List of top Questions asked in JEE Main- 2020

If the mean and the standard deviation of the data \(3, 5, 7, a, b\) are \(5\) and \(2\) respectively, then \(a\) and \(b\) are the roots of the equation :

If \(x=1\) is a critical point of the function \( f(x)=(3x^2+ax-2-a)e^x \), then :

There are 3 sections in a question paper and each section contains 5 questions. A candidate has to answer a total of 5 questions, choosing at least one question from each section. Then the number of ways, in which the candidate can choose the questions, is :

The area (in sq. units) of the region \( A=\{(x,y):(x-1)[x]\le y\le2\sqrt{x},\ 0\le x\le2\} \), where [t] denotes the greatest integer function, is :

\( \lim_{x\to0}\frac{x\left(e^{\left(\sqrt{1+x^2+x^4}-1\right)/x}-1\right)}{\sqrt{1+x^2+x^4}-1} \)

If the system of linear equations
\( x+y+3z=0 \)
\( x+3y+k^2z=0 \)
\( 3x+y+3z=0 \)
has a non-zero solution \((x, y, z)\) for some \(k\in R\), then \( x+\left(\frac{y}{z}\right) \) is equal to :

If the length of the chord of the circle, \( x^2+y^2=r^2 \) (\(r>0\)) along the line, \( y-2x=3 \) is r, then \(r^2\) is equal to :

If \( \int \frac{\cos\theta}{5+7\sin\theta-2\cos^2\theta}\,d\theta = A\log_e|B(\theta)|+C \), where C is a constant of integration, then \( \frac{B(\theta)}{A} \) can be :

If the sum of the second, third and fourth terms of a positive term G.P. is 3 and the sum of its sixth, seventh and eighth terms is 243, then the sum of the first 50 terms of this G.P. is :

The value of \( \left(\frac{-1+i\sqrt{3}}{1-i}\right)^{30} \) is :

If \( \alpha \) and \( \beta \) are the roots of the equation, \( 7x^2-3x-2=0 \), then the value of \( \frac{\alpha}{1-\alpha^2}+\frac{\beta}{1-\beta^2} \) is equal to :

The number of chiral carbon(s) present in peptide, Ile-Arg-Pro, is _____.

A soft drink was bottled with a partial pressure of \(\mathrm{CO_2}\) of 3 bar over the liquid at room temperature. The partial pressure of \(\mathrm{CO_2}\) over the solution approaches a value of 30 bar when 44 g of \(\mathrm{CO_2}\) is dissolved in 1 kg of water at room temperature. The approximate pH of the soft drink is ______ \(\times\) \(10^{-1}\).
(First dissociation constant of \(\mathrm{H_2CO_3}\) = \(4.0\times 10^{-7}\); \(\log 2 = 0.3\); density of the soft drink = 1 g \(\mathrm{mL^{-1}}\)) .

The total number of coordination sites in ethylenediaminetetraacetate (\(\mathrm{EDTA^{4-}}\)) is _____.

The equation that represents the water-gas shift reaction is :

An Ellingham diagram provides information about :

An oxidation-reduction reaction in which 3 electrons are transferred has a \(\Delta G^\circ\) of 17.37 kJ \(\mathrm{mol^{-1}}\) at 25 \(^\circ\)C. The value of \(E^\circ_{\mathrm{cell}}\) (in V) is ______ \(\times\) \(10^{-2}\).
(1 F = 96,500 C \(\mathrm{mol^{-1}}\))

Identify the correct molecular picture showing that happens at the critical micellar concentration (CMC) of an aqueous solution of a surfactant (polar head: shaded circle; non-polar tail: wavy line; water: black dot).

The minimum number of moles of \(\mathrm{O_2}\) required for complete combustion of 1 mole of propane and 2 moles of butane is _____.

The condition that indicates a polluted environment is :

The potential energy curve for the \(\mathrm{H_2}\) molecule as a function of internuclear distance is :

In the following reaction sequence the major products A and B are :

If a person is suffering from the deficiency of nor-adrenaline, what kind of drug can be suggested?

In the sixth period, the orbitals that are filled are :

The values of the crystal field stabilization energies for a high spin \(d^6\) metal ion in octahedral and tetrahedral fields, respectively, are :