List of top Questions asked in JEE Main- 2020

The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word 'SYLLABUS' such that two letters are distinct and two letters are alike, is :

Four fair dice are thrown independently 27 times. Then the expected number of times, at least two dice show up a three or a five, is _________.

The natural number \(m\), for which the coefficient of \(x\) in the binomial expansion of \(\left(x^{m}+\frac{1}{x^{2}}\right)^{22}\) is 1540, is ............. .

Three different processes that can occur in an ideal monoatomic gas are shown in the \(P\) vs \(V\) diagram. The paths are labelled as \(A\rightarrow B\), \(A\rightarrow C\) and \(A\rightarrow D\). The change in internal energies during these process are taken as \(E_{AB}\), \(E_{AC}\) and \(E_{AD}\) and the work done as \(W_{AB}\), \(W_{AC}\) and \(W_{AD}\).
The correct relation between these parameters are :

Number of molecules in a volume of \(4\ \mathrm{cm^3}\) of a perfect monoatomic gas at some temperature \(T\) and at a pressure of \(2\ \mathrm{cm}\) of mercury is close to?
(Given, mean kinetic energy of a molecule (at \(T\)) is \(4\times10^{-14}\) erg, \(g = 980\ \mathrm{cm/s^2}\), density of mercury \(= 13.6\ \mathrm{g/cm^3}\))

Let \(f(x)=x\cdot\left[\frac{x}{2}\right]\), for \(-10\lt x\lt 10\), where \([t]\) denotes the greatest integer function. Then the number of points of discontinuity of \(f\) is equal to ______.

If the line, \(2x-y+3=0\) is at a distance \(\frac{1}{\sqrt{5}}\) and \(\frac{2}{\sqrt{5}}\) from the lines \(4x-2y+\alpha=0\) and \(6x-3y+\beta=0\), respectively, then the sum of all possible values of \(\alpha\) and \(\beta\) is :

If the common tangent to the parabolas, \(y^2=4x\) and \(x^2=4y\) also touches the circle, \(x^2+y^2=c^2\), then \(c\) is equal to :

If \(2^{10}+2^{9}\cdot 3^{1}+2^{8}\cdot 3^{2}+\ldots+2\cdot 3^{9}+3^{10}=S-2^{11}\), then \(S\) is equal to :

If the volume of a parallelopiped, whose coterminus edges are given by the vectors \(\vec{a}=\hat{i}+\hat{j}+n\hat{k}\), \(\vec{b}=2\hat{i}+4\hat{j}-n\hat{k}\) and \(\vec{c}=\hat{i}+n\hat{j}+3\hat{k}\) \((n\ge 0)\), is 158 cu. units, then :

The negation of the Boolean expression \(x\leftrightarrow\ \sim y\) is equivalent to :

The value of \(\displaystyle\int_{-\pi/2}^{\pi/2}\frac{1}{1+e^{\sin x}}\,dx\) is:

If \((a,\ b,\ c)\) is the image of the point \((1,\ 2,\ -3)\) in the line \(\frac{x+1}{2}=\frac{y-3}{-2}=\frac{z}{-1}\), then \(a+b+c\) is :

If the point \(P\) on the curve, \(4x^2+5y^2=20\) is farthest from the point \(Q(0,-4)\), then \(PQ^2\) is equal to:

If the four complex numbers \(z,\ \overline{z},\ \overline{z}-2\,\mathrm{Re}(z)\) and \(z-2\,\mathrm{Re}(z)\) represent the vertices of a square of side 4 units in the Argand plane, then \(|z|\) is equal to :

A survey shows that \(73\%\) of the persons working in an office like coffee, whereas \(65\%\) like tea. If \(x\) denotes the percentage of them, who like both coffee and tea, then \(x\) cannot be :

If \(\alpha\) is positive root of the equation, \(p(x)=x^2-x-2=0\), then
\( \lim_{x\to\alpha^+}\frac{\sqrt{1-\cos\left(p(x)\right)}}{x+\alpha-4} \)
is equal to :

The product of the roots of the equation \(9x^2-18|x|+5=0\) is :

If \(3^{2\sin2\alpha-1}\), \(14\) and \(3^{4-2\sin2\alpha}\) are the first three terms of an A.P. for some \(\alpha\), then the sixth term of this A.P. is:

If the co-ordinates of two points \(A\) and \(B\) are \(\left(\sqrt7,0\right)\) and \(\left(-\sqrt7,0\right)\) respectively and \(P\) is any point on the conic, \(9x^2+16y^2=144\), then \(PA+PB\) is equal to :

If \(S\) is the sum of the first 10 terms of the series
\( \tan^{-1}\left(\frac{1}{3}\right)+\tan^{-1}\left(\frac{1}{7}\right)+\tan^{-1}\left(\frac{1}{13}\right)+\tan^{-1}\left(\frac{1}{21}\right)+\dots \)
then \(\tan(S)\) is equal to :

If
\( \int\left(e^{2x}+2e^x-e^{-x}-1\right)e^{\left(e^x+e^{-x}\right)}dx = g(x)\,e^{\left(e^x+e^{-x}\right)}+c \)
where \(c\) is a constant of integration, then \(g(0)\) is equal to :

Let \(\lambda\in R\). The system of linear equations
\(2x_1-4x_2+\lambda x_3=1\)
\(x_1-6x_2+x_3=2\)
\(\lambda x_1-10x_2+4x_3=3\)
is inconsistent for:

If the minimum and the maximum values of the function \( f:\left[\frac{\pi}{4},\frac{\pi}{2}\right]\to R \), defined by
\( f(\theta)=\begin{vmatrix} -\sin^2\theta & -1-\sin^2\theta & 1 \\ -\cos^2\theta & -1-\cos^2\theta & 1 \\ 12 & 10 & -2 \end{vmatrix} \)
are \(m\) and \(M\) respectively, then the ordered pair \((m, M)\) is equal to :

If \(y=y(x)\) is the solution of the differential equation
\( \frac{5+e^x}{2+y}\cdot\frac{dy}{dx}+e^x=0 \)
satisfying \(y(0)=1\), then a value of \(y(\log_e 13)\) is :