List of top Questions asked in JEE Main

A cylinder of radius R is surrounded by a cylindrical shell of inner radius R and outer radius 2R. The thermal conductivity of the material of the inner cylinder is \(K_1\) and the of the outer cylinder is \(K_2\). Assuming no loss of heat, the effective thermal conductivity of the system for heat flowing along the length of the cylinder is :

Two electric bulbs, rated at (25 W, 220 V) and (100 W, 220 V), are connected in series across a 220 V voltage source. If the 25 W and 100 W bulbs draw powers \(P_1\) and \(P_2\) respectively, then :

Two light identical springs of spring constant k are attached horizontally at the two ends of a uniform horizontal rod AB of length \(\ell\) and mass m. The rod is pivoted at its centre 'O' and can rotate freely in horizontal plane. The other ends of the two springs are fixed to rigid supports as shown in figure. The rod is gently pushed through a small angle and released. The frequency of resulting oscillation is :

A point source of light, S is placed at distance L in front of the centre of plane mirror of width d which is hanging vertically on a wall. A man walks in front of the mirror along a line parallel to the mirror, at a distance 2L as shown below. The distance over which the man can see the image of the light source in the mirror is

The position vector of the centre of mass \(\vec{r}_{cm}\) of an asymmetric uniform bar of negligible area of crosssection as shown in figure is :

The least count of the main scale of a screw gauge is 1 mm. The minimum number of divisions on its circular scale required to measure 5 \(\mu\)m diameter of a wire is :

The galvanometer deflection, when key \(K_1\) is closed but \(K_2\) is open, equals \(\theta_0\) (see figure). On closing \(K_2\) also and adjusting \(R_2\) to \(5\,\Omega\), the deflection in galvanometer becomes \(\frac{\theta_0}{5}\). The resistance of the galvanometer is, then, given by [Neglect the internal resistance of battery] :

Let \(C_1\) and \(C_2\) be the centres of the circles \(x^2 + y^2 - 2x - 2y - 2 = 0\) and \(x^2 + y^2 - 6x - 6y + 14 = 0\) respectively. If P and Q are the points of intersection of these circles, then the area (in sq. units) of the quadrilateral \(PC_1QC_2\) is :

There is a uniform spherically symmetric surface charge density at a distance \(R_0\) from the origin. The charge distribution is initially at rest and starts expanding because of mutual repulsion. The figure that represents best the speed \(V(R(t))\) of the distribution as a function of its instantaneous radius \(R(t)\) is :

If a variable line, \(3x + 4y - \lambda = 0\) is such that the two circles \(x^2 + y^2 - 2x - 2y + 1 = 0\) and \(x^2 + y^2 - 18x - 2y + 78 = 0\) are on its opposite sides, then the set of all values of \(\lambda\) is the interval :

The perpendicular distance from the origin to the plane containing the two lines, \(\frac{x+2}{3} = \frac{y-2}{5} = \frac{z+5}{7}\) and \(\frac{x-1}{1} = \frac{y-4}{4} = \frac{z+4}{7}\), is :

The sum of the distinct real values of \(\mu\), for which the vectors, \(\mu\hat{i} + \hat{j} + \hat{k},\ \hat{i} + \mu\hat{j} + \hat{k},\ \hat{i} + \hat{j} + \mu\hat{k}\) are co-planar, is :

Let \(S_k = \frac{1 + 2 + 3 + \dots + k}{k}\). If \(S_1^2 + S_2^2 + \dots + S_{10}^2 = \frac{5}{12}A\), then A is equal to :

The maximum value of \(3\cos\theta + 5\sin\left(\theta - \frac{\pi}{6}\right)\) for any real value of \(\theta\) is :

If the vertices of a hyperbola be at \((-2, 0)\) and \((2, 0)\) and one of its foci be at \((-3, 0)\), then which one of the following points does not lie on this hyperbola?

\(\displaystyle\lim_{x \to \pi/4} \frac{\cot^3 x - \tan x}{\cos\left(x + \frac{\pi}{4}\right)}\) is :

The area (in sq. units) of the region bounded by the parabola, \(y = x^2 + 2\) and the lines, \(y = x + 1\), \(x = 0\) and \(x = 3\), is

The maximum area (in sq. units) of a rectangle having its base on the x-axis and its other two vertices on the parabola, \(y = 12 - x^2\) such that the rectangle lies inside the parabola, is :

A tetrahedron has vertices \(P(1, 2, 1)\), \(Q(2, 1, 3)\), \(R(-1, 1, 2)\) and \(O(0, 0, 0)\). The angle between the faces OPQ and PQR is :

An ordered pair \((\alpha, \beta)\) for which the system of linear equations
\((1 + \alpha)x + \beta y + z = 2\)
\(\alpha x + (1 + \beta)y + z = 3\)
\(\alpha x + \beta y + 2z = 2\)
has a unique solution, is :

If \(\lambda\) be the ratio of the roots of the quadratic equation in \(x\), \(3m^2x^2 + m(m - 4)x + 2 = 0\), then the least value of \(m\) for which \(\lambda + \frac{1}{\lambda} = 1\), is

Let \(P = \begin{bmatrix} 1 & 0 & 0\\ 3 & 1 & 0\\ 9 & 3 & 1\end{bmatrix}\) and \(Q = [q_{ij}]\) be two \(3 \times 3\) matrices such that \(Q - P^5 = I_3\). Then \(\frac{q_{21} + q_{31}}{q_{32}}\) is equal to :

Let \(S = \{1, 2, 3, \ldots, 100\}\). The number of non-empty subsets \(A\) of \(S\) such that the product of elements in \(A\) is even is :

Let \(f\) and \(g\) be continuous functions on \([0, a]\) such that \(f(x) = f(a - x)\) and \(g(x) + g(a - x) = 4\), then \(\int_0^a f(x)g(x)\,dx\) is equal to :

Let \(S\) be the set of all points in \((-\pi, \pi)\) at which the function, \(f(x) = \min\{\sin x, \cos x\}\) is not differentiable. Then \(S\) is a subset of which of the following ?