List of top Questions asked in JEE Main

In a class of $140$ students numbered $1$ to $140$, all even numbered students opted mathematics course, those whose number is divisible by $3$ opted Physics course and those whose number is divisible by $5$ opted Chemistry course. Then the number of students who did not opt for any of the three courses is :

Let $z \in C$ with Im(z) = 10 and it satisfies $\frac{2z-n}{2z+n} = 2i -1$ for some natural number $n$.Then :

The value of $\cos \frac{\pi}{2^{2}} .\cos \frac{\pi}{2^{3} } . ...... .\cos \frac{\pi}{2^{10}} .\sin \frac{\pi}{2^{10}} $ is :

The solution of the differential equation , $\frac{dy}{dx} = \left(x-y\right)^{2} , $ when $y(1) = 1$, is :

In a game, a man wins Rs. $100$ if he gets $5$ of $6$ on a throw of a fair die and loses Rs. $50$ for getting any other number on the die. If he decides to throw the die either till he gets a five or a six or to a maximum of three throws, then his expected gain/ loss (in rupees) is :

Consider a class of $5$ girls and $7$ boys. The number of different teams consisting of $2$ girls and $3$ boys that can be formed from this class, if there are two specific boys $A$ and $B$, who refuse to be the members of the same team, is :

If $m$ is chosen in the quadratic equation $(m^2 + 1) x^2 - 3x + (m^2 + 1)^2 = 0$ such that the sum of its roots is greatest, then the absolute difference of the cubes of its roots is :

The value of cos $^2 10^{\circ} - cos10^{\circ} cos50^{\circ} + cos^2 50^{\circ}$

Calculate the limit of resolution of a telescope objective having a diameter of $200\, cm$, if it has to detect light of wavelength $500\, nm$ coming from a star :

Diameter of the objective lens of a telescope is $250\, cm$. For light of wavelength $600\,nm$. coming from a distant object, the limit of resolution of the telescope is close to :

Ice at $-20^{\circ} C$ os added tp $50\, g$ of water at $40^{\circ}C$. When the temperature of the mixture reaches $0^{\circ}C$, it is found that $20\, g$ of ice is still unmelted. The amount of ice added to the water was close to (Specific heat of water = $4.2 \; J/g/^{\circ}C$) Specific heat of Ice = $2.1 \; J/g/^{\circ}C$ Heat of fusion of water at $0^{\circ}C = 334 \; J/g$)

The correct figure that shows, schematically, the wave pattern produced by superposition of two waves of frequencies $9 \,Hz$ and $11\, Hz$ is :

The length of the chord of the parabola $x^2 = 4y$ having equation $x - \sqrt{2} y + 4 \sqrt{2} = 0$ is :

1 g of non-volatile non-electrolyte solute is dissolved in 100g of two different solvents A and B whose ebullioscopic constants are in the ratio of 1 : 5. The ratio of the elevation in their boiling points, $\frac{\Delta T_b(A)}{\Delta T_b (B)}$, is:

In the following skew conformation of ethane, $H'-C-C-H''$ dihedral angle is :

Which of the following compounds is not aromatic ?

An aromatic compound $'A'$ having molecular formula ${C7H6O2}$ on treating with aqueous ammonia and heating forms compound $'B'$. The compound $'B'$ on reaction with molecular bromine and potassium hydroxide provides compound $'C'$ having molecular formula ${C_6H_7N}$. The structure of $'A'$ is :

Arrange the following amines in the decreasing order of basicity:

Four identical particles of mass $M$ are located at the corners of a square of side $'a'$. What should be their speed if each of them revolves under the influence of other?s gravitational field in a circular orbit circumscribing the square?

If the angular momentum of a planet of mass $m$, moving around the Sun in a circular orbit is $L$, about the center of the Sun, its areal velocity is :

A particle undergoing simple harmonic motion has time dependent displacement given by $x(t) = A \sin \frac{\pi t}{90}$. The ratio of kinetic to potential energy of this particle at $t\, =\, 210\, s$ will be :

A rod of mass $'M'$ and length $'2L'$ is suspended at its middle by a wire. It exhibits torsional oscillations; If two masses each of $'m'$ are attached at distance $'L/2'$ from its centre on both sides, it reduces the oscillation frequency by $20\%$. The value of ratio $m/M$ is close to :

If a unit vector $\vec{a}$ makes angles $\pi/3$ with $\hat{i} , \pi /4$ with $\hat{j}$ and $\theta \in (0 , \pi)$ with $\hat{k}$, then a value of $\theta$ is : -

If $0 \le x < \frac{\pi}{2}$ , then the number of values of $ x$ for which $sin \,x-sin\,2x+sin\,3x = 0$, is

Among the following species, the diamagnetic molecule is