List of top Questions asked in JEE Main

The major product 'Y' in the following reaction is :

In an experiment, brass and steel wires of length \(1\ \mathrm{m}\) each with areas of cross section \(1\ \mathrm{mm^2}\) are used. The wires are connected in series and one end of the combined wire is connected to a rigid support and other end is subjected to elongation. The stress required to produce a net elongation of \(0.2\ \mathrm{mm}\) is, [Given, the Young's Modulus for steel and brass are, respectively, \(120\times10^{9}\ \mathrm{N/m^2}\) and \(60\times10^{9}\ \mathrm{N/m^2}\)]

In a Young's double slit experiment, the ratio of the slit's width is \(4:1\). The ratio of the intensity of maxima to minima, close to the central fringe on the screen, will be :

A submarine experiences a pressure of \(5.05\times10^{6}\ \mathrm{Pa}\) at a depth of \(d_1\) in a sea. When it goes further to a depth of \(d_2\), it experiences a pressure of \(8.08\times10^{6}\ \mathrm{Pa}\). Then \(d_2-d_1\) is approximately (density of water \(=10^{3}\ \mathrm{kg/m^3}\) and acceleration due to gravity \(=10\ \mathrm{ms^{-2}}\)) :

When heat \(Q\) is supplied to a diatomic gas of rigid molecules, at constant volume its temperature increases by \(\Delta T\). The heat required to produce the same change in temperature, at a constant pressure is :

The figure represents a voltage regulator circuit using a Zener diode. The breakdown voltage of the Zener diode is 6 V and the load resistance is, \(R_L=4\,\mathrm{k}\Omega\). The series resistance of the circuit is \(R_i=1\,\mathrm{k}\Omega\). If the battery voltage \(V_B\) varies from 8 V to 16 V, what are the minimum and maximum values of the current through Zener diode?

A coil of self inductance 10 mH and resistance \(0.1\ \Omega\) is connected through a switch to a battery of internal resistance \(0.9\ \Omega\). After the switch is closed, the time taken for the current to attain 80% of the saturation value is: [take \(\ln5=1.6\)]

Space between two concentric conducting spheres of radii a and b (b > a) is filled with a medium of resistivity \(\rho\). The resistance between the two spheres will be :

The time dependence of the position of a particle of mass \(m=2\) is given by \(\vec{r}(t)=2t\hat{i}-3t^2\hat{j}\). Its angular momentum, with respect to the origin, at time \(t=2\) is

If the plane \(2x-y+2z+3=0\) has the distances \(\frac13\) and \(\frac23\) units from the planes \(4x-2y+4z+\lambda=0\) and \(2x-y+2z+\mu=0\), respectively, then the maximum value of \(\lambda+\mu\) is equal to :

If the tangent to the curve \(y=\frac{x}{x^2-3}\), \(x\in\mathbb{R},\ (x\ne\pm\sqrt3)\), at a point \((\alpha,\beta)\ne(0,0)\) on it is parallel to the line \(2x+6y-11=0\), then :

If the line \(ax+y=c\), touches both the curves \(x^2+y^2=1\) and \(y^2=4\sqrt{2}\,x\), then \(|c|\) is equal to :

A square loop is carrying a steady current I and the magnitude of its magnetic dipole moment is m. if this square loop is changed to a circular loop and it carries the same current, the magnitude of the magnetic dipole moment of circular loop will be:

A spaceship orbits around a planet at a height of 20 km from its surface. Assuming that only gravitational field of the planet acts on the spaceship, what will be the number of complete revolutions made by the spaceship in 24 hours around the planet?
[Given ; Mass of planet = \(8\times10^{22}\) kg, Radius of planet = \(2\times10^{6}\) m, Gravitational constant \(G=6.67\times10^{-11}\ \mathrm{Nm^2/kg^2}\)]

The angles A, B and C of a triangle ABC are in A.P. and \(a:b=1:\sqrt{3}\). If \(c=4\) cm, then the area (in sq. cm) of this triangle is :

A perpendicular is drawn from a point on the line \(\frac{x-1}{2}=\frac{y+1}{-1}=\frac{z}{1}\) to the plane \(x+y+z=3\) such that the foot of the perpendicular Q also lies on the plane \(x-y+z=3\). Then the co-ordinates of Q are :

If \(5x+9=0\) is the directrix of the hyperbola \(16x^2-9y^2=144\), then its corresponding focus is :

The smallest natural number n, such that the coefficient of x in the expansion of \(\left(x^2+\frac{1}{x^3}\right)^n\) is \(^{n}\mathrm{C}_{23}\), is :

The negation of the Boolean expression \(\sim s \vee (\sim r \wedge s)\) is equivalent to :

The locus of the centres of the circles, which touch the circle, \(x^2+y^2=1\) externally, also touch the y-axis and lie in the first quadrant, is :

Lines are drawn parallel to the line \(4x-3y+2=0\), at a distance \(\dfrac35\) from the origin. Then which one of the following points lies on any of these lines ?

The integral \(\displaystyle\int_{\pi/6}^{\pi/3}\sec^{2/3}x\;\mathrm{cosec}^{4/3}x\,dx\) is equal to :

The area (in sq. units) of the region bounded by the curves \(y=2^x\) and \(y=|x+1|\), in the first quadrant is :

If \(\cos^{-1}x-\cos^{-1}\dfrac{y}{2}=\alpha\), where \(-1\le x\le1\), \(-2\le y\le2\), \(x\le\dfrac{y}{2}\), then for all \(x,y\), \(4x^2-4xy\cos\alpha+y^2\) is equal to :

Let \(y=y(x)\) be the solution of the differential equation \(\dfrac{dy}{dx}+y\tan x=2x+x^2\tan x\), \(x\in\left(-\frac{\pi}{2},\frac{\pi}{2}\right)\), such that \(y(0)=1\). Then :