Science-Class-12 Physics and Chemistry DPP Talent Search Examinations

Physics & Chemistry-XII 1. A charge +Q is uniformly distributed in a spherical volume of radius R. A particle of charge +q and mass m is projected with velocity v0 from the surface of the spherical volume to its centre. The minimum value of v0 such that it just reaches the centre (assume that there is no resistance on the particle except electrostatic force) of the spherical volume is Qq Qq 2Qq Qq (a) 20 mR (b)  0 mR (c) 0 mR (d) 40 mR 2. Two fixed charges –2Q and + Q are located at points (–3a, 0) and (+3a, 0) respectively. Which of the following statement is wrong? (a) points where the electric potential due to the two charges is zero, lie on a circle of radius 4a and centre (5a, 0) (b) potential is zero at x = a and x = 9a (c) if a particle of charge +q is released from the centre of the circle obtained in part (a), it will eventually cross the circle. (d) points where the electric potential due to the two charges is zero, lie on a circle of radius 4a and centre (–5a, 0) 3. The variation of electric field between the two charges q1 and q2 along the line joining the charge is plotted against distance from q1 (taking rightward direction of electric field as positive) as shown in the figure. Then the correct statement is (a) q1 and q2 are positive and q1 < q2 (b) q1 and q2 are positive and q1 > q2 (c) q1 is positive and q2 is negative and q1 < q2 (d) q1 and q2 are negative and q1 < q2 E q1 q2 - : Rough Space : - [2] Physics & Chemistry-XII 4. A capacitor of capacity C is charged to a potential difference V and another capacitor of capacity 2 C is charged to a potential difference 4 V. The charging batteries are disconnected and the two capacitors are connected with reverse polarity (i.e., positive plate of the first capacitor is connected to negative plate of the second capacitor and the negative plate of the first capacitor is connected to the positive plate of the second capacitor). The heat produced during the redistribution of charge between the capacitors will be (a) 125CV2 3 (b) 50 CV2 3 (c) 2 CV2 (d) 25CV2 3 5. In the circuit shown, the switch S is thrown to position 1 at t = 0. When the current in the resistor is 1 A, the switch S is shifted to position 2. The heat generated in the circuit after shifting to position 2 is (a) zero (b) 625 µJ (c) 1250 µJ (d) none of these 10V 1 S 2 25µF 5V 6. A wire of mass 100 g carrying a current of 2A towards increasing x is in the form of y = x2, (–2m  x  +2m). This wire is placed in a magnetic field B = –0.02 k T. The acceleration of the wire (in m/s2) is (a) –1.6 j (b) –3.2 j (c) 1.6 j (d) 2.4 j 7. A charged particle of unit mass and unit charge moves with velocity v = (8i + 6j) m/s in a magnetic field of B = 2kT. Then choose the wrong statement (a) the path of the particle may be x2 + y2 – 4x – 21 = 0 (b) the path of the particle may be x2 + y2 = 25 (c) the path of the particle may be y2 + z2 = 25 (d) The time period of the particle will be 3.14 s. - : Rough Space : - [3] Physics & Chemistry-XII 8. A conducting rod is moving with a constant velocity over the parallel conducting rails which are connected at the ends through a resistor R and capacitor C, as shown in the figure. Magnetic field B is directed into the plane of the paper. Consider the following statements. I. Current in loop AEFBA is anticlockwise II. Current in loop AEFBA is clockwise III. Current through the capacitor is zero IV. Energy stored in the capacitor is 1/2 CB2L2V2 × E × ×A × H × × C× R × × which of the following options is correct. × F × ×B × G × (a) statements I and III only are correct (b) statements II and IV only are correct (c) statements I, III and IV only are correct (d) all of these 9. Two parallel long straight conductors lie on a smooth plane surface. Two other parallel conductors rest on them at right angles so as to form a square of side a. A uniform magnetic field B exists at right angle to the plane containing the conductors. Now conductors start moving outward with a constant velocity v0 at t = 0. Then induced current in the loop at any time t is ( is resistance per unit length of the conductors) (a) aBv0 (a  v0t) (b) aBv0 2 (c) Bv0  (d) Bv0 2 10. In the given branch AB of a circuit, a current I = (10 t + 5)A is following, where t is time in second. At t = 0, the potential difference (VA – VB) is (a) 15 V (b) – 5 V (c) –15 V (d) 5 V B 10V L= 1H I A - : Rough Space : - [4] Physics & Chemistry-XII 11. A uniform but time varying magnetic field exists in a cylindrical region, as shown in the figure. The direction of magnetic field is into the plane of the paper and its magnitude is decreasing at a constant of 2 × 10–3 T/s. A particle of charge 1 µC is moved slowly along a square of side 1 m by an external force, as shown in the figure. The plane of the square lies on the plane of the paper and it is concentric with the cylindrical region. The work done by the external force in moving this charge along the square will be × × × × × × × × × × × (a) zero (b) 2 × 10–9 J (c) –2 × 10–9 J (d) 2 × 10–6 J 12. In the circuit shown, the switch S is closed at t = 0. The change in flux in the inductor from t = 0 to an instant when it reaches steady state is (a) 2 Wb (b) 1.5 Wb (c) 0 Wb (d) none of these 20V × 5 500mH 5 S × × × × × × × × 5 10V × 50µF  dI  13. In an LC circuit, the capacitor has maximum charge q0. The maximum value of  dt  is q (a) 0 LC q0 L C (b) LC (c) (c) q0 1 LC (d) (d) q0  1 LC 14. A L - R circuit is connected to a battery at time t = 0. The energy stored in the inductor reaches half its maximum value at time R ln  2  L ln  2  1 L ln  2  R ln  2  1 (a) L  2  1 (b) R  2  (c) R  2 1 (d) L  2          - : Rough Space : - [5] Physics & Chemistry-XII 15. A complex current wave is given by i = (5 + 5 sin 100 t) A. Its average value over one time period is given as (a) 10 A (b) 5 A (c) 50 A (d) 0 16. In the circuit shown, R = L C . Consider the following statements and choose the correct option. R L I. R.M.S. value of current through AC source is II. Impedance of the circuit is independent of . III. Impedance of the circuit depends on . Vrms Vrms 2 R R C IV. Current through the source is R 2  2 L2 (a) only III and IV are correct (b) only II is correct (c) only I and II are correct (d) only IV are correct. 17. Two parallel plane mirrors are 3 m apart. A person standing x m from the 1 L2 right mirror sees a series of images. The distance between the first and second image is 4 m. The value of x is (a) 2 m (b) 6 m x (c) 1 m (d) 8 m 18. A bird in air looks at a fish directly below it inside a transparent liquid in a tank. If the distance of the fish as estimated by the bird is h1 and that of the bird as estimated by the fish is h2, then refractive index of liquid is (a) h2 (b) 1 h1 (c) 2 h1  h2 h1  h2 (d) h1  h2 h1  h2 - : Rough Space : - [6] Physics & Chemistry-XII 19.  number of identical equilateral prisms are kept in contact, as shown in the figure. If deviation through a single prism is , then consider the following statements (m is an integer) 2 4 1 3 5 I. if ( = 2 m), deviation through  prisms is zero II. if ( = 2 m +1), deviation through  prisms is  III. if  = 2 m, deviation through  prisms is  IV. if  = (2 m +1), deviation through  prisms is zero (a) statements I and III are true (b) statements I and II are true (c) statement I and IV are true (d) statements III and IV are true 20. An object is kept on the top of a glass slab A of thickness 20 cm and refractive index 1.5. The slab covers the top of a container B containing water of refractive index = 4/3 up to height 30 cm. The container is placed over a concave mirror C, as shown in the figure. Now the slab and container is replaced by a slab of thickness 50 cm and refractive index = 1.4 and placed over the same concave mirror. The shift position of final image in second condition with respect to initial condition is (a) zero (b) upward (c) downward (d) cannot be determined A µ=3/2 µ=4/3 B C 21. Two light rays 1 and 2 are incident on two faces AB and AC on an isosceles prism, as shown in the figure. The rays emerge from the side BC. Then (a) minimum deviation of the ray 1 > minimum deviation of ray 2 (b) minimum deviation of the ray 1 < minimum deviation the ray 2 (c) minimum deviation of the ray 1 = minimum deviation of the ray 2 (d) can not be determined. 1 A 30° 2 B 75° 75° C - : Rough Space : - [7] Physics & Chemistry-XII 22. A double slit of separation 0.1 cm is illuminated by white light. A coloured interference pattern is formed on a screen 100 cm away. If a pin hole is located in this screen at a distance of 2 mm from the central fringe the wavelengths in the visible spectrum which will be absent in the light transmitted through the pin hole are (a) 5714 Å and 4444 Å (b) 6000 Å and 5000 Å (c) 5500 Å and 4500Å (d) 5200 Å and 4200 Å 23. In a sample of hydrogen like atoms all of which are in ground state, a photon beam containing photons of various energies are passed. In absorption spectrum, five dark lines ar observed. The number of bright lines in the emission spectrum will be (assume that all transitions take place) (a) 5 (b) 10 (c) 15 (d) none of these 24. Hydrogen atoms absorb radiations of wavelength 0 and consequently emit radiations of six different wavelengths of which two wavelengths are shorter than 0. Choose the wrong statement (a) the final excited state of the atoms is n = 4 (b) the initial state of the atoms may be n = 2 (c) the initial state of the atoms may be n = 3 (d) there are three transitions belonging to Lyman series. 25. If the frequency of k x-ray emitted by the element with atomic number 41 be f, then the frequency of k x-ray emitted from the element with atomic number 61 will be (a) 1681 f (b) 3721 f (c) 9 f (d) 4 f 3721 1681 4 9 26. The wavelengths of k x-ray from lead isotopes Pb204, Pb206; Pb208 and 1, 2 and 3 respectively, choose the correct alternative (a) 1 < 2 < 3 (b) 1 > 2 > 3 (c) 1 = 2 = 3 (d) none of these - : Rough Space : - [8] Physics & Chemistry-XII 27. A nucleus X initially at rest, undergoes alpha decay according to equation 232 X  A Y  what fraction of the total energy released in the decay will be the kinetic energy of the alpha particle? (a) 90 92 (b) 228 232 (c) 228 1 232 (d) 2 28. Radon decays to polonium according to the decay scheme Rn222 decay Po218 , which of the following statement is false 88 3.8 days 86 (a) If the original mass of radon in a closed container was 1 mg, the amount of random left after 11.4 days will be 0.125 mg (b) Activity of radon after 7.6 days will be N = (5.3 × 10–7 No)s–1, where No is the original number of atoms of radon. (c) the decay constant of radon is 2.1 × 10–6s–1 (d) 60% of the radon will decay in 10 days approximately. 29. In a Young’s double slit experiment, let  be the fringe width and let I0 be the intensity at the central bright fringe. At a distance x from the central bright fringe, the intensity will be  x  (a) I0 cos    (b) I0 cos2  x      x  (c) I0 cos2    (d) (d)  I0 cos 4 2  x               30. When photons of energy 4.25 eV strikes the surface of a metal, the ejected photoelectrons have maximum kinetic energy TA eV and the de-Broglie’s wavelength A. The maximum kinetic energy of photoelectrons liberated from another metal B by photons of energy 4.7 eV is TB = (TA – 1.5)eV. If the de-Broglie wavelength of these photoelectrons is B = 2A, then (a) the work function of A is 2.25 eV (b) the work function of B is 3.00 eV (c) TB = 1.70 eV (d) none of these - : Rough Space : - [9] Physics & Chemistry-XII 31. A solution containing 0.319 g of complex CrCl3 . 6H2O was passed through cation exchanger and the solution given out was neutralised by 28.5 ml of 0.125 M NaOH. The correct formula of complex is (a) [Cr(H2O)4Cl2] Cl (b) [Cr(H2O)6]Cl3 (c) [Cr(H2O)5Cl]Cl2 (d) [Cr(H2O)3Cl3] 32. A metal complex having composition Cr(NH3)4 Cl2Br has been isolated in two forms (A) and (B). The form (A) reacts with AgNO3 to give a white precipitate readily soluble in dilute aqueous ammonia, whereas (B) gives a pale yellow precipitate soluble in concentrated ammonia. The formula of (A) and (B) are respectively. (a) [Cr(NH3)4 Cl2]Br and [Cr(NH3)4 Br . Cl]Cl (b) [Cr(NH3)4 Br . Cl]Cl and [Cr(NH3)4 Cl2]Br (c) [Cr(NH3)4 Cl2]Br of each (A) and (B) (d) [Cr(NH3)4 Br . Cl]Cl of each (A) and (B) 33. In the above question (i.e., 32), magnetic moments (spin only value) in each (A) and (B) will be (a) 3.87 B.M. in each (A) and (B) (b) 2.87 B.M. in (A) and 3.87 B.M. in (B) (c) 0 in (A) and 3.87 B.M. in (B) (d) 3.87 B.M. in (A) and 0 in (B) 34. The molarity and molality of a solution are M and m respectively. If the molecular weight of the solute is M´, the density of the solution in terms of M, m and M´ is (a) M  1 + M'  (b) m  1 + M'  (c) M '  1 + M  (d) M '  1 + 1000 m 1000   M 1000   m 1000   M  35. 3.75 g of a mixture of CaCO3 and MgCO3 is dissolved in 1 litre of 0.1 N HCl to liberate 0.04 mole of CO2. The % of each constituent of the mixture are: (a) 45% CaCO3 and 55% MgCO3 (b) 55% CaCO3 and 45% MgCO3 (c) 65% CaCO3 and 35% MgCO3 (d) 75% CaCO3 and 25% MgCO3 - : Rough Space : - [10] Physics & Chemistry-XII 36. In the above question (i.e. 35), the mole of acid used is (a) 0.2 mole (b) 0.02 mole (c) 0.025 mole (d) 0.03 mole 37. Which of these compounds is amphoteric? I. Al(OH)3 II. Ba(OH)2 III. Zn(OH)2 (a) I only (b) II only (c) I and III only (d) II and III only 38. Which substance participates readily in both acid-base and oxidation-reduction reactions? (a) Na2CO3 (b) KOH (c) KMnO4 (d) H2C2O4 39. The triple point of CO2 occurs at 5.1 atm and –56°C. Its critical temperature is 31°C. Solid CO2 is more dense than liquid CO2. Under which combination of pressure and temperature is liquid CO2 stable at equilibrium? (a) 10 atm and –25°C (b) 5.1 atm and –25°C (c) 10 atm and 33° C (d) 5.1 atm and –100°C 40. The vapour pressure of water at 20°C is 17.54 mmHg. What will be the vapour pressure of the water in the apparatus shown after the piston is lowered, decreasing the volume of the gas above the liquid to one half of its initial volume? (Assume no temperature change) (a) 8.77 mm Hg (b) 17.54 mm Hg (c) 35.08 mm Hg (d) between 8.77 and 17.54 mm Hg 41. Al3+(aq) + 3e–  Al(s); E° = –1.66 V Cu2+(aq) + 2e–  Cu(s); E° = +0.34 V What voltage is produced under standard conditions by combining the half-reductions with these Standard Electrode Potentials? (a) 1.32 V (b) 2.00 V (c) 2.30 V (d) 4.34 V - : Rough Space : - [11] Physics & Chemistry-XII 42. For which of these oxidation/reduction pairs will the reduction potential vary with pH? AmO2+ I. AmO+ II. II. AmO2+ Am4 III. III. Am4 Am2 (a) I only (b) II only (c) I and II only (d) I, II and III 43. 2Ag+(aq) + Cu(s)  Cu2+(aq) + 2Ag(s). The standard potential for this reaction is 0.46 V. Which change will increase the potential the most? (a) Doubling the [Ag+] (b) Halving the [Cu2+] (c) Doubling the size of the Cu(s) electrode (d) Decreasing the size of the Ag electrode by one half O O 44. B 1) N2H4  Zn-Hg/ HCl  A O In the above reactions, A and B are respectively (a) O (A) O and O O (B) O O (b) in both the case (c) O O and (A) O O (B) (d) and (A) O O (B) - : Rough Space : - [12] Physics & Chemistry-XII 45. Rank the following in decreasing order of their acidic strengths. O N OH N H H (A) H (B) (C) CH3 (D) (a) A > C > B > D (b) A > D > B > C (c) A > D > C > B (d) D > A > C > B 46. (I) Br, which is not correct about (I) (a) I is more soluble than bromocyclopropane in water or in polar protic solvent (b) I gives pale yellow ppt. on addition with AgNO3 (c) I is having lower dipole moment than bromocyclo propane (d) I have more ionic character than Br 47. Which of the following rings is highly strained? (a) O O (b) O O (c) O O (d) N H O 48. Arrange the following in order of C – Br bond strength in polar solvent. Br CH3 II. Br Br III. CH Br IV. H (a) I < II < III < IV (b) II < IV < I < III (c) IV < III < II < I (d) II < I < III < IV - : Rough Space : - [13] Physics & Chemistry-XII 49. O  ROH/ H+ P (major organic product). Then product P is OR OR OR (a) (b) O OR O (c) O CH3 OR (d) O 50. Which of the following is strongest base? (a) H3C N CH3 (b) H3C N CH3 CH3 (c) H3C N CH3 CH3 (d) H3C N CH3 CH3 51. Arrange decreasing order of reactivity of these compounds for nucleophilic substitution reaction O || I. CH3CH2O – S– CF3 II. CH3CH2O – TsCl III. || O CH3 – CH – CH3 | OH IV. CH3 – CH – OH | C6 H5 (a) III > IV> I >II (b) III > IV > II >I (c) I > II > III > IV (d) I > II > IV > III 52. About the, Hydrolysis of isocyanides, which of the following statements is incorrect? (a) Acidic hydrolysis of isocyanides leads to the formation of a primary amine and formic acid (b) Alkaline hydrolysis of isocyanides leads to the formation of a primary amine and salt of formic acid (c) In the hydrolysis of isocyanides, electrophile and nucleophile attack on the same site. (d) none of these - : Rough Space : - [14] Physics & Chemistry-XII 53. O 1 equiv. OH OH C H O A NaBH4  B  H3O  D. In the above sequence, ‘D’ is (a) H OH C H O O (b) H OH CH2 – OH OCH2 – CH2 – OH (c) C H O (d) CH2 – O – CH2 – CH2 – OH 54. An ideal solution has two components A and B. A is more volatile than B i.e., po > po and po > p . A B If XA and YA are mole fractions of components A in liquid and vapour phase, then A total (a) XA = YA (b) XA > YA (c) XA < YA (d) data insufficient 55. The freezing point of a solution containing 0.2 g of acetic acid in 20.0 g benzene is lowered by 0.45°C. Calculate the degree of dimerization of acetic acid in benzene. Kf for benzene is 5.12 K mol–1 kg (a) 0.527 (b) 0.80 (c) 0.945 (d) none of these 56. What Fraction (n/N) of the lattice sites are vacant at 298 K for a crystal for which the energy required to make a defect is 1 eV. (1 eV = 1.602 × 10–19J) (a) 1.24 × 10–17 (b) 1.24 × 10–18 (c) 1.24 × 10–19 (d) none of these - : Rough Space : - [15] Physics & Chemistry-XII 57. The approach to the following equilibrium was observed kinetically from both directions. d[PtCl2 ] PtCl42– + H2O   Pt(H2O)Cl3– + Cl– at 25°C. It was found that – 4 = (3.9 × 10–5) dt [PtCl42–] – (2.1 × 10–3) [Pt(H2O)Cl3–][Cl–]. The equilibrium constant for the complexation of the fourth Cl– by Pt(II) is w (a) 52.85 (b) 53.85 (c) 54.85 (d) none of these 58. Bicyclohexane was found to undergo two parallel first order rearrangements. At 730 K, the first order rate constant for the formation of cyclohexene was measured as 1.26 × 10–4 s–1, and for the formation of methyl cyclopentene the rate constant was 3.8 × 10–5 s–1. The percentage distribution of cyclohexene and methyl cyclopentene are respectively (a) 21% and 79% (b) 77% and 23% (c) 25% and 75% (d) 27% and 73% 59. For the precipitation of positively charged colloidal sol, which of the following has maximum floculation value? (a) SO42– (b) PO43– (c) [Fe(CN)6]4– (d) Cl– O 60. NH H+ / H2O Product. Which of the following is correct about the product? (a) product obtained is the monomer of polyamide known as nylon-6, 6, which is thermosetting plastic (b) product obtained is the monomer of polyamide known as nylon-6, which is thermoplastic. (c) product obtained is the monomer of polyamide known as nylon-6, which is thermosetting plastic (d) product obtained is the monomer of polyamide known as nylon-6, 6, which is thermo plastic 🙤🙦🙥🙧 - : Rough Space : - [16]