List of top Questions asked in JEE Main

The area (in sq. units) of the region \(\{(x,y)\in\mathbb{R}^2: x^2\le y\le3-2x\}\), is :

The mirror image of the point \((1,2,3)\) in a plane is \(\left(-\dfrac73,-\dfrac43,-\dfrac13\right)\). Which of the following points lies on this plane ?

Let S be the set of all functions \(f:[0,1]\to\mathbb{R}\), which are continuous on \([0,1]\) and differentiable on \((0,1)\). Then for every \(f\) in S, there exists a \(c\in(0,1)\), depending on \(f\), such that

If \(I=\displaystyle\int_1^2\dfrac{dx}{\sqrt{2x^3-9x^2+12x+4}}\), then :

\(\displaystyle\lim_{x\to0}\dfrac{\int_0^x t\sin(10t)\,dt}{x}\) is equal to

Let \(f:(1,3)\to\mathbb{R}\) be a function defined by \(f(x)=\dfrac{x[x]}{1+x^2}\), where \([x]\) denotes the greatest integer \(\le x\). Then the range of \(f\) is

Let S be the set of all real roots of the equation, \(3^x(3^x-1)+2=|3^x-1|+|3^x-2|\). Then S :

If the \(10^{\text{th}}\) term of an A.P. is \(\dfrac{1}{20}\) and its \(20^{\text{th}}\) term is \(\dfrac{1}{10}\), then the sum of its first 200 terms is

Let \(\alpha=\dfrac{-1+i\sqrt3}{2}\). If \(a=(1+\alpha)\displaystyle\sum_{k=0}^{100}\alpha^{2k}\) and \(b=\displaystyle\sum_{k=0}^{100}\alpha^{3k}\), then \(a\) and \(b\) are the roots of the quadratic equation :

If \(A=\begin{pmatrix}2&2\\9&4\end{pmatrix}\) and \(I=\begin{pmatrix}1&0\\0&1\end{pmatrix}\), then \(10A^{-1}\) is equal to :

Among the gases (a) – (e), the gases that cause greenhouse effect are :
(a) \(\mathrm{CO_2}\)
(b) \(\mathrm{H_2O}\)
(c) CFCs
(d) \(\mathrm{O_2}\)
(e) \(\mathrm{O_3}\)

What would be the electrode potential for the given half cell reaction at pH = 5? ______
\(2\mathrm{H_2O} \to \mathrm{O_2} + 4\mathrm{H}^{+} + 4e^{-}\) ; \(E^0_{red} = 1.23\) V
(R = 8.314 J mol\(^{-1}\) K\(^{-1}\) ; Temp = 298 K ; oxygen under std. atm. pressure of 1 bar)

The number of chiral centres in penicillin is _________.

The strength of an aqueous NaOH solution is most accurately determined by titrating :
(Note : consider that an appropriate indicator is used)

When gypsum is heated to 393 K, it forms :

As per Hardy-Schulze formulation, the flocculation values of the following for ferric hydroxide sol are in the order :

The third ionization enthalpy is minimum for :

For the Balmer series in the spectrum of H atom,
\(\bar{\nu}=R_H\left\{\frac{1}{n_1^2}-\frac{1}{n_2^2}\right\}\),
the correct statements among (I) to (IV) are :
(I) As wavelength decreases, the lines in the series converge
(II) The integer \(n_1\) is equal to 2
(III) The lines of longest wavelength corresponds to \(n_2=3\)
(IV) The ionization energy of hydrogen can be calculated from wave number of these lines

The predominant intermolecular forces present in ethyl acetate, a liquid, are:

The rate of a certain biochemical reaction at physiological temperature (T) occurs \(10^6\) times faster with enzyme than without. The change in the activation energy upon adding enzyme is :

The first ionization energy (in kJ/mol) of Na, Mg, Al and Si respectively, are :

A flask contains a mixture of isohexane and 3-methylpentane. One of the liquids boils at \(63^\circ\mathrm{C}\) while the other boils at \(60^\circ\mathrm{C}\). What is the best way to separate the two liquids and which one will be distilled out first ?

When photon of energy 4.0 eV strikes the surface of a metal A, the ejected photoelectrons have maximum kinetic energy \(T_A\) eV and de-Broglie wavelength \(\lambda_A\). The maximum kinetic energy of photoelectrons liberated from another metal B by photon of energy 4.50 eV is \(T_B=(T_A-1.5)\) eV. If the de-Broglie wavelength of these photoelectrons \(\lambda_B=2\lambda_A\), then the work function of metal B is :

Arrange the following compounds in increasing order of C-OH bond length :
methanol, phenol, p-ethoxyphenol

A particle is moving along the x-axis with its coordinate with the time 't' given be \(x(t)=10+8t-3t^2\). Another particle is moving the y-axis with its coordinate as a function of time given by \(y(t)=5-8t^3\).
At \(t=1\) s, the speed of the second particle as measured in the frame of the first particle is given as \(\sqrt{v}\). Then \(v\) (in m/s) is ______.