Practice Questions

Q12.A diatomic ideal gas is used in a Car engine as the working substance. If during the adiabatic expansion part of the cycle, volume of the gas increases from V to 32 V the efficiency of the engine is (1) 0.5 (2) 0.75 (3) 0.99 (4) 0.25

Q13.The equation of a wave on a string of linear mass density 0.04 kg m−1 is given by y = 0.02( m) sin [2π ( 0.04(t s) − 0.50(x m) )]. The tension in the string is (1) 4.0 N (2) 12.5 N (3) 0.5 N (4) 6.25 N

Q14.A thin semi-circular ring of radius r has a positive charge q distributed uniformly over it. The net field →E at the centre O is (1) q ^j (2) − q ^j 4π2ε0r2 4π2ε0r2 (3) − q ^j (4) q ^j 2π2ε0r2 2π2ε0r2

Q16.Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of 30∘ with each other. When suspended in a liquid of density 0.8 g cm−3 , the angle remains the same. If density of the material of the sphere is 16 g cm−3 , the dielectric constant of the liquid is (1) 4 (2) 3 (3) 2 (4) 1

Q17.Let C be the capacitance of a capacitor discharging through a resistor R. Suppose t1 is the time taken for the energy stored in the capacitor to reduce to half its initial value and t2 is the time taken for the charge to reduce to one-fourth its initial value. Then the ratio t1/t2 will be (1) 1 (2) 1 2 (3) 1 (4) 2 4

Q18.Two long parallel wires are at a distance 2 d apart. They carry steady equal current flowing out of the plane of the paper as shown. The variation of the magnetic field along the line XX ' is given by (1) (2) (3) (4)

Q19.A rectangular loop has a sliding connector PQ of length ℓ and resistance RΩ and it is moving with a speed v as shown. The set-up is placed in a uniform magnetic field going into the plane of the paper. The three currents I1, I2 and I are (1) I1 = −I2 = BℓvR , I = 2 BℓvR (2) I1 = I2 = Bℓv3R , I = 2 3RBℓv (3) l1 = I2 = I = BℓvR (4) I1 = I2 = Bℓv6R , I = Bℓv3R JEE Main 2010 JEE Main Previous Year Paper

Q20.In the circuit shown below, the key K is closed at t = 0 . The current through the battery is (1) VR1R2 at t = 0 and V at t = ∞ (2) V at t = 0 and V (R1+R2) at t = ∞ √R21+R22 R2 R2 R1R2 (3) V at t = 0 and V R1R2 at t = ∞ (4) V (R1+R2) at t = 0 and V at t = ∞ R2 √R21+R22 R1R2 R2

Q21.In a series LCR circuit R = 200Ω and the voltage and the frequency of the main supply is 220 V and 50 Hz respectively. On taking out the capacitance from the circuit the current lags behind the voltage by 30∘ . On taking out the inductor from the circuit the current leads the voltage by 30∘ . The power dissipated in the LCR circuit is (1) 305 W (2) 210 W (3) Zero W (4) 242 W

Q22.If a source of power 4 kW produces 1020 photons/second, the radiation belong to a part of the spectrum called (1) X-rays (2) ultraviolet rays (3) microwaves (4) γ -rays

Q25.An initially parallel cylindrical beam travels in a medium of refractive index μ(I) = μ0 + μ2I , where μ0 and μ2 are positive constants and I is the intensity of the light beam. The intensity of the beam is decreasing with increasing radius. The speed of light in the medium is (1) minimum on the axis of the beam (2) the same everywhere in the beam (3) directly proportional to the intensity I (4) maximum on the axis of the beam JEE Main 2010 JEE Main Previous Year Paper

Q26.Statement-1 : When ultraviolet light is incident on a photocell, its stopping potential is V0 and the maximum kinetic energy of the photoelectrons is Kmax . When the ultraviolet light is replaced by X− rays, both V0 and Kmax increase. Statement-2 : Photoelectrons are emitted with speeds ranging from zero to a maximum value because of the range of frequencies present in the incident light. Of the four choices given after the statements, choose the one that best describes the two statements. (1) Statement-1 is true, Statement-2 is true; (2) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-2 is not the correct explanation of Statement-1. Statement- 1. (3) Statement-1 is false, Statement-2 is true. (4) Statement-1 is true, Statement- 2 is false.

Q27.A nucleus of mass M + Δm is at rest and decays into two daughter nuclei of equal mass M2 each. Speed of light is c. 40. The binding energy per nucleon for the parent nucleus is E1 and that for the daughter nuclei is E2 . Then (1) E2 = 2E1 (2) E1 > E2 (3) E2 > E1 (4) E1 = 2E2

Q29.A radioactive nucleus (initial mass number A and atomic number Z) emits 3α-particles and 2 positrons. The ratio of number of neutrons to that of protons in the final nucleus will be (1) A−Z−8 (2) A−Z−4 Z−4 Z−8 (3) A−Z−12 (4) A−Z−4 Z−4 Z−2

Q31.Ionisation energy of He+ is 19.6 × 10−18 Jatom−1 . The energy of the first stationary state (n = 1) of Li2+ is (1) 4.41 × 10−16 Jatom−1 (2) −4.41 × 10−17 Jatom −1 (3) −2.2 × 10−15 Jatom−1 (4) 8.82 × 10−17 Jatom −1

Q33.The standard enthalpy of formation of NH3 is −46.0 kJ mol−1 . If the enthalpy of formation of H2 from its atoms is −436 kJ mol−1 and that of N2 is −712 kJ mol−1 , the average bond enthalpy of N −H bond in NH3 JEE Main 2010 JEE Main Previous Year Paper is (1) −964 kJ mol−1 (2) +352 kJ mol−1 (3) +1056 kJ mol−1 (4) −1102 kJ mol−1

Q34.The energy required to break one mole of Cl −Cl bonds in Cl2 is 242 kJ mol−1 . The longest wavelength of light capable of breaking a single Cl −Cl bond is (c = 3 × 108 ms−1 and NA = 6.02 × 1023 mol−1) (1) 594 nm (2) 640 nm (3) 700 nm (4) 494 nm

Q36.In aqueous solution the ionization constants for carbonic acid are K1 = 4.2 × 10−7 and K2 = 4.8 × 10−11 Select the correct statement for a saturated 0.034M solution of the carbonic acid. (1) The concentration of CO2−3 is 0.034M. (2) The concentration of CO2−3 is greater than that of HCO−3 . (3) The concentration of H+ and HCO−3 are (4) The concentration of H+ is double that of CO2−3 . approximately equal.

Q37.Solubility product of silver bromide is 5.0 × 10−13 . The quantity of potassium bromide (molar mass precipitation of AgBr is (1) 1.2 × 10−10 g (2) 1.2 × 10−9 g (3) 6.2 × 10−5 g (4) 5.0 × 10−8 g

Q38.At 25∘C, the solubility product of Mg(OH)2 is 1.0 × 10−11 . At which pH, will Mg2+ ions start precipitating in the form of Mg(OH)2 from a solution of 0.001MMg2+ ions ? (1) 9 (2) 10 (3) 11 (4) 8 Q39. 29.5mg of an organic compound containing nitrogen was digested according to Kjeldahl's method and the evolved ammonia was absorbed in 20 mL of 0.1MHCl solution. The excess of the acid required 15 mL of 0.1MNaOH solution for complete neutralization. The percentage of nitrogen in the compound is (1) 59.0 (2) 47.4 (3) 23.7 (4) 29.5

Q40.The correct order of increasing basicity of the given conjugate bases (R = CH3) is –––––– (1) RCOO < HC = C < R < NH2 (2) R < HC ≡C < RCOO < NH2 ––––– (3) RCOO < NH2 < HC ≡C < R (4) RCOO < HC ≡C < NH2 < R

Q41.Out of the following, the alkene that exhibits optical isomerism is (1) 3-methyl-2-pentene (2) 4-methyl-1-pentene (3) 3-methyl-1-pentene (4) 2-methyl-2-pentene JEE Main 2010 JEE Main Previous Year Paper ⟶ ?

Q42.The main product of the following reaction is C6H5CH2CH(OH)CH(CH3)2 conc. H2SO4 (1) (2) (3) (4)

Q43.The edge length of a face centered cubic cell of an ionic substance is 508pm. If the radius of the cation is 110pm, the radius of the anion is (1) 288pm (2) 398pm (3) 618pm (4) 144pm

Q44.Percentage of free space in cubic close packed structure and in body centred packed structure are respectively (1) 30% and 26% (2) 26% and 32% (3) 32% and 48% (4) 48% and 26%