JEE (Advanced) 2019 Paper - 2 - JEE MCQ

A small particle of mass m moving inside a heavy,hollow and straight tube along the tube axis undergoes elastic collision at two ends. The tube has no friction and it is closed at one end by a flat surface while the other end is fitted with a heavy movable flat piston as shown in figure. When the distance of the piston from closed end is L = L₀ the particle speed is v = v₀. The piston is moved inward at a very low speed V such that , where dL is the infinitesimal displacement of the piston. which of the following statement(s) is/are correct?

Three glass cylinders of equal height H = 30 cm and same refractive index n = 1.5 are placed on a horizontal surface as shown in figure. Cylinder I has a flat top, cylinder II has a convex top and cylinder III has a concave top. The radii of curvature of the two curved tops are same (R = 3m). If H1, H2 and H3 are the apparent depths of a point X on the bottom of the three cylinders, respectively, the correct statement(s) is/are:

An electric dipole with dipole moment  is held fixed at the origin O in the presence of an uniform electric field of magnitude E0.If the potential is constant on a circle of radius R centered at the origin as shown in figure, then the correct statement(s) is/are:

( ∈₀ is permittivity of free space. R >> dipole size)

A ball is thrown from ground at an angle θ with horizontal and with an initial speed u₀. For the resulting
projectile motion, the magnitude of average velocity of the ball up to the point when it hits the ground for
the first time is V1. After hitting the ground, the ball rebounds at the same angle θ but with a reduced speed
of u0/α. Its motion continues for a long time as shown in figure. If the magnitude of average velocity of the
ball for entire duration of motion is 0.8 V1, the value of α is________.

A 10 cm long perfectly conducting wire PQ is moving with a velocity 1 cm/s on a pair of horizontal rails of zero resistance. One side of the rails is connected to an inductor L = 1 mH and a resistance R = 1Ω as shown in the figure. The horizontal rails, L and R lie in the same plane with a uniform magnetic field B = 1 T perpendicular to the plane. If the key S is closed at certain instant, the current in the circuit after 1 millisecond is x * 10^-3 A, where the value of x is ________

[Assume the velocity of wire PQ remains constant (1 cm/s) after key S is closed. Given: e^-1 = 0.37, where e
is base of the natural logarithm]

A perfectly reflecting mirror of mass M mounted on a spring constitutes a spring-mass system of angular frequency Ω such that 4πMΩ/h =10²⁴ m^-2 with h as Planck’s constant. N photons of wavelength λ = 8π * 10^-6 m strike the mirror simultaneously at normal incidence such that the mirror gets displaced by 1 µm. If the value of N is x * 10¹²  then the value of x is _________. [Consider the spring as massless]

A monochromatic light is incident from air on a refracting surface of prism of angle 75° and refractive index n₀ = √3 . The other refracting surface of the prism is coated by a thin film of material of refractive index n as shown in figure.
The light suffers total internal reflection at the coated prism surface for an incidence angle of θ ≤ 60°. The value of n2 is _______

An optical bench has 1.5 m long scale having four equal divisions in each cm. While measuring the focal length of a convex lens, the lens is kept at 75 cm mark of the scale and the object pin is kept at 45 cm mark.The image of the object pin on the other side of the lens overlaps with image pin that is kept at 135 cm mark. In this experiment, the percentage error in the measurement of the focal length of the lens is_______.

Q. If the tension in each string is T₀, the correct match for the highest fundamental frequency in f₀ units will be, Options

Q. 

Q. If the process carried out on one mole of monatomic ideal gas is as shown in figure in the PV-diagram with P₀V₀  =1/3 RT₀, the correct match is

Q. If the process on one mole of monatomic ideal gas is as shown in the TV-diagram with P₀V₀ = 1/3  RT₀, the correct match is,

Choose the correct option(s) that give(s) an aromatic compound as the major product

Consider the following reactions (unbalanced)

Choose the correct option(s)

Which of the following reactions produce(s) propane as a major product?

Choose the correct option(s) from the following:

The ground state energy of hydrogen atom is – 13.6 eV. Consider an electronic state ψ of He+ whose
energy, azumuthal quantum number and magnetic quantum number are -3.4 eV, 2 and 0, respectively.
Which of the following statement(s) is(are) true for the state ψ ?

The cyanide process of gold extraction involves leaching out gold from its ore with CN^- in the presence of
Q in water to form R. Subsequently, R is treated with T to obtain Au and Z. Choose the correct option(s)

With reference to aqua regia, choose the correct option(s)

Choose the correct option(s) for the following reaction sequence

Total number of isomers, considering both structural and stereoisomers, of cyclic ethers with the molecular
formula C4H8O is_______

The mole fraction of urea in an aqueous urea solution containing 900 g of water is 0.05. If the density of the
solution is 1.2 g cm-3, the molarity of urea solution is______
(Given data: Molar masses of urea and water are 60 g mol-1 and 18 g mol-1, respectively)\

Total number of cis N-Mn-Cl bond angles (that is, Mn – N and Mn – Cl bonds in cis positions) present in a
molecule of cis-[Mn(en)2Cl2] complex is______(en = NH2CH2CH2NH2)

The amount of water produced (in g) in the oxidation of 1 mole of rhombic sulphur by conc. HNO3 to a
compound with the highest oxidation state of sulphur is______
(Given data : Molar mass of water = 18 g mol-1)