List of top Questions asked in JEE Main- 2023

Let $M$ be the maximum value of the product of two positive integers when their sum is 66. Let the sample space $S =\left\{x \in Z : x(66-x) \geq \frac{5}{9} M\right\}$ and the event $A =\{x \in S : x$ is a multiple of 3$\}$. Then $P ( A )$ is equal to

Isomeric amines with molecular formula C₈ H₁₁N give the following tests
Isomer (P) ⇒ Can be prepared by Gabriel phthalimide synthesis
Isomer (Q) ⇒ Reacts with Hinsberg’s reagent to give solid insoluble in NaOH
Isomer (R) ⇒ Reacts with HONO followed by β-naphthol in NaOH to give red dye.
Isomers (P), (Q) and (R) respectively are

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R:
S-1 $\rightarrow$ Steel is used in construction of a bridge and house.
S–2 $\rightarrow$ Modulus of elasticity of steel is high.
In the light of the above statements, choose the correct answer from the options given below

Spherical insulating ball and a spherical metallic ball of same size and mass are dropped from the same height Choose the correct statement out of the following (Assume negligible air friction)

A parallel plate capacitor of capacitance 2 F is charged to a potential V. The energy stored in the capacitor is E. The capacitor is now connected to another uncharged identical capacitor in parallel combination. The energy stored in the combination is E₅. The ratio $ E_5 / E_1 $ is:

If $f(x)=x^3-x^2 f^{\prime}(1)+x f^{\prime \prime}(2)-f^{\prime \prime \prime}(3), x \in R$, then

For three low density gases $A , B , C$ pressure versus temperature graphs are plotted while keeping them at constant volume, as shown in the figure.

The temperature corresponding to the point ' $K$ ' is :

Let A = {2, 3, 4} and B = {8, 9, 12}. Then the number of elements in the relation R = {((a₁, b₁), (a₂, b₂)) ∈ (A × B, A × B) : a₁ divides b₂ and a₂ divides b₁} is

Find out the major products from the following reaction sequence.

If 1000 droplets of water of surface tension 0.07 N/m, having same radius 1 mm each, combine to from a single drop In the process the released surface energy is - (Take π=$\frac {22}{7}$)

If $a_1,a_2,.......a_n$ are in arithmetic progression with common difference $d>n$, then find limit $\lim_{n \to \infty}\sqrt{\frac{d}{n}}(\frac{1}{\sqrt{a_1}+\sqrt{a_2}})+\frac{1}{\sqrt{a_2}+\sqrt{a_3}}+.......+\frac{1}{\sqrt{a_n}+\sqrt{a_{n-1}}})$ is____.

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 ______

If $A(1, 1, 1), B(0, λ, 0), C(λ + 1, 0, 1), D(2, -2, 2)$ are co-planer then $\sum (\lambda_i + 2)^2$ is equal to

Let $S=\{1,2,3,4,5,6\}$ Then the number of one-one functions $f: S \rightarrow P ( S )$, where $P ( S )$ denote the power set of $S$, such that $f(m) \subset f(m)$ where $n < m$ is _______

Let $x, y, z>1$ and $A=\begin{bmatrix}1 & \log _x y & \log _x z \\ \log _y x & 2 & \log _y z \\ \log _z x & \log _z y & 3\end{bmatrix}$ Then ∣adj(adjA2)∣ is equal to

$2 \sin \left(\frac{\pi}{22}\right) \sin \left(\frac{3 \pi}{22}\right) \sin \left(\frac{5 \pi}{22}\right) \sin \left(\frac{7 \pi}{22}\right) \sin \left(\frac{9 \pi}{22}\right)$is equal to

Let $P$ be a square matrix such that $P^2 = I - P$. For $\alpha, \beta, \gamma, \delta \in \mathbb{N}$, if $P^\alpha + P^\beta = \gamma I - 29P$ and $P^\alpha - P^\beta = \delta I - 13P$, then $\alpha + \beta + \gamma - \delta$ is equal to:

The number of ways of selecting two numbers $a$ and $b, a \in\{2,4,6, \ldots , 100\}$ and $b \in\{1,3,5, \ldots , 99\}$ such that 2 is the remainder when $a+b$ is divided by 23 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 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.

If the system of linear equations
7x +11y + αz = 13
5x + 4y + 7z = β
175x + 194y + 57z = 361
has infinitely many solutions, then α + β + 2 is equal to:

Let a, b, c be three distinct positive real numbers such that (2a)^log_^e^a = (bc)^log_^e^b and b^log_^e² = a^log_^e^c. Then 6a + 5bc is equal to _____.

In a metallic conductor, under the effect of applied electric field, the free electrons of the conductor

Which one of the following elements will remain as liquid inside pure boiling water?

Let $λ∈Z ,→a=λ\^i+\^j =/^ k λ ∈$ and $\overrightarrow{ b} = 3 \^i− \^j + 2 \^k$ . be a vector such that ( $\overrightarrow{ a}+\overrightarrow{ b}+\overrightarrow{ c}$ ) × $\overrightarrow{ c}=\overrightarrow{ 0},\overrightarrow{ a}.\overrightarrow{ c}$ and $\overrightarrow{ b}.\overrightarrow{ C}=-20$ Then $ | \overrightarrow{c} + ( λ \^i + \^j + \^k ) | ^2 $ is equal to