List of top Questions asked in JEE Main- 2020

A uniform thin rope of length 12 m and mass 6 kg hangs vertically from a rigid support and a block of mass 2 kg is attached to its free end. A transverse short wavetrain of wavelength 6 cm is produced at the lower end of the rope. What is the wavelength of the wavetrain (in cm) when it reaches the top of the rope ?
Magnitude of magnetic field (in SI units) at the centre of a hexagonal shape coil of side 10 cm, 50 turns and carrying current I (Ampere) in units of \(\frac{\mu_0 I}{\pi}\) is :
A charged particle carrying charge \(1\ \mu\)C is moving with velocity \((2\hat i + 3\hat j + 4\hat k)\) ms\(^{-1}\). If an external magnetic field of \((5\hat i + 3\hat j - 6\hat k) \times 10^{-3}\) T exists in the region where the particle is moving then the force on the particle is \(\vec F \times 10^{-9}\) N. The vector \(\vec F\) is :
The value of \((0.16)^{\log_{2.5}\left(\frac{1}{3} + \frac{1}{3^2} + \ldots \text{to } \infty\right)}\) is equal to _______ .
Let \(A = \begin{bmatrix} x & 1 \\ 1 & 0 \end{bmatrix}\), \(x \in \mathbb{R}\) and \(A^4 = [a_{ij}]\). If \(a_{11} = 109\), then \(a_{22}\) is equal to _______ .
If \(\lim_{x \to 0}\left\{\frac{1}{x^8}\left(1 - \cos\frac{x^2}{2} - \cos\frac{x^2}{4} + \cos\frac{x^2}{2}\cos\frac{x^2}{4}\right)\right\} = 2^{-k}\), then the value of k is _______ .
When a diode is forward biased, it has a voltage drop of 0.5 V. The safe limit of current through the diode is 10 mA. If a battery of emf 1.5 V is used in the circuit, the value of minimum resistance to be connected in series with the diode so that the current does not exceed the safe limit is
If \(\left(\frac{1+i}{1-i}\right)^{\frac{m}{2}} = \left(\frac{1+i}{1-i}\right)^{\frac{n}{3}} = 1\), \((m, n \in N)\) then the greatest common divisor of the least values of \(m\) and \(n\) is _______ .
The foot of the perpendicular drawn from the point (4, 2, 3) to the line joining the points (1, \(-\)2, 3) and (1, 1, 0) lies on the plane :
A dice is thrown two times and the sum of the scores appearing on the die is observed to be a multiple of 4. Then the conditional probability that the score 4 has appeared atleast once is :
If the first term of an A.P. is 3 and the sum of its first 25 terms is equal to the sum of its next 15 terms, then the common difference of this A.P. is :
The diameter of the circle, whose centre lies on the line \(x + y = 2\) in the first quadrant and which touches both the lines \(x = 3\) and \(y = 2\), is _______ .
Let [t] denote the greatest integer \(\le\) t. If for some \(\lambda \in \mathbb{R} - \{1, 0\}\),
\(\lim_{x \to 0}\left|\frac{1 - x + |x|}{\lambda - x + [x]}\right| = L\), then L is equal to :
The proposition \(p \to \sim(p \wedge \sim q)\) is equivalent to :
A hyperbola having the transverse axis of length \(\sqrt{2}\) has the same foci as that of the ellipse \(3x^2 + 4y^2 = 12\), then this hyperbola does not pass through which of the following points?
The lines
\(\vec{r} = (\hat{i} - \hat{j}) + l(2\hat{i} + \hat{k})\)
and
\(\vec{r} = (2\hat{i} - \hat{j}) + m(\hat{i} + \hat{j} + \hat{k})\)
If \(y^2 + \log_e(\cos^2 x) = y\), \(x \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right)\), then :
The solution curve of the differential equation, \((1 + e^{-x})(1 + y^2)\frac{dy}{dx} = y^2\), which passes through the point \((0, 1)\), is :
The value of (\(2\cdot{}^{1}P_0 - 3\cdot{}^{2}P_1 + 4\cdot{}^{3}P_2 \ldots\) up to 51th term) + (\(1! - 2! + 3! - \ldots\) up to 51th term) is equal to :
\(2\pi - \left(\sin^{-1}\frac{4}{5} + \sin^{-1}\frac{5}{13} + \sin^{-1}\frac{16}{65}\right)\) is equal to :
If \(\alpha\) and \(\beta\) are the roots of the equation \(x^2 + px + 2 = 0\) and \(\frac{1}{\alpha}\) and \(\frac{1}{\beta}\) are the roots of the equation \(2x^2 + 2qx + 1 = 0\), then \(\left(\alpha - \frac{1}{\alpha}\right)\left(\beta - \frac{1}{\beta}\right)\left(\alpha + \frac{1}{\beta}\right)\left(\beta + \frac{1}{\alpha}\right)\) is equal to :
Consider the two sets :
\(A = \{m \in \mathbb{R} : \text{both the roots of } x^2 - (m + 1)x + m + 4 = 0 \text{ are real}\}\)
and \(B = [-3, 5)\).
Which of the following is not true?
If the number of integral terms in the expansion of \((3^{1/2} + 5^{1/8})^n\) is exactly 33, then the least value of \(n\) is :
If \(\Delta = \begin{vmatrix} x - 2 & 2x - 3 & 3x - 4 \\ 2x - 3 & 3x - 4 & 4x - 5 \\ 3x - 5 & 5x - 8 & 10x - 17 \end{vmatrix} = Ax^3 + Bx^2 + Cx + D\), then \(B + C\) is equal to :
\(\int_{-\pi}^{\pi} \left| \pi - |x| \right| dx\) is equal to :