List of top Questions asked in JEE Main

Block sliding down... moving up... distance S before stopping is _____.

Three parallel plate capacitors each with area \(A\) and separation \(d\) are filled with two dielectric (\(k_1\) and \(k_2\)) in the following fashion. (\(k_1>k_2\)) Which of the following is true? 

A simple pendulum has a bob with mass \(m\) and charge \(q\). The pendulum string has negligible mass. When a uniform and horizontal electric field \( \vec{E} \) is applied, the tension in the string changes. The final tension in the string, when pendulum attains an equilibrium position is _______.
(\( g \): acceleration due to gravity)
In a double slit experiment the distance between the slits is 0.1 cm and the screen is placed at 50 cm from the slits plane. When one slit is covered with a transparent sheet having thickness t and refractive index n(=1.5), the central fringe shifts by 0.2 cm. The value of t is_________ cm.
Two resistors of $100\,\Omega$ each are connected in series with a $9\,\text{V}$ battery. A voltmeter of $400\,\Omega$ resistance is connected to measure the voltage drop across one of the resistors. The voltmeter reading is ___ V.

The strain-stress plot for materials A, B, C and D is shown in the figure. Which material has the largest Young's modulus? 

Which one of the following is not a measurable quantity?
Consider two identical metallic spheres of radius $R$ each having charge $Q$ and mass $m$. Their centers have an initial separation of $4R$. Both the spheres are given an initial speed of $u$ towards each other. The minimum value of $u$, so that they can just touch each other is :
(Take $k = \frac{1}{4 \pi \epsilon_0}$ and assume $kQ^2>Gm^2$ where $G$ is the Gravitational constant)
Refer to the circuit diagram given below. The heat generated across the $6\ \Omega$ resistance in 100 second is $\frac{\alpha}{100}\ J$. The value of $\alpha$ is ________. (Nearest integer)
When 300 J of heat is given to an ideal gas with \( C_p = \frac{7}{2}R \), its temperature rises from 20°C to 50°C keeping its volume constant. The mass of the gas is (approximately) ______ g. (R = 8.314 J/mol K)

The figure shows a pipe with cross-section area 10 \( cm^2 \). Water flows from one end with velocity 20 cm/s. The other end of the pipe is closed and consists of 10 holes each of area 30 \( mm^2 \). Find the velocity of water coming out from each hole: 

An unpolarised light is incident at an interface of two dielectric media having refractive indices of $2$ (incident medium) and $2\sqrt{3}$ (refracted medium) respectively. To satisfy the condition that reflected and refracted rays are perpendicular to each other, the angle of incidence is ___.
An inductor of inductance $10 \text{ mH}$ having resistance of $100 \text{ } \Omega$ is connected to battery of E.M.F. $1.0 \text{ V}$ through a switch as shown in the figure below. After switch is closed, the ratio of instantaneous voltages across the inductor when the current passing through it is $2 \text{ mA}$ and $4 \text{ mA}$ is ________.
Let \( f(x) = \begin{cases} x^3 + 8 & x < 0 \\ x^2 - 4 & x \ge 0 \end{cases} \) and \( g(x) = \begin{cases} (x-8)^{1/3} & x < 0 \\ (x+4)^{1/2} & x \ge 0 \end{cases} \) then find number of points of discontinuity of \( g(f(x)) \).
Let \(O\) be the vertex of the parabola \(y^2 = 4x\). Let \(P\) and \(Q\) be two points on parabola such that chords \(OP\) and \(OQ\) are perpendicular to each other. If the locus of mid-point of segment \(PQ\) is a conic \(C\), then latus rectum of \(C\) is
A river of width 200 m is flowing from west to east with a speed of 18 km/h. A boat, moving with speed of 36 km/h in still water, is made to travel one-round trip (bank to bank of the river). Minimum time taken by the boat for this journey and also the displacement along the river bank are _________ and _________} respectively.
A point light source emits E.M. waves in free space. A detector, placed at a distance of $L$ m, measures the intensity as $I_0$. The detector is now shifted to another location on the same spherical surface ensuring the angle between original location and new location as $45^{\circ}$. The measured intensity at new location will be ————.
The energy released when $\frac{7}{17.13} \text{ kg}$ of ${}^7_3\text{Li}$ is converted into ${}^4_2\text{He}$ by proton bombardment is $\alpha \times 10^{32} \text{ eV}$. The value of $\alpha$ is ____. (Nearest integer)
(Mass of ${}^7_3\text{Li} = 7.0183 \text{ u}$, mass of ${}^4_2\text{He} = 4.004 \text{ u}$, mass of proton $= 1.008 \text{ u}$ and $1 \text{ u} = 931 \text{ MeV}/c^2$ and Avogadro number $= 6.0 \times 10^{23}$)
If \( 26 \left( \dfrac{2^3 \cdot \binom{12}{2}}{3} + \dfrac{2^5 \cdot \binom{12}{4}}{5} + \dots + \dfrac{2^{13} \cdot \binom{12}{12}}{13} \right) = 3^{13 - \alpha} \), then find the value of \( \alpha \).
If \(\int_0^{\pi/4} \left[ \cot(x - \frac{\pi}{3}) - \cot(x + \frac{\pi}{3}) + 1 \right] dx = \alpha \log(\sqrt{3} - 1)\) then \(9\alpha\) is

The value of \[ \int_0^{2} \sqrt{\frac{x(x^2+x+1)}{(x+1)(x^4+x^2+1)}} \, dx \] is 

The mean & variance of \(x_1, x_2, x_3, x_4\) is 1 and 13 respectively and the mean and variance of \(y_1, y_2, \dots, y_6\) be 2 and 1 respectively, the variance of \(x_1, x_2, \dots, x_4, y_1, y_2, \dots, y_6\) will be
The number of values of \(z \in \mathbb{C}\) satisfying \(|z-4-8i| = \sqrt{10}\) and \(|z-3-5i| + |z-5-11i| = 4\sqrt{5}\) is
Locus of the mid-point of chord of circle \(x^2 + y^2 - 6x - 8y - 11 = 0\), subtending a right angle at the center is
Let \( \frac{x^2}{f(a^2 + 2a + 7)} + \frac{y^2}{f(3a + 14)} = 1 \) represent an ellipse. The major axis of the given ellipse is the y-axis and \( f \) is a decreasing function. If the range of \( a \) is \( R - [\alpha, \beta] \), then \( \alpha + \beta \) is: