List of top Questions asked in JEE Main- 2020

Let a, \(\mathrm{b}\in\mathbf{R}\) and \(\mathrm{a}>0\). If the tangent at the point \((2,2)\) to the circle \(x^{2}+y^{2}=8\) touches the parabola \(y^{2}=4\mathrm{a}(x-\mathrm{b})\), then \(\mathrm{b}-\mathrm{a}\) is equal to ________.

If the line joining the points \((-1,2,5)\) and \((3,4,-10)\) intersects the \(xy\)-plane at the point \((x, y, z)\), then \(\dfrac{y}{x}\) is equal to ________.

If the total number of ways in which 8-digit numbers can be formed by using all the digits \(0,1,2,3,4,5,7,9\) such that no two even digits appear together is \((5!)\,k\), then \(k\) is equal to ________.

If \(\int \mathrm{e}^{2x}(\cos x+7\sin x)\,\mathrm{d}x=\mathrm{e}^{2x}g(x)+\mathrm{c}\), where c is a constant of integration, then \(g(0)+g\left(\frac{\pi}{2}\right)\) is equal to ________.

Let a function, \(f:(-1,3) \rightarrow \mathbf{R}\) be defined as \(f(x)=\min \{x[x],|x[x]-2|+2\}\), where \([x]\) denotes the greatest integer \(\leq x\). Then \(f\) is :

A ray of light is projected from the origin at angle of \(60^{\circ}\) with the positive direction of \(x\)-axis towards the line, \(y=2\), which gets reflected from the point \((\alpha, 2)\). Then the distance of the reflected ray of light from the point \((2,2)\) is :

Let \(\mathrm{A}=\left[\begin{array}{cc}x & 2 y \\ -1 & y\end{array}\right]\); \(x, y \in \mathbf{R}\).
If \(\mathrm{AA}^{\mathrm{T}}=\left[\begin{array}{ll}1 & 0 \\ 0 & \alpha\end{array}\right]\) \((\alpha \in \mathbf{R})\), then \(\alpha+y^{2}\) is equal to :

The function \(f(x)=\mathrm{e}^{x+1}\left(4 x^{2}-16 x+11\right)\) is :

If \(x=x(y)\) is the solution of the differential equation, \(y\,\mathrm{d}x-\left(x+2y^{2}\right)\mathrm{d}y=0\), with \(x(-\pi)=\pi^{2}\), then \(x\) is equal to :

A bag contains 6 red balls and 10 green balls. 3 balls are drawn from it one by one randomly without replacement. If the 3^rd drawn ball is red, then the probability that the first two drawn balls are green is :

Which of the following is not equivalent to \(\sim p \wedge q\) ?

If a variable plane in 3-dimensional space moves in such a way that the sum of the reciprocals of its intercepts on the \(x\) and \(y\)-axes exceeds the reciprocal of its intercept on the \(z\)-axis by 2, then all such planes will pass through the point :

Find the correct match :

(P)	Aligarh	(I)	Silk Sarees
(Q)	Firozabad	(II)	Brass product
(R)	Kanjeevaram	(III)	Bangles
(S)	Moradabad	(IV)	Locks

The area (in sq. units) of the region \(\left\{(x, y): \frac{1}{2} \leq y \leq \sin x,\ 0 \leq x \leq \pi\right\}\) is :

Topographical map of an area is used to understand :

Which of the following Ministers has never held the portfolio of Urban Development ?

The headquarters of International Labour Organisation (ILO) is located in which city ?

Sustainable Development takes care of the present and :

With what amongst the given option is "The White Revolution" in India associated ?

The figure shows floors as 1, 2, 3, 4 on each plot A, B, C, D, E, F. Plot A, D and E are commercial on all floors. B, C and F are residential on all floors. Find the percentage of total floors that are commercial and residential respectively :

Statement I :
Exposure to computer based learning is common in most schools today.
Statement II :
Most jobs require at least basic computer literacy.
Pick the correct option :

Which is the First Airport in India ?

The Eastern coast of India is also known as :

When was the first United Nations Conference on ‘Human Settlements Habitat I’ held ?

In a survey of tourists in a city, 120 tourists were women of which 35% stayed in the city for more than one day. Which of the following is the correct conclusion for this data ?