List of top Questions asked in JEE Main

A transverse wave is represented by : $y = \frac{10}{\pi} \sin \left(\frac{2\pi}{T}t-\frac{2\pi}{\lambda}x\right)$ For what value of the wavelength the wave velocity is twice the maximum particle velocity ?

The total length of a sonometer wire between fixed ends is $110\, cm$. Two bridges are placed to divide the length of wire in ratio $6 : 3 : 2$. The tension in the wire is $400\, N$ and the mass per unit length is $0.01\, kg/m$. What is the minimum common frequency with which three parts can vibrate ?

The correct statement for the molecule, $CsI_3$ is

The angular frequency of the damped oscillator is given by, $\omega = \sqrt{\left(\frac{k}{m} - \frac{r^{2}}{4m^{2}}\right)}$ where $k$ is the spring constant, $m$ is the mass of the oscillator and $r$ is the damping constant. If the ratio $\frac{r^{2}}{mk}$ is $8\%$, the change in time period compared to the undamped oscillator is approximately as follows :

Dissolving $120 \,g$ of a compound of (mol. wt. $60$) in $1000 \,g$ of water gave a solution of density $1.12 \,g/mL$. The molarity of the solution is :

Among the following organic acids, the acid present in rancid butter is :

For the compounds $CH_3Cl, \, CH_3Br,\,CH_3I$ and $CH_3F,$ the correct order of increasing $C$-halogen bond length is :

During an adiabatic compression, $830\, J$ of work is done on $2$ moles of a diatomic ideal gas to reduce its volume by $50\%$. The change in its temperature is nearly : $(R = 8.3 JK^{-1}\, mol^{-1})$

The image of the line $\frac{x-2}{3}=\frac{y+1}{4} = \frac{z-2}{12}$ in the plane $2x - y + z + 3 = 0$ is the line

The initial speed of a bullet fired from a rifle is $630\, m/ s$. The rifle is fired at the centre of a target $700\, m$ away at the same level as the target. How far above the centre of the target the rifle must be aimed in order to hit the target ?

From a tower of height $H$, a particle is thrown vertically upwards with a speed $u$. The time taken by the particle to hit the ground, is $n$ times that taken by it to reach the highest point of its path. The relation between $H, u$ and $n$ is

If $f$ and $g$ are differentiable functions in $(0, 1)$ satisfying $f (0) = 2 = g (1), g (0) = 0$ and $f (1) = 6$, then for some $c \in ] 0, 1 [$

Considering the basic strength of amines in aqueous solution, which one has the smallest $pK_b$ value?

For the reaction, $ SO_2 ( g) + \frac{1}{2} O_2 \, ( g) \rightleftharpoons SO_3 \, ( g) $ if $ K_P = K_C \, ( RT)^x $ X where, the symbols have usual meaning, then the value of x is (assuming ideality)

If a line intercepted between the coordinate axes is trisected at a point $A(4, 3)$, which is nearer to $x$-axis, then its equation is :

Which one of the following acids does not exhibit optical isomerism?

Let $f\left(n\right) = \left[\frac{1}{3} + \frac{3n}{100}\right]{n},$ where $\left[n\right]$ denotes the greatest integer less than or equal to n. Then $\sum\limits^{56}_{n = 1} \Delta_{r} f\left(n\right)$ is equal to :

The average mass of rain drops is $3.0 \times 10^{-5}$ kg and their average terminal velocity is $9\, m/s.$ Calculate the energy transferred by rain to each square metre of the surface at a place which receives $100\, cm$ of rain in a year.

An object is located in a fixed position in front of a screen. Sharp image is obtained on the screen for two positions of a thin lens separated by $10\, cm$. The size of the images in two situations are in the ratio 3 : 2. What is the distance between the screen and the object ?

An ideal monoatomic gas is confined in a cylinder by a spring loaded piston of cros section $8.0 \times 10^{-3} \, m^2$. Initially the gas is at 300K and occupies a volume of $2.4 \times 10^{-3} \, m^3$ and the spring is in its relaxed state as shown in figure. The gas is heated by a small heater until the piston moves out slowly by $0.1\, m$. The force constant of the spring is $8000\, N/m$ and the atmospheric pressure is $1.0 \times 10^5 \, N/m^2$. The cylinder and the piston are thermally insulated. The piston and the spring are massless and there is no friction between the piston and the cylinder. The final temperature of the gas will be : (Neglect the heat loss through the lead wires of the heater. The heat capacity of the heater coil is also negligible)

What happens when an inert gas is added to an equilibrium keeping volume unchanged ?

If $m$ and $e$ are the mass and charge of the revolving electron in the orbit of radius $r$ for hydrogen atom, the total energy of the revolving electron will be :

A particle moves with simple harmonic motion in a straight line. In first $\tau$ sec, after starting from rest it travels a distance a and in next $\tau$ sec, it travels $2a$, in same direction, then

A person climbs up a stalled escalator in $60\, s$ . If standing on the same but escalator running with constant velocity he takes $40\, s$. How much time is taken by the person to walk up the moving escalator ?

The total number of octahedral void(s) per atom present in a cubic close packec structure is :-