List of top Questions asked in JEE Main- 2020

A body A of mass \(m\) is moving in a circular orbit of radius \(R\) about a planet. Another body B of mass \(\frac{m}{2}\) collides with A with a velocity which is half \(\left(\frac{\vec{v}}{2}\right)\) the instantaneous velocity \(\vec{v}\) of A. The collision is completely inelastic. Then, the combined body :

A quantity \(f\) is given by \(f=\sqrt{\frac{hc^5}{G}}\) where \(c\) is speed of light, \(G\) universal gravitational constant and \(h\) is the Planck's constant. Dimension of \(f\) is that of :

Three harmonic waves having equal frequency \(\nu\) and same intensity \(I_0\), have phase angles 0, \(\frac{\pi}{4}\) and \(-\frac{\pi}{4}\) respectively. When they are superimposed the intensity of the resultant wave is close to :

If the vectors, \(\vec{p} = (a+1)\hat{i} + a\hat{j} + a\hat{k}\), \(\vec{q} = a\hat{i} + (a+1)\hat{j} + a\hat{k}\) and \(\vec{r} = a\hat{i} + a\hat{j} + (a+1)\hat{k}\) \((a \in R)\) are coplanar and \(3(\vec{p}\cdot\vec{q})^2 - \lambda|\vec{r}\times\vec{q}|^2 = 0\), then the value of \(\lambda\) is ______.

The product \(2^{\frac{1}{4}} \cdot 4^{\frac{1}{16}} \cdot 8^{\frac{1}{48}} \cdot 16^{\frac{1}{128}} \cdots\) to \(\infty\) is equal to :

Negation of the statement :
\(\sqrt{5}\) is an integer or 5 is an irrational is :

The number of distinct solutions of the equation \(\log_{\frac{1}{2}}|\sin x| = 2 - \log_{\frac{1}{2}}|\cos x|\) in the interval \([0, 2\pi]\), is ____.

The coefficient of \(x^4\) is the expansion of \((1 + x + x^2)^{10}\) is _____.

The projection of the line segment joining the points \((1, -1, 3)\) and \((2, -4, 11)\) on the line joining the points \((-1, 2, 3)\) and \((3, -2, 10)\) is ____________.

If for \(x \ge 0\), \(y = y(x)\) is the solution of the differential equation \((x+1)\,dy = \left((x+1)^2 + y - 3\right)dx\), \(y(2) = 0\), then \(y(3)\) is equal to ______.

Let the observations \(x_i\ (1\le i\le10)\) satisfy the equations,
\(\sum_{i=1}^{10}(x_1-5)=10\) and \(\sum_{i=1}^{10}(x_1-5)^2=40\).
If \(\mu\) and \(\lambda\) are the mean and the variance of the observations, \(x_1-3,x_2-3,\dots,x_{10}-3\), then the ordered pair \((\mu,\lambda)\) is equal to :

A circle touches the y-axis at the point \((0, 4)\) and passes through the point \((2, 0)\). Which of the following lines is not a tangent to this circle?

If for some \(\alpha\) and \(\beta\) in R, the intersection of the following three places
\(x + 4y - 2z = 1\)
\(x + 7y - 5z = b\)
\(x + 5y + \alpha z = 5\)
is a line in \(\mathbb{R}^3\), then \(\alpha + \beta\) is equal to :

If the matrices \(A = \begin{bmatrix}1&1&2\\1&3&4\\1&-1&3\end{bmatrix}\), \(B = \mathrm{adj}A\) and \(C = 3A\), then \(\frac{|\mathrm{adj}B|}{|C|}\) is equal to :

The number of real roots of the equation,
\(e^{4x}+e^{3x}-4e^{2x}+e^x+1=0\) is :

If \(f'(x) = \tan^{-1}(\sec x + \tan x)\), \(-\frac{\pi}{2} \lt x \lt \frac{\pi}{2}\), and \(f(0) = 0\), then \(f(1)\) is equal to :

Let C be the centroid of the triangle with vertices (3, \(-1\)), (1, 3) and (2, 4). Let P be the point of intersection of the lines \(x+3y-1=0\) and \(3x-y+1=0\). Then the line passing through the points C and P also passes through the point :

In a box, there are 20 cards, out of which 10 are lebelled as A and the remaining 10 are labelled as B. Cards are drawn at random, one after the other and with replacement, till a second A-card is obtained. The probability that the second A-card appears before the third B-card is :

The value of
\(\int_0^{2\pi}\frac{x\sin^8x}{\sin^8x+\cos^8x}\,dx\)
is equal to :

The integral
\(\int\frac{dx}{(x+4)^{\frac87}(x-3)^{\frac67}}\)
is equal to :
(where C is a constant of integration)

Let \(f\) be any function continuous on [a, b] and twice differentiable on (a, b). If for all \(x\in(a,b)\), \(f'(x)>0\) and \(f''(x)<0\), then for any \(c\in(a,b)\),
\(\frac{f(c)-f(a)}{f(b)-f(c)}\)
is greater than :

If
\(f(x)=\begin{cases}\dfrac{\sin(a+2)x+\sin x}{x}; & x<0\\[2mm] b\ ; & x=0\\[2mm] \dfrac{(x+3x^2)^{\frac13}-x^{\frac13}}{x^{\frac43}}; & x>0\end{cases}\)
is continuous at x = 0, then a + 2b is equal to :

If the number of five digit numbers with distinct digits and 2 at the 10^th place is 336 k, then k is equal to :

The value of
\(\cos^3\left(\frac{\pi}{8}\right)\cos\left(\frac{3\pi}{8}\right)+\sin^3\left(\frac{\pi}{8}\right)\sin\left(\frac{3\pi}{8}\right)\)
is :

If for all real triplets (a, b, c), \(f(x)=a+bx+cx^2\); then
\(\int_0^1 f(x)\,dx\)
is equal to :