List of top Questions asked in JEE Main

Let \(a_1,a_2,a_3,\ldots\ldots,a_n,\ldots\) be in A.P. If \(a_3+a_7+a_{11}+a_{15}=72\), then the sum of its first 17 terms is equal to :

If \(A=\begin{bmatrix}-4&-1\\3&1\end{bmatrix}\), then the determinant of the matrix \((A^{2016}-2A^{2015}-A^{2014})\) is :

\(\displaystyle\lim_{x\to0}\frac{(1-\cos2x)^2}{2x\tan x-x\tan2x}\) is :

If the coefficients of \(x^{-2}\) and \(x^{-4}\) in the expansion of \(\left(x^{\frac{1}{3}}+\frac{1}{2x^{\frac{1}{3}}}\right)^{18}\), \((x>0)\), are \(m\) and \(n\) respectively, then \(\frac{m}{n}\) is equal to :

Let \(a,b\in\mathbf{R}\), \((a\neq0)\). If the function \(f\) defined as
\(f(x)=\begin{cases}\frac{2x^2}{a}, & 0\leq x<1\\ a, & 1\leq x<\sqrt{2}\\ \frac{2b^2-4b}{x^3}, & \sqrt{2}\leq x<\infty\end{cases}\)
is continuous in the interval \([0,\infty)\), then an ordered pair \((a,b)\) is :

If \(x\) is a solution of the equation, \(\sqrt{2x+1}-\sqrt{2x-1}=1\), \(\left(x\geq\frac{1}{2}\right)\), then \(\sqrt{4x^2-1}\) is equal to :

Let A be a \(3\times3\) matrix such that \(A^2-5A+7I=O\).
Statement - I : \(A^{-1}=\frac{1}{7}(5I-A)\).
Statement - II : The polynomial \(A^3-2A^2-3A+I\) can be reduced to \(5(A-4I)\).
Then :

The test to distinguish primary, secondary and tertiary amines is :

The most appropriate method of making egg-albumin sol is :

Identify the correct trend given below :
(Atomic No. = Ti : 22, Cr : 24 and Mo : 42)

BOD stands for :

The hydrocarbon with seven carbon atoms containing a neopentyl and a vinyl group is :

5 L of an alkane requires 25 L of oxygen for its complete combustion. If all volumes are measured at constant temperature and pressure, the alkane is :

The gas evolved on heating \(\mathrm{CH_3MgBr}\) in methanol is :

Which one of the following complexes will consume more equivalents of aqueous solution of \(\mathrm{Ag(NO_3)}\) ?

Which one of the following species is stable in aqueous solution ?

Match the items in Column I with its main use listed in Column II :

Column I	Column II
(A) Silica gel	(i) Transistor
(B) Silicon	(ii) Ion-exchanger
(C) Silicone	(iii) Drying agent
(D) Silicate	(iv) Sealant

The plot shows the variation of \(-\ln K_p\) versus temperature for the two reactions \(\mathrm{M(s)}+\frac{1}{2}\mathrm{O_2(g)}\rightarrow\mathrm{MO(s)}\) and \(\mathrm{C(s)}+\frac{1}{2}\mathrm{O_2(g)}\rightarrow\mathrm{CO(s)}\).

Identify the correct statement :

The correct order of the solubility of alkaline-earth metal sulphates in water is :

The group of molecules having identical shape is :

A reaction at 1 bar is non-spontaneous at low temperature but becomes spontaneous at high temperature. Identify the correct statement about the reaction among the following :

For the reaction, A(g) + B(g) \(\rightarrow\) C(g) + D(g), \(\Delta H^\circ\) and \(\Delta S^\circ\) are, respectively, \(-29.8\ \mathrm{kJ\ mol^{-1}}\) and \(-0.100\ \mathrm{kJ\ K^{-1}\ mol^{-1}}\) at 298 K. The equilibrium constant for the reaction at 298 K is :

Which intermolecular force is most responsible in allowing xenon gas to liquefy ?

The reaction of ozone with oxygen atoms in the presence of chlorine atoms can occur by a two step process shown below :
\(\mathrm{O_3(g)+Cl^{\bullet}(g)\rightarrow O_2(g)+ClO^{\bullet}(g)}\) ____ (i)
\(k_i=5.2\times10^{9}\ \mathrm{L\ mol^{-1}\ s^{-1}}\)
\(\mathrm{ClO^{\bullet}(g)+O^{\bullet}(g)\rightarrow O_2(g)+Cl^{\bullet}(g)}\) ____ (ii)
\(k_{ii}=2.6\times10^{10}\ \mathrm{L\ mol^{-1}\ s^{-1}}\)
The closest rate constant for the overall reaction \(\mathrm{O_3(g)+O^{\bullet}(g)\rightarrow 2\,O_2(g)}\) is :

What will occur if a block of copper metal is dropped into a beaker containing a solution of 1M \(\mathrm{ZnSO_4}\) ?