List of top Questions asked in JEE Main- 2020

An ideal gas in a closed container is slowly heated. As its temperature increases, which of the following statements are true?
(A) the mean free path of the molecules decreases.
(B) the mean collision time between the molecules decreases.
(C) the mean free path remains unchanged.
(D) the mean collision time remains unchanged.

The height 'h' at which the weight of a body will be the same as that at the same depth 'h' from the surface of the earth is (Radius of the earth is R and effect of the rotation of the earth is neglected)

The equation of the normal to the curve
\(y = (1+x)^{2y} + \cos^{2}(\sin^{-1}x)\) at \(x = 0\) is :

For a positive integer \(n\),
\(\left(1+\frac{1}{x}\right)^{n}\) is expanded
in increasing powers of \(x\). If three consecutive
coefficients in this expansion are in the ratio,
\(2 : 5 : 12\), then \(n\) is equal to _______.

If \(y=\displaystyle\sum_{k=1}^{6} k\cos^{-1}\left\{\frac{3}{5}\cos kx-\frac{4}{5}\sin kx\right\}\), then \(\frac{dy}{dx}\) at \(x=0\) is _______.

Let \([t]\) denote the greatest integer less than or equal to \(t\). Then the value of
\(\displaystyle\int_{1}^{2}\left|2x-[3x]\right|dx\) is _______.

Let the position vectors of points \(A\) and \(B\) be \(\hat{i}+\hat{j}+\hat{k}\) and \(2\hat{i}+\hat{j}+3\hat{k}\), respectively. A point \(P\) divides the line segment \(AB\) internally in the ratio \(\lambda : 1\) (\(\lambda \gt 0\)). If \(O\) is the origin and
\(\overrightarrow{OB}\cdot\overrightarrow{OP}-3\left|\overrightarrow{OA}\times\overrightarrow{OP}\right|^{2}=6\), then \(\lambda\) is equal to _______.

If the variance of the terms in an increasing A.P.,
\(b_1, b_2, b_3, \ldots, b_{11}\) is 90, then the common difference of this A.P. is _______.

A plane passing through the point \((3, 1, 1)\) contains two lines whose direction ratios are \(1, -2, 2\) and \(2, 3, -1\) respectively. If this plane also passes through the point \((\alpha, -3, 5)\), then \(\alpha\) is equal to:

Let a, b, c \(\in \mathbb{R}\) be all non-zero and satisfy \(a^3+b^3+c^3=2\). If the matrix \(A=\begin{pmatrix} a & b & c \\ b & c & a \\ c & a & b \end{pmatrix}\) satisfies \(A^TA = I\), then a value of abc can be :

\(\lim\limits_{x\to0}\left(\tan\left(\frac{\pi}{4}+x\right)\right)^{\frac1x}\) is equal to :

Let \(n > 2\) be an integer. Suppose that there are n Metro stations in a city located along a circular path. Each pair of stations is connected by a straight track only. Further, each pair of nearest stations is connected by blue line, whereas all remaining pairs of stations are connected by red line. If the number of red lines is 99 times the number of blue lines, then the value of n is :

The set of all possible values of \(\theta\) in the interval
\((0, \pi)\) for which the points \((1, 2)\) and \((\sin\theta, \cos\theta)\) lie
on the same side of the line \(x + y = 1\) is :

If the sum of first 11 terms of an A.P., \(a_1, a_2, a_3, \ldots\) is 0 \((a_1 \ne 0)\), then the sum of the A.P., \(a_1, a_3, a_5, \ldots, a_{23}\) is \(ka_1\), where k is equal to :

Let \(f : \mathbb{R} \to \mathbb{R}\) be a function which satisfies \(f(x+y) = f(x) + f(y)\ \forall\ x, y \in \mathbb{R}\). If \(f(1) = 2\) and \(g(n) = \sum\limits_{k=1}^{(n-1)} f(k)\), \(n \in \mathbb{N}\), then the value of n, for which \(g(n) = 20\), is :

The imaginary part of \(\left(3+2\sqrt{-54}\right)^{\frac12}-\left(3-2\sqrt{-54}\right)^{\frac12}\) can be :

Let \(E^C\) denote the complement of an event E. Let \(E_1\), \(E_2\) and \(E_3\) be any pairwise independent events with \(P(E_1) > 0\) and \(P(E_1 \cap E_2 \cap E_3) = 0\).
Then \(P\left(E_2^C \cap E_3^C / E_1\right)\) is equal to :

If a curve \(y = f(x)\), passing through the point \((1, 2)\), is the solution of the differential equation, \(2x^2\,dy = (2xy + y^2)\,dx\), then \(f\left(\frac{1}{2}\right)\) is equal to :

Consider a region \(R = \{(x, y) \in \mathbb{R}^2 : x^2 \le y \le 2x\}\). If a line \(y = \alpha\) divides the area of region R into two equal parts, then which of the following is true?

If the equation \(\cos^4\theta + \sin^4\theta + \lambda = 0\) has real solutions for \(\theta\), then \(\lambda\) lies in the interval :

Let \(A = \{X = (x, y, z)^T : PX = 0 \text{ and } x^2+y^2+z^2 = 1\}\) where \(P = \begin{bmatrix} 1 & 2 & 1 \\ -2 & 3 & -4 \\ 1 & 9 & -1 \end{bmatrix}\), then the set A :

For some \(\theta \in \left(0, \frac{\pi}{2}\right)\), if the eccentricity of the hyperbola, \(x^2 - y^2\sec^2\theta = 10\) is \(\sqrt{5}\) times the eccentricity of the ellipse, \(x^2\sec^2\theta + y^2 = 5\), then the length of the latus rectum of the ellipse, is :

The mass of gas adsorbed, x, per unit mass of adsorbate, m, was measured at various pressures, p. A graph between \(\log \frac{x}{m}\) and \(\log p\) gives a straight line with slope equal to 2 and the intercept equal to 0.4771. The value of \(\frac{x}{m}\) at a pressure of 4 atm is :
(Given \(\log 3 = 0.4771\))

The metal mainly used in devising photoelectric cells is :

The Gibbs change (in J) for the given reaction at [Cu²⁺] = [Sn²⁺] = 1 M and 298 K is :
Cu(s) + Sn²⁺(aq.) \(\to\) Cu²⁺(aq.) + Sn(s);
(\(E^0_{\mathrm{Sn^{2+}|Sn}} = -0.16\) V, \(E^0_{\mathrm{Cu^{2+}|Cu}} = 0.34\) V)
Take F = 96500 C mol^-1