JEE Advanced 2019 Paper 1 Offline

In a radioactive sample, \({}_{19}^{40}K\) nuclei either decay into stable \({}_{20}^{40}Ca\) nuclei with decay constant 4.5 \(\times\) 10-10 per year or into stable \({}_{18}^{40}Ar\) nuclei with decay constant 0.5 \(\times\) 10-10 per...

A parallel plate capacitor of capacitance C has spacing d between two plates having area A. The region between the plates is filled with N dielectric layers, parallel to its plates, each with thickness, \(\delta = {d \over N}\). The dielec...

Two identical moving coil galvanometers have 10\(\Omega\) resistance and full scale deflection at 2\(\mu\)A current. One of them is converted into a voltmeter of 100 mV full scale reading and the other into an ammeter of 1 mA full scale c...

In the circuit shown, initially there is no charge on the capacitors and keys S1 and S2 are open. The values of the capacitors are C1 = 10\(\mu\)F, C2 = 30\(\mu\)F and C3 = C4 = 80\(\mu\)F. Which of the statement(s) is/are correct?

A conducting wire of parabolic shape, initially y = x2, is moving with velocity \(v = {v_0}\widehat i\) in a non-uniform magnetic field \(B = {B_0}\left( {1 + {{\left( {{y \over L}} \right)}^\beta }} \right)\widehat k\), as shown in figure....

A charged shell of radius R carries a total charge Q. Given \(\phi\) as the flux of electric field through a closed cylindrical surface of height h, radius r and with its center same as that of the shell. Here, center of the cylinder is a ...

A thin spherical insulating shell of radius R carries a uniformly distributed charge such that the potential at its surface is V0. A hole with a small area \(\alpha\)4\(\pi\)R2(\(\alpha\) << 1) is made on the shell without affecting the ...

A planar structure of length L and width W is made of two different optical media of refractive indices n1 = 1.5 and n2 = 1.44 as shown in figure. If L >> W, a ray entering from end AB will emerge from end CD. CD only if the total internal ...

A thin convex lens is made of two materials with refractive indices n1 and n2, as shown in the figure. The radius of curvature of the left and right spherical surfaces are equal. f is the focal length of the lens when n1 = n2 = n. The focal...

Consider a spherical gaseous cloud of mass density \(\rho\)(r) in free space where r is the radial distance from its center. The gaseous cloud is made of particles of equal mass m moving in circular orbits about the common center with the ...

One mole of a monatomic ideal gas goes through a thermodynamic cycle, as shown in the volume versus temperature (V-T) diagram. The correct statement(s) is/are [R is the gas constant]

A liquid at 30\(^\circ\)C is poured very slowly into a Calorimeter that is at temperature of 110\(^\circ\)C. The boiling temperature of the liquid is 80\(^\circ\)C. It is found that the first 5 gm of the liquid completely evaporates. Aft...

A current carrying wire heats a metal rod. The wire provides a constant power (P) to the rod. The metal rod is enclosed in an insulated container. It is observed that the temperature (T) in the metal rod changes with time (t) as $$T(t) = {T...

A cylindrical capillary tube of 0.2 mm radius is made by joining two capillaries T1 and T2 of different materials having water contact angles of 0\(^\circ\) and 60\(^\circ\), respectively. The capillary tube is dipped vertically in water ...

A block of weight 100 N is suspended by copper and steel wires of same cross-sectional area 0.5 cm2 and length \(\sqrt 3\) m and 1 m, respectively. Their other ends are fixed on a ceiling as shown in figure. The angles subtended by copper ...

Let us consider a system of units in which mass and angular momentum are dimensionless. If length has dimension of L, which of the following statement(s) is/are correct?

A train S1, moving with a uniform velocity of 108 km/h, approaches another train S2 standing on a platform. An observer O moves with a uniform velocity of 36 km/h towards S2, as shown in figure. Both the trains are blowing whistles of same...

A particle is moved along a path AB-BC-CD-DE-EF-FA, as shown in figure, in presence of a force \(F = (\alpha y\widehat i + 2\alpha x\widehat j)\) N, where x and y are in meter and \(\alpha\) = \(-\)1 Nm-1. The work done on the particle b...