Practice Questions

Q25.A thin convex lens L (refractive index = 1.5 ) is placed on a plane mirror M. When a pin is placed at A , such that OA = 18 cm, its real inverted image is formed at A itself, as shown in figure. When liquid of refractive index μl is put between the lens and the mirror, the pin has to be moved to A', such that OA' = 27 cm, to get its inverted real image at A' itself. The value of μl will be (1) 4 (2) √3 3 (3) 3 (4) √2 2

Q25.An upright object is placed at a distance of 40 cm in front of a convergent lens of focal length 20 cm . A convergent mirror of focal length 10 cm is placed at a distance of 60 cm on the other side of the lens. The position and size of the final image will be: JEE Main 2019 (08 Apr Shift 1) JEE Main Previous Year Paper (1) 40 cm from the (2) 20 cm from the (3) 40 cm from the (4) 20 cm from the convergent lens, twice convergent mirror, convergent lens, same convergent mirror, the size of the object twice the size of the size of the object same size of the object object

Q25.In a double-slit experiment, green light (5303 A) falls on a double slit having a separation of 19.44μm and a width of 4.05μm. The number of bright fringes between the first and the second diffraction minima is (1) 10 (2) 5 (3) 4 (4) 9

Q26.A convex lens (of focal length 20 cm ) and a concave mirror, having their principal axes along the same lines, are kept 80 cm apart from each other. The concave mirror is to the right of the convex lens. When an object is kept at a distance of 30 cm to the left of the convex lens, its image remains at the same position even if the concave mirror is removed. The maximum distance of the object for which this concave mirror, by itself would produce a virtual image would be: (1) 30 cm (2) 25 cm (3) 20 cm (4) 10 cm JEE Main 2019 (08 Apr Shift 2) JEE Main Previous Year Paper

Q26.In an electron microscope, the resolution that can be achieved is of the order of the wavelength of electrons used. To resolve a width of 7.5 × 10−12 m, the minimum electron energy required is close to: (1) 100 keV (2) 25 keV (3) 1 keV (4) 500 keV

Q26.A particle of mass m moves in a circular orbit in a central potential field U(r) = 12 kr2. If Bohr's quantization conditions are applied, radii of possible orbitals and energy levels vary with quantum number n as: (1) rn ∝n2, En ∝ n21 (2) rn ∝√n, En ∝n (3) rn ∝n, En ∝n (4) rn ∝√n, En ∝1n

Q26.Consider a Young's double slit experiment as shown in figure. What should be the slit separation d in terms of wavelength λ such that the first minima occurs directly in front of the slit (S1) ? (1) λ (2) λ (5−√2) 2(√5−2) (3) λ (4) λ 2(5−√2) √5−2

Q28.An NPN transistor operates as a common emitter amplifier, with a power gain of 60 dB . The input circuit resistance is 100 Ω and the output load resistance is 10 kΩ . The common emitter current gain β is: (1) 6 × 102 (2) 102 (3) 104 (4) 60

Q28.In Li+ + ,electron in first Bohr orbit is excited to a level by a radiation of wavelength λ.When the ion gets de excited to the ground state in all possible ways (including intermediate emissions), a total of six spectral lines are observed. What is the value of λ ? (Given: ℎ= 6.63 × 10-34 J s ; 𝑐= 3 × 108 m s-1 ) (1) 10.8 nm (2) 9.4 nm (3) 11.4 nm (4) 12.3 nm

Q28.Consider a tank made of glass (refractive index 1.5 ) with a thick bottom. It is filled with a liquid of refractive index 𝜇. A student finds that, irrespective of what the incident angle 𝑖 (see figure) is for a beam of light entering the liquid, the light reflected from the liquid glass interface is never completely polarized. For this to happen, the minimum value of 𝜇 is: 3 4 (1) (2) √5 3 5 5 (3) (4) √3 √ 3

Q28.An excited He+ ion emits two photons in succession, with wavelengths 108.5 nm and 30.4 nm in making a transition to the ground state. The quantum number n, corresponding to its initial excited state is 1240 eV (for a photon of wavelength λ, energy E = ) λ ( in nm ) (1) n = 6 (2) n = 5 (3) n = 7 (4) n = 4

Q30.The figure represents a voltage regulator circuit using a Zener diode. The breakdown voltage of the Zener diode is 6 V and the load resistance is, RL = 4 kΩ . The series resistance of the circuit is Ri = 1 kΩ . If the battery voltage VB varies from 8 V to 16 V , what are the minimum and maximum values of the current through Zener diode? (1) 0.5 mA; 6 mA (2) 1 mA; 8.5 mA (3) 0.5 mA; 8.5 mA (4) 1.5 mA; 8.5 mA

Q30.In a meter bridge, the wire of length 1 m has a non-uniform cross-section such that, the variation dRdl of its resistance R with length l is dRdl ∝ √l1 . Two equal resistances are connected as shown in the figure. The galvanometer has zero deflection when the jockey is at point P. What is the length AP? JEE Main 2019 (12 Jan Shift 1) JEE Main Previous Year Paper (1) 0.2 m (2) 0.35 m (3) 0.3 m (4) 0.25 m o

Q30.A load of mass M kg is suspended from a steel wire of length 2m and radius 1.0 mm in Searle's apparatus experiment. The increase in length produced in the wire is 4.0 mm. Now the load is fully immersed in a liquid of relative density 2. The relative density of the material of load is 8. The new value of increase in length of the steel wire is: (1) 4.0 mm (2) Zero (3) 5.0mm (4) 3.0mm Q31. 8 g of NaOH is dissolved in 18g of H2O. Mole fraction of NaOH in solution and molality (in mol kg−1 ) of the solution respectively are: (1) 0.167, 11.11 (2) 0.167, 22.20 (3) 0.2, 11.11 (4) 0.2, 22.20 JEE Main 2019 (12 Jan Shift 2) JEE Main Previous Year Paper

Q30.In the experimental set up of metre bridge shown in the figure, the null point is obtaine data distance of 40 cm from A. If a 10Ω resistor is connected in series with R1, the null point shifts by 10 cm. The resistance that should be connected in parallel with (R1 + 10)Ω such that the null point shifts back to its initial position is (1) 20Ω (2) 40Ω (3) 60Ω (4) 30Ω Q31. 25 mL of the given HCl solution requires 30 mL of 0.1M sodium carbonate solution. What is the volume of this HCl solution required to titrate 30 mL of 0.2M aqueous NaOH solution? (1) 25 mL (2) 75 mL (3) 50 mL (4) 12.5 mL JEE Main 2019 (11 Jan Shift 2) JEE Main Previous Year Paper

Q35.The entropy change associated with the conversion of 1 kg of ice at 273 K to water vapours at 383 K is: (Specific heat of water liquid and water vapour are 4.2 kJ K − and 2.0 kJ K −1kg−1 ; heat of liquid fusion and vaporization of water are 334 kJ kg−1 and 2491 kJ kg−1 , respectively). ( log 273 = 2.436, log 373 = 2.572, log 383 = 2.583 ) (1) 9.26 kJ kg−1K −1 (2) 2.64 kJ kg−1K −1 (3) 8.49 kJ kg−1K −1 (4) 7.90 kJ kg−1K −1

Q36.A mixture of 100 m mol of Ca (OH)2 and 2 g of sodium sulphate was dissolved in water and the volume was made up to 100 mL. What is the mass of calcium sulphate formed and the concentration of OH− in resulting solution, respectively? (Molar mass of Ca (OH)2, Na2 SO4 and CaSO4 are 74, 143 and 136 g mol−1, respectively; Ksp of Ca (OH)2 is 5 .5 ×10−6 ) (1) 1 .9 g, 0 .14 mol L−1 (2) 13 .6 g, 0 .28 mol L−1 (3) 1 .9 g, 0 .28 mol L−1 (4) 13 .6 g, 0 .14 mol L−1

Q36.The molar solubility of Cd(OH)2 is 1.84 × 10−5M in water. The expectes solunility of Cd(OH)2 in a buffer solution of pH = 12 is: (1) 2.49 × 10−10M (2) 2.491.84 × 10−9M (3) 1.84 × 10−9M (4) 6.23 × 10−11M

Q36.In order to oxidize a mixture of one mole of each of FeC2O4, Fe2 ( C2O4 ) 3, FeSO4 and Fe2 ( SO4 ) 3 in acidic medium, the number of moles of KMnO4 is: (1) 1 (2) 2 (3) 3 (4) 1.5

Q37.Consider the following statements (a) The pH of a mixture containing 400 mL of 0.1 M H2SO4 and 400 mL of 0.1 M NaOH will be approximately 1.3. (b) Ionic product of water is temperature dependent. (c) A monobasic acid with Ka = 10−5 has a pH = 5 . The degree of dissociation of this acid is 50% . (d) The Le Chatelier's principle is not applicable to common-ion effect. The correct statements are: (1) (b) and (c) (2) (a), (b) and (d) (3) (a) and (b) (4) (a), (b) and (c)

Q37.Two solids dissociate as follows: A (s) ⇌B (g) + C (g); KP1 = x atm2 D (s) ⇌C (g) + E (g); KP2 = y atm2 The total pressure when both the solids dissociate simultaneously is: (1) √x + y atm (2) x2 + y2 atm (3) (x + y) atm (4) 2(√x + y) atm Q38. 50 mL of 0 .5 M oxalic acid is needed to neutralize 25 mL of sodium hydroxide solution. What is the amount of NaOH in 50 mL of the given sodium hydroxide solution? (1) 2 g (2) 4 g (3) 1 g (4) 8 g

Q42.Which one of the following alkenes when treated with HCl yields majorly an anti Markovnikov product? (1) CH3O - CH = CH2 (2) Cl - CH = CH2 (3) H2N - CH = CH2 (4) F3C - CH = CH2

Q43.Heating of 2-chloro-1-phenylbutane with EtOK/EtOH gives X as the major product. Reaction X with Hg(OAc)2/H2O followed by NaBH4 gives Y as the major product. Y is: (1) (2) (3) (4)

Q43.Consider the given plot of enthalpy of the following reaction between A and B. A + B →C + D. Identify the incorrect statement. JEE Main 2019 (09 Apr Shift 2) JEE Main Previous Year Paper (1) Formation of A and B from C has highest enthalpy of activation. (2) D is kinetically stable product. (3) C is the thermodynamically stable product. (4) Activation enthalpy to form C is 5 kJ mol−1 less than that to form D. Q44. 10 mL of 1 mM surfactant solution forms a monolayer covering 0.24 cm2 on a polar substrate. If the polar head is approximated as a cube, what is its edge length? (1) 1.0 pm (2) 0.1 nm (3) 2.0 pm (4) 2.0 nm

Q45.Molecules of benzoic acid (C6H5 COOH) dimerise in 30 g of benzene. ' w ' g of benzoic acid shows a depression in freezing point equal to 2 K. If the percentage association of the acid to form dimer in the solution is 80, then w is: ( Given that Kf = 5 Kmol−1 , molar mass of benzoic acid = 122 gmol−1) (1) 1.0g (2) 2.4g (3) 1.8g (4) 1.5g Q46. ∧om for NaCl, HCl and NaA are 126.4, 425.9 and 100 .5 S cm2 mol−1 respectively. If the conductivity of 0 .001 M HA is 5 × 10−5S cm−1 , degree of dissociation of HA is (1) 0.125 (2) 0.75 (3) 0.25 (4) 0.50