List of top Questions asked in JEE Main- 2020

Particle A of mass \(m_1\) moving with velocity \((\sqrt3\,\hat i+\hat j)\ \mathrm{ms^{-1}}\) collides with another particle B of mass \(m_2\) which is at rest initially. Let \(\vec V_1\) and \(\vec V_2\) be the velocities of particles A and B after collision respectively. If \(m_1=2m_2\) and after collision \(\vec V_1=(\hat i+\sqrt3\,\hat j)\), the angle between \(\vec V_1\) and \(\vec V_2\) is :

When a particle of mass \(m\) is attached to a vertical spring of spring constant \(k\) and released, its motion is described by \(y(t)=y_0\sin^2\omega t\), where \(y\) is measured from the lower end of unstretched spring. Then \(\omega\) is :

The linear mass density of a thin rod AB of length \(L\) varies from A to B as \(\lambda(x)=\lambda_0\left(1+\dfrac{x}{L}\right)\), where \(x\) is the distance from A. If \(M\) is the mass of the rod then its moment of inertia about an axis passing through A and perpendicular to the rod is :

Two identical electric point dipoles have dipole moments \(\vec{p}_1=p\hat{i}\) and \(\vec{p}_2=-p\hat{i}\) and are held on the x axis at distance \(a\) from each other. When released, they move along the x-axis with the direction of their dipole moments remaining unchanged. If the mass of each dipole is \(m\), their speed when they are infinitely far apart is :

A circuit to verify Ohm's law uses ammeter and voltmeter in series or parallel connected correctly to the resistor. In the circuit :

A square loop of side \(2a\) and carrying current I is kept in xz plane with its centre at origin. A long wire carrying the same current I is placed parallel to z-axis and passing through point \((0, b, 0)\), \((b \gt\gt a)\). The magnitude of torque on the loop about z-axis will be :

Three rods of identical cross-section and lengths are made of three different materials of thermal conductivity \(K_1\), \(K_2\) and \(K_3\), respectively. They are joined together at their ends to make a long rod (see figure). One end of the long rod is maintained at \(100^\circ\mathrm{C}\) and the other at \(0^\circ\mathrm{C}\) (see figure). If the joints of the rod are at \(70^\circ\mathrm{C}\) and \(20^\circ\mathrm{C}\) in steady state and there is no loss of energy from the surface of the rod, the correct relationship between \(K_1\), \(K_2\) and \(K_3\) is :

A double convex lens has power \(P\) and same radii of curvature \(R\) of both the surfaces. The radius of curvature of a surface of a plano-convex lens made of the same material with power \(1.5\,P\) is :

Suppose that a function \(f : R \to R\) satisfies \(f(x + y) = f(x)f(y)\) for all \(x, y \in R\) and \(f(1) = 3\). If \(\sum_{i=1}^{n} f(i) = 363\) then n is equal to ________ .

The number of words (with or without meaning) that can be formed from all the letters of the word “LETTER” in which vowels never come together is ________ .

Two planets have masses M and 16 M and their radii are \(a\) and \(2a\), respectively. The separation between the centres of the planets is \(10a\). A body of mass m is fired from the surface of the larger planet towards the smaller planet along the line joining their centres. For the body to be able to reach at the surface of smaller planet, the minimum firing speed needed is :

Consider the statement :
“For an integer n, if \(n^3 - 1\) is even, then n is odd.”
The contrapositive statement of this statement is :

The sum of distinct values of \(\lambda\) for which the system of equations
\((\lambda - 1)x + (3\lambda + 1)y + 2\lambda z = 0\)
\((\lambda - 1)x + (4\lambda - 2)y + (\lambda + 3)z = 0\)
\(2x + (3\lambda + 1)y + 3(\lambda - 1)z = 0\)
has non-zero solutions, is ________ .

Consider the data on x taking the values \(0, 2, 4, 8, \ldots, 2^n\) with frequencies \({}^nC_0, {}^nC_1, {}^nC_2, \ldots, {}^nC_n\) respectively. If the mean of this data is \(\frac{728}{2^n}\), then n is equal to ________ .

The angle of elevation of the summit of a mountain from a point on the ground is \(45^\circ\). After climbing up one km towards the summit at an inclination of \(30^\circ\) from the ground, the angle of elevation of the summit is found to be \(60^\circ\). Then the height (in km) of the summit from the ground is :

A plane P meets the coordinate axes at A, B and C respectively. The centroid of \(\Delta ABC\) is given to be \((1, 1, 2)\). Then the equation of the line through this centroid and perpendicular to the plane P is :

If the tangent to the curve, \(y = f(x) = x\log_e x\), \((x \gt 0)\) at a point \((c, f(c))\) is parallel to the line-segment joining the points \((1, 0)\) and \((e, e)\), then \(c\) is equal to :

The probabilities of three events A, B and C are given by \(P(A)=0.6\), \(P(B)=0.4\) and \(P(C)=0.5\). If \(P(A\cup B)=0.8\), \(P(A\cap C)=0.3\), \(P(A\cap B\cap C)=0.2\), \(P(B\cap C)=\beta\) and \(P(A\cup B\cup C)=\alpha\), where \(0.85\le\alpha\le0.95\), then \(\beta\) lies in the interval :

If the normal at an end of a latus rectum of an ellipse passes through an extremity of the minor axis, then the eccentricity \(e\) of the ellipse satisfies :

If \(\alpha\) and \(\beta\) are the roots of the equation \(2x(2x+1)=1\), then \(\beta\) is equal to :

If \(y = \left(\frac{2}{\pi}x - 1\right)\mathrm{cosec}\,x\) is the solution of the differential equation,
\(\frac{dy}{dx} + p(x)\,y = \frac{2}{\pi}\mathrm{cosec}\,x\), \(0 \lt x \lt \frac{\pi}{2}\),
then the function \(p(x)\) is equal to :

Let \(f:\mathbb{R}\to\mathbb{R}\) be a function defined by \(f(x)=\max\{x,x^2\}\). Let S denote the set of all points in \(\mathbb{R}\), where f is not differentiable. Then :

Let \(z=x+iy\) be a non-zero complex number such that \(z^2=i|z|^2\), where \(i=\sqrt{-1}\), then z lies on the :

Let \(\theta=\frac{\pi}{5}\) and \(A=\begin{bmatrix}\cos\theta & \sin\theta\\ -\sin\theta & \cos\theta\end{bmatrix}\). If \(B=A+A^4\), then det (B) :

If the constant term in the binomial expansion of \(\left(\sqrt{x}-\frac{k}{x^2}\right)^{10}\) is 405, then \(|k|\) equals :