List of top Questions asked in JEE Main- 2023

The slope of tangent at any point (x, y) on a curve y = y(x) is \(\frac{x^2+y^2}{2xy},x>0\) If y(2) = 0, then a value of y(8) is
 

Let the ellipse \(E : x^2 + 9y^2 = 9\) intersect the positive x- and y-axes at the points A and B respectively Let the major axis of E be a diameter of the circle C. Let the line passing through A and B meet the circle C at the point P. If the area of the triangle which vertices A, P and the origin O is m/n , where m and n are coprime, then m – n is equal to 

A line segment AB of length λ moves such that the points A and B remain on the periphery of a circle of radius λ. Then the locus of the point, that divides the line segment AB in the ratio 2 : 3, is a circle of radius

Let two vertices of triangle ABC be (2, 4, 6) and (0, –2, –5), and its centroid be (2, 1, –1). If the image of third vertex in the plane x + 2y + 4z = 11 is (α, β, γ), then αβ + βγ + γα is equal to

Let P be the point of intersection of the line \(\frac{x+3}{3}=\frac{y+2}{1}=\frac{1-z}{2}\) and the plane x + y + z = 2. If the distance of the point P from the plane 3x – 4y + 12z = 32 is q, then q and 2q are the roots of the equation 

Let O be the origin and the position vector of the point P be \(\hat i-2\hat j+3\hat k\). If the position vectors of the points A, B and C are \(-2\hat i+\hat j-3\hat k,2\hat i+4\hat j-2\hat k\) and \(-4\hat i+2\hat j-\hat k\) respectively then the projection of the vector \(\overrightarrow{OP}\) on a vector perpendicular to the vectors \(\overrightarrow{ AB}\) and \(\overrightarrow {AC}\) is

The shortest distance between the lines \(\frac{x+2}{1}=\frac{y}{-2}=\frac{z-5}{2}\) and \(\frac{x-4}{1}=\frac{y-1}{2}=\frac{z+3}{0}\) is

An arc PQ of a circle subtends a right angle at its centre O. The mid point of the arc PQ is R. If OP = μ, OR=v and OQ=αv+βv, then α, β² are the roots of the equation

\(96\cos\frac{π}{33}\cos \frac{2π}{33}\cos\frac{4π}{33}\cos\frac{8π}{33}\cos\frac{16π}{33}\) is equal to

The negation of the statement
(p v q) ∧ (q v(∼r)) is

Let a, b, c be three distinct positive real numbers such that (2a)^log_ea = (bc)^log_eb and b^log_e2 = a^log_ec. Then 6a + 5bc is equal to _____.

The number of elements in the set \(\{n ∈ Z : n^2-10n+19| < 6\}\) is __.

Let f : (-2, 2) → IR be defined by \(f(x) =   \begin{cases}     x[x]       & \quad -2<x<0\\     (x-1)[x],  & \quad 0\leq x<2   \end{cases}\)
Where [x] denotes the greatest integer function. If m and n respectively are the number of points in (-2, 2) at which y = |f(x)| is not continuous and not differentiable, then m + n is equal to ______.

Let y = p(x) be the parabola passing through the points (–1, 0), (0, 1) and (1, 0). If the area of the region \(\{x,y):(x+1)^2+(y-1)^2≤1,y≤p(x)\}\) is A, then 12(π-4A) is equal to__.

Let a common tangent to the curves y² = 4x and (x – 4)² + y² = 16 touch the curves at the points P and Q. Then (PQ)² is equal to ________.

The distance between two plates of a capacitor is \(d\) and its capacitance is \(C_1\), when air is the medium between the plates. If a metal sheet of thickness \(\frac {2d}{3}\) and of the same area as plate is introduced between the plates, the capacitance of the capacitor becomes \(C_2\). The ratio \(\frac {C_2}{C_1}\) is

For a periodic motion represented by the equation y = sin ωt + cos ωt, the amplitude of the motion is

A gas mixture consists of 2 moles of oxygen and 4 moles of neon at temperature T. Neglecting all vibrational modes, the total internal energy of the system will be,

A gas is compressed adiabatically, which one of the follwing statement is NOT true.

Young's moduli of the material of wires A and B are in the ratio of 1:4, while its area of cross section are in the ratio of 1:3. If the same amount of load is applied to both the wires, the amount of elongation produced in the wires A and B will in the ratio of
[Assume length of wires A and B are same]

Given below are two statement:
statement I : Rotation of the earth shows effect on the value of acceleration due to gravity (g).
statement II : The effect of rotation of the earth on the value of 'g' at the equator is minimum and that at the pole is maximum.
In the light of the above statements , choose the correct answer from the options given below

The time period of a satellite revolving above earth's surface at a height equal to R will be
(given: \(g= \pi^2 \ m/s^2\), R= radius of earth)

Two projectiles are projected at 30° and 60° with the horizontal with the same speed. The ratio of the maximum height attained by the two projectiles respectively is :

A rectangular block of mass 5 kg attached to an horizontal spiral spring executes simple harmonic motion of amplitude 1 m and time period 3.14s. The maximum force exerted by spring on block is _____N.

Figure below shows a liquid being pushed out of the tube by a piston having area of cross section 2.0 cm². The area of cross section at the oulet is 10 mm². If the piston is pushed at a speed of 4 cm s^-1, the speed of outgoing fluid is ______ cm s^-1.