List of top Questions asked in JEE Main

If \(\{p\}\) denotes the fractional part of the number \(p\), then
\(\left\{\frac{3^{200}}{8}\right\}\), is equal to :

\(\displaystyle\lim_{x\to 1}\left(\frac{\int_{0}^{(x-1)^2} t\cos\left(t^2\right)dt}{(x-1)\sin(x-1)}\right)\)

The region represented by
\(\{z=x+iy\in C : |z|-\mathrm{Re}(z)\le 1\}\) is also given by the inequality :
\(\{z=x+iy\in C : |z|-\mathrm{Re}(z)\le 1\}\)

Let a, b, c, d and p be any non zero distinct real numbers such that
\((a^2+b^2+c^2)p^2-2(ab+bc+cd)p+(b^2+c^2+d^2)=0\). Then :

The values of \(\lambda\) and \(\mu\) for which the system of linear equations
\(x+y+z=2\)
\(x+2y+3z=5\)
\(x+3y+\lambda z=\mu\)
has infinitely many solutions are, respectively:

If \(\alpha\) and \(\beta\) be two roots of the equation \(x^2-64x+256=0\). Then the value of
\(\left(\dfrac{\alpha^3}{\beta^5}\right)^{1/8}+\left(\dfrac{\beta^3}{\alpha^5}\right)^{1/8}\)
is :

If \(\displaystyle\sum_{i=1}^{n}(x_i-a)=n\) and \(\displaystyle\sum_{i=1}^{n}(x_i-a)^2=na\) \((n, a>1)\) then the standard deviation of n observations \(x_1, x_2, \ldots, x_n\) is :

Two families with three members each and one family with four members are to be seated in a row. In how many ways can they be seated so that the same family members are not separated?

The area (in sq. units) of the region
\(A=\{(x, y) : |x|+|y|\le 1,\ 2y^2\ge |x|\}\)

Out of 11 consecutive natural numbers if three numbers are selected at random (without repetition), then the probability that they are in A.P. with positive common difference, is :

The position of a moving car at time t is given by \(f(t)=at^2+bt+c,\ t>0\), where a, b and c are real numbers greater than 1. Then the average speed of the car over the time interval \([t_1,\ t_2]\) is attained at the point :

Let m and M be respectively the minimum and maximum values of
\(\begin{vmatrix}\cos^2 x & 1+\sin^2 x & \sin 2x\\ 1+\cos^2 x & \sin^2 x & \sin 2x\\ \cos^2 x & \sin^2 x & 1+\sin 2x\end{vmatrix}\)
Then the ordered pair (m, M) is equal to :

For a dimerization reaction,
\(\mathrm{2A(g) \to A_2(g)}\)
at 298 K, \(\Delta U^\circ = -20\ \mathrm{kJ\ mol^{-1}}\), \(\Delta S^\circ = -30\ \mathrm{J\,K^{-1}\,mol^{-1}}\),
then the \(\Delta G^\circ\) will be _____ J.

The volume, in mL, of 0.02 M \(\mathrm{K_2Cr_2O_7}\) solution required to react with 0.288 g of ferrous oxalate in acidic medium is _______.
(Molar mass of Fe = 56 g mol^-1)

For a reaction \(\mathrm{X + Y \rightleftharpoons 2Z}\), 1.0 mol of X, 1.5 mol of Y and 0.5 mol of Z were taken in a 1 L vessel and allowed to react. At equilibrium, the concentration of Z was 1.0 mol L^-1. The equilibrium constant of reaction is \(\frac{x}{15}\). The value of x is _________.

Considering that \(\Delta_0 \gt P\), the magnetic moment (in BM) of \(\mathrm{[Ru(H_2O)_6]^{2+}}\) would be _________.

Hydrogen peroxide, in the pure state, is :

Which one of the following polymers is not obtained by condensation polymerisation?

The one that is NOT suitable for the removal of permanent hardness of water is :

Reaction of ammonia with excess \(\mathrm{Cl_2}\) gives :

Adsorption of a gas follows Freundlich adsorption isotherm. If x is the mass of the gas adsorbed on mass m of the adsorbent, the correct plot of \(\frac{x}{m}\) versus p is :

The following molecule acts as an :

The final major product of the following reaction is :

(3-methylaniline treated with (i) \(\mathrm{Ac_2O}\)/Pyridine, (ii) \(\mathrm{Br_2/FeCl_3}\), (iii) \(\mathrm{OH^{-}/\Delta}\))

Boron and silicon of very high purity can be obtained through :

The major product of the following reaction is :