List of top Questions asked in JEE Main- 2023

Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R
Assertion (A) : Benzene is more stable than hypothetical cyclohexatriene
Reason (R) : The delocalised π-electrons cloud is attracted more strongly by the nuclei of the carbon atoms than the electron cloud localised between two carbon atoms.
In the light of the above statements, choose the correct answer from the options given below

The metal which is extracted by oxidation and subsequent reduction from its ore is:

$K_2Cr_2O_7$ paper acidified with dil. $H_2SO_4$ turns green when exposed to :

Choose the correct options based on the column shown below.

1.	TV signal	(P)	12 GHz
2.	Satellite	(Q)	30 MHz
3.	AM	(R)	88 MHz
4.	FM	(S)	1 MHz

If frequency can be represented as f = (radius)a (density)b (surface tension)c. Find a, b, c?

S₁: Be⁺² has higher SRP than other alkaline earth metals.
S₂: Be⁺² has higher hydration energy and greater △aH (atomisation enthalpy) than other alkaline earth metals.

Let $f: R -\{2,6\} \rightarrow R$ be real valued function defined as $f(x)=\frac{x^2+2 x+1}{x^2-8 x+12}$ Then range of $f$ is

Two isolated metallic solid spheres of radii $R$ and $2 R$ are charged such that both have same charge density $\sigma$. The spheres are then connected by a thin conducting wire. If the new charge density of the bigger sphere is $\sigma^{\prime}$ The ratio $\frac{\sigma^{\prime}}{\sigma}$ is :

The sum $\displaystyle\sum_{n=1}^{21} \frac{3}{(4 n-1)(4 n+3)}$ is equal to

$\displaystyle\lim _{n \rightarrow \infty} \frac{1}{2^n}\left(\frac{1}{\sqrt{1-\frac{1}{2^n}}}+\frac{1}{\sqrt{1-\frac{2}{2^n}}}+\frac{1}{\sqrt{1-\frac{3}{2^n}}}+\ldots +\frac{1}{\sqrt{1-\frac{2^n-1}{2^n}}}\right)$ is equal to

The number of functions $f:\{1,2,3,4\} \rightarrow\{ a \in: Z|a| \leq 8\}$ satisfying $f(n)+\frac{1}{n} f( n +1)=1, \forall n \in\{1,2,3\}$ is

If $A$ and $B$ are two events such that $P ( A )=\frac{1}{3}, P ( B )=\frac{1}{5}$ and $P ( A \cup B )=\frac{1}{2}$, then $P \left( A \mid B ^{\prime}\right)+ P \left( B \mid A ^{\prime}\right)$ is equal to

Let $[t]$ denote the greatest integer less than or equal to t Then the value of the integral $\int\limits_{-3}^{101}\left([\sin (\pi x)]+e^{[\cos (2 \pi x)]}\right) d x$ is equal to

The equations of two sides of a variable triangle are $x-0$ and $y=3$, and its third side is a tangent to the parabola $y^2=6 x$. The locus of its circumcentre is:

Let a smooth curve $y=f(x)$ be such that the slope of the tangent at any point $(x, y)$ on it is directly proportional to $\left(\frac{-y}{x}\right)$ If the curve passes through the point $(1,2)$ and $(8,1)$, then $\left|y\left(\frac{1}{8}\right)\right|$ is equal to

If the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ meets the line $\frac{x}{7}+\frac{y}{2 \sqrt{6}}=1$ on the $x$-axis and the line $\frac{x}{7}-\frac{y}{2 \sqrt{6}}=1$ on the $y$-axis, then the eccentricity of the ellipse is

Let $T$ and $C$ respectively be the transverse and conjugate axes of the hyperbola $16 x^2-y^2+64 x+4 y$ $+44=0$. Then the area of the region above the parabola $x^2=y+4$, below the transverse axis $T$ and on the right of the coujugate axis $C$ is:

The tangents at the point $A (1,3)$ and $B (1,-1)$ on the parabola $y^2-2 x-2 y=1$ meet at the point $P$ Then the area (in unit $^2$ ) of $\triangle PAB$ is :-

Let the foci of the ellipse $\frac{x^2}{16}+\frac{y^2}{7}=1$ and the hyperbola $\frac{x^2}{144}-\frac{y^2}{\alpha}=\frac{1}{25}$ coincide Then the length of the latus rectum of the hyperbola is:-

The number of numbers, strictly between 5000 and 10000 can be formed using the digits 1,3,5,7,9 without repetition, is