List of top Questions asked in JEE Main

If the function f given by \(f(x)=x^3-3(a-2)x^2+3ax+7\), for some \(a\in R\) is increasing in (0, 1] and decreasing in [1, 5), then a root of the equation, \(\frac{f(x)-14}{(x-1)^2}=0\ (x\ne1)\) is :

In a class of 60 students, 40 opted for NCC, 30 opted for NSS and 20 opted for both NCC and NSS. If one of these students is selected at random, then the probability that the students selected has opted neither for NCC nor for NSS is :

The integral \(\int_1^e \left\{\left(\frac{x}{e}\right)^{2x}-\left(\frac{e}{x}\right)^{x}\right\}\log_e x\,dx\) is equal to :

The molecule that has minimum /no role in the formation of photochemical smog, is :

Water samples with BOD values of 4 ppm and 18 ppm, respectively are :

A metal on combustion in excess air forms X. X upon hydrolysis with water yields \(\mathrm{H_2O_2}\) and \(\mathrm{O_2}\) along with another product. The metal is :

The correct order for acid strength of compounds :
\(\mathrm{CH\equiv CH}\), \(\mathrm{CH_3{-}C\equiv CH}\) and \(\mathrm{CH_2{=}CH_2}\) is as follows

The major product of the following reaction is

The volume of gas A is twice than that of gas B. The compressibility factor of gas A is thrice than that of gas B at same temperature. The pressures of the gases for equal number of moles are -

The standard electrode potential \(E^\circ\) and its temperature coefficient \(\left(\frac{dE^\circ}{dT}\right)\) for a cell are 2 V and \(-5\times10^{-4}\ \mathrm{VK^{-1}}\) at 300 K respectively. The cell reaction is
\(\mathrm{Zn(s) + Cu^{2+}(aq) \rightarrow Zn^{2+}(aq) + Cu(s)}\)
The standard reaction enthalpy \((\Delta_rH^\circ)\) at 300 K in \(\mathrm{kJ\ mol^{-1}}\) is, [Use \(R = 8\ \mathrm{JK^{-1}mol^{-1}}\) and \(F = 96{,}000\ \mathrm{C\ mol^{-1}}\)]

The major product of the following reaction is \(-\)

Among the following four aromatic compounds, which one will have the lowest melting point ?

can not be prepared by \(-\)
(The structure shown is \(\mathrm{CH_3CH_2C(OH)(Ph)CH_3}\), i.e. 2-phenylbutan-2-ol.)

The element with Z = 120 (not yet discovered) will be an/a \(-\)

What is the work function of the metal if the light of wavelength \(4000\ \mathrm{\AA}\) generates photoelectrons of velocity \(6\times 10^{5}\ \mathrm{ms^{-1}}\) from it ?
(Mass of electron = \(9\times 10^{-31}\) kg;
Velocity of light = \(3\times 10^{8}\ \mathrm{ms^{-1}}\)
Plank's constant = \(6.626\times 10^{-34}\) Js;
Charge of electron = \(1.6\times 10^{-19}\ \mathrm{JeV^{-1}}\))

The pair of metal ions that can give a spin only magnetic moment of 3.9 BM for the complex \(\mathrm{[M(H_2O)_6]Cl_2}\), is \(-\)

The increasing order of reactivity of the following compounds towards reaction with alkyl halides directly is

(The figure shows four structures labelled (A) benzamide, (B) phthalimide, (C) 2-aminobenzonitrile, (D) aniline.)

In the following reaction, products A and B are \(-\)

In the following reaction :
\(\text{Aldehyde} + \text{Alcohol} \xrightarrow{\ \mathrm{HCl}\ } \text{Acetal}\)

Aldehyde	Alcohol
HCHO	tBuOH
\(\mathrm{CH_3CHO}\)	MeOH

The best combination is

A 100 V carrier wave is made to vary between 160 V and 40 V by a modulating signal. What is the modulation index ?

Decomposition of X exhibits a rate constant of \(0.05\ \mu\mathrm{g/year}\). How many year are required for the decomposition of \(5\ \mu\mathrm{g}\) of X into \(2.5\ \mu\mathrm{g}\)?

A light wave is incident normally on a glass slab of refractive index 1.5. If 4 % of light gets reflected and the amplitude of the electric field of the incident light is 30 V/m, then the amplitude of the electric field for the wave propagating in the glass medium will be :

A particle A of mass 'm' and charge 'q' is accelerated by a potential difference of 50 V. Another particle B of mass '4 m' and charge 'q' is accelerated by a potential difference of 2500 V. The ratio of de-Broglie wavelengths \(\dfrac{\lambda_A}{\lambda_B}\) is close to :

As shown in the figure, two infinitely long, identical wires are bent by \(90^\circ\) and placed in such a way that the segments LP and QM are along the x-axis, while segments PS and QN are parallel to the y-axis. If OP = OQ = 4 cm, and the magnitude of the magnetic field at O is \(10^{-4}\) T, and the two wires carry equal currents (see figure), the magnitude of the current in each wire and the direction of the magnetic field at O will be (\(\mu_0 = 4\pi \times 10^{-7}\ \mathrm{NA^{-2}}\)) :

In the figure shown, a circuit contains two identical resistors with resistance \(R = 5\,\Omega\) and an inductance with \(L = 2\,\text{mH}\). An ideal battery of 15 V is connected in the circuit. What will be the current through the battery long after the switch is closed ?