List of top Questions asked in JEE Main- 2023

A car is moving on a circular path of radius \(600\ m\) such that the magnitudes of the tangential acceleration and centripetal acceleration are equal. The time taken by the car to complete first quarter of revolution, if it is moving with an initial speed of \(54 \ km/hr\) is \(𝑡(1−𝑒^{−\frac \pi2})\ 𝑠\). The value of \(t\) is _____ .

Unpolarised light is incident on the boundary between two dielectric media, whose dielectric constants are 2.8 (medium −1 ) and 6.8 (medium −2 ), respectively. To satisfy the condition, so that the reflected and refracted rays are perpendicular to each other, the angle of incidence should be $ tan^{−1}(1+\frac{10}\theta )^{\frac{1} 2}$, then the value of 𝜃 is _______.
(Given for dielectric media, $ \mu_r=1$ )

A null point is found at 200 cm in potentiometer when cell in secondary circuit is shunted by 5Ω. When a resistance of 15Ω is used for shunting, null point moves to 300 cm. The internal resistance of the cell is _______ Ω.

An inductor of inductance \(2\mu H\) is connected in series with a resistance, a variable capacitor and an AC source of frequency \(7\ kHz\). The value of capacitance for which maximum current is drawn into the circuit is \(\frac 1x\) F, where the value of \(𝑥 \) is ______. (Take \(\pi=\frac {22}{7}\) )

A particle of mass 100 g is projected at time \(𝑡=0\) with a speed \(20\,ms^{−1}\) at an angle \(45°\) to the horizontal as given in the figure. The magnitude of the angular momentum of the particle about the starting point at time \(𝑡=2 s\) is found to be \(\sqrt{K}\  kgm^2/s.\) The value of \(K\) is ________. (Take \(g=10\) \(ms^{−2}\))

A particle of mass 250 g executes a simple harmonic motion under a periodic force F=(−25𝑥)N. The particle attains a maximum speed of 4 m/s during its oscillation. The amplitude of the motion is ______ cm.

For a charged spherical ball, electrostatic potential inside the ball varies with 𝑟 as $V=2𝑎𝑟^2+𝑏$. Here, 𝑎 and 𝑏 are constant and r is the distance from the center. The volume charge density inside the ball is −𝜆𝑎𝜀. The value of 𝜆 is ______. 
(𝜀= permittivity of the medium)

When two resistances 𝑅₁ and 𝑅₂ connected in series and introduced into the left gap of a meter bridge and a resistance of 10Ω is introduced into the right gap, a null point is found at 60 cm from left side. When 𝑅₁ and 𝑅₂ are connected in parallel and introduced into the left gap, a resistance of 3Ω is introduced into the right-gap to get null point at 40 cm from left end. The product of 𝑅₁𝑅₂ is _______ Ω².

A metal block of base area \(0.20 \,m^2\) is placed on a table, as shown in figure. A liquid film of thickness \(0.25\, mm\) is inserted between the block and the table. The block is pushed by a horizontal force of 0.1 N and moves with a constant speed. If the viscosity of the liquid is \(5.0×10^{−3}Pl\), the speed of block is  ________ \(×10^{−3}m/s\)

The volume of HCl, containing $73 g L^{−1}$, required to completely neutralise NaOH obtained by reacting $0.69 g$ of metallic sodium with water, is _______ mL.( Nearest Integer)
(Given : molar Masses of Na, Cl, O, H, are 23,35.5,16 and 1 $g mol^{−1}$ respectively)

When 0.01 mol of an organic compound containing 60% carbon was burnt completely, 4.4 g of $CO_2$ was produced. The molar mass of compound is _______ $gmol^{−1}$. (Nearest integer).

For conversion of compound \(A→B\), the rate constant of the reaction was found to be $4.6×10^{−5} L mol^{−1} s^{−1}$. The order of the reaction is _____ .

On heating, $LiNO_3$ gives how many compounds among the following?
$Li_2O,N_2,O_2,LiNO_2,NO_2 $

A metal 𝑀 forms hexagonal close-packed structure. The total number of voids in 0.02 mol of it is _______ $×10^{21}$. (Nearest integer).
( Given $N_A=6.02×10^{23}$)

Total number of acidic oxides among $N_2O_3,NO_2, N_2O,Cl_2O_7,SO_2,CO,CaO,Na_2O$ and NO is ____ .

At \(298\ K\)
\(N_2( g)+3H_2( g)⇌2NH_3( g),K_1=4×10^5\)
\(N_2( g)+O_2( g)⇌2NO(g),K_2=1.6×10^{12}\)
\(H_2( g)+1 2O_2( g)⇌H_2O(g),K_3=1.0×10^{−13}\)
Based on above equilibria, the equilibrium constant of the reaction, 
\(2NH_3( g)\)+\(\frac5 {2}\) \(O_2( g)⇌2NO(g)+3H_2O(g)\) is _______ \(×10^{−33 }\). (Nearest integer)

The denticity of the ligand present in the Fehling's reagent is ____ .

The equilibrium constant for the reaction
\(Zn(s)+Sn^{2+}(aq)⇌Zn^{2+}(aq)+Sn(s)\, is\, 1×10^{20}\) at \(298 K\). 
The magnitude of standard electrode potential of \(Sn/Sn^{2+}\) if \(E^{\degree}_{ Zn^{2+}/Zn}= –0.76V \) is _______ \(×10^{−2} V\). (Nearest integer).
(Given : \(\frac{2.303RT}{ F}\) \(=0.059 V \))

Assume that the radius of the first Bohr orbit of hydrogen atom is $0.6Å$. The radius of the third Bohr orbit of $He^+$is _______ picometer. (Nearest Integer)

The total number of 4-digit numbers whose greatest common divisor with 54 is 2 , is ____.

If the equation of the normal to the curve \(𝑦= 𝑥−𝑎 (𝑥+𝑏)(𝑥−2)\) at the point \((1,−3)\) is \(𝑥−4𝑦=13\), then the value of \(𝑎+𝑏\) is equal to ___ .

Let \(𝑋={11,12,13,…,40,41}\) and \(𝑌={61,62,63,…,90,91}\) be the two sets of observations. If \(\bar 𝑥\) and \(\bar 𝑦\) are their respective means and \(σ^2\) is the variance of all the observations in \(𝑋∪𝑌\), then \(|\bar 𝑥+\bar 𝑦−σ^2|\) is equal to ____ .

A triangle is formed by the tangents at the point \((2,2)\) on the curves \(𝑦^2=2𝑥\) and \(𝑥^2+𝑦^2=4𝑥\), and the line \(𝑥+𝑦+2=0\). If \(𝑟\) is the radius of its circumcircle, then \(𝑟^2\) is equal to ____ .

Let \(α_1,α_2,….,α_7\) be the roots of the equation \(𝑥^7+3𝑥^5−13𝑥^3−15𝑥=0\) and \(|α_1|≥|α_2|≥⋯≥ |α_7|\). Then \(α_1α_2−α_3α_4+α_5α_6\) is equal to ____.

Let \(A\) be a symmetric matrix such that \(|A|=2\) and \(\begin{bmatrix} 2 & 1 \\[0.3em] 3 & \frac 32 \\[0.3em] \end{bmatrix}𝐴−\begin{bmatrix} 1 & 2 \\[0.3em] α & β \\[0.3em] \end{bmatrix}\). If the sum of the diagonal elements of \(A\) is \(s\), then \(\frac {βs}{α^2}\) is equal to ____ .