List of top Questions asked in JEE Main- 2023

The magnetic moment of a transition metal compound has been calculated to be 3.87 B.M. The metal ion is

Let $S_1$ and $S_2$ be respectively the sets of all $a \in R -\{0\}$ for which the system of linear equations $ a x+2 a y-3 a z=1$ $ (2 a+1) x+(2 a+3) y+(a+1) z=2$ $(3 a+5) x+(a+5) y+(a+2) z=3$ has unique solution and infinitely many solutions Then

Let $x=2$ be a local minima of the function $f(x)=2 x^4-18 x^2+8 x+12$, $x \in(-4,4)$ If $M$ is local maximum value of the function $f$ in $(-4,4)$, then $M =$

Some amount of dichloromethane $\left( CH _2 Cl _2\right)$ is added to $671.141 \,mL$ of chloroform $\left( CHCl _3\right)$ to prepare $2.6 \times 10^{-3} M$ solution of $CH _2 Cl _2$ (DCM) The concentration of DCM is ______$ppm$ (by mass) Given: atomic mass : $C =12$ $H =1$ $Cl =35.5$ density of $CHCl _3=1.49\, g \,cm ^{-3}$

Let the six numbers $a_1, a_2, a_3, a_4, a_5, a_6$, be in AP and $a_1+a_3=10$ If the mean of these six numbers is $\frac{19}{2}$ and their variance is $\sigma^2$, then $8 \sigma^2$ is equal to :

For two different photosensitive materials having work function and 2 respectively, are illuminated with light of sufficient energy to emit electrons. If the graph of stopping potential versus frequency is drawn, for these two different photosensitive materials the ratio of slope of graph for these two materials is

If de-Broglie wavelength is $\lambda$ when energy is E. Find the wavelength at $\frac{E}{4}$ (Kinetic Energy).

$y=f(x)$ is a quadratic function passing through (–1, 0) and tangent to it at (1, 1) is $y=x$. Find x intercept by normal at point (𝛂, 𝛂 + 1), (𝛂 > 0)

$20 \,mL$ of $01 \,M \,NH _4 OH$ is mixed with $40\, mL$ of $005\, M \,HCl$ The $pH$ of the mixture is nearest to: (Given: $K _{ b }\left( NH _4 OH \right)=1 \times 10^{-5}, \log 2=030$, $\log 3=048, \log 5=069, \log 7=084$, $\log 11=104$ )

During the reaction of permanganate with thiosulphate, the change in oxidation of manganese occurs by value of 3. Identify which of the below medium will favour the reaction

Let the quadratic curve passing through the point $ (-1, 0) $ and touching the line $ y = x $ at $ (1, 1) $ be $ y = f(x) $. Then the x-intercept of the normal to the curve at the point $ (\alpha, \alpha + 1) $ in the first quadrant is:

Let the line $L: \frac{x-1}{2}=\frac{y+1}{-1}=\frac{z-3}{1}$ intersect the plane $2 x+y+3 z=16$ at the point $P$ Let the point $Q$ be the foot of perpendicular from the point $R(1,-1,-3)$ on the line $L$ If $\alpha$ is the area of triangle $P Q R$, then $\alpha^2$ is equal to

A uniform electric field of $10 N / C$ is created between two parallel charged plates (as shown in figure) An electron enters the field symmetrically between the plates with a kinetic energy $05 eV$ The length of each plate is $10 cm$ The angle $(\theta)$ of deviation of the path of electron as it comes out of the field is ___ (in degree)

The separation of two coloured substances was done by paper chromatography The distances travelled by solvent front, substance $A$ and substance $B$ from the base line are $3.25\, cm. 2.08 \, cm$ and $1.05\, cm$ respectively. The ratio of $R_f$ values of $A$ to $B$ is _______

The equations of the sides $AB$ and $AC$ of a triangle $ABC$ are $(\lambda+1) x+\lambda y=4$ and $\lambda x+(1-\lambda) y+\lambda=0$ respectively Its vertex $A$ is on the $y$ - axis and its orthocentre is $(1,2)$ The length of the tangent from the point $C$ to the part of the parabola $y^2=6 x$ in the first quadrant is :

The value of the integral $\int \limits_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \frac{x+\frac{\pi}{4}}{2-\cos 2 x} d x$is :

A condenser of $2 \,\mu F$ capacitance is charged steadily from $0$ to $5 C$ Which of the following graph represents correctly the variation of potential difference $(V)$ across it's plates with respect to the charge $( Q )$ on the condenser?

A Particle is projected vertically upward reaches 136 m height. What will be the maximum range for the particle projected with same speed ?

An object is allowed to fall from a height $R$ above the earth, where $R$ is the radius of earth Its velocity when it strikes the earth's surface, ignoring air resistance, will be

A lift of mass $M =500 kg$ is descending with speed of $2 ms ^{-1}$ Its supporting cable begins to slip thus allowing it to fall with a constant acceleration of $2 ms ^{-2}$ The kinetic energy of the lift at the end of fall through to a distance of $6 m$ will be ___ $kJ$

$\displaystyle\sum_{k=0}^6{ }^{51-k} C_3$ is equal to

A particle starts with an initial velocity of 10.0 m/s along x-direction and accelerates uniformly at the rate of 2.0 m/s$^2$. The time taken by the particle to reach the velocity of 60.0 m/s is

Two projectiles u₁ and u₂, with speed of 40 m/s and 60 m/s respectively are thrown at a certain angle, u₁ with 30^o and u₂ with 60^o, what is the ratio of range?

If $sin^{-1}x=2\,tan^{-1}x$ , then the number of integral values of x is equal to:

A body is released from a height equal to the radius (r) of the earth. The velocity of the body when it strikes the surface of the earth will be: