List of top Questions asked in JEE Main- 2020

Let the function \(f: \mathrm{N} \rightarrow \mathrm{R}\) satisfy \(f(x+y)=f(x) \cdot f(y)\) for all \(x, y \in \mathrm{N}\) and \(f(1)=2\). If \(\sum_{\mathrm{k}=1}^{50} f(4+\mathrm{k})=\lambda\left(2^{\beta}-1\right)\), then \(\lambda+\beta\) is equal to ________.

Let the circle, \((x-\mathrm{a})^{2}+(y-\mathrm{b})^{2}=8\) and the parabola, \(y^{2}=4 x\) have a common tangent at the point \(\mathrm{P}(1,2)\). If \(\mathrm{C}\) is the centre of the circle and \(\mathrm{S}\) is the focus of the parabola, then the area (in sq. units) of \(\triangle \mathrm{CPS}\) is equal to ________.

If a hyperbola has length of its transverse axis \(=\sqrt{2}\) and it has the same foci as that of the ellipse \(4x^{2}+3y^{2}=24\), then this hyperbola also passes through the point whose coordinates are :

Which one of the following is a tautology ?

A six faced biased dice is so loaded that in any of its toss getting any of even scores is equally likely and the probability of getting an even score is three times the probability of getting an odd score. This dice is tossed repeatedly until a six is obtained. If X denotes the number of tosses required, then \(\mathrm{P}(\mathrm{X}<4)\) is :

If \(2 \sin x-\cos 2 x=1\), then :

Let P be the point of intersection of the plane \(4x-6y+14z=57\) with the line joining the points A\((2,3,5)\) and B\((1,-1,4)\). If \(BP=\lambda\,AP\), then the value of \(\lambda\) is :

Let \(\vec{a}, \vec{b}, \vec{c}\) be any three non-coplanar vectors. If the points \(\mathrm{A}(-2 \vec{a}+3 \vec{b}+5 \vec{c})\), \(\mathrm{B}(\vec{a}+2 \vec{b}+3 \vec{c})\) and \(\mathrm{C}(7 \vec{a}-\lambda \vec{c})\) are collinear, then \(\lambda\) is equal to :

The area (in sq. units) of the region \(\{(x,y)\in\mathbb{R}^{2}:2|x|+|y|\le 2\text{ and }x+y\ge 1\}\) is :

Let ABC be a triangle such that the vertex A has coordinates \((-3,1)\). If the equation of the median through B be \(2x+y-3=0\) and the equation of the bisector of angle C be \(7x-4y-1=0\), then the equation of the line BC is :

If \(y(x)=\int_{\pi^{2}/16}^{x^{2}}\frac{\sin x\,\sin\sqrt{\theta}}{1+\cos^{2}\sqrt{\theta}}\,d\theta\), then \(y'\left(\frac{\pi}{4}\right)\) is equal to :

If the ellipse centered at the origin has a focus at \((0,3)\) and the corresponding directrix is \(y=9\), then which one of the following is not true for this ellipse ?

Let \(f(x)=\left(2x^{2}-9x+11\right)\cdot e^{x},\ -\infty<x<\infty\). Then \(f\) has :

If for \(x>0\), \(\int \frac{e^{\sqrt{x}}\sin\left(\frac{\pi}{4}+\sqrt{x}\right)}{\sqrt{x}}\,dx=e^{\sqrt{x}}\cdot f(x)+C\), where \(C\) is a constant of integration, then \(f(x)\) is equal to :

Who amongst the following designed The Falling Waters ?

Draw from imagination a highway on which cars and trucks are moving in both directions.
OR
Draw from imagination an interior of cinema hall.
OR
Draw from memory your best teacher's face.

In the space provided for the answer of this question, draw an aesthetic composition appropriate to this space using only rectangles. There is no restriction to numbers, sizes, placement and directions of these shapes. Color this composition so that it becomes visually exciting.

Who amongst the following designed Indian Institute of Management ?

Which one of the following is the most suitable material for toilet floors ?

Let the functions \(f\) and \(g\) be defined as \(f(x)=2\cos|x-2|+3|x|\sin|x|\) and \(g(x)=x^{5}+x\). If S be the set of points where the function \((f\circ g)(x)\) is not differentiable, then S is equal to :

Let \(f\) be a twice differentiable function on \(\mathbb{R}\) such that \(f(0)=4\) and the function, \(g(x)=\frac{1}{2}f^{2}(x)+3x^{3}-5\) is monotonically increasing in \(\mathbb{R}\). Then \(f(1)\) cannot be :

If \(z=-1+i\sqrt{2}\), then which one of the following is not true ?

Let \(a_1, a_2, a_3, a_4\) and \(a_5\) be in A.P. with the common difference greater than 2. If \(\sum_{i=1}^{5}a_i=30\) and \(a_1\cdot a_2\cdot a_3\cdot a_4\cdot a_5=3840\), then \(a_1\cdot a_5\) is equal to :

Let \(A=\begin{pmatrix}\alpha & 1 & 2\\ 1 & 2 & 3\\ 3 & 1 & 1\end{pmatrix}\), \(\alpha\in\mathbb{R}\) and \(B=[b_{ij}]_{3\times3}\) such that \(AB=rI\), \(r\neq0\) in \(\mathbb{R}\). If \(b_{32}=-\frac{3}{2}r\) and \(|\operatorname{adj}B|=r^{5}\), then \(|\operatorname{adj}(AB)|\) equals :

For \(\theta\in(0,\pi/2)\), \(\theta\in(\pi,2\pi)\) and \(\beta\in\mathbb{R}\), the value of the determinant
\(\begin{vmatrix}\cos 2\alpha & \cos(\alpha+\theta) & -\sin(\alpha+\theta)\\ \sin\alpha & \sin\theta & \cos\theta\\ \beta\cos\alpha & -\cos\theta & \sin\theta\end{vmatrix}\) :