List of top Questions asked in JEE Main

The number of solutions of the equation \(\sin 2x - 2\cos x + 4\sin x = 4\) in the interval \([0, 5\pi]\) is :

The sum of the rational terms in the binomial expansion of \(\left(2^{\frac{1}{2}} + 3^{\frac{1}{5}}\right)^{10}\) is :

The sum of the series : \((2)^2 + 2(4)^2 + 3(6)^2 + \ldots\) upto 10 terms is :

If \(a_1, a_2, a_3, \ldots, a_n, \ldots\) are in A.P. such that \(a_4 - a_7 + a_{10} = m\), then the sum of first 13 terms of this A.P., is :

The least integral value \(\alpha\) of \(x\) such that \(\dfrac{x-5}{x^2+5x-14} \gt 0\), satisfies :

The polymer used for optical lenses is :

Which of the following statements about aspirin is not true?

A molecule \(M\) associates in a given solvent according to the equation \(\mathrm{M} \rightleftharpoons (\mathrm{M})_n\). For a certain concentration of M, the van't Hoff factor was found to be 0.9 and the fraction of associated molecules was 0.2. The value of \(n\) is :

What is the structure of the major product when phenol is treated with bromine water?

Amongst the following alcohols which would react fastest with conc. \(\mathrm{HCl}\) and \(\mathrm{ZnCl_2}\) ?

Which of the following statements is incorrect?

Flocculation value of \(\mathrm{BaCl_2}\) is much less than that of \(\mathrm{KCl}\) for sol A and flocculation value of \(\mathrm{Na_2SO_4}\) is much less than that of \(\mathrm{NaBr}\) for sol B. The correct statement among the following is :

In Williamson synthesis of mixed ether having a primary and a tertiary alkyl group if tertiary halide is used, then :

Clemmensen reduction of a ketone is carried out in the presence of :

Which of the following would not give 2-phenylbutane as the major product in a Friedel-Crafts alkylation reaction ?

Which one of the following arrangements represents the correct order of solubilities of sparingly soluble salts \(\mathrm{Hg_2Cl_2}\), \(\mathrm{Cr_2(SO_4)_3}\), \(\mathrm{BaSO_4}\) and \(\mathrm{CrCl_3}\) respectively?

NaOH is a strong base. What will be pH of \(5.0\times10^{-2}\) M NaOH solution ? (\(\log 2 = 0.3\))

Values of dissociation constant, \(K_a\) are given as follows :

Acid	\(K_a\)
HCN	\(6.2\times10^{-10}\)
HF	\(7.2\times10^{-4}\)
\(\mathrm{HNO_2}\)	\(4.0\times10^{-4}\)

Correct order of increasing base strength of the base \(\mathrm{CN^-}\), \(\mathrm{F^-}\) and \(\mathrm{NO_2^-}\) will be :

The solubility order for alkali metal fluoride in water is :

The half-life of a radioactive element A is the same as the mean-life of another radioactive element B. Initially both substances have the same number of atoms, then :

The wave number of the first emission line in the Balmer series of H-Spectrum is : (\(R\) = Rydberg constant)

The reaction \(\mathrm{X} \to \mathrm{Y}\) is an exothermic reaction. Activation energy of the reaction for X into Y is 150 kJ mol^-1. Enthalpy of reaction is 135 kJ mol^-1. The activation energy for the reverse reaction, \(\mathrm{Y} \to \mathrm{X}\) will be :

Given

Reaction	Energy Change (in kJ)
\(\mathrm{Li(s)} \to \mathrm{Li(g)}\)	161
\(\mathrm{Li(g)} \to \mathrm{Li^+(g)}\)	520
\(\frac{1}{2}\mathrm{F_2(g)} \to \mathrm{F(g)}\)	77
\(\mathrm{F(g)} + \mathrm{e^-} \to \mathrm{F^-(g)}\)	(Electron gain enthalpy)
\(\mathrm{Li^+(g)} + \mathrm{F^-(g)} \to \mathrm{LiF(s)}\)	\(-1047\)
\(\mathrm{Li(s)} + \frac{1}{2}\mathrm{F_2(g)} \to \mathrm{LiF(s)}\)	\(-617\)

Based on data provided, the value of electron gain enthalpy of fluorine would be :

Bond order normally gives idea of stability of a molecular species. All the molecules viz. \(\mathrm{H_2}\), \(\mathrm{Li_2}\) and \(\mathrm{B_2}\) have the same bond order yet they are not equally stable. Their stability order is :

The focal length of the objective and the eyepiece of a telescope are 50 cm and 5 cm respectively. If the telescope is focussed for distinct vision on a scale distant 2 m from its objective, then its magnifying power will be :