JEE Main 2020 Question Paper with Solutions

If momentum (P), area (A) and time (T) are taken to be the fundamental quantities then the dimensional formula for energy is

Two uniform circular discs are rotating independently in the same direction around their common axis passing through their centres. The moment of inertia and angular velocity of the first disc are 0.1 kg-m 2 and 10 rad s –1 respectively while those for the second one are 0.2 kg-m 2 and 5 rad s –1 respectively. At some instant they get stuck together and start rotating as a single system about their common axis with some angular speed. The kinetic energy of the combined system is :

The displacement time graph of a particle executing S.H.M is given in figure : (sketch is schematic and not to scale) Which of the following statements is/are true for this motion? (A) The force is zero at t = ${{3T} \over 4}$ (B) The acceleration is maximum at t = T (C) The speed is maximum at t = ${{T} \over 4}$ (D) The P.E. is equal to K.E. of the oscillation at t = ${{T} \over 2}$

The height ‘h’ at which the weight of a body will be the same as that at the same depth ‘h’ from the surface of the earth is (Radius of the earth is R and effect of the rotation of the earth is neglected)

An ideal gas in a closed container is slowly heated. As its temperature increases, which of the following statements are true? (A) the mean free path of the molecules decreases. (B) the mean collision time between the molecules decreases. (C) the mean free path remains unchanged. (D) the mean collision time remains unchanged.

Three elements X, Y and Z are in the 3 rd period of the periodic table. The oxides of X, Y and Z, respectively, are basic, amphoteric and acidic. The correct order of the atomic numbers of X, Y and Z is :

The shape / structure of [XeF 5 ] – and XeO 3 F 2 , respectively, are

Two elements A and B have similar chemical properties. They don’t form solid hydrogencarbonates, but react with nitrogen to form nitrides. A and B, respectively, are :

The number of subshells associated with n = 4 and m = –2 quantum numbers is

If you spill a chemical toilet cleaning liquid on your hand, your first aid would be

The area (in sq. units) of an equilateral triangle inscribed in the parabola y 2 = 8x, with one of its vertices on the vertex of this parabola, is :

Let f : R → R be a function which satisfies f(x + y) = f(x) + f(y) ∀ x, y ∈ R. If f(1) = 2 and g(n) = ∑ k = 1 ( n − 1 ) f ( k ) , n ∈ N then the value of n, for which g(n) = 20, is :

If the equation cos 4 $\theta$ + sin 4 $\theta$ + $\lambda$ = 0 has real solutions for $\theta$ , then $\lambda$ lies in the interval :

Let n > 2 be an integer. Suppose that there are n Metro stations in a city located along a circular path. Each pair of stations is connected by a straight track only. Further, each pair of nearest stations is connected by blue line, whereas all remaining pairs of stations are connected by red line. If the number of red lines is 99 times the number of blue lines, then the value of n is :

The imaginary part of ${\left( {3 + 2\sqrt { - 54} } \right)^{{1 \over 2}}} - {\left( {3 - 2\sqrt { - 54} } \right)^{{1 \over 2}}}$ can be :

A wire carrying current I is bent in the shape ABCDEFA as shown, where rectangle ABCDA and ADEFA are perpendicular to each other. If the sides of the rectangles are of lengths a and b, then the magnitude and direction of magnetic moment of the loop ABCDEFA is

An inductance coil has a reactance of 100 Ω . When an AC signal of frequency 1000 Hz is applied to the coil, the applied voltage leads the current by 45 o . The self-inductance of the coil is

A charge Q is distributed over two concentric conducting thin spherical shells radii r and R (R > r). If the surface charge densities on the two shells are equal, the electric potential at the common centre is :

A small point mass carrying some positive charge on it, is released from the edge of a table. There is a uniform electric field in this region in the horizontal direction. Which of the following options then correctly describe the trajectory of the mass? (Curves are drawn schematically and are not to scale).

In the following digital circuit, what will be the output at ‘Z’, when the input (A, B) are (1, 0), (0, 0), (1, 1,), (0, 1)

Let A = {X = (x, y, z) T : PX = 0 and x 2 + y 2 + z 2 = 1} where P = [ 1 2 1 − 2 3 − 4 1 9 − 1 ] , then the set A :

Let E C denote the complement of an event E. Let E 1 , E 2 and E 3 be any pairwise independent events with P(E 1 ) > 0 and P(E 1 $\cap$ E 2 $\cap$ E 3 ) = 0. Then P( $E_2^C \cap E_3^C/{E_1}$ ) is equal to :

If a curve y = f(x), passing through the point (1, 2), is the solution of the differential equation, 2x 2 dy= (2xy + y 2 )dx, then $f\left( {{1 \over 2}} \right)$ is equal to :

Consider a region R = {(x, y) $\in$ R : x 2 $\le$ y $\le$ 2x}. if a line y = $\alpha$ divides the area of region R into two equal parts, then which of the following is true?

$\mathop {\lim }\limits_{x \to 0} {\left( {\tan \left( {{\pi \over 4} + x} \right)} \right)^{{1 \over x}}}$ is equal to :

Amongst the following statements regarding adsorption, those that are valid are (a) $\Delta$ H becomes less negative as adsorption proceeds (b) On a given adsorbent, ammonia is adsorbed more than nitrogen gas (c) On adsorption, the residual force acting along the surface of the adsorbent increases (d) With increase in temperature, the equilibrium concentration of adsorbate increases

The results given in the below table were obtained during kinetic studies of the following reaction 2A + B $\to$ C + D X and Y in the given table are respectively :

The major product obtained from E 2 - elimination of 3-bromo-2-fluoropentane is

Arrange the following labelled hydrogens in decreasing order of acidity :

The major product of the following reaction is :