# CBSE - Kinematics

## Transcription

CBSE - Kinematics

http://iitscholars.com http://iitvidya.com http://iitscholar.com 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. MATHEMATICS If a line OP through the origin O makes angles , 45° and 60° with x, y and z axis respectively then the 12. direction cosines of OP are (A) 1/ 2, 1/ 2, 1/ 2 (B) 1/2,1/2, 1/ 2 (C) 1/2, 1/ 2 , 1/2 (D) none of these An equation of z–axis is (A) z = 0, x = 0 (B) z = 0, y = 0 (C) x = 0, y = 0 (D) x = k, y = –k., (k 0) The ratio in which the yz plane divides the segment joining the points (–2, 4, 7) and (3, –5, 8) is (A) 2 : 3 (B) 3 : 2 (C) 4 : 5 (D) –7 : 8 The coordinates of a point equidistant from the points (a, 0, 0), (0, a, 0), (0, 0, a) and (0, 0, 0) are (A) (a/3, a/3, a/3) (B) (a/2, a/2, a/2) (C) (a, a, a) (D) (2a, 2a, 2a) 13. If O is the origin and the line OP of length r makes an angle with x–axis and lies in the xz plane, then the 14. coordinate of P are (A) (r cos , 0, r sin ) (B) (0, 0, r sin) (C) (0, 0, r cos) (D) (r cos, 0, 0) If a line is equally inclined with the coordinate axes, then the angle of inclination is (A) cos–1 (1/2) (B) cos–1 1 / 2 (C) cos–1 (1/ 3 ) (D) cos–1( 3 / 2) A line makes an angle of 60° with each of x and y axis, the angle which it makes with z axis is (A) 30° (B) 45° 15. (C) 60° (D) none of these If a1, a2, … form a G.P. and ai > 0 for all i 1, then log a m log a m 1 log a m 2 log a m 3 log a m 4 log a m 5 is equal to log a m 6 log a m 7 log a m 8 (A) log (am + 8) – log (am) (B) log (am + 8) + log (am) (C) zero 16. (D) log2am+ 4 If the system of equations x + ay + az = 0; bx + y + bz = 0; cx + cy + z = 0, where a, b, c are non–zero and non– unity has a non–trival solution, then the value of 17. a b c is 1 a 1 b 1 c (A) zero (B) 1 abc (C) –1 (D) 2 a b2 c2 x 2 3x x 1 x 3 If px4 + qx3 + rx2 + sx + t = x 2 1 2 x x 3 then 18. x 2 3 x 4 3x p is equal to (A) –5 (B) –4 (C) –3 (D) –2. If A and B are symmetric matrices then AB – BA is a (A) symmetric matrix (B) skew symmetric matrix (C) diagonal matrix (D) null matrix. 19. 3 1 1 1 2 If P 2 ,A and Q = P AP' then P' 1 3 0 1 2 2 (Q2005) P is equal to 1 2005 (A) 1 0 3 (B) 2 0 2005 1 1 3 1 2 1 (C) (D) 2 . 3 1 2005 2 2005 If A is matrix such that A2 + A + 2I = 0, then (A) A is non-singular (B) A is symmetric (C) A = 0 (D) none of these If a, b and c are all different from zero such that 1 1 1 a 1 1 1 0 , then the matrix A 1 1 b 1 a b c 1 1 1 c is (A) symmetric (B) singular (C) a skew symmetric matrix (D) none of these Consider the system of equation ax1 + b1y + c1z = 0, a2x a1 b1 c1 + b2y + c2z = 0, a3x + b3y + c3z = 0 if a 2 b 2 c2 0, a 3 b 3 c3 then the system has (A) infinite number of solutions (B) only one solution (C) no solution (D) none of these If A and B are two invertible matrices of the same order, then the adjoint of AB is equal to (A) (adj A) + (adj B) (B) (adj B) (adj A) (C) adj (BA) (D) none of these Consider an infinite geometric series with first term a and common ratio r. If its sum is 4 and the second term is 3/4, then 7 3 (A) a , r (B) a = 2, r = 3/8 4 7 3 1 (C) a , r (D) a = 3, r = 1/4 2 2 Let S1, S2, … be squares such that for each n 1, the length of a side of Sn equals the length of the diagonal of Sn+1. If the length of a side of Si is 10 cm, then for which of the following values of n is the area of Sn less than 1 sq. cm? (A) 7 (B) 8 (C) 11 (D) none of these If cos (x – y), cosx and cos (x + y) are in H.P., then cosx y sec is equal to 2 http://iitscholars.com http://iitvidya.com http://iitscholar.com http://iitscholars.com http://iitvidya.com http://iitscholar.com (A) (C) 2 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 2 (B) 1 31. 2 (D) none of these If log3 2, log3 (2x – 5) and log3 (2x – 7/2) are in A.P., then x is equal to (A) 2 (B) 3 (C) 4 (D) 2, 3 If a, b, c are in arithmetic progression then 1 1 1 are in , , a b a c b c (A) A.P. (B) G.P. (C) H.P. (D) none of these If (m + 1)th, (n + 1)th and (r + 1)th term of an A.P. are in G.P. and m, n, r are in H.P., then the ratio of the first term of the A.P. to its common difference in terms of n is (A) n/2 (B) –n/2 (C) n/3 (D) –n/3 The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is (A) 6 (B) 18 (C) 12 (D) 9 A person wishes to make up as many different parties as he can out of 20 friends, each party consisting of the same number. The number of persons he should invite at a time is (A) 8 (B) 10 (C) 12 (D) none of these. The number of ways in which 30 marks can be allotted to 8 questions if each question carries at least 2 marks, is (A) 115280 (B) 117280 (C) 116280 (D) none of these. In a network of railways, a small island has 15 stations. The number of different types of tickets to be printed for each class, if every station must have tickets for other station, is (A) 230 (B) 210 (C) 340 (D) none of these. A father with 8 children takes them 3 at a time to the zoological garden, as he can without taking the same 3 children together more than once. Then (A) number of times he will go is 56 (B) number of times each child will go is 21 (C) number of times a particular child will not go is 35 32. 33. 34. 35. A particle is moving on a straight line, where its position s, in meters, as a function of time t in seconds is given by s = t3 + at2 + bt + c where a, b, c are constants. It is known that at t = 1 sec; the position of the particle is s = 7m, velocity is 7 m/s and acceleration is 12 m/s2. The values of a, b, c are respectively (A) 3, 2, 5 (B) -3, 2, 5 (C) 3, -2, 5 (D) none of these A and B play a game of tennis. The situation of the game is as follows; if one scores two consecutive points after a deuce he wins; if loss of a point is followed by win of a point, it is deuce. The chance of a server to win a point is 2/3. The game is at deuce and A is serving. Probability that A will win the match is, (serves are changed after each game) (A) 3/5 (B) 2/5 (C) 1/2 (D) 4/5 A die is thrown three times and the sum of three numbers obtained is 15. The probability of first throw being 4 is (A) 1/18 (B) 1/5 (C) 4/5 (D) 17/18 Six different balls are put in three different boxes, no box being empty. The probability of putting balls in the boxes in equal numbers is (A) 3/10 (B) 1/6 (C) 1/5 (D) none of these Fifteen coupons are numbered 1, 2, 3, .... 15. Seven coupons are selected at random one at a time with replacement. The probability that the largest number appearing on the selected coupon is 9, is 6 36. 37. (D) all of these. 38. A boat is to be manned by eight men of whom 2 can only row on bow side and 1 can only row on stroke side; the number of ways in which the crew can be arranged is (A) 4360 (B) 5760 (C) 5930 (D) none of these. 39. The number of proper divisors of 2520 is (A) 46 (B) 52 (C) 64 (D) none of these A man who swims at the rate of 5 m/s in still water wishes to cross a river of breadth 20 m flowing at the rate of 3 m/s. The time taken by man to cross the river is (A) 8s (B) 6s 40. (C) 5s (D) 4s 7 9 8 (A) (B) 16 15 7 7 9 8 (C) (D) none of these 157 Three persons A1, A2 and A3 are to speak at a function along with 5 other persons. If the person speak in random order, the probability that A1 speaks before A2 and A2 speaks before A3 is (A) 1/6 (B) 3/5 (C) 3/8 (D) none of these A fair coin is tossed a fixed number of times. If the probability of getting 7 heads is equal to getting 9 heads, then the probability of getting 2 heads is, (A) 15/28 (B) 2/15 13 (C) 15/2 (D) none of these ˆ ˆ ˆ ˆ If a i j k,b 4i 3jˆ 4kˆ and c ˆi ˆj kˆ are linearly dependent vectors and | c | = 3 , then (A) = 1, = -1 (B) = 1, 1 (C) = -1, 1 (D) = 1, = 1 Let a 2iˆ ˆj 2kˆ and b ˆi ˆj . If c is a vector such that a.c = | c |, | c - a | = 2 2 and the angle between a b and c is 30°, then a b c is equal to (A) 2/3 (C) 2 (B) 3/2 (D) 3 Let a 2iˆ ˆj kˆ , b ˆi 2jˆ kˆ and a unit vector c be coplanar. If c is perpendicular to a , then c is equal to http://iitscholars.com http://iitvidya.com http://iitscholar.com http://iitscholars.com http://iitvidya.com http://iitscholar.com ˆj kˆ 2 1 41. 42. 43. 1 ˆ ˆ ˆ i j k 3 1 ˆ ˆ 1 ˆ ˆ ˆ (C) (D) i 2j i j k 5 2 51. The distance in meters described by a particle in t seconds is given by s = aet + be-t. The acceleration of the particle at instant t is 52. (A) s m/s2 (B) ab m/s2 (C) s/(a2 + b2) m/s2 (D) none of these If a both moves so that the distance sm which it moves in t seconds is given by the relation s = at3. The time t when magnitude of the velocity and acceleration are equal, is 53. (A) 2s (B) 3s (C) 4s (D) none of these If and are unit vectors, then c a, b (A) 2 (B) 2 2 a b b c c a does not exceed (A) 4 (C) 8 44. 45. 46. 47. (B) 9 (D) 6 If a r b ta and a.r 3, where a 2iˆ ˆj kˆ and b ˆi 2jˆ kˆ then r equals 7 2 7 1 (A) ˆi ˆj (B) ˆi ˆj 6 5 6 3 7ˆ 2ˆ 1 ˆ (C) i j k (D) none of these 6 3 3 If | a b | | a |, then b.(2a b) equals (A) 0 (B) 1 (C) 2a.b (D) none of these Two equal forces P and P act at a point and their resultant is P. The angle between the forces is (A) /3 (B) 2/3 (C) /2 (D) /6 The angle at which two forces of magnitude P + Q and P - Q ( P Q) must act so that their resultant is of magnitude P Q is 2 49. 50. 55. 56. 57. (B) tan-1 (1/20) (D) tan-1 (1/120) CHEMISTRY Corundum is: (A) SrO2 (B) Al2O3 (C) CaCl2 (D) Cu2Cl2. By which process Pb and Sn are extracted respectively? (A) Carbon reduction — self reduction (B) Self reduction — carbon reduction (C) Electrolytic reduction — cyanide process (D) Cyanide process — electrolytic reduction. When MnO2 is fused with KOH, a coloured compound is formed, the compound and its colour is: (A) K2MnO4, purple green (B) KMnO4, purple (C) Mn2O3, brown (D) Mn3O4, black. The metal that cannot be obtained by electrolysis of the aqueous solution of their salts is: (A) Ag (B) Mg (C) Cu (D) Cr. The chemical composition of ‘slag’ formed during the smelting process in the extraction of copper is: (A) Cu2O + FeS (B) FeSiO3 (C) CuFeS2 (D) Cu2S + FeO. Carbon monoxide reduction process is used for the extraction of : (A) Cu (B) Ag (C) Na (D) K. Which represents calcination? 2AgCl + H2O (A) 2Ag + 2HCl + [O] 2ZnO (B) 2Zn + O2 2ZnO + 2SO2 (C) 2ZnS + 3O2 58. 2 P 2 Q2 (A) cos-1 2 2 2(P Q ) 2(P 2 Q2 ) (B) cos-1 2 2 2P 4Q 48. 54. (A) tan-1 (1/10) (C) tan-1 (1/30) 59. 60. (C) /2 (D) none of these When two equal forces are inclined at an angle 2, their resultant is twice as great as when they act at an angle 2. 61. The ratio |cos /cos| is equal to (A) 2 (B) 3 (C) 1/2 (D) 1/ 3 If the resultant of two velocities u = 2 cm/s and v = 4 62. cm/s is w = 2 3 cm/s, then angle between u and v is given by 63. (A) 30° (B) 60° (C) 90° (D) 120° A thief, when detected, jumps out of a running train at right angles to its direction with velocity 5m/min. If the velocity of the train is 36 km/h, the direction in which the 64. thief falls makes an angle of with the direction of the train where is MgO + CO2. (D) MgCO3 The hardness of water is due to …. Metal ions (A) Cu2+ and Na+ (B) Mg2+ and K+ (C) Ca2+ and Mg2+ (D) Zn2+ and Ba2+. When silicon is boiled with caustic soda solution, the gas evolved is: (A) O2 (B) SiH4 (C) H2 (D) None of these. The volume strength of 1.5 N H2O2 solution is: (A) 4.8 (B) 8.4 (C) 3.0 (D) 8.0. An inorganic compound liberates O2 when heated, turns an acid solution of KI brown and reduces acidified KMnO4. The substance is: (A) H2O2 (B) D2O (C) KNO3 (D) Pb(NO3)2. Temporary hardness is caused due to the presence of : (A) CaSO4 (B) CaCl2 (C) CaCO3 (D) Ca(HCO3)2. Both temporary and permanent hardness are removed on boiling water with: (A) Ca(OH)2 (B) Na2CO3 (C) CaCO3 (D) CaO. Para hydrogen is: (A) less stable than ortho hydrogen (B) more stable than ortho hydrogen http://iitscholars.com http://iitvidya.com http://iitscholar.com http://iitscholars.com http://iitvidya.com http://iitscholar.com 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. (C) as stable as ortho hydrogen (D) none of the above. An inorganic compound gives off O2 when heated, turns an acid solution of KI violet, and reduces acidified KMnO4. The compound is : (A) SO3 (B) KNO3 (C) H2O2 (D) all of these. Point out the incorrect statement (A) Hardness of water depends upon its soap consuming power (B) Temporary hardness is due to bicarbonates of calcium and magnesium (C) Permanent hardness is due to soluble sulphates, chlorides and nitrates of Ca and Mg. (D) Permanent hardness can be removed by boiling water. Ordinary hydrogen is a mixture of: (A) 75% ortho –H2 + 25% para-H2 (B) 25% ortho – H2 + 75% para – H2 (C) 50% orhto – H2 + 50% para – H2 (D) 99% para – H2 + 1% ortho – H2. A given solution of H2O2 is 30 volume. Its concentration in terms of molarity is: (A) 9.1 M (B) 2.68 M (C) 2.5 M (D) 26.8 M. The following compounds have been arranged in order of their increasing thermal stabilites. Identify the correct order. K2CO3 (I) MgCO3(II) CaCO3(III) BeCO3(IV) (A) I < II < III < IV (B) IV < II < III < I (C) IV < II < I < III (D) II < IV < III < I. When orthoboric acid (H3BO3) is heated the residue left is: (A) boron (B) metaboric acid (C) boric anhydride (D) borax. Borax on heating with cobalt oxide forms a blue bead of : (A) Co(BO2)2 (B) CoBO2 (C) Co3(BO3)2 (D) Na3Co(BO3)2. The borax bead is chemically: (A) B2O3 (B) Na2B4O7 (C) Na3BO3 (D) B2O3 + NaBO2. Which species doe not exist? (A) [BF6]3– (B) [AlF6]3– 3– (C) [GaF6] (D) [InF6]3–. H3BO3 is: (A) monobasic and Lewis acid (B) monobasic and Bronsted acid (C) monobasic and strong lewis acid (D) tribasic and weak Bronsted acid. H2O is dipolar whereas BeF2 is not. It is because (A) the electronegativity of F is greater than O (B) H2O involves H-honding whereas BeF2 is discrete molecule (C) H2O is linear and BeF2 is angular (D) H2O is angular and BeF2 is linear. Which acid is formed when SiF4 reacts with water? (A) H2SO4 (B) H2SiF4 (C) H2SiF6 (D) None of these. Which of the following shows bond in silicone? (A) Si—C—Si—O—Si (B) Si—C—Si—C—Si | | | (C) —Si— O — Si— O — Si— (D) Si—Si—Si—Si. 78. 79. 80. 81. 82. 83. 84. 85. 86. 87. 88. 89. 90. Which is formed when SiCl4 vapours are passed over hot Mg? (A) SiCl2 + MgCl2 (B) Si + MgCl2 (C) Mg2Si + Cl2 (D) MgSiCl6. The number of P—O—P bonds in cyclic metaphosphoric acid is: (A) zero (B) two (C) three (D) four. P4O10 has short and long P—O bonds. The number of short P—O bonds in this compound is: (A) 1 (B) 2 (C) 3 (D) 4. The number of S—S bonds in sulphur trioxide trimer (S3O9) is: (A) three (B) two (C) one (D) zero. The correct order of bond angles in H2S, NH3, BF3, and SiH4 is: (A) H2S < NH3 < BF3 < SiH4 (B) NH3 < H2S < SiH4 < BF3 (C) H2S < NH3 < SiH4 < BF3 (D) H2S < SiH4 < NH3 < BF3. Generally H2O exists as a liquid while H2S as a gas because: (A) H2O shows hydrogen bonding (B) molecular weight of H2S is higher (C) bond angle in H2O is larger (D) size of ‘O’ atom is smaller than ‘S’ atom. In the species O2, O2+, O2– and O22+, the correct decreasing order of bond strength is: (A) O2 > O2+ > O2– > O22(B) O2+ > O2 > O2– > O22(C) O22– > O2– > O2+ > O2 (D) O22+ > O2– > O2 > O2+. Which of the following statements is correct? (A) All halogens form oxoacids (B) Only chlorine and bromine form oxoacids (C) All halogens except fluorine form oxoacids (D) Only iodine forms oxoacid. Increasing order of strength of oxoacids of chlorine is: (A) HClO < HClO2 < HClO4 < HClO3 (B) HClO4 < HClO2 < HClO < HClO3 (C) HClO < HClO2 < HClO3 < HClO4 (D) none of these. Thermal stability of hydrogen halide follows the order: (A) HI > HBr > HCl > HF (B) HI > HF > HBr > HCl (C) HI > HBr > HF > HCl (D) HF > HCl > HBr > HI. XeF6 on complete hydrolysis gives: (A) XeO3 (B) XeO (C) XeO2 (D) Xe. Which noble gas is most soluble in water? (A) He (B) Ar (C) Ne (D) Xe. How many lone pair of electrons are present on Xe in XeOF4? (A) 1 (B) 2 http://iitscholars.com http://iitvidya.com http://iitscholar.com http://iitscholars.com http://iitvidya.com http://iitscholar.com (C) 3 (D) 4. 91. Which is planar molecule? (A) XeO4 (B) XeF4 (C) XeOF4 (D) XeO2F2. 92. The stability of the following alkali metal chlorides follows the order: (A) LiCl > KCl > NaCl > CsCl (B) CsCl > KCl > NaCl > LiCl (C) NaCl > KCl > LiCl > CsCl (D) KCl > CsCl > NaC > LiCl. 93. Baking soda is: (A) NaHCO3 (B) NaHCO36H2O (C) Na2CO3 (D) Na2CO3 . 10H2O. 94. The role of fluorispar (CaF2) which is added in small quantities in the electrolytic reduction of alumina dissolved in fused cryolite (Na3AlF6) is: (A) as a catalyst (B) to make the fused mixture very conducting (C) to increase the temperature of the melt (D) to decrease the rate of oxidation of carbon at the anode. 95. Which statement is correct? (A) BCl3 and AlCl3 are both Lewis acids and BCl3 is stronger than AlCl3 (B) BCl3 and AlCl3 are both Lewis acids and AlCl3 is stronger than BCl3 (C) BCl3 and AlCl3 are both equally strong Lewis acids (D) Both BCl3 and AlCl3 are not Lewis acids. 96. Potash alum is water soluble and ionizes in aqueous solution to give: (A) an aluminium salt (B) a cobalt salt (C) a copper salt (D) a nickel salt. 97. ClO2 is an anhydride of: (A) chlorous acid (HClO2) (B) chloric acid (HClO3) (C) mixed anhydride of HClO2 and HClO3 (D) none of the above. 98. Strongest reducing agent is: (A) H2O (B) H2S (C) H2Se (D) H2Te 99. The strongest oxidizing agent is (A) HNO3 (B) H2SO4 (C) H2SO3 (D) H2S2O3. 100. In silicon dioxide: (A) each silicon atom is surrounded by four oxygen atoms and each oxygen atom is bonded to two silicon atoms (B) each silicon atom is surrounded by two oxygen atoms and each oxygen atom is bonded to two silicon atoms (C) silicon atom is bonded to oxygen atoms (D) there are double bonds between silicon and oxygen atoms. PHYSICS B v R M 102. 103. 104. 105. Q (A) zero 1 (B) BR 2 , and M is at a higher potential 2 (C) RB, and Q is at a hither potential (D) 2RB, and Q is at a hither potential The magnitude of earth’s magnetic field at a plane is B0 and the angle of dip is . A horizontal conductor of length , lying north-south, moves eastwards with a velocity . The emf induced across the rod is (A) zero (B) B0 (C) B0 sin (D) B0 cos A horizontal ring of radius r spins about its axis with an angular velocity in a uniform vertical magnetic field of magnitude B. The emf induced in the ring is (A) zero (B) r 2 R 1 2 (C) (D) Br 2 Br 2 A long solenoid of N turns has a self-inductance L and area of cross-section A. When a current i flows through the solenoid, the magnetic field inside it has magnitude B. The current i is equal to BAN (A) (B) BANL L BN B (C) (D) AL ANL The network shown in the figure is part of a complete circuit. If at a certain instant, the current I is 5 A, and is decreasing at a rate 103 A/s then VB – VA is 5 m H 1 + B A I1 5 V (A) 20 V (B) 15 V (C) 10 V (D) 5 V 106. In the circuit shown, the cell is ideal. The coil has an inductance of 4 H and zero resistance. F is a fuse of zero resistance and will blow when the current through it reaches 5 A. The switch is closed at t = 0. The fuse will blow F =2V L =4H S (A) almost at once (B) after 2 s (C) 5 s (D) after 10 s 107. In the circuit shown, S is joined to Y for a long time, and then X is joined to Z. The total heat produced in R2 is R2 101. A thin semicircular conducting ring of radius R is falling with its plane vertical in a horizontal magnetic induction B . At the position MNQ, the speed of the ring is . The potential difference developed across the ring is L X Z Y R1 http://iitscholars.com http://iitvidya.com http://iitscholar.com http://iitscholars.com http://iitvidya.com http://iitscholar.com (A) L 2 2R 12 (B) L 2 2R 22 114. L 2 R 2 L 2 (D) 2 2 3 2R1 R 2 2R1 108. Two coils of inductances L1 and L2 are linked such that their mutual inductance is M (A) M = L1 + L2 1 115. (B) M (L1 L2 ) 2 (C) the maximum value of M is (L1 + L2) (D) the maximum value of M is L1L2 109. In the circuit shown, the coil has inductance and resistance. When X is joined to Y, the time constant is during growth of current. When the steady state is 116. reached, heat is produced in the coil at a rate P. X is now joined to Z (C) Y X Z (A) the total heat produced in the coil is P 1 117. (B) the total heat produced in the coil is P 2 (C) the total heat produced in the coil is 2P (D) the data given is not sufficient to reach a conclusion 110. A charged capacitor discharged through a resistance R with time constant . The two are now placed in series 118. 1 across an AC source of angular frequency . The impedance of the circuit will be R (A) (B) R 2 (C) (D) 2R 2R 111. An electric lamp designed for operation on 110V AC is 119. connected to a 220 V AC supply, through a choke coil of inductance 2H, for proper operation. The angular frequency of the AC is 100 10 rad/s. If a capacitor is to be used in place of the choke coil, its capacitance must be (A) 1 F (B) 2 F (C) 5 F (D) 10 F 112. A resistance R draws P power when connected to an AC 120. source. If an inductance is now placed in series with the resistance, such that the impedance of the circuit becomes Z, the power drawn will be 2 R R (A) P (B) P Z Z 121. R (C) P (D) P Z 113. An inductance L, a capacitance C and a resistance R may be connected to an AC source of angular frequency , in three different combinations of RC, RL and LC in series. 122. 1 Assume that L . The power drawn by the three C combinations are P1, P2, P3 respectively. then, (A) P1 P2 P3 (B) P1 P2 P3 (C) P1 P2 P3 (D) P1 P2 P3 An electrical heater and a capacitor are joined in series across a 220 V, 50 Hz AC supply. The potential difference across the heater is 90 V. The potential difference across the capacitor will be about (A) 200 V (B) 130 V (C) 110 V (D) 90 V In an AC circuit, the reactance is equal to the resistance. The power factor of the circuit will be 1 (A) 1 (B) 2 1 (C) (D) zero 2 P is a point on the axis of a concave mirror. The image of P, formed by the mirror, coincides with P. A rectangular glass slab of thickness t and refractive index is now introduced between P and the mirror. For the image of P to coincide with P again, the mirror must be moved (A) towards P by ( - 1)t (B) away from P by ( - 1)t (C) towards P by t (1 – 1/) (D) away from P by t (1 – 1/) The light reflected by a plane mirror may form a real image, (A) if the rays incident on the mirror are converging (B) if the rays incident on the mirror are diverging (C) if the object is placed very close to the mirror (D) under no circumstances A transparent sphere of radius R and refractive index is kept in air. At what distance from the surface of the sphere should a point object be placed so as to form a real image at the same distance from the sphere ? (A) R/ (B) R R R (C) (D) 1 1 An air bubble is inside water. The refractive index of water is 4/3. At what distance from the air bubble should a point object be placed so as to form a real image at the same distance from the bubble ? (A) 2R (B) 3R (C) 4R (D) the air bubble cannot form a real image A point source of light at the surface of a sphere causes a parallel beam of light to emerge from the opposite surface of the sphere. The refractive index of the material of the sphere is (A) 1.5 (B) 5/3 (C) 2 (D) 2.5 A thin lens of refractive index 1.5 has a focal length of 15 cm in air. When the lens is placed in a medium of refractive index 4/3, its focal length will become (A) 30 cm (B) 45 cm (C) 60 cm (D) 75 cm A double convex lens, made of a material of refractive index 1, is placed inside two liquids of refractive indices 2 and 3, as shown. 2 > 1 > 3. A wide, parallel beam http://iitscholars.com http://iitvidya.com http://iitscholar.com http://iitscholars.com http://iitvidya.com http://iitscholar.com of light is incident on the lens from the left. The lens will give rise to 2 2 131. 1 3 3 (A) a single convergent beam (B) two different convergent beams 132. (C) two different divergent beams (D) a convergent and a divergent beam 123. A convex lens of focal length 40 cm, a concave lens of focal length 40 cm and a concave lens of focal length 15 cm are placed in contact. The power of this combination in dioptres is 133. (A) + 1.5 (B) - 1.5 (C) + 6.67 (D) - 6.67 124. A short linear object of length b lies along the axis of a concave mirror of focal length f, at a distance u from the mirror. The size of the image is approximately u f (A) b f 1 2 f (B) b u f 1 2 2 125. 126. 127. 128. 129. f u f (C) b (D) b f u f A boy of height 1 m stands in front of a convex mirror. His distance from the mirror is equal to its focal length. The height of his image is (A) 0.25 m (B) 0.33 m (C) 0.5 m (D) 0.67 m A ray of light is incident normally on one of the faces of a prism of apex angle 30º and refractive index 2 . The angle of deviation of the ray is (A) 0º (B) 12.5º (C) 15º (D) 22.5º A ray of light is incident normally on one face of an equilateral prism of refractive index 1.5. The angle of deviation is (A) 30º (B) 45º (C) 60º (D) 75º An astronomical telescope has an angular magnification of magnitude 5 for distant objects. The separation between the objective and the eyepiece is 36 cm. The final image is formed at infinity. The focal lengths f0 of the objective and fe of the eyepiece are (A) 45 cm and –9 cm respectively (B) 50 cm and 10 cm respectively (C) 7.2 cm and 5 cm respectively (D) 30 cm and 6 cm respectively In an astronomical telescope in normal adjustment, a straight black line of length L is drawn on the objective lens. The eyepiece forms a real image of this line. The length of this image is . The magnification of the telescope is L L (A) (B) 1 134. 135. 136. 137. 138. 139. L L 140. 130. Two coherent monochromatic light beams of intensities I and 4I are superposed. The maximum and minimum possible intensities in the resulting beam are (C) L 1 (D) (A) 5I and I (B) 5I and 3I (C) 9I and I (D) 9I and 3I In an Young’s double-slit experiment using identical slits, the intensity at a bright fringe is I0. If one of the slits is now covered, the intensity at any point on the screen will be (A) I0 (B) I0/2 (C) I0/4 (D) I0/(2 2 ) In a Young’s double-slit experiment, the centre bright fringe can be identified (A) as it has greater intensity than the other bright fringe (B) as it is wider than the other bright fringes (C) as it is narrower than the other bright fringes (D) by using white light instead of monochromatic light In a Young’s double-slit experiment, if the slits are of unequal width, (A) fringes will not be formed (B) the positions of minimum intensity will not be completely dark (C) bright fringe will not be formed at the centre of the screen (D) distance between two consecutive bright fringes will not be equal to the distance between two consecutive dark fringes A bird flies down vertically towards a water surface. To a fish inside the water, vertically below the bird, the bird will appear to (A) be farther away than its actual distance (B) be closer than its actual distance (C) move slower than its actual speed (D) none of these. Two coils x and y are placed in a circuit such that a current changes by 2 A in coil x and magnetic flux change of 0.4 Wb occurs in y. The value of mutual inductance of the coils is : (A) 0.8 H (B) 0.2 H (C) 0.5 H (D) 5 H. At what angle should an unpolarized beam be incident on a crystal of 3 , so that reflected beam is polarized ? (A) 45º (B) 60º (C) 90º (D) 0º. The angle of the prism for which there is no emergent ray, if its critical angle is ic, will be : (A) greater than ic (B) less than ic (C) 2ic (D) greater than 2ic. The focal length of the objective of a telescope is 60 cm. To obtain a magnification of 20, the focal length of the eyepiece should be : (A) 2 cm (B) 3 cm (C) 4 cm (D) 5 cm. A ray of light passes through a plane glass slab of thickness t and refractive index = 1.5. The angle between incident ray and emergent ray will be (A) 0º (B) 30º (C) 45º (D) 60º. Magnetic flux in Weber in a closed circuit of resistance 10 varies with time t (s) as = 6t2 – 5t + 1. The magnitude of induced current at t = 0.25 s is (A) 0.2 A (B) 0.6 A http://iitscholars.com http://iitvidya.com http://iitscholar.com http://iitscholars.com http://iitvidya.com http://iitscholar.com 141. 142. 143. 144. (C) 1.2 A (D) 0.8 A. An alternating voltage E (in volt) = 200 2 sin100 t is connected to 1F capacitor through an AC ammeter. The reading of ammeter will be (A) 10 mA (B) 22 mA (C) 40 mA (D) 80 mA. Upto what height should water be filled into a vessel of height 21 cm such that it appears half filled when viewed from above ? 4 for water = 3 (A) 8 cm (B) 10.5 cm (C) 12 cm (D) 14 cm. The magnifying power of an astronomical telescope is 8 and the distance between the two lenses is 54 cm. The focal lengths of eye lens and objective lens will be respectively (A) 6 cm and 48 cm (B) 48 cm and 6 cm (C) 8 cm and 64 cm (D) 64 cm and 8 cm. Two short magnets are placed on a piece of cork which floats on water. The magnets are so placed that the axis of one produced bisects the axis of other at right angles. Then, the cork : 146. A thin, symmetric double-convex lens of power P is cut into three parts A, B and C as shown. The power of A B C (A) A is P 147. 148. 149. Cork 150. (A) rotates only (B) moves along a straight line only (C) has neither translational nor rotational motion (D) has both translational and rotational motion. 145. A far–sighted man cannot focus distinctly on object closer than 120 cm. The lens that will permit him to read from a distance of 40 cm will have a focal length : (A) +30 cm (B) –30 cm (C) +60 cm (D) –60 cm. (B) A is 2P P (C) B is 2P (D) B is 4 Which of the following form virtual and erect images for all positions of the object ? (A) convex lens (B) concave lens (C) concave mirror (D) none of these Two thin lenses, when in contact, produce a combination of power + 10 dioptres. When they are 0.25 m apart, the power is reduced to + 6 dioptres. The powers of the lenses in dioptres, are (A) 1 to 9 (B) 2 and 8 (C) 4 to 6 (D) 5 each A converging lens of focal length f1 is placed in front of and coaxially with a convex mirror of focal length f2. Their separation is d. A parallel beam of light incident on the lens returns as a parallel beam from the arrangement (A) the beam diameter of the incident and reflected beams must be the different (B) d = f1 – 2 | f2 | (C) d = f1 + 2 | f2 | (D) if the entire arrangement is immersed in water, the conditions will remains unaltered. A non-conducting ring of radius r has charge Q. A magnetic field perpendicular to the plane of the ring dB changes at the rate . The torque experience by the dt ring is dB (A) zero (B) Qr 2 dt 1 2 dB dB 2 (C) (D) r Q Qr 2 dt dt ANSWER KEY MATHS 1. 2. 3. 4. 5. 6. 7. 8. 9 10. 11. 12. 13. 14. (C) (C) (A) (B) (A) (C) (B) (C) (C) (B) (B) (A) (A) (A) CHEMISTRY 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. (B) (B) (A) (B) (B) (A) (D) (C) (C) (B) (A) (D) (B) (A) PHYSICS 101. 102. 103. 104. 105. 106. 107. 108. 109. 110. 111. 112. 113. 114. http://iitscholars.com http://iitvidya.com http://iitscholar.com (D) (C) (A) (A) (B) (D) (A) (D) (B) (C) (C) (A) (B) (A) 15. 16 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. (A) (B) (D) (B) (A) (B) (A) (B) (B) (B) (C) (B) (D) (B) (A) (C) (C) (C) (B) (B) (C) (A) (C) (D) (B) (A) (A) (A) (B) (D) (A) (B) (A) (A) (D) (D) 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98. 99. 100. (C) (D) (A) (B) (B) (C) (A) (D) (A) (A) (D) (C) (C) (B) (C) (D) (D) (C) (A) (B) (C) (C) (D) (A) (D) (A) (B) (D) (A) (B) (A) (C) (C) (D) (A) (A) 115. 116. 117. 118. 119. 120. 121. 122. 123. 124. 125. 126. 127. 128. 129. 130. 131. 132. 133. 134. 135. 136. 137. 138. 139. 140. 141. 142. 143. 144. 145. 146. 147. 148. 149. 150. (C) (D) (A) (C) (D) (C) (C) (D) (D) (D) (C) (C) (C) (D) (A) (C) (C) (D) (B) (A) (B) (B) (D) (B) (A) (A) (B) (D) (A) (C) (C) (A) (B) (B) (B) (C)