List of top Questions asked in JEE Main

This question has Statement-1 and Statement-2. Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement 1: No work is required to be done to move a test charge between any two points on an equipotential surface.
Statement 2: Electric lines of force at the equipotential surfaces are mutually perpendicular to each other.

A parallel plate capacitor having a separation between the plates d, plate area A and material with dielectric constant K has capacitance \(C_0\). Now one-third of the material is replaced by another material with dielectric constant 2 K, so that effectively there are two capacitors one with area \(\frac{1}{3}\)A, dielectric constant 2 K and another with area \(\frac{2}{3}\)A and dielectric constant K. If the capacitance of this new capacitor is C then \(\frac{C}{C_0}\) is

The gravitational field in a region is given by: \(\vec{E} = (5\ N/kg)\hat{i} + (12\ N/kg)\hat{j}\). If the potential at the origin is taken to be zero, then the ratio of the potential at the points \((12\ \mathrm{m}, 0)\) and \((0, 5\ \mathrm{m})\) is :

Six equal resistances are connected between points P, Q and R as shown in figure. Then net resistance will be

maximum between :

In a transverse wave the distance between a crest and neighbouring trough at the same instant is 4.0 cm and the distance between a crest and trough at the same place is 1.0 cm. The next crest appears at the same place after a time interval of 0.4 s. The maximum speed of the vibrating particles in the medium is:

A uniform cylinder of length L and mass M having cross-sectional area A is suspended, with its length vertical, from a fixed point by a massless spring, such that it is half submerged in a liquid of density \(\sigma\) at equilibrium position. When the cylinder is given a downward push and released, it starts oscillating vertically with a small amplitude. The time period T of the oscillations of the cylinder will be :

In the isothermal expansion of 10 g of gas from volume V to 2V the work done by the gas is 575 J. What is the root mean square speed of the molecules of the gas at that temperature?

A sample of gas expands from \(V_1\) to \(V_2\). In which of the following, the work done will be greatest?

A ring of mass \(M\) and radius \(R\) is rotating about its axis with angular velocity \(\omega\). Two identical bodies each of mass \(m\) are now gently attached at the two ends of a diameter of the ring. Because of this, the kinetic energy loss will be :

A wind-powered generator converts wind energy into electrical energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. For wind speed \(v\), the electrical power output will be most likely proportional to

If the events A and B are mutually exclusive events such that \(P(A)=\frac{3x+1}{3}\) and \(P(B)=\frac{1-x}{4}\), then the set of possible values of \(x\) lies in the interval :

The maximum range of a bullet fired from a toy pistol mounted on a car at rest is \(R_0=40\) m. What will be the acute angle of inclination of the pistol for maximum range when the car is moving in the direction of firing with uniform velocity \(v=20\) m/s on a horizontal surface? (\(g=10\ \mathrm{m/s^2}\))

Let ABC be a triangle with vertices at points \(A(2,3,5),\ B(-1,3,2)\) and \(C(\lambda,5,\mu)\) in three dimensional space. If the median through A is equally inclined with the axes, then \((\lambda,\mu)\) is equal to:

Let \(f:[-2,3]\to[0,\infty)\) be a continuous function such that \(f(1-x)=f(x)\) for all \(x\in[-2,3]\). If \(R_1\) is the numerical value of the area of the region bounded by \(y=f(x),\ x=-2,\ x=3\) and the axis of \(x\) and \(R_2=\int_{-2}^{3}xf(x)\,dx\), then :

Let \(\vec a=2\hat i+\hat j-2\hat k,\ \vec b=\hat i+\hat j\). If \(\vec c\) is a vector such that \(\vec a\cdot\vec c=|\vec c|,\ |\vec c-\vec a|=2\sqrt2\) and the angle between \(\vec a\times\vec b\) and \(\vec c\) is \(30^\circ\), then \(|(\vec a\times\vec b)\times\vec c|\) equals:

The equation of the curve passing through the origin and satisfying the differential equation \((1+x^2)\frac{dy}{dx}+2xy=4x^2\) is

The equation of a plane through the line of intersection of the planes \(x+2y=3,\ y-2z+1=0\), and perpendicular to the first plane is :

Let \(f(1) = -2\) and \(f'(x) \ge 4.2\) for \(1 \le x \le 6\). The possible value of \(f(6)\) lies in the interval :

A spherical balloon is being inflated at the rate of 35cc/min. The rate of increase in the surface area (in \(\mathrm{cm^2}\)/min.) of the balloon when its diameter is 14 cm, is :

If an equation of a tangent to the curve, \(y - \cos(x + y) = 0,\ -1 \le x \le 1 + \pi\), is \(x + 2y = k\) then \(k\) is equal to :

For \(0 \le x \le \frac{\pi}{2}\), the value of \(\displaystyle\int_0^{\sin^2 x}\sin^{-1}(\sqrt{t})\,dt+\int_0^{\cos^2 x}\cos^{-1}(\sqrt{t})\,dt\) equals :

In a set of \(2n\) observations, half of them are equal to 'a' and the remaining half are equal to '\(-a\)'. If the standard deviation of all the observations is 2 ; then the value of \(|a|\) is :

Let \(S=\left\{\begin{pmatrix}a_{11}&a_{12}\\a_{21}&a_{22}\end{pmatrix}: a_{ij}\in\{0,1,2\},\ a_{11}=a_{22}\right\}\). Then the number of non-singular matrices in the set \(S\) is :

Consider the function : \(f(x)=[x]+|1-x|,\ -1\le x\le3\) where \([x]\) is the greatest integer function. Statement 1 : \(f\) is not continuous at \(x=0,1,2\) and \(3\) Statement 2 : \(f(x)=\begin{cases}-x, & -1\le x\lt0\\ 1-x, & 0\le x\lt1\\ 1+x, & 1\le x\lt2\\ 2+x, & 2\le x\le3\end{cases}\)

Let \(p\) and \(q\) be any two logical statements and \(r : p \rightarrow (\sim p \vee q)\). If \(r\) has a truth value \(F\), then the truth values of \(p\) and \(q\) are respectively: