List of top Questions asked in JEE Main- 2023

If the maximum distance of normal to the ellipse $\frac{x^2}{4}+\frac{y^2}{b^2}=1, b<2$, from the origin is 1 , then the eccentricity of the ellipse is

If area bounded by region ${x, y)| |x^{2}-2| ≤ y ≤ x}$ is A, then 6A + 16$\sqrt{2}$ is?

A particle is thrown vertically upward with initial velocity of 150m/s. Find the ratio of its speed at t=3s and t=5s. (Take g=10 $ms^{-2}$)

Among the statements :
$(S1)$ $(( p \vee q ) \Rightarrow r ) \Leftrightarrow( p \Rightarrow r )$
$(S2)$$(( p \vee q ) \Rightarrow r ) \Leftrightarrow(( p \Rightarrow r ) \vee( q \Rightarrow r ))$

Three dice are thrown. Then the probability that no outcomes is similar is p/q then q – p is (where p and q are co-prime)

The sum of all the four-digit numbers that can be formed using all the digits 2, 1, 2, 3 is equal to ______.

Let a circle of radius 4 be concentric to the ellipse $ 15x^2 + 19y^2 = 285 $. Then the common tangents are inclined to the minor axis of the ellipse at the angle:

Let a die be rolled $ n $ times. Let the probability of getting odd numbers seven times be equal to the probability of getting odd numbers nine times. If the probability of getting even numbers twice is $ \frac{k}{2^{15}} $, then $ k $ is equal to:

The area enclosed by $y = |x-1| + |x-2|$ and $y = 3$

Orthocentre of triangle having vertices as A (1,2), B(3,-4), C(0,6) is

If n $\in$ [10,100] and n $\in$ N, then how many such n are possible where 3n - 3 is divisible by 7?

Let the image of the point P(1, 2, 6) in the plane passing through the points A(1, 2, 0), B(1, 4, 1) and C(0, 5, 1) be Q (α, β, γ). Then (α² + β² + γ²) is equal to

For the system of linear equations
$x+y+z=6$
$\alpha x+\beta y+7 z=3$
$x+2 y+3 z=14$.
which of the following is NOT true ?

If the sum and product of four positive consecutive terms of a GP, are 126 and 1296, respectively, then the sum of common ratios of all such GPs is

If gcd $ (m, n) = 1 $ and \[ 1^2 - 2^2 + 3^2 - 4^2 + \cdots + (2022)^2 - (2023)^2 = 1012 \, m^2 n \] then $ m^2 - n^2 $ is equal to:

Let a differentiable function $f$ satisfy $f(x)+\int\limits_3^x \frac{f(t)}{t} d t=\sqrt{x+1}, x \geq 3$ Then $12 f(8)$ is equal to :

Among the statements:

The system of the equations
$x + y + z = 6$
$x + 2y + \alpha z = 5 $
$x + 2y + 6z = $$ \beta$ has

The total number of three-digit numbers, divisible by 3, which can be formed using the digits 1,3,5,8, if repetition of digits is allowed, is

A proton with a kinetic energy of 2.0 eV moves into a region of uniform magnetic field of magnitude $\dfrac{\pi}{2} \times 10^{-3} \text{T}$. The angle between the direction of magnetic field and velocity of proton is 60°. The pitch of the helical path taken by the proton is \_\_\_\ cm.

Let the determinant of a square matrix A of order $ m $ be $ m - n $, where $ m $ and $ n $ satisfy $ 4m + n = 22 $ and $ 17m + 4n = 93 $. If $ \text{det} (n \, \text{adj}(\text{adj}(mA))) = 3^a 5^b 6^c $, then $ a + b + c $ is equal to:

For all $z \in C$ on the curve $C_1:|z|=4$, let the locus of the point $z+\frac{1}{z}$ be the curve $C_2$ Then:

For reaction : $SO _2( g )+\frac{1}{2} O _2( g )= SO _3( g )$$K _{ p }=2 \times 10^{12}$ at $27^{\circ} C$ and 1 atm pressure The $K _{ c }$ for the same reaction is ____$\times 10^{13}$ (Nearest integer)(Given $R =0.082 \,L \,atm \,K ^{-1} \,mol ^{-1}$ )

Group-13 elements react with O₂ in amorphous form to form oxides of type M₂O₃ (M = element). Which among the following is the most basic oxide?

The oxidation state of phosphorus in hypophosphoric acid is + _____