List of top Questions asked in JEE Main- 2023

Major product of the following reaction is

Let $f(x)=\begin{cases}x^2 \sin \left(\frac{1}{x}\right) & , x \neq 0 \\ 0 & , x=0\end{cases}$Then at $x=0$

Match the terms in Column-I with their description in Column-II and choose the correct option:

Column I (Chemical reactions)		Column II (Enzymes used)
(i)	Glucose → CO₂+ Ethanol	a	Pepsin
(ii)	Sucrose→Glucose + Fructose	b	Diastase
(iii)	Starch →Maltose	c	Zymase
(iv)	Protein→Amino acids	d	Invertase

If f(x) = [a+13 sinx] & x ε (0, $\pi$), then number of non-differentiable points of f(x) are [where 'a' is integer]

A solid sphere and a ring have equal masses and equal radius of gyration. If the sphere is rotating about its diameter and ring about an axis passing through and perpendicular to its plane, then the ratio of radius is $\sqrt{\frac{x}{2} }$ then find the value of x.

The number of solutions of cos4θ – 2cos2θ + 3sin6θ + 1 = 0 in [0,2π] is

Let $H$ be the hyperbola, whose foci are $(1 \pm \sqrt{2}, 0)$ and eccentricity is $\sqrt{2}$. Then the length of its latus rectum 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 $a_0$

Consider the lines $L_1$ and $L_2$ given by
$L_1: \frac{x-1}{2}=\frac{y-3}{1}=\frac{z-2}{2} $
$L_2: \frac{x-2}{1}=\frac{y-2}{2}=\frac{z-3}{3} $
A line $L_3$ having direction ratios $1,-1,-2$, intersects $L_1$ and $L_2$ at the points $P$ and $Q$ respectively Then the length of line segment $P Q$ is

A faulty thermometer reads $5^{\circ} C$ in melting ice and $95^{\circ} C$ in stream.The correct temperature on absolute scale will be_______ $K$ (when the faulty thermometer reads $41^{\circ} C$).

A triangle is formed by $X$-axis, $Y$-axis and the line $3 x+4 y=60$ Then the number of points $P ( n , b )$ which lie strictly inside the triangle, where a is an integer and $b$ is a multiple of a, is ____

It is observed that characteristic $X$-ray spectra of elements show regularity When frequency to the power " $n$ " ie $v^n$ of $X$-rays emitted is plotted against atomic number " $Z$ ", following graph is obtained

If the two metals $A$ and $B$ are exposed to radiation of wavelength $350 mm$. The work functions of metals $A$ and $B$ are $4.8 eV$ and $2.2 eV$. Then choose the correct option

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:

The increasing order of metallic character

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?

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?

If $\int \sqrt{\sec 2 x-1} d x=\alpha \log _e\left|\cos 2 x+\beta+\sqrt{\cos 2 x\left(1+\cos \frac{1}{\beta} x\right)}\right|+$ constant, then $\beta-\alpha$ is equal to_______

In the given circuit, the equivalent resistance between the terminal $A$ and $B$ is __$\Omega$

In the given circuit, the equivalent resistance between the terminal A and B is Ω

Number of compounds giving (i) red colouration with ceric ammonium nitrate and also (ii) positive iodoform test from the following is_____

The correct order of melting points of dichlorobenzenes is

Compound $( X )$ undergoes following sequence of reactions to give the Lactone $( Y )$

Two circles having radius $r_1$ and $r_2$ touch both the coordinate axes. Line $x+y=2$ makes intercept 2 on both the circles. The value of $r_{1}^{2} + r_{2}^{2} - r_{1}r_{2}$ is:

Which one amongst the following are good oxidizing agents?
(A) $ \text{Sm}^{\text{2+}}$
(B) $\text{Ce}^{\text{2+}}$
(C)$ \text{Ce}^{\text{4+}}$
(D) $\text{Tb}^{\text{4+}}$
Choose the most appropriate answer from the options given below:

1 L, 0.02 M solution of [Co(NH₃)₅SO₄]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