List of top Questions asked in JEE Main- 2023

The amplitude of a particle executing SHM is $3 \,cm$ The displacement at which its kinetic energy will be $25 \%$ more than the potential energy is:_______ $cm$

N>40000, where N is divisible by 5. How many such 5 digit numbers can be formed using 0,1,3,5,7,9 without repetition.

If the sum of all the solutions of $\tan ^{-1}\left(\frac{2 x}{1-x^2}\right)+\cot ^{-1}\left(\frac{1-x^2}{2 x}\right)=\frac{\pi}{3},-1 < x < 1, x \neq 0$, is $\alpha-\frac{4}{\sqrt{3}}$, then $\alpha$ is equal to ___

Let $\vec{a}$ = 2$\widehat{i}$+3$\widehat{j}$+4$\widehat{k}$, $\vec{b}$ = $\widehat{i}$-2$\widehat{j}$-2$\widehat{k}$, $\vec{c}$ = -$\widehat{i}$+4$\widehat{j}$+3$\widehat{k}$ and $\vec{d}$ is a vector perpendicular to $\vec{b}$ and $\vec{c}$, $\vec{a}$.$\vec{d}$ = 18, then find |$\vec{a}$x$\vec{d}$|²

An inductor of $0.5 mH$, a capacitor of $20 \mu F$ and resistance of $20 \Omega$ are connected in series with a $220 V$ ac source If the current is in phase with the emf, the amplitude of current of the circuit is $\sqrt{x}$ A The value of $x$ is -

$\frac{dy}{dx}$ + $\frac{5}{x(1+x^5)}$y = $\frac{(1+x^5)^2}{x^7}$ If y(1) = 2, then the value of y(2) is:

Let $\vec{u}=\hat{i}-\hat{j}-2 \hat{k}, \vec{v}=2 \hat{i}+\hat{j}-\hat{k}, \vec{v} \cdot \vec{w}=2$ and $\vec{v} \times \vec{w}=\vec{u}+\lambda \vec{v}$. Then $\vec{u} \cdot \vec{w}$ is equal to

Let $\vec{a}=\hat{i}+2 \hat{j}+\lambda \hat{k}, \vec{b}=3 \hat{i}-5 \hat{j}-\lambda \hat{k}, \vec{a} \cdot \vec{c}=7,2 \vec{b} \cdot \vec{c}+43=0, \vec{a} \times \vec{c}=\vec{b} \times \vec{c}$. Then $|\vec{a} \cdot \vec{b}|$ is equal to

Let a and b are roots of $x^2 – 7x – 1 = 0$. The value of $\frac{(a_{21} + b_{21} + a_{17} + b_{17})}{(a_{19} + b_{19})}$ is?

$56.0 \,L$ of nitrogen gas is mixed with excess of hydrogen gas and it is found that $20\, L$ of ammonia gas is produced The volume of unused nitrogen gas is found to be _______ $L$

Number of 4-digit numbers that are less than or equal to 2800 and either divisible by 3 or by 11 , is equal to

Let $a_1=8, a_2, a_3, \ldots, a_n$ be an AP If the sum of its first four terms is $50$ and the sum of its last four terms is $170$ , then the product of its middle two terms is______

Let S = $\{z \in C-\{i,2i\}:\frac{z^2+8iz-15}{z^2-3iz-2}\in R\}$ if $\alpha-\frac{13}{11}i\in S, a \in R-{0}$, then $242\alpha^2$ is equal to ____.

Determine the amount of urea (NH₂CONH₂) to be added in 1000 g of water to decrease its vapour pressure by 25%.

Let $\vec{a}=5 \hat{i}-\hat{j}-3 \hat{k}$ and $\vec{b}=\hat{i}+3 \hat{j}+5 \hat{k}$ be two vectors Then which one of the following statements is TRUE ?

Let $\sum_{n=0}^{\infty }\frac{n^{3}((2n)!+(2n-1)(n!))}{(n!)((2n)!)}=ae+\frac{b}{e}+c$, where $a, b, c \in Z$ and $e=\displaystyle\sum_{n=0}^{\infty} \frac{1}{n !}$ Then $a^2-b+c$ is equal to _______

The pair of lanthanides will exceptionally high 3^rd ionisation enthalpy than neighbouring elements:

Let $a_1, a_2, a_3, \ldots$ be an AP If $a_7=3$, the product $a_1 a_4$ is minimum and the sum of its first $n$ terms is zero, then $n !-4 a_{n(n+2)}$ is equal to :

Let $\vec{a}, \vec{b}, \vec{c}$ be three vectors such that $|\vec{a}|=\sqrt{31}, 4|\vec{b}|=|\vec{c}|=2$ and $2(\vec{a} \times \vec{b})=3(\vec{c} \times \vec{a})$ If the angle between $\vec{b}$ and $\vec{c}$ is $\frac{2 \pi}{3}$, then $\left(\frac{\vec{a} \times \vec{c}}{\vec{a} \cdot \vec{b}}\right)^2$ is equal to _____

Rank of the word PUBLIC is?

Let a and b are roots of x² – 7x – 1 = 0. The value of $\frac{a^{21} + b^{21} + a^{17} + b^{17}}{a^{19} + b^{19}}$ is?

The energy levels of an hydrogen atom are shown below. The transition corresponding to emission of shortest wavelength is