List of top Questions asked in JEE Main- 2020

A transverse wave travels on a taut steel wire with a velocity of \(v\) when tension in it is \(2.06 \times 10^4\) N. When the tension is changed to \(T\), the velocity changed to \(v/2\). The value of \(T\) is close to :

The number of 4 letter words (with or without meaning) that can be formed from the eleven letters of the word 'EXAMINATION' is _______.

The sum, \(\sum_{n=1}^{7} \frac{n(n+1)(2n+1)}{4}\) is equal to ________.

If \(\frac{\sqrt{2}\sin\alpha}{\sqrt{1 + \cos 2\alpha}} = \frac{1}{7}\) and \(\sqrt{\frac{1 - \cos 2\beta}{2}} = \frac{1}{\sqrt{10}}\), \(\alpha, \beta \in \left(0, \frac{\pi}{2}\right)\), then \(\tan(\alpha + 2\beta)\) is equal to _____.

Let a line \(y = mx\) \((m \gt 0)\) intersect the parabola, \(y^2 = x\) at a point P, other than the origin. Let the tangent to it at P meet the x-axis at the point Q. If area \((\Delta OPQ) = 4\) sq. units, then m is equal to __________.

If a line, \(y = mx + c\) is a tangent to the circle, \((x - 3)^2 + y^2 = 1\) and it is perpendicular to a line \(L_1\), where \(L_1\) is the tangent to the circle, \(x^2 + y^2 = 1\) at the point \(\left(\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)\), then :

The differential equation of the family of curves, \(x^2=4b(y+b)\), \(b\in\mathbb{R}\), is :

The length of the perpendicular from the origin, on the normal to the curve, \(x^2+2xy-3y^2=0\) at the point \((2,2)\) is

The area (in sq. units) of the region \(\{(x,y)\in\mathbb{R}^2: x^2\le y\le3-2x\}\), is :

The mirror image of the point \((1,2,3)\) in a plane is \(\left(-\dfrac73,-\dfrac43,-\dfrac13\right)\). Which of the following points lies on this plane ?

If \(I=\displaystyle\int_1^2\dfrac{dx}{\sqrt{2x^3-9x^2+12x+4}}\), then :

Let S be the set of all functions \(f:[0,1]\to\mathbb{R}\), which are continuous on \([0,1]\) and differentiable on \((0,1)\). Then for every \(f\) in S, there exists a \(c\in(0,1)\), depending on \(f\), such that

Let \(f:(1,3)\to\mathbb{R}\) be a function defined by \(f(x)=\dfrac{x[x]}{1+x^2}\), where \([x]\) denotes the greatest integer \(\le x\). Then the range of \(f\) is

\(\displaystyle\lim_{x\to0}\dfrac{\int_0^x t\sin(10t)\,dt}{x}\) is equal to

If the \(10^{\text{th}}\) term of an A.P. is \(\dfrac{1}{20}\) and its \(20^{\text{th}}\) term is \(\dfrac{1}{10}\), then the sum of its first 200 terms is

Let \(\alpha=\dfrac{-1+i\sqrt3}{2}\). If \(a=(1+\alpha)\displaystyle\sum_{k=0}^{100}\alpha^{2k}\) and \(b=\displaystyle\sum_{k=0}^{100}\alpha^{3k}\), then \(a\) and \(b\) are the roots of the quadratic equation :

Let S be the set of all real roots of the equation, \(3^x(3^x-1)+2=|3^x-1|+|3^x-2|\). Then S :

If \(A=\begin{pmatrix}2&2\\9&4\end{pmatrix}\) and \(I=\begin{pmatrix}1&0\\0&1\end{pmatrix}\), then \(10A^{-1}\) is equal to :

Among the gases (a) – (e), the gases that cause greenhouse effect are :
(a) \(\mathrm{CO_2}\)
(b) \(\mathrm{H_2O}\)
(c) CFCs
(d) \(\mathrm{O_2}\)
(e) \(\mathrm{O_3}\)

What would be the electrode potential for the given half cell reaction at pH = 5? ______
\(2\mathrm{H_2O} \to \mathrm{O_2} + 4\mathrm{H}^{+} + 4e^{-}\) ; \(E^0_{red} = 1.23\) V
(R = 8.314 J mol\(^{-1}\) K\(^{-1}\) ; Temp = 298 K ; oxygen under std. atm. pressure of 1 bar)

The number of chiral centres in penicillin is _________.

The strength of an aqueous NaOH solution is most accurately determined by titrating :
(Note : consider that an appropriate indicator is used)

As per Hardy-Schulze formulation, the flocculation values of the following for ferric hydroxide sol are in the order :

When gypsum is heated to 393 K, it forms :

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 :