let $\vec{a}, \vec{b}$ and $\vec{c}$ be three non zero vectors such that $\vec{b} \cdot \vec{c}=0$ and $\vec{a} \times(\vec{b} \times \vec{c})=\frac{\vec{b}-\vec{c}}{2}$ If $\vec{d}$ be a vector such that $\vec{b} \cdot \vec{d}=\vec{a} \cdot \vec{b}$, then $(\vec{a} \times \vec{b}) \cdot(\vec{c} \times \vec{d})$ is equal to

Let $x=\sin \left(2 \tan ^{-1} \alpha\right)$ and $y=\sin \left(\frac{1}{2} \tan ^{-1} \frac{4}{3}\right)$ If $S =\left\{\alpha \in R : y ^2=1- x \right\}$, then $\displaystyle\sum_{\alpha \in S } 16 \alpha^3$ is equal to ______

Compound A from the following reaction sequence is

Br2 , C S 2 0 − 5 ° C 0 − 5 ° 𝐶 → 𝐵 𝑟 2 , 𝐶 𝑆 2 B. N a N O 2 / H C l

The coefficient of x and x$^2$ in (1 + x)$^p$ (1 – x)$^q$ are 4 and – 5, then 2p + 3q is

A passenger sitting in a train A moving at 90 km/h observes another train B moving in the opposite direction for 8 s. If the velocity of train B is 54 km/h, then the length of train B is:

The electric potential at the center of two concentric half rings of radii $R_1$ and $R_2$, having same linear charge density $\lambda$ is :

Suppose $\displaystyle\sum_{r=0}^{2023} r^{22023} C_r=2023 \times \alpha \times 2^{2022}$ Then the value of $\alpha$ is

In the given circuit $C_1 = 2μF, C_2 = 0.2μF, C_3 = 2μF, C_4 = 4μF, C_5 = 2μF, C_6 = 2μF$. The charge stored on capacitor $C_4$ is _____ $μC$

A vehicle travels $4 \, km$ with speed of $3\, km / h$ and another $4 \, km$ with speed of $5\, km / h$, then it's average speed is

Two long parallel wires carrying currents $8 A$ and $15 A$ in opposite directions are placed at a distance of $7 cm$ from each other A point $P$ is at equidistant from both the wires such that the lines joining the point $P$ to the wires are perpendicular to each other The magnitude of magnetic field at $P$ is___$\times 10^{-6} T$(Given : $\sqrt{2}=1.4$ )

Let $ \alpha, \beta $ be the roots of the equation $ x^2 - \sqrt{2}x + 2 = 0 $, then $ \alpha^{14} + \beta^{14} $ is equal to:

Let S = {1, 2, 3, 4, 5, 6}. Then the number of one-one functions $f : S → P(S)$, where $P(S)$ denotes the power set of S, such that $f(n) ⊂ f(m)$ where $n < m,$ is:

A square loop of area $25\ cm^2$ has a resistance of $10\ Ω$. The loop is placed in uniform magnetic field of magnitude $40.0 \ T$. The plane of loop is perpendicular to the magnetic field. The work done in pulling the loop out of the magnetic field slowly and uniformly in $1.0$ sec, will be

The integral $\int \left(\frac{x}{2}\right)^x + \left(\frac{2}{x}\right)^x \log x \, dx$ is equal to:

Let $A$ be a $3 \times 3$ matrix such that $|\operatorname{adj}(\operatorname{adj}(\operatorname{adj} A ))|=12^4$ Then $\mid A ^{-1}$ adj $A \mid$ is equal to

If $\vec{P}=3 \hat{i}+\sqrt{3} \hat{j}+2 \hat{k}$ and $\vec{Q}=4 \hat{i}+\sqrt{3} \hat{j}+25 \hat{k}$ then, The unit vector in the direction of $\vec{P} \times \vec{Q}$ is $\frac{1}{x}(\sqrt{3} i+\hat{j}-2 \sqrt{3} \hat{k})$ The value of $x$ is

Let $S=\{\theta \in[0,2 \pi): \tan (\pi \cos \theta)+\tan (\pi \sin \theta)=0\}$ Then $\displaystyle\sum_{\theta \in s } \sin ^2\left(\theta+\frac{\pi}{4}\right)$ is equal to _______

If the function $f(x)=\begin{cases}(1+|\cos x|) \frac{\lambda}{|\cos x|} & , 0 < x < \frac{\pi}{2} \\\mu & , \quad x=\frac{\pi}{2} \\\frac{\cot 6 x}{e^{\cot 4 x}} & \frac{\pi}{2}< x< \pi\end{cases}$is continuous at $x=\frac{\pi}{2}, then 9 \lambda+6 \log _{ e } \mu+\mu^6- e ^{6 \lambda}$ is equal to

On a temperature scale X, the boiling point of water is 65° X and the freezing point is 15° X. Assume that the X scale is linear. The equivalent temperature corresponding to 95° X on the Fahrenheit scale would be: