List of top Questions asked in JEE Main

In a building there are $15$ bulbs of $45\, W, 15$ bulbs of $100\, W$, $15$ small fans of $10\, W$ and $2$ heaters of $1\, kW$. The voltage of electric main is $220\, V$. The minimum fuse capacity (rated value) of the building will be:

A vessel of depth $2\,h$ is half filled with a liquid of refractive index $2\sqrt{2}$ and the upper half with another liquid of refractive index $\sqrt{2}$ The liquids are immiscible. The apparent depth of the inner surface of the bottom of vessel will be :

Consider a sphere of radius $R$ which carries a uniform charge density $\rho$. If a sphere of radius $\frac{R}{2}$ Ls carved out of it, as shown, the ratio $\frac{\left|\overrightarrow{E_{A}}\right|}{\left|\overrightarrow{E_{B}}\right|}$ of magnitude of electric field $\overrightarrow{E_{A}}$ and $\overrightarrow{E}_{B}$ respectively, at points A and B due to the remaining portion is :

An ideal fluid flows (laminar flow) through a pipe of non-uniform diameter. The maximum and minimum diameters of the pipes are $6.4\, cm$ and $4.8\, cm$, respectively. The ratio of the minimum and the maximum velocities of fluid in this pipe is :

If the potential energy between two molecules is given by $U = - \frac{ A }{ r ^{6}}+\frac{ B }{ r ^{12}},$ then at equilibrium, separation between molecules, and the potential energy are :

In finding the electric field using Gauss law the formula $\left|\overrightarrow{E}\right|= \frac{q_{enc}}{\epsilon_{0}\left|A\right|}$ is applicable. In the formula $\epsilon_{0}$ is permittivity of free space, $A$ is the area of Gaussian surface and $ q_{enc}$ is charge enclosed by the Gaussian surface. This equation can be used in which of the following situation ?

The inverse function of $f\left(x\right) = \frac{8^{2x}-8^{-2x}}{8^{2x} + 8^{-2x}}, x\epsilon \left(-1, 1\right),$ is __________.

Let $\vec{a}=\hat{i}-2\,\hat{j}+\hat{k}$ and $\vec{b}=\hat{i}-\hat{j}+\hat{k}$ be two vectors. If $\vec{c}$ is a vector such that $\vec{b}\times\vec{c}=\vec{b}\times\vec{a}$ and $\vec{c}\cdot\vec{a}=0,$ then $\vec{c} \cdot \vec{b}$ is equal to :

If the volume of a parallelepiped whose coterminous edges are $\vec{a}=\hat{i}+\hat{j}+2\,\hat{k}, \vec{b}=2\,\hat{i}+\lambda\,\hat{j}+\hat{k}$ and $\vec{c}=2\,\hat{i}+2\hat{j}+\lambda\hat{k}$ is 35 cu.m, then a value of $\vec{a}\cdot\vec{b}+\vec{b}\cdot\vec{c}-\vec{c}\cdot\vec{a}$ is :

The probability that a randomly chosen 5 -digit number is made from exactly two digits is :

Let the ellipse, $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1, a > b,$ pass through the point (2, 3) and have eccentricity equal to $\frac{1}{2}$. Then equation of the normal to this ellipse at $(2,3)$ is :

The number of bonds between sulphur and oxygen atoms in $S_2O^{2-}_8$ and the number of bonds between sulphur and sulphur atoms in rhombic sulphur, respectively, are:

The system of linear equations $\lambda x+2y+2z=5$ $2\lambda x+3y+5z=8$ $4x+\lambda y+6z=10$ has :

A particle of mass m is projected with a speed $u$ from the ground at an angle $\theta=\frac{\pi}{3}$ w.r.t. horizontal (x-axis). When it has reached its maximum height, it collides completely inelastically with another particle of the same mass and velocity $u\,\hat{i}$. The horizontal distance covered by the combined mass before reaching the ground is :

$\displaystyle\lim_{x \to 0} \left(\frac{3x^{2}+2}{7x^{2}+2}\right)^{\frac {1}{x^2}}$ is equal to :

Which one of the following is a tautology ?

Cast iron is used for the manufacture of :

Starting from the origin at time $t=0$, with initial velocity $5 \hat{ j } \,ms ^{-1},$ a particle moves in the $x - y$ plane with a constant acceleration of $(10 \hat{ i }+4 \hat{ j }) ms ^{-2} .$ At time $t$, its coordinates are (20 $\left. m , y _{0} m \right)$. The values of $t$ and $y _{0}$, are respectively

The coefficient of $x^7$ in the expression $\left(1+x\right)^{10}+x\left(1+x\right)^{9}+x^{2}\left(1+x\right)^{8}+...+x^{10}$ is :

The major product formed in the following reaction is : $CH _{3} CH = CHCH \left( CH _{3}\right)_{2} \stackrel{ HBr }{\longrightarrow}$

The mean and variance of 7 observations are 8 and $16,$ respectively. If five observations are $2,4,10,12,14,$ then the absolute difference of the remaining two observations is :

If enthalpy of atomisation for $Br_{2(I)}$ is $x \,kJ/mol$ and bond enthalpy for $Br_2$ is $y\, kj/mol$, the relation between them :

The IUPAC name of the complex $[Pt(NH_3)_2Cl(NH_2CH_3)]Cl$ is :

For $a > 0$, let the curves $C_1 : y^2 = ax$ and $C_2 : x^2= ay$ intersect at origin O and a point P. Let the line $x = b (0 < b < a)$ intersect the chord OP and the x-axis at points Q and R, respectively. If the line x = b bisects the area bounded by the curves, $C_1$ and $C_2$, and the area of $\Delta OQR = \frac{1}{2},$ then 'a' satisfies the equation :

The sum of the values of $x$ satisfying the equation, $\sqrt{x}\left(\sqrt{x}-4\right)-3\left|\sqrt{x}-2\right|+6=0 \left(x\,\ge\,0\right),$ is :