List of top Questions asked in JEE Main- 2023

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 D_k=\(\begin{vmatrix} 1 & 2k & 2k-1\\ n & n^2+n+2 & n^2 \\ n & n^2+n & n^2+n+2 \end{vmatrix} \) If \(∑^n_{k=1} D_k=96,\) The n is equal to

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_____.

Let the plane x+3y–2z+6=0 meet the co-ordinate axes at the points A,B,C. If the orthocentre of the triangle ABC is\( (α,β,\frac{6 }{7} ), \) then 98(α + β)² is equal to___.

A fair n (n>1) faces die is rolled repeatedly until a number less than n appears. If the mean of the number of tosses required is \(\frac{n}{9}\), then n is equal to_____.

A compass needle of oscillation magnetometer oscillates 20 times per minute at a place P of dip 30°. The number of oscillations per minute become 10 at another place Q of 60° dip. The ratio of the total magnetic field at the two places respectively is \(\frac{4}{√x}\) The value of x is 

To maintain a speed of 80 km/h by a bus of mass 500 kg on a plane rough road for 4 km distance, the work done by the engine of the bus will be ____KJ. [The coefficient of friction between tyre of bus and road is 0.04].

For a rolling spherical shell, the ratio of rotational kinetic energy and total kinetic energy is \(\frac{x}{5}\). The value of x is____.

Glycerine of density 1.25 × 10³ kg m^-3 is flowing through the conical section of pipe. The area of cross-section of the pipe at its ends is 10 cm2 and 5 cm2 and pressure drop across its length is 3 Nm^-2. The rate of flow of glycerine through the pipe is x x10^-5 m3 s^-1. The value of x is____.

For a certain organ pipe, the first three resonance frequencies are in the ratio of 1:3:5 respectively. If the frequency of fifth harmonic is 405 Hz and the speed of sound in air is 324 ms^-1 the length of the organ pipe is ___ m.

The current flowing through a conductor connected across a source is 2A and 1.2 A at 0°C and 100°C respectively. The current flowing through the conductor at 50°C will be ______x10² mA.

A conducting circular loop is placed in a uniform magnetic field 0.04 T with its plane perpendicular to the magnetic field. Somehow, the radus of the loop starts expanding at a constant rate of 1 mm/s. The magnitude of induced emf in the loop at an instant when the radius of the loop is 2 cm will be ___μV

At 600K, the root mean square (rms) speed of gas X (molar mass = 40) is equal to the most probable speed of gas Y at 90K. The molar mass of the gas Y is ____ g mol^-1. (Nearest integer)

One mole of an ideal gas at 350K is in a 2.0 L vessel of thermally conducting walls, which are in contact with the surroundings. It undergoes isothermal reversible expansion from 2.0L to 3.0L against a constant pressure of 4 atm. The change in entropy of the surroundings (ΔS) is JK (Nearest integer) Given: R = 8.314 J K^-1 Mol^-1.

80 mole percent of MgCl₂ is dissociated in aqueous solution. The vapour pressure of 1.0 molal aqueous solution of M_gCl₂ at 38°C is ____mm Hg. (Nearest integer)
Given : Vapour pressure of water at 38°C is 50 mm Hg.