List of top Questions asked in JEE Main

The commercial name for calcium oxide is :

The point $(2, 1)$ is translated parallel to the line $L : x-y = 4$ by $2\sqrt{3}$ units. If the new point $Q$ lies in the third quadrant, then the equation of the line passing through $Q$ and perpendicular to $L$ is :

The species in which the $N$ atom is in a state of $sp$ hybridization is :

The sum $\displaystyle\sum^{10}_{r=1}(r^2 + 1) \times (r!)$ is equal to :

Two closed bulbs of equal volume $(V)$ containing an ideal gas initially at pressure $p_i$ and temperature $T_1$ are connected through a narrow tube of negligible volume as shown in the figure below. The temperature of one of the bulbs is then raised to $T_2$. The final pressure $p_f$ is :

Two particles are performing simple harmonic motion in a straight line about the same equilibrium point. The amplitude and time period for both particles are same and equal to $A$ and $T$, respectively. At time $t = 0$ one particle has displacement $A$ while the other one has displacement $\frac{-A}{2}$ and they are moving towards each other. If they cross each other at time $t$, then $t$ is :

Two sides of a rhombus are along the lines, $x - y + 1 = 0$ and $7x - y - 5 = 0$. If its diagonals intersect at $(-1, -2)$, then which one of the following is a vertex of this rhombus?

The sum of coefficients of integral powers of $x$ in the binomial expansion $(1-2\sqrt x)^{50}$ is

Addition of phosphate fertilisers to water bodies causes :

If the mean and the variance of a binomial variate $X$ are $2$ and $1$ respectively, then the probability that $X$ takes a value greater than or equal to one is :

$A +2 B +3 C \rightleftharpoons AB _{2} C _{3}$ Reaction of $6.0\, g$ of $A , 6.0 \times 10^{23}$ atoms of $B$, and $0.036\, mol$ of $C$ yields $4.8\, g$ of compound $AB _{2} C _{3}$. If the atomic mass of $A$ and $C$ are 60 and 80 amu respectively, the atomic mass of $B$ is (Avogadro no. $=6 \times 10^{23}$ ):

A simple harmonic oscillator of angular frequency $2 \,rad \,s^{-1}$ is acted upon by an external force $F= \sin\, t \,N$. If the oscillator is at rest in its equilibrium position at $t\, =\, 0$, its position at later times is proportional to :

An ellipse passes through the foci of the hyperbola, $9x^2? 4y^2 = 36$ an and minor axes lie along the transverse and conjugate axes of the hyperbola respectively. If the product of eccentricities of the two conics is $\frac{1}{2},$ then which of the following points does not lie on the ellipse ?

If $y + 3x = 0$ is the equation of a chord of the circle, $x^2 + y^2 - 30x = 0$, then the equation of the circle with this chord as diameter is :

Let k be a non-zero real number. If

\( f(x) = \begin{cases} \dfrac{(e^x - 1)^2}{\sin\left(\frac{x}{k}\right)\log\left(1+\frac{x}{4}\right)}, & x \ne 0 \\[2ex] 12, & x = 0 \end{cases} \)

is a continuous function, then the value of \( k \) is:

Let $O$ be the vertex and $Q$ be any point on the parabola, $x^2$ = 8y. If the point $P$ divides the line segment $OQ$ internally in the ratio $1 : 3$, then the locus of $P$ is

Let $PQ$ be a double ordinate of the parabola, $y^2= - 4x$, where P lies in the second quadrant. If R divides $PQ$ in the ratio $2 : 1$, then the locus of R is :

Locus of the image of the point $(2, 3)$ in the line $\left(2x - 3y + 4\right) + k\left(x - 2y + 3\right) = 0, k \in R,$ is a

Which of the following compounds is not an antacid?

In Carius method of estimation of halogens $250\, mg$ of an organic compound gave $141\, mg$ of $AgBr$. The percentage of bromine in the compound is (atomic mass $Ag\, =\, 108, Br \,= \,80$)

An experiment takes $10\, min$ to raise the temperature of water in a container from $0^{\circ} C$ to $100^{\circ} C$ and another $55\, min$ to convert it totally into steam by a heater supplying heat at a uniform rate. Neglecting the specific heat of the container and taking specific heat of water to be $1\, cal / g { }^{\circ} C$, the heat of vaporisation according to this experiment will come out to be

When $5\,V$ potential difference is applied across a wire of length $0.1\,m$, the drift speed of electrons is $2.5\times10^{-4}$ $ms^{-1}$. If the electron density in the wire is $8\times10^{28}\, m^{-3}$ the resistivity of the material is close to

For plane electromagnetic waves propagating in the $z$ direction, which one of the following combination gives the correct possible direction for $\vec{E}$ and $\vec{B}$ field respectively ?

A solution at $20^{\circ}$C is composed of $1.5\, mol$ of benzene and $3.5\, mol$ of toluene. If the vapour pressure of pure benzene and pure toluene at this temperature are $74.7$ torr and $22.3$ torr, respectively, then the total vapour pressure of the solution and the benzene mole fraction in equilibrium with it will be, respectively :

Choose the incorrect formula out of the four compounds for an element X below :