List of top Questions asked in JEE Main- 2023

A thin infinite sheet charge and an infinite line charge of respective charge densities +σ and +λ are placed parallel at 5 m distance from each other. Points ‘P’ and ‘Q’ are at \(\frac{3}{π} \)m and \(\frac{4}{π}\) m perpendicular distance from line charge towards sheet charge, respectively. ‘E_P’ and ‘E_Q’ are the magnitudes of resultant electric field intensities at point ‘P’ and ‘Q’, respectively. If \(\frac{E_p}{E_Q} =\frac{ 4}{a}\) for 2|σ| = |λ|. Then the value of a is _______.

The elastic potential energy stored in a steel wire of length 20 m stretched through 2 cm is 80 J. The cross sectional area of the wire is______ mm² . (Given, y = 2.0 x 10¹¹ Nm^-2)

A solid sphere is rolling on a horizontal plane without slipping. If the ratio of angular momentum about axis of rotation of the sphere to the total energy of moving sphere is π : 22 then, the value of its angular speed will be ______ rad/s.

When a resistance of 5Ω is shunted with a moving coil galvanometer, it shows a full scale deflection for a current of 250 mA, however when 1050Ω resistance is connected with it in series, it gives full scale deflection for 25 volt. The resistance of galvanometer is _____Ω .

From the given transfer characteristic of a transistor in CE configuration, the value of power gain of this configuration is 10^x, for R_B = 10 kΩ, and R_c = 1 kΩ. The value of x is_____.

KMnO₄ is titrated with ferrous ammonium sulphate hexahydrate in presence of dilute H₂SO₄. Number of water molecules produced for 2 molecules of KMnO₄ is______.

A certain quantity of real gas occupies a volume of 30.15 dm3 at 100 atm and 500 K when its compressibility factor is 1.07. Its volume at 300 atm and 300K (When its compressibility factor is 1.4) is _____ x 10-4 dm3 (Nearest integer)

A₂+B₂→2AB. \(ΔH^0_f\)= -200 kJ mol^-1 AB, A2 and B2 are diatomic molecule. If the bond enthalpies of A₂, B₂ and AB are in the ratio 1:0.5:1, then the bond enthalpy of A₂ is ___ kJmol^-1 (Nearest integer)

Solution of 12 g of non-electrolyte (A) prepared by dissolving it in 1000 mL of water exerts the same osmotic pressure as that of 0.05 M glucose solution at the same temperature. The empirical formula of A is CH₂O. The molecular mass of A is ____ g. (Nearest integer)

25.0 mL of 0.050 M Ba(NO₃)₂ is mixed with 25.0 mL of 0.020 M NaF. K_sp of BaF₂ is 0.5 x 10^-6 at 298 K. The ratio of [Ba2+] [F^-]² and K_sp is__ (Nearest integer)

A metal surface of 100 cm2 area has to be coated with nickel layer of thickness 0.001mm. A current of 2A was passed through a solution of Ni (NO₃)₂ for 'x' seconds to coat the desired layer. The value of x is_____ (Nearest integer)
 (P_Ni (density of Nickel) is 10 gmL^-1, Molar mass of Nickel is 60 gmol^-1 F = 96500 C mol^-1)

For the given reaction

The total number of possible products formed by tertiary carbocation of A is____.

20 mL of calcium hydroxide was consumed when it was reacted with 10 mL of unknown solution of H₂SO4. Also 20 mL standard solution of 0.5 M HCI containing 2 drops of phenolphthalein was titrated with calcium hydroxide the mixture showed pink colour when burette displayed the value of 35.5 mL whereas the burette showed 25.5 mL initially. The concentration of H₂SO₄ is_____M (Nearest integer)

Let A = {1, 2, 3, 4,.....10} and B = {0, 1, 2, 3, 4}. The number of elements in the relation R = {(a, b) ∈ A × A: 2(a – b)2 + 3(a – b) ∈ B} is______.

Let the point (p, p+1) lie inside the region \(E = \{(x,y):3-x≤y≤\sqrt{9-x^2}, 0 ≤ x ≤ 3\} \)If the set of all values of p is the interval (a,b). then b2 + b - a2 is equal to_____

Let a∈ Z and [t] be the greatest integer t. Then the number of points, where the function f(x)=[a+13 sin x], x ∈ (0, π) is not differentiable, is ____

If the area of the region \( S={(x,y) : 2y-y^2 ≤ x^2 ≤ 2y, x ≥ y}\) is equal to \(\frac{ n+2}{n+1}−\frac{π}{n−1}\), then the natural number n is equal to _____.

Let the tangent to the curve x² + 2x – 4y + 9 = 0 at the point P(1, 3) on it meet the y-axis at A. Let the line passing through P and parallel to the line x – 3y = 6 meet the parabola y² = 4x at B. If B lies on the line 2x – 3y = 8. then (AB)² is equal to___

Let y = y(x) be a solution of the differential equation (x cos x)dy +(xy sin x + y cos x – l)dx = 0, 0 < x < \(\frac{π}{2}\). If\(\frac{π}{3}y(\frac{π}{3})=\sqrt3\), then \(| \frac{π}{6 }y“( \frac{π}{6})+2 y'( \frac{π}{6})| \) is equal to______.

Consider the graph of Gibbs free energy G vs Extent of reaction. The number of statement/s from the following which are true with respect to points (a), (b) and (c) is…

A. Reaction is spontaneous at (a) and (b)  
B. Reaction is at equilibrium at point (b) and nonspontaneous at point (c)  
C. Reaction is spontaneous at (a) and nonspontaneous at (c)  
D. Reaction is non-spontaneous at (a) and (b)

For the adsorption of hydrogen on platinum, the activation energy is 30 kJ mol^-1 and for the adsorption of hydrogen on nickel, the activation energy is 41.4 kJ mol^-1 . The logarithm of the ratio of the rates of chemisorption on equal areas of the metals at 300 K is ……… (Nearest integer) Given: ln 10 = 2. 3  R = 8.3 JK^-1 mol^-1

The number of relations, on the set {1,2,3} containing (1,2) and (2,3), which are reflexive and transitive but not symmetric, is______

Let the digits a, b, c be in A.P. Nine-digit numbers are to be formed using each of these three digits thrice such that three consecutive digits are in A.P. at least once. How many such numbers can be formed?

Let [x] be the greatest integer ≤ x. Then the number of points in the interval (-2,1), where the function f(x)=|[x]|+√x−[x] is discontinuous is _____.

Let I(x) = \(∫√\frac{x+7}{x} dx\) and I (9) = 12 + 7 loge 7. If I (1) = α + 7 loge (1 + 2√2), then α4 is equal to_____.