List of top Questions asked in JEE Main

The value of $\lim_{x \to 0} \frac{x^2 \sin^2 x}{x^2 - \sin^2 x}$ is:

The question figure shows the 3D view of the object. Choose the correct 2D view (Elevation) of the object looking in the direction of the arrow

Consider an A.P. $a_1,a_2,\ldots,a_n$ with $a_1>0$, $a_2-a_1=-\dfrac{3}{4}$ and $a_n=\dfrac{a_1}{4}$. If \[ \sum_{i=1}^{n} a_i=\frac{525}{2}, \] then find $\sum_{i=1}^{17} a_i$.

Consider the following statements for [Ni(dmg)$_2$]: (A) It is a red coloured compound.
(B) It is readily soluble in water at pH = 9.
(C) Central metal ion has two unpaired electrons.
(D) It has four, 5-membered metal containing rings.

Match the list-I with list-II

1 mole of He and 1 mole A are taken in a 10 L rigid container at 400 K, and equilibrium $ A \rightleftharpoons B $ is established. Calculate the partial pressure of He and B at equilibrium if $ K_c = 4 $.

Let $ A = \{1, 2, 3, 4, 5\} $ and $ B = \{a, b, c\} $. Then the number of functions which are not onto are:

A solution contains 0.25 moles of non-volatile solute dissolved in one mole of solvent. Then calculate the % vapor pressure of solution relative to the vapor pressure of pure solvent.

A screw gauge has a pitch of 0.1 mm and 100 divisions on its circular scale. When its both jaws touch, the fifth division of its circular scale coincides with zero. When a sphere is placed between the jaws, the reading of the linear scale is 5 mm and the 50th division of the circular scale coincides with zero of the main scale. Find the diameter of the sphere.

Which of the following pair of species have different Lewis structures? (A) $ \mathrm{SO_3^{2-}, CO_3^{2-}} $
(B) $ \mathrm{O_2^{2-}, F_2} $
(C) $ \mathrm{CN^- , CO} $
(D) $ \mathrm{NH_3, H_3O^+} $
(E) $ \mathrm{MnO_4^- , CrO_4^{2-}} $

The maximum rated power of the LED is $2 \text{ mW}$ and it is used in the circuit with input voltage of $5 \text{ V}$ as shown in the figure below. The current through resistance $R$ is $0.5 \text{ mA}$. The minimum value of the resistance $R_s$, to ensure that the LED is not damaged is ______ $\text{k}\Omega$.

In the provided circuit, the input voltage is $5 \text{ V}$, a series resistor $R_s$ is connected, and the circuit then branches into two parallel paths: one with a resistor $R = 1 \text{ k}\Omega$ in series with a Zener diode, and another with the LED.

Find speed given to particle at lowest point so that tension in string at point A becomes zero.

The pairs among $A = [SO_3^{2-}, CO_3^{2-}]$, $B = [O_2^-, F_2]$, $C = [CN^-, CO]$, $D = [NH_3, H_3O^+]$ and $E = [MnO_4^-, CrO_4^{2-}]$ that do not have similar Lewis dot structure are

Identify the total number of surfaces in the given 3D object.

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)

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 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 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