List of top Questions asked in JEE Main

A ray of light along \(x + \sqrt{3}\,y = \sqrt{3}\) gets reflected upon reaching \(X\)-axis, the equation of the reflected ray is :

If \(y=\sec\left(\tan^{-1}x\right)\), then \(\dfrac{dy}{dx}\) at \(x=1\) is equal to :

If \(\displaystyle\int f(x)\,dx=\psi(x)\), then \(\displaystyle\int x^5 f(x^3)\,dx\) is equal to

If \(x,y,z\) are in A.P. and \(\tan^{-1}x,\tan^{-1}y\) and \(\tan^{-1}z\) are also in A.P., then :

Statement-1 : The value of the integral \(\displaystyle\int_{\pi/6}^{\pi/3}\frac{dx}{1+\sqrt{\tan x}}\) is equal to \(\pi/6\)
Statement-2 : \(\displaystyle\int_a^b f(x)\,dx=\int_a^b f(a+b-x)\,dx\).

The area (in square units) bounded by the curves \(y=\sqrt{x}\), \(2y-x+3=0\), \(x\)-axis, and lying in the first quadrant is :

Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of \(A \times B\) having 3 or more elements is :

\(\displaystyle\lim_{x\to 0}\frac{(1-\cos 2x)(3+\cos x)}{x\tan 4x}\) is equal to

For gaseous state, if most probable speed is denoted by $c *$, average speed by $\overline{C}$ and root square speed by $c$, then for a large number of molecules, the ratios of these speeds are

Number of atoms in the following samples of substances is largest in :

Experimentally it was found that a metal oxide has formula $ M_{0.98}O. $ Metal $M$, present as $ M^{2+} $ and $ M^{3+} $ in its oxide.Fraction of the metal which exists as $ M^{3+} $ would be

Which of the following is diamagnetic?

Which of the following arrangements does not represent the correct order of the property stated against it?

Copper crystallises in fcc with a unit length of $361\,pm$. What is the radius of copper atom ?

A solution of $(-) 1-chloro-1-$phenylethane in toluene racemises slowly in the presence of a small amount of $SbCl_5$, due to the formation of

Electron gain enthalpy with negative sign of fluorine is less than that of chlorine due to :

Calcination is the process in which:

A major component of Borsch reagent is obtained by reacting hydrazine hydrate with which of the following ?

A compound with molecular mass $180$ is acylated with $CH_3COCl$ to get a compound with molecular mass $390$. The number of amino groups present per molecule of the former compound is

A gaseous hydrocarbon gives upon combustion $0.72\, g$ of water and $3.08\, g$ of $CO_2$. The empirical formula of the hydrocarbon is

Consider the following reaction, $xMnO_4^- + yC_2O_4^{2-}+zH^+ \rightarrow xMn^{2+}+2yCO_2 + \frac{z}{2}H_2O$ The values of x, y and z in the reaction are, respectively

Which of the following represents the correct order of increasing first ionisation enthalpy for $Ca, Ba, S, Se$ and $Ar$?

Vapour pressure of pure benzene is $119$ torr and that of toluene is $37.0$ torr at the same temperature. Mole fraction of toluene in vapour phase which is in equilibrium with a solution of benzene and toluene having a mole fraction of toluene $0.50$, will be :

Glycosidic linkage is actually an :

Formaldehyde can be distinguished from acetaldehyde by the use of :