List of top Questions asked in JEE Main- 2023

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 ______

The minimum value of the function $f(x)=\int\limits_0^2 e^{|x-t|} d t$ is :

The major product P formed in the given reaction is:

If the coefficient of $x^{15}$ in the expansion of $\left(a x^3+\frac{1}{b x^{1 / 3}}\right)^{15}$ is equal to the coefficient of $x^{-15}$ in the expansion of $\left(a x^{1 / 3}-\frac{1}{b x^3}\right)^{15}$, where a and $b$ are positive real numbers, then for each such ordered pair $(a, b)$ :

A spherical drop of liquid splits into 1000 identical spherical drops If $u _{ i }$ is the surfice energy of the original drop and $u_f$ is the total surface energy of the resulting drops, the (ignoring evaporation), $\frac{u_f}{u_i}=\left(\frac{10}{x}\right)$ Then value of $x$ is ___

4,11,21,34….. Find the value of \(\frac{(S_{29}-S_{9})}{60}\)?

If the solution of the equation $\log _{\cos x} \cot x+4 \log _{\sin x} \tan x=1, x \in\left(0, \frac{\pi}{2}\right)$, is $\sin ^{-1}\left(\frac{\alpha+\sqrt{\beta}}{2}\right)$, where $\alpha$, $\beta$ are integers, then $\alpha+\beta$ is equal to :

$\displaystyle\lim _{x \rightarrow \infty} \frac{(\sqrt{3 x+1}+\sqrt{3 x-1})^6+(\sqrt{3 x+1}-\sqrt{3 x-1})^6}{\left(x+\sqrt{x^2-1}\right)^6+\left(x-\sqrt{x^2-1}\right)^6} x^3$

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?

\(max\\{0≤x≤π}\) \(\{x−2\,\, sin. x \,\,cos+\frac{1}{3} sin\,\, 3x \}=\)

The number of units, which are used to express concentration of solutions from the following is _______
Mass percent, Mole, Mole fraction, Molarity, ppm, Molality

1 L, 0.02 M solution of [Co(NH₃)₅ SO₄]Br is mixed with 1 L, 0.02 M solution of [Co(NH₃)₅Br]SO₄.  The resulting solution is divided into two equal parts (X) and treated with excess of AgNO₃ solution and BaCl₂ solution respectively as shown below:
1 L Solution (X) + AgNO₃ solution (excess) →  Y  
1 L Solution (X) + BaCl₂ solution (excess) → Z
The number of moles of Y and Z respectively are

The total pressure observed by mixing two liquids $A$ and $B$ is $350 \, mm$ Hg when their mole fractions are $0.7$ and $0.3$ respectively The total pressure becomes $410 \,mm \,Hg$ if the mole fractions are changed to $0.2$ and $0.8$ respectively for $A$ and $B$ The vapour pressure of pure $A$ is _________$mm \,Hg$ (Nearest integer) Consider the liquids and solutions behave ideally.

What is the mass ratio of ethylene glycol \((C _2H _6O_2\), molar mass \(62\ g/mol)\) required for making \(500\ g\) of \(0.25\) molal aqueous solution and \(250\ ml\) of \(0.25\) molal aqueous solution?

Which transition in the hydrogen spectrum would have the same wavelength as the Balmer type transition from $n =4$ to $n =2$ of $He ^{+}$spectrum

Given below are two statements: one is labeled as Assertion (A) and the other is labeled as Reason (R).
Statement-1: According to Bohr’s Model, angular momentum is Quantized for stationary orbits.
Statement-2: Bohr’s Model doesn’t follow Heisenberg’s Uncertainty Principle.
In the light of the above statements, write the detailed answer:

Arrange the following orbitals in decreasing order of energy
A. $n=3, l =0, m =0$
B. $n =4, l =0, m =0$
C. $n =3, l =1, m =0$
D. $n =3, l =2, m =1$
The correct option for the order is :

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason $R$:
Assertion A: Acetal / Ketal is stable in basic medium
Reason R: The high leaving tendency of alkoxide ion gives the stability to acetal ketal in basic medium
In the light of the above statements, choose the correct answer from the options given below :

Maximum number of electrons that can be accommodated in shell with $n=4$ are:

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

The wave function $(\Psi)$ of $2 s$ is given by $\Psi_{2 n }=\frac{1}{2 \sqrt{2 \pi}}\left(\frac{1}{a_0}\right)^{1 / 2}\left(2-\frac{r}{a_0}\right) e^{-\frac{r}{2 a_0}}$ At $r=r_0$, radial node is formed Thus, $r_0$ in terms of $a_0$

The IUPAC nomenclature of an element with electronic configuration $[ Rn ] 5 f ^{14} 6 d ^1 7 s ^2$ is :

Which of the following sets of quantum numbers is not allowed?

If the radius of ground state hydrogen is 51 pm, find out the radius of 5th orbit of Li²⁺ ions. (closest integer)