List of top Questions asked in JEE Main

Let \(\ell\), r, C and V represent inductance, resistance, capacitance and voltage, respectively. The dimension of \(\frac{\ell}{rCV}\) in SI units will be :

The mean intensity of radiation on the surface of the Sun is about \(10^8\) W/m². The rms value of the corresponding magnetic field is closet to :

When a certain photosensitive surface is illuminated with monochromatic light of frequency v, the stopping potential for the current is \(-V_0/2\). When the surface is illuminated by monochromatic light of frequency v/2, the stopping potential is \(-V_0\). The threshold frequency for photoelectric emission is :

Two satellites, A and B, have masses m and 2m respectively. A is in a circular orbit of radius R, and B is in a circular orbit of radius 2R around the earth. The ratio of their kinetic energies, \(T_A/T_B\), is ;

The charge on a capacitor plate in a circuit, as a function of time, is shown in the figure :

What is the value of current at t = 4 s ?

A simple harmonic motion is represented by :
\(y=5(\sin3\pi t+\sqrt3\cos3\pi t)\) cm
The amplitude and time period of the motion are :

Two particles A, B are moving on two concentric circles of radii \(R_1\) and \(R_2\) with equal angular speed \(\omega\). At t = 0, their positions and direction of motion are shown in the figure.

The relative velocity \(\vec V_A-\vec V_B\) at \(t=\frac{\pi}{2\omega}\) is given by :

A parallel plate capacitor with plates of area 1 m² each, are at a separation of 0.1 m. If the electric field between the plates is 100 N/C, the magnitude of charge on each plate is :
(Take \(\varepsilon_0=8.85\times10^{-12}\ \frac{\mathrm{C^2}}{\mathrm{N\,m^2}}\))

In the above circuit, \(C=\frac{\sqrt3}{2}\,\mu\mathrm{F}\), \(R_2=20\,\Omega\), \(L=\frac{\sqrt3}{10}\) H and \(R_1=10\,\Omega\). Current in L-\(R_1\) path is \(I_1\) and in C-\(R_2\) path it is \(I_2\). The voltage of A.C. source is given by, \(V=200\sqrt2\sin(100t)\) volts. The phase difference between \(I_1\) and \(I_2\) is :

The equation of a tangent to the parabola, \(x^2=8y\), which makes an angle \(\theta\) with the positive directions of x-axis, is :

Let S be the set of all real values of \(\lambda\) such that a plane passing through the points \((-\lambda^2,1,1)\), \((1,-\lambda^2,1)\) and \((1,1,-\lambda^2)\) also passes through the point \((-1,-1,1)\). Then S is equal to :

If the angle of elevation of a cloud from a point P which is 25 m above a lake be 30^o and the angle of depression of reflection of the cloud in the lake from P be 60^o, then the height of the cloud (in meters) from the surface of the lake is :

If the sum of the first 15 terms of the series \(\left(\frac{3}{4}\right)^3+\left(1\frac{1}{2}\right)^3+\left(2\frac{1}{4}\right)^3+3^3+\left(3\frac{3}{4}\right)^3+\ldots\) is equal to 225 k, then k is equal to :

Let \(\vec a,\vec b\) and \(\vec c\) be three unit vectors, out of which vectors \(\vec b\) and \(\vec c\) are non-parallel. If \(\alpha\) and \(\beta\) are the angles which vector \(\vec a\) makes with vectors \(\vec b\) and \(\vec c\) respectively and \(\vec a\times(\vec b\times\vec c)=\frac12\vec b\), then \(|\alpha-\beta|\) is equal to :

\(\lim_{x\to\infty}\left(\dfrac{n}{n^2+1^2}+\dfrac{n}{n^2+2^2}+\dfrac{n}{n^2+3^2}+\ldots+\dfrac{1}{5n}\right)\) is equal to :

If an angle between the line, \(\frac{x+1}{2}=\frac{y-2}{1}=\frac{z-3}{-2}\) and the plane, \(x-2y-kz=3\) is \(\cos^{-1}\left(\frac{2\sqrt{2}}{3}\right)\), then a value of k is :

If \(\sin^4\alpha+4\cos^4\beta+2=4\sqrt2\,\sin\alpha\cos\beta;\ \alpha,\beta\in[0,\pi]\), then \(\cos(\alpha+\beta)-\cos(\alpha-\beta)\) is equal to :

The mean and the variance of five observations are 4 and 5.20, respectively. If three of the observations are 3, 4 and 4 ; then the absolute value of the difference of the other two observations, is :

\(\lim_{x\to1^-}\dfrac{\sqrt\pi-\sqrt{2\sin^{-1}x}}{\sqrt{1-x}}\) is equal to :

Let f be a differentiable function such that \(f(1)=2\) and \(f'(x)=f(x)\) for all \(x\in R\). If \(h(x)=f(f(x))\), then \(h'(1)\) is equal to :

The tangent to the curve \(y=x^2-5x+5\), parallel to the line \(2y=4x+1\), also passes through the point :

If the function f given by \(f(x)=x^3-3(a-2)x^2+3ax+7\), for some \(a\in R\) is increasing in (0, 1] and decreasing in [1, 5), then a root of the equation, \(\frac{f(x)-14}{(x-1)^2}=0\ (x\ne1)\) is :

If \(A=\begin{bmatrix}1&\sin\theta&1\\-\sin\theta&1&\sin\theta\\-1&-\sin\theta&1\end{bmatrix}\); then for all \(\theta\in\left(\frac{3\pi}{4},\frac{5\pi}{4}\right)\), \(\det(A)\) lies in the interval :

The number of integral values of m for which the quadratic expression, \((1+2m)x^2-2(1+3m)x+4(1+m)\), \(x\in R\), is always positive, is :

If \(^nC_4,\ ^nC_5\) and \(^nC_6\) are in A.P., then n can be :