List of top Questions asked in JEE Main- 2020

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 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 ?

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 :

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 ______.

Four resistances of \(15\,\Omega\), \(12\,\Omega\), \(4\,\Omega\) and \(10\,\Omega\) respectively in cyclic order to form Wheatstone's network. The resistance that is to be connected in parallel with the resistance of \(10\,\Omega\) to balance the network is ______ \(\Omega\).

The magnifying power of a telescope with tube 60 cm is 5. What is the focal length of its eye piece ?

A leak proof cylinder of length 1 m, made of a metal which has very low coefficient of expansion is floating vertically in water at \(0^\circ\mathrm{C}\) such that its height above the water surface is 20 cm. When the temperature of water is increased to \(4^\circ\mathrm{C}\), the height of the cylinder above the water surface becomes 21 cm. The density of water at \(T=4^\circ\mathrm{C}\), relative to the density at \(T=0^\circ\mathrm{C}\) is close to :

Consider a uniform rod of mass M = 4m and length \(\ell\) pivoted about its centre. A mass m moving with velocity v making angle \(\theta = \frac{\pi}{4}\) to the rod's long axis collides with one end of the rod and sticks to it. The angular speed of the rod-mass system just after the collision is :

An urn contains 5 red marbles, 4 black marbles and 3 white marbles. Then the number of ways in which 4 marbles can be drawn so that at the most three of them are red is ___________.

Effective capacitance of parallel combination of two capacitors \(C_1\) and \(C_2\) is 10 \(\mu\)F. When these capacitors are individually connected to a voltage source of 1V, the energy stored in the capacitor \(C_2\) is 4 times that of \(C_1\). If these capacitors are connected in series, their effective capacitance will be :

Consider a solid sphere of radius R and mass density
\(\rho(r) = \rho_0\left(1 - \frac{r^2}{R^2}\right)\), \(0 \lt r \le R\)
The minimum density of a liquid in which it will float is :

The sum \(\displaystyle\sum_{k=1}^{20} (1 + 2 + 3 + \ldots + k)\) is :

Let the normal at a point P on the curve \(y^2 - 3x^2 + y + 10 = 0\) intersect the y-axis at \(\left(0, \frac{3}{2}\right)\). If m is the slope of the tangent at P to the curve, then \(|m|\) is equal to

If \(c\) is a point at which Rolle's theorem holds for the function,
\(f(x)=\log_e\left(\frac{x^2+\alpha}{7x}\right)\)
in the interval \([3,4]\), where \(\alpha\in R\), then \(f''(c)\) is equal to

Let the line \(y=mx\) and the ellipse \(2x^2+y^2=1\) intersect at a ponit \(P\) in the first quadrant. If the normal to this ellipse at \(P\) meets the co-ordinate axes at
\(\left(-\frac{1}{3\sqrt2},0\right)\) and \((0,\beta)\), then \(\beta\) is equal to :

The least positive value of 'a' for which the equation \(2x^2 + (a - 10)x + \frac{33}{2} = 2a\) has real roots is

The number of all \(3 \times 3\) matrices A, with entries from the set \(\{-1, 0, 1\}\) such that the sum of the diagonal elements of \(AA^T\) is 3, is

If the equation, \(x^2+bx+45=0\) (\(b\in R\)) has conjugate complex roots and they satisfy \(|z+1|=2\sqrt{10}\), then :

Let \(f(x) = (\sin(\tan^{-1}x)+\sin(\cot^{-1}x))^2-1\), \(|x|>1\).
If \(\frac{dy}{dx}=\frac12\frac{d}{dx}\left(\sin^{-1}(f(x))\right)\) and \(y(\sqrt3)=\frac{\pi}{6}\), then \(y(-\sqrt3)\) is equal to :

Let \(f:\mathbf{R}\to\mathbf{R}\) be such that for all \(x\in\mathbf{R}\)
\((2^{1+x}+2^{1-x})\), \(f(x)\) and \((3^x+3^{-x})\) are in A.P.,
then the minimum value of \(f(x)\) is

The mean and the standard deviation (s.d.) of 10 observations are 20 and 2 resepectively. Each of these 10 observations is multiplied by \(p\) and then reduced by \(q\), where \(p\ne0\) and \(q\ne0\). If the new mean and new s.d. become half of their original values, then \(q\) is equal to