http://iitscholars.com http://iitvidya.com http://iitscholar.com x 2 y2 1. If (h, k) is the point of intersection of a 2 b2 MATHEMATICS the normals at P and Q, then k is equal to 1. Co-ordinates of the focus of the parabola x – 4x – 8y – 4 = 0 are (A) (0, 2) (B) (2, 1) (C) (1, 2) (D) (-2, -1) 2. The equation of the directrix of the parabola y2 + 4y + 10. 4x + 2 = 0 is (A) x = -1 (B) x = 1 3 3 (C) x (D) x 2 2 3. If the line x – 1 = 0 is the directrix of the parabola y2 – kx + 8 = 0, then one of the values of k is 11. 1 (A) (B) 8 8 1 (C) 4 (D) 4 4. 5. 6. If y = mx + c touches the parabola y2 = 4a(x + a), then a a (A) c (B) c am m m a (C) c a (D) none of these m 12. 13. A man running round a race course notes that the sum of the distance of two flag-posts from him is always 10 meters and the distance between the flag posts is 8 meters. The area of the path he encloses in square meters is (A) 15 (B) 12 (C) 18 (D) 8 14. The radius of the circle passing through the foci of (B) 3 (D) 7/2 x2 y2 1 10 a 4 a 15. 7. The equation 8. ellipse if (A) a < 4 (B) a > 4 (C) 4 < a < 10 (D) a > 10 The value of m for which y = mx + 6 is tangent to represents an x2 y2 1 is 16. 100 49 17 20 (A) (B) 20 17 3 20 (C) (D) 20 3 Let P a sec , b tan and Q a sec , b tan , where the hyperbola 9. a 2 b2 a (B) (C) a 2 b2 b (D) , 2 a 2 b2 b PQ and RS are two perpendicular chords of the rectangular hyperbola xy = c2. If C is the centre of this hyperbola then product of the slopes of CP, CQ, CR and CS is (A) 1 (B) –1 (C) 0 (D) none The locus of the mid–point of the line segment joining the focus to a moving point on the parabola y2 = 4ax is another parabola with directrix (1) x = –a (2) x = – a/2 (3) x = 0 (4) x = a/2 If x, y, z are the three geometric means between 6 and 54, then z = (A) 9 3 (B) 18 (C) 18 3 (D) 27 If a1 , a2 , a3 ,.... are in A.P. such that a1 a5 a10 a15 a20 a24 225 then a1 a2 a3 .... a23 a24 (A) 909 (C) 750 (B) 75 (D) 900 If H 1 , H 2 ,....., H n are ‘n’ harmonic means between ‘a’ and ‘b’ then the value of H1 a H n b H1 a H n b x 2 y2 the ellipse 1, and having its centre (0, 3) 16 9 is (A) 4 (C) 12 a 2 b2 a (A) 2 (A) n + 1 (B) n – 1 (C) 2n (D) 2n + 3 If a, b, c are in A.P., p, q, r are in H.P and ap, bq, cr are in G.P., then p r = r p (A) a c c a (B) a c c a (C) b q q b (D) b a q p The interior angles of a polygon are in A.P. If the smallest angle is 100 o and the common difference is 4 o , then the number of sides is (A) 5 (B) 7 (C) 36 (D) 44 be two points on the hyperbola http://iitscholars.com http://iitvidya.com http://iitscholar.com http://iitscholars.com http://iitvidya.com http://iitscholar.com 17. For a real number x, [.] denotes the greatest integer. The value of (x) 1 (B) A = , z 2 f (x) 1 1 1 1 2 1 99 ... 2 2 100 2 100 2 100 is: (A) 49 (C) 48 18. If f ( x y, x y) xy , then the arithmetic mean of f x, y and f y, x is (A) y (B) x (C) 0 (D) xy 19. 20. (C) A (B) 50 (D) 51 1 1 If 3 f ( x) 5 f 3, x( 0) R then f ( x) x x 1 3 (A) 5x 6 14 x 1 3 (B) 5x 6 16 x 1 3 (C) 5x 6 14 x 3 (D) 5 x 6 x 25. (B) [2, 3] (D) [2, 3) (C) A = 22. x 26. (C) (2,3] (D) (3, 9) (1 x)dx ex x 2 (1 e2x x 2 ) (D) A = – 2 1 x x dx = A 1 – x 2 1 Bcos 1 x c 1 x 2 1 tan 1(xe x ) c x (B) 1 tan 1 (e x ) c x xe (C) 1 tan 1(xe x ) c x xe (C) A 1, B = 1 4 –1 2 (B) A B (D) A A curve passing through (1, 0) whose gradient (B) E 1 e (D) 1 e 1 e 2ln x dx 0 1 4 1 2 1 (D) 4 (A) 0 1 1 ,B 4 4 (C) {f (x). '(x) f '(x).(x)} f (x).(x) {log (x) log f (x)}dx A(log z)2 C (A) – e (C) 27. (A) A 1, B is equal to is then 23. (B) (0, ) 1 log x , has local max value = 2 x (B) A = 2 1 2 dx f (x) c. then range of f(x) is (D) xex tan 1(xex ) c ln(1 x) 1 x dx = A ln (1 + x) dx + c then (A) A = 4 3 log x) (x) f(x) (A) (,0) (A) f ( x) log10 [1 log10 ( x 2 5 x 16)] is 21. e2(x The domain of the function (A) (2, 3) (C) (2, 3] 1 (x) z= 2 f (x) (D) A 1, z = 24. 2 (B) 1 3 / 4 28. tan 2 xdx 0 then (A) 1 then (C) (x) (A) A = 1, z = f (x) / 2 29. 0 4 1 4 (B) 1 (D) 4 cos x dx (1 sin x)(2 sin x) http://iitscholars.com http://iitvidya.com http://iitscholar.com 4 http://iitscholars.com http://iitvidya.com http://iitscholar.com 38. The area bounded by the curves y = |x| - 1 and 1 (B) log |x| + 1 is 3 4 3 3 (C) log 4 (A) log (D) None of these 39. / 2 30. 1 cos x / 3 (1 cos x)5/ 2 dx 5 2 1 (C) 2 3 2 2 (D) 5 (A) 1 31. sin 0 1 (B) 2x dx 2 1 x 2 log 2 2 (C) log 2 4 (A) 32. 40. 2 log 2 2 (D) log 2 4 (B) If the equations x2 + ax + b = 0 and x2 + bx + a = 0 have exactly one common root, then the numerical value of a + b is (A) 1 (B) – 1 (C) 0 (D) None of these 41. 33. The set of the values of a for which the inequality x2 + ax + a2 + 6a < 0 is satisfied for all x (1, 2) lies in the interval (A) (1, 2) (B) [1, 2] (C) [-7, 4] (D) None of these 34. If ax2 + bx + 6 = 0 does not have two distinct real roots, then the least value of 3a + b is (A) 2 (B) –2 (C) 1 (D) – 1 35. Let p and q be the roots of the equation x2 – 2x + A = 0 and let r and s be the roots of the equation x2 – 18x + B = 0. If p < q < r < s are in arithmetic progression then the value of A and B are given by 43. (A) A = 3, B = 77 (B) A = 3, B = 7 (C) A = –3, B = 77 (D) A = 3, B = –7 36. If the inequality R, then (A) 1 < m < 5 (C) 1 < m < 6 37. 42. mx 2 3x 4 5 is satisfied for all x 44. x2 2x 2 (B) –1 < m < 5 (D) m The area of the quadrilateral formed by the tangents at the end points of latus recta to the ellipse 5x2 + 9y2 = 45 is 27 (A) sq. units (B) 9 sq. units 4 27 (C) sq. units (D) 27 sq. units. 2 (A) 1 sq. unit (B) 2 sq. units (C) 2 2 sq. units (D) 4 sq. units. Let f(x) = min. x 1, 1 x , then area bounded by f(x) and x-axis is 1 5 (A) sq. units (B) sq. units 6 6 7 11 (C) sq. units (D) sq. units 6 6 3 The area bounded by the curve y = 2 - |2 – x|, y = |x| is 5 4 ln 2 (A) sq. units 3 4 ln 3 (B) sq units 2 4 3 ln 3 (C) sq. units 2 3 ln 3 4 (D) sq. units 2 Let f(x) be a continuous function such that the area bounded by the curve y = f(x), the x-axis and then two a2 a ordinates x = 0 and x = a is sin a cos a, 2 2 2 then f(/2) is 1 1 (A) (B) 2 2 (C) 2 (D) -2 45. The maximum value of (cos 1)(cos 2) . . . . . (cos n) under the restriction 0 1, 2, . . . n and (cot 1) (cot 2) . . . . (cot 2 n) = 1 is 1 1 (A) n / 2 (B) n 2 2 1 (C) n1 (D) 1 2 If + = /2 and + = , then tan equals (A) 2(tan + tan ) (B) (tan + tan ) (C) (tan + 2 tan ) (D) 2 tan + tan If sin cos3 > sin3 cos , then lies in (A) 0, (B) (0, ) 2 (C) 0, 4 71 24 y=- (D) (0, 2) If z be any complex number such that |3z – 2| + |3z + 2| = 4, then locus of z is (A) an ellipse (B) a circle (C) a line-segment (D) a parabola http://iitscholars.com http://iitvidya.com http://iitscholar.com 46. 47. http://iitscholars.com http://iitvidya.com http://iitscholar.com The complex numbers z1, z2 and z3 satisfying (C) (CH3)3 CCOCH3 (D) (CH3)2C = C(CH3)2 z1 z3 1 3i are the vertices of a triangle which z2 z3 2 53. is (A) of area zero (B) equilateral (C) right angled isosceles (D) obtuse angled isosceles If z1 and z2 be the nth roots of unity which subtend right angle at the origin. Then n must be of the form (where k N) (A) 4k + 1 (B) 4k + 2 (C) 4k + 3 (D) 4k 54. 48. 49. For all complex numbers z1, z2 satisfying | z1 | = 12 and | z2 – 3 – 4i | = 5, the minimum and maximum value of |z1 – z2| is (A) 0, 2 (B) 2, 22 (C) 7, 17 (D) 2, 17 If |z| = 1, z 1, then the real part of w = (A) (C) 50. 2 (B) | z 1 |2 1 Consider the following transformation conc.HI CH3CH CH O CH2CH3 heat The major product(s) formed is (are) (A) CH3CH CHI and CH3CH2I (B) CH3CH CHI and CH3CH2OH (C) CH3CH2CHO and CH3CH2I (D) CH3CH 2CH O CH 2CH3 | I Consider the following sequence of reactions : The products (A) and (B) are, respectively O H a n d N H O H (A) z 1 z 1 (B) is 1 (C) | z 1 |2 If z = x + iy, = N O H H = N O H a n d = N O H a n d N = O O N O (D) 0 | z 1| 2 H S O 2 4 h e a t + H N O H O A 2 h e a tB (D) 1 iz , then | | = 1 implies that : z i (A) z lies on imaginary axis (B) z lies on real axis (C) z lies on unit circle (D) None of these 55. = N O Ha n d N H How many isomers of monochloride can be obtained CH3 from CH3—C—CH2—CH3 on monochlorination CH3 CHEMISTRY 56. 51. Consider the following chlorides (A) C H C l 2 (B) C H 3 C H C l 2 57. CH2=CHCl reacts with HCl to form major product (A) CH2Cl—CH2Cl (B) CH3—CHCl2 (C) CH2=CHCl.HCl (D) None C H C l 2 58. The order of reactivity of A, B, C and D towards hydrolysis by SN1 mechanism is (A) A < B < C < D (B) D < C < B < A (C) D < A < B < C (D) C < B < A < D 2-bromopentane is heated with potassium ethoxide in ethanol. The major product is (A) Trans - pent-2-ene (B) 2-ethoxy pentane (C) Pent-1-ene (D) cis-pent-2-ene 59. Gem dihalide on hydrolysis gives (A) Acetone (B) Aldehyde (C) Ketone (D) None 60. The reaction with ethyl alcohol and methyll magnesium bromide gives (A) CH4 (B) C2H6 (C) C3H8 (D) None (C) C H O 3 (D) O N 2 52. (A) 1 (B) 2 (C) 3 (D) 4 Butane nitrile may be prepared by heating: (A) Propyl alcohol with KCN (B) Butyl alcohol with KCN (C) Butyl chloride with KCN (D) Propyl chloride with KCN C H C l 2 NaNO2 The reaction (CH 3 )2 C C (CH 3 )2 dil . H 2 SO4 | | OH NH2 Produces only (A) (CH 3 )2 C C (CH 3 )2 | | OH OH (B) two moles of (CH3)2 C = O http://iitscholars.com http://iitvidya.com http://iitscholar.com 61. 62. http://iitscholars.com http://iitvidya.com http://iitscholar.com (A) Heisenberg uncertainty Principle The maximum kinetic energy of the photo(B) Hund’s rule electrons is found to be –19 (C) Pauli;s exclusion Principle 6.63 10 J. When the metal is irradiated with a (D) Bohr’s postulates of stationary orbits. radiation of frequency 15 2 10 Hz. The threshold frequency of the metal 70. The ionization energy of a hydrogen atom is 13.6 is about 15 –1 15 –1 eV. The energy of the third-lowest electronic level (A) 1 10 s (B) 2 10 s 15 –1 15 –1 in doubly ionized lithium (Z = 3) is (C) 3 10 s (D) 1.5 10 s (A) – 28.7 eV (B) –54.4 Ev (C) – 122.4 eV (D) –13.6 eV How fast is an electron moving if it has a wavelength equal to the distance it travels in one second ? h m (A) (B) m h h h (C) (D) p 2(KE) 63. Hund’s rule deals with the distribution of electrons in (A) a quantum shell (B) an orbit (C) an orbital (D) degenerate orbitals 64. If traveling at equal speeds, the longest wavelength of the following matter waves is that of: (A) electron (B) proton (C) neutron (D) alpha particles 65. How many moles of electrons weigh one kilogram? [Mass of electron = 9.1 10-31 kg, Avagadro’s number = 6.023 1023] 1 (A) 6.023 1023 (B) 1031 9.1 6.023 1 54 (C) (D) 10 108 9.1 9.1 6.023 66. 67. 68. A 200 g cricket ball is thrown with a speed of 3 103 cm/s. The de Broglie wavelength of the ball is (A) 1.1 10-32 cm (B) 2.2 10-32 cm -32 (C) 0.55 10 cm (D) 11.0 10-32 cm If the wavelength of the first line of the Balmer series of hydrogen atom is 656.1 nm, the wavelength of the second line of this series would be (A) 218.7 nm (B) 328.0 nm (C) 486.0 nm (D) 640.0 nm 71. The wavelength of the third line of the Balmer series for a hydrogen atom is 21 100 (A) (B) 100R H 21R H 21R H 100R H (C) (D) 100 21 72. The correct set of quantum for the unpaired electron of a chlorine atom is (Cl = 17) 1 1 (A) 2, 0, 0, (B) 2,1, 1, 2 2 1 1 (C) 3,1, 1, (D) 3, 0, 0, 2 2 The value of the magnetic moment of a particular ion is 2.83 Bohr magneton. The ion is (Atomic No. of Mn = 25, Fe = 26, Co = 27, Ni = 28) (A) Fe2+ (B) Ni2+ 2+ (C) Mn (D) Co3+ 73. 74. If the radius of first Bohr orbit of H-atom is x then de-Broglie wave length of electron in 3rd orbit is nearly: (A) 2x (B) 6x (C) 9x (D) x/3. 75. Magnetic moment of V (z = (z = 24), Mn (z = 25) are x, y, z hence (A) x = y = z (B) x < y < z (C) x < z < y (D) z < y < x. 76. Magnetic moment of Xn+ (Z = 26) is 24 B.M. Hence no. of unpaired electrons and value of ‘n’ respectively are (A) 4, 2 (B) 2, 4 (C) 3, 1 (D) 0, 2 77. The longest energy transition in the Balmer series corresponds to (A) n = 2 to n = 1 (B) n = 3 to n = 1 (C) n = 3 to n = 2 (D) n = 5 to n = 4 78. A photon of 3000Å is absorbed by a gas and reemitted two photons. One photon has wavelength of 4500Å. What would be the wavelength of other photon? Which of the following is violation of Pauli’s exclusion principle? (a) 23), Cr (b) (c) (d) 69. If the electronic configuration of nitrogen had 1s7, it would have energy lower than that of normal ground state configuration 1s2 2s2 2p3 because the electrons would be closer to the nucleus. Yet 1s7 would be not observed because it violates http://iitscholars.com http://iitvidya.com http://iitscholar.com 79. http://iitscholars.com http://iitvidya.com http://iitscholar.com (A) 4500Å (B) 2500Å 86. A first order reaction (C) 9000Å (D) 3000Å 2H2O2 2H2O + O2 is 75 percent complete in 100 sec. What is the half – life of the reaction? Which describes orbital: (A) 200 sec (B) 50 sec (A) (B) 2 (C) 400 sec (D) 150 sec (C) |2| 80. 81. (D) none Which of the expressions given below gives I.E of H – 87. atom in terms of Rydberg’s constant: (A) RHhc (B) RHNA.hc (C) RH. (2hc) (D) RH.C Consider the reaction mechanism A2 2A (fast) A + B P (slow) where A is the intermediate. The rate law for the reaction is (A) k2[A][B] (B) k2k1/2[A2]1/2[B] (C) k2k1/2[A][B] (D) k2k1/2[A]2[B] 82. 83. The saturated reduction potential for Cu+2/Cu is + 0.34 Volt. Calculate reduction potential at pH = 14 For the above couple Ksp of Cu(OH)2 is 1 × 10-19. (A) 0.2214 V (B) -0.2214 V (C) 2.214 V (D) 0.1107 V 88. Aqueous NH4NO2 decomposes according to the first-order reaction 89. NH4NO2(aq) N2(g) + 2H2O(l) After 20 minutes the volume of N2 collected during such a reaction is 20 mL, and that collected after a very long time is 40 mL. The rate constant for the reaction is (A) 1.435 10-2 min-1 (B) 3.466 10-2 min-1 90. (C) 3.465 10-2 min-1 -1 (D) 6.93 min The reaction C(g) + D(g) is an A(g) + 2B(g) elementary process. In an experiment involving this reaction, the initial partial pressure of A and B are pA = 0.60 atm and pB = 0.80 atm respectively. 91. When pC = 0.20 atm, the rate of reaction relative to the initial rate is (A) 1/6 (B) 1/12 (C) 1/36 (D) 1/18 84. If in the fermentation of sugar in an enzymatic 92. solution that is initially 0.12 M the concentration of sugar is reduced to 0.06 M in 10 hr and to 0.03M is 20 hr, what is the order of the reaction? (A) 0 (B) 1 (C) 2 (D) 3 85. The following first order reaction is 50 percent complete in 24 hours at 300K 2N2O5 4NO2 + O2 How many grams of N2O5 will remain after a period of 4 days? [Given : [N2O5]0 = 10 g] (A) 1.77 g (B) 1/25 g (C) 0.63 g (D) 0.500 g 93. Calculate emf of silver. Silver chloride electrode immersed in 1M KCL of 25oC. Given Ksp of AgCl = 1.8×10-10, Eo Ag+/Ag = 0.799 volt. (A) 2.23 volt (B) -0.223 volt (C) 0.223 volt (D) none. Electrolysis of a solution of HSO4- ions produces S2O8-2. Assuming 75% current efficiency, what current should be employed to achive a production rate of 1 mole of S2O8-2 per hour ? (A) - 71.5 amp (B) 35.7 amp (C) 53.0 amp (D) 44.3 amp Electrolysis of dil H2SO4 liberates gases at anode and cathode (A) O2 & SO2 respectively (B) SO2 & O2 respectively (C) O2 & H2respectively (D) H2 & O2 respectively Stronger the oxidizing agent, greater is the (A) Standard reduction potential (B) Standard oxidation potential (C) Ionic nature (D) None Zn | Zn+2 (C1) || Zn+2 (C2) | Zn For this cell G is negative if (A) C1 = C2 (B) C1 > C2 (D) C2 > C1 (D) both (A) & (C) are correct Emf of the cell Ni | Ni2+ (0.1M) || Au3+ (1.0M) | Au will be 0 ENi 0.25, / Ni 2 (A) 1.75 V (C) +0.7795 V 94. EA0u / Au3 1.5V (B) +1.7795 V (D) –1.7795 V How much time is required for complete decomposition of two moles of water using a current of 2 ampere http://iitscholars.com http://iitvidya.com http://iitscholar.com http://iitscholars.com http://iitvidya.com http://iitscholar.com 103. Cathode rays may not be deflected by (A) 1.93 10 sec (B) 2.93 105 sec 5 5 (a) Magnetic field (C) 0.93 10 sec (D) 4.93 10 sec 5 95. 96. A 0.2 M KOH solution is electrolysed for 1.5 hr using a current of 8 amp. How many mol of O2 were produced at the anode (A) 0.48 (B) 0.224 (C) 0.112 (D) 0.0224 When a lead storage battery is discharged: (A) SO2 is evolved (B) Lead is formed (C) lead sulphate is formed (D) sulphuric acid is formed 97. Which of the following alkanes may be synthesized from a single alkyl halide by a process involving coupling reaction ? (A) 1-Methylbutane (B) 2-Methylpropane (C) 2, 3-Dimethylbutane (D) Propane 98. An equimolar mixture of methyl iodide and ethyl iodide is heated with sodium in dry ether. The expected alkane is (A) propane (B) ethane (C) butane (D) all of these 99. 100 (b) Electric field (c) Perpendicular magnetic field & electric field (A) Only (a) (B) Only (a) & (b) (C) Only (c) (D) (a), (b) & (c) 104. In Millikan’s oil drop experiment, a charged drop of mass 1.8 × 10–14 kg is stationary between its plates. The distance between the plates is 0.90 cm. The potential difference is 2 kV. The mass of excess electrons on this drop is (in kg) (A) 500 × 10–28 (B) 5 (C) 50 × 10–41 (D) 5 × 9.1 × 10–31 105. Light of frequency 1.5 times the threshold frequency is incident on a photosensitive material. If the frequency is halved and the intensity is doubled, the photoelectric current becomes (A) Four times (B) Double (C) Half (D) Zero 106. The momentum of a photon of frequency v is hv c2 (C) hv c (A) hv c (D) hv c2 (B) 107. A photon of wavelength 1 × 10–7 m has energy 12.3 eV. If cis –2, 3-Diphenyl-2-butane is allowed to react light of wavelength 5000 Å, having intensity I, falls on a with H2 in the presence of palladium catalyst. The metal surface, the saturation current is 0.40 A and the major product will be stopping potential is 1.3 V. The work function of the (A) meso-2, 3-diphenylbutane metal is (B) (+)-2, 3-diphenylbutane (A) 2.47 eV (B) 1.36 eV (C) (-)-2, 3-diphenylbutante (C) 1.16 eV (D) 0.43 eV (D) ()-2, 3-diphenylbutane 1-butene on reaction with HBr gives mainly (A) 1-bromobutane (B) 2-bromobutane (C) ()-2-bromobutane (D) 3-bromobutane 108. The ratio of the de-Broglie wavelengths of a proton and particle will be 2 : 4 if there (A) Kinetic energies are in the ratio 1 : 8 (B) Kinetic energies are in the ratio 8 : 1 (C) Velocities are in the ratio 1 : 8 (D) Velocities are in the ratio 8 : 1 109. The ratio of the area of the orbit swept by an electron of H-atom in 2nd state and 3rd excited state is PHYSICS (A) 2 : 3 (B) 4 : 9 101. The ratio of the specific charge of the electron to that of (C) 4 : 16 (D) 1 : 16 the hydrogen ion is approximately (1) 1 : 1 (B) 1840 : 1 110. Consider the spectral lien resulting from the transition (C) 1 : 1840 (D) None of these from n = 2 to n = 1 in the atoms and ions given below. 102. How many minimum number of NAND gates are only The shortest wavelength is produced by required to form OR gate? (A) Hydrogen atom (A) One (B) Two (B) Deutron atom (C) Three (D) Four (C) Singly ionized helium http://iitscholars.com http://iitvidya.com http://iitscholar.com http://iitscholars.com http://iitvidya.com http://iitscholar.com (D) Doubly ionized lithium 119. If 10% of a radioactive material decays in 5 days, then the amount of original material left after 111. If the electron in a hydrogen atom jumps from the third 20 days is approximately orbit to the second orbit, the emitted radiation has (A) 60% (B) 65% wavelength (R is Rydberg’s constant) (C) 70% (D) 75% 36 5R (A) (B) 5R 36 120. What fraction of the original amount of a radioactive 6 5R (C) (D) substance will have disintegrated after a time equal to its 5R 6 mean life? 112. If elements with principal quantum number n > 4 were not (A) 0.368 (B) 0.632 allowed in nature, the number of possible elements would (C) 0.101 (D) ½ be (A) 60 (B) 32 121. Which of the following has highest binding energy per (C) 4 (D) 64 nucleon? (A) He3 (C) He2 (B) He4 (D) All of have equal value 113. The potential difference applied to an x-ray tube is decreased. As a result, in the emitted radiation 122. Nuclear forces are (a) The intensity increases (A) Charge dependent (B) Spin independent (b) The minimum wavelength increases (C) Charge independent (D) Long – range (c) The intensity remains unchanged (d) The minimum wavelength decreases 123. Nuclear volume of a nucleus (A) (c) & (d) (B) (a) & (c) (A) Varies inversely with mass number (C) (b) & (c) (D) All of these (B) Varies directly with square of mass number (C) Is constant for all nuclei 114. In the Bohr model of hydrogen atom, let PE represents (D) Varies directly with mass number potential energy and TE represent total energy of an electrons. In going from a lower to higher orbit 124. The circuit shown in the figure contains two diodes each (A) PE decreases, TE increases with a forward resistance of 50 and with infinite (B) PE increases, TE increases backward resistance. If the battery of 6V is connected in the circuit, the current through the 100 resistance in (C) PE decreases, TE decreases (amp.) is (D) PE increases, TE decreases 12 115. Suppose the potential energy between electron and proton Ke 2 at a distance r is given by 3 . Use Bohr’s theory. Find 3r centripetal force (A) Ke 2 r3 (B) Ke 2 r4 (C) Ke 2 r2 (D) Ke 2 r 50 6V (A) Zero (C) 0.030 100 (B) 0.02 (D) 0.037 125. A p-type semiconductor has acceptor level 57 m eV above the valence band. The maximum wavelength of light required to create a hole is 116. If 200 MeV of energy is released in the fission of one (A) 57Å (B) 57 × 10–3Å nucleus of 92U235, how many nuclei must undrgo fission (C) 217100 Å (D) 11.61 × 10–33Å per second to produce a power of 1 KW? (A) 3.125 × 1016 (B) 3.125 × 1013 126. If A – B C and | A || B || C | then what should be the 9 (C) 3.125 × 10 (D) 3.12 × 102 angle between A and B ? 117. The nuclei 6C13 and 7N14 can be described as (A) Isobars (B) Isotones (C) Isotopes of carbon (D) Isotopes of nitrogen (A) 0 (C) 2 3 (B) 3 (D) 127. Dimensional formula of a physical quantity x is [M–1L3T– 2 ]. The errors in measuring the quantities M, L and T 118. The end product of the decay of 90Th232 is 82Pb208. The respectively are 2%, 3% and 2%. The maximum number of and particles emitted are, respectively percentage error that occurs in measuring the quantity x (A) 3, 3 (B) 6, 4 is: (C) 6, 0 (D) 4, 6 http://iitscholars.com http://iitvidya.com http://iitscholar.com http://iitscholars.com http://iitvidya.com http://iitscholar.com (A) 6 (B) 7 (C) 10 (D) 15 128. A train starts from station A, uniformly accelerates for 1 2 minute then moves uniformly for 2 minutes and retards uniformly for 1 minute to rest to reach station B 2200 meters away. The acceleration of the train in metres/ minute2 will be: 6 33 (A) 1600 (B) (C) 1200 (D) None of these increases linearly y 2 1 x (A) T1 > T2 (C) u1 > u2 (B) T1 < T2 (D) u1 < u2 with 135. The average acceleration vector (taken over a full circle) for a particle having a uniform circular motion is:- 130. Two stones are projected with the same speed but making different angles with horizontal. Their ranges are equal. If the angle of projection of one is and its maximum 3 height is h1 then the maximum height of the other will be:(A) 3h1 (B) 2h1 h (C) 1 2 v1 v12 v2 2 (D) g vv (C) 1 2 g 134. Trajectories of two projectiles are shown in figure. Let T1 and T2 be the time of flights and u1 and u2 their speeds of projection. Then: 129. The velocity of a particle increases linearly with displacement. The particle starts with some velocity then out of the following statements the wrong statement is: (A) the ratio of acceleration and velocity is a constant (B) Displacement increases exponentially with time (C) Velocity increases linearly with time (D) Acceleration velocity time with a speed v12 v2 2 then the horizontal displacement of the ball is v2 v2 (A) 1 (B) 2 g g h (D) 1 3 (A) a constant vector of magnitude v2 r (B) a null vector v2 r (C) a vector of magnitude the plane motion (D) equal vector to of the the given directed normal to uniform instantaneous circular acceleration 136. A mass is supported on a frictionless horizontal surface . It is attached to a string and rotates about a fixed centre at 131. A projectile is projected from ground with some velocity an angular velocity 0 . If the length of the string and and at some angle with horizontal so that its time of flight angular velocity are doubled, the tension in the string is ‘T’. The time interval between two points on the path which was initially T0, is now: 3 where elevation is of maximum elevation is: T 4 (A) T0 (B) 0 T 4 3T (C) 2 2 T 2 T (D) 3 (A) (B) (C) 4T0 (D) 8T0 137. The slope of the smooth banked horizontal road is p. If the radius of the curve is r, the maximum velocity with which a car can negotiate the curve is given by: 132. The trajectory of a projectile in a vertical plane is y = px – 2, qx where p and q are constants and x & y are (A) prg (B) prg respectively horizontal and vertical distances of the (C) p / rg (D) p / rg projectile from the point of projection. The maximum height attained by the particle and the angle of projection from the horizontal are respectively 138. A uniform circular ring is rotated about an axis 2 2 perpendicular to the plane and touching the ring with a q p , tan –1 (q) , tan –1 (2 p) (A) (B) constant angular velocity. The ratio of acceleration of 2p q points B and C is [ diameters AC and BD are 2 2 perpendicular] p 2p –1 –1 (C) 4q , tan ( p) (D) q , tan ( p) 133. A ball is projected horizontally with velocity v1 from top of a tower. The ball strikes the ground after some http://iitscholars.com http://iitvidya.com http://iitscholar.com http://iitscholars.com http://iitvidya.com http://iitscholar.com 20 2 B (C) (D) g g 3 3 A C 144. A chain of n links is placed on a smooth horizontal surface. Each link is of mass m. A force F is applied to the first link. The force applied by the second last link to the last link will be:- D (A) 1 (C) (B) 1 2 F n nF (C) m (D) 2 2 F m Fm (D) n (A) 139. 1 g wt is numerically same as (A) 98 g cm/s2 (B) 980 dyne 2 (C) 980 gm/s (D) 9.8 N (B) 145. A boy standing on a weighing machine notices his weight as 400N. When he suddenly jumps on it, the weight shown by the machine becomes 600N. The acceleration with which the boy jumps up is: 140. A bird flying at some height is carrying a stone. The bird (A) zero (B) 4.5 ms–2 is flying horizontally with a constant speed. If it releases (C) 3.4 ms–2 (D) 4.9 ms–2 the stone and keeps on flying horizontal. The path of the stone as seen by the bird and a man standing on ground 146. A rod of length L and mass M is acted on by two unequal respectively are: forces F1 and F2(<F1) as shown in the following figure. (A) straight line making an acute angle with horizontal, C B A parabola. F1 F 2 (B) vertical straight line, parabola y (C) vertical straight line, straight line making an acute L angle with horizontal The tension in the rod at a distance y from the end A is given by: (D) parabola, parabola 141. The horizontal acceleration that should be given to a 1 smooth inclined plane of angle sin–1 to keep an l object stationary on the plane relative to the inclined plane is:(A) g / l 2 1 (C) (B) g l 2 1 l 1 / g y y F2 L L y y (B) F2 1 F1 L L y (C) F1 F2 L (A) F1 1 (D) none of these (D) g / l 1 2 2 147. A block of mass m is kept on a rough inclined plane of inclination 45 . The block slips down with 142. A small sphere is suspended by a string from the ceiling of a car. The tension in the string is T0 when the car is at rest. When the car begins to move with a constant acceleration, the tension developed in the string is: (A) T = T0 (B) T > T0 (C) T < T0 (D) T = 0 constant speed. The same block is pushed against a vertical wall of roughness identical to inclined plane so that block does not slip. The minimum horizontal force required is: (A) mg (B) 2mg (C) 3 mg 2 (D) 3 mg 143. Three equal weights A, B, & C of mass 5kg each are hanging on a string passing over a fixed frictionless pulley as shown in the figure. The tension in the string 148. A small heavy ball of mass m is suspended from a point connecting weights B and C is: by a thread of length 1 metre. The thread is having a breaking tension of T0(>mg). The maximum angular displacement of the ball so that the ball can oscillate in the vertical plane is:- A 3 T0 mg (A) cos 1 B C (A) 5 g 3 3 2 T0 2mg T0 mg (B) cos 1 (B) 10 g 3 (C) cos 1 2 http://iitscholars.com http://iitvidya.com http://iitscholar.com http://iitscholars.com http://iitvidya.com http://iitscholar.com 3T0 2mg (D) cos 1 149. Which of the following statements about reading of the spring balance shown in figure are correct? [take the pulley and the string to be massless and frictionless] (A) Reading 10 kg. (B) Reading 10 kg (C) Reading 10 kg (D) Reading 5 kg of A is 5 kg and reading of B is of A is 10 kg and reading of B is of A is 20kg and reading of B is of A is 10 kg and reading of B is 150. A man is pulling a rope attached to a block on a smooth horizontal table. The tension in the rope will be the same at all points. (A) if and only if the rope is not accelerated (B) if and only if the rope is massless A 10 kg (C) if either the rope is not acceleration or is massless (D) always B ANSWER KEY MATHS 1. 2. 3. 4. 5. 6. 7. 8. 9 10. 11. 12. 13. 14. 15. 16 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32 33. 34. 35. 36. 37. (B) (D) (C) (B) (A) (A) (A) (A) (D) (A) (C) (C) (D) (C) (A) (A) (B) (C) (B) (A) (A) (C) (C) (B) (C) (D) (C) (A) (A) (B) (A) (B) (D) (B) (C) (D) (D) CHEMISTRY 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83. 84. 85. 86. 87. (A) (C) (C) (B) (C) (D) (B) (A) (B) (A) (A) (A) (D) (A) (D) (A) (C) (D) (C) (C) (B) (C) (B) (B) (C) (A) (C) (C) (B) (A) (B) (B) (A) (B) (C) (B) (B) PHYSICS 101. 102. 103. 104. 105. 106. 107. 108. 109. 110. 111. 112. 113. 114. 115. 116. 117. 118. 119. 120. 121. 122. 123. 124. 125. 126. 127. 128. 129. 130. 131. 132. 133. 134. 135. 136. 137. http://iitscholars.com http://iitvidya.com http://iitscholar.com (B) (C) (D) (D) (D) (B) (C) (D) (D) (D) (A) (A) (C) (B) (B) (B) (B) (B) (B) (B) (B) (C) (D) (D) (C) (B) (D) (A) (C) (D) (B) (C) (C) (D) (B) (D) (B) 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. (B) (C) (C) (A) (A) (C) (C) (C) (B) (B) (D) (B) (B) 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98. 99. 100. (C) (A) (C) (A) (C) (B) (A) (C) (C) (C) (D) (A) (B) 138. 139. 140. 141. 142. 143. 144. 145. 146. 147. 148. 149. 150. (B) (B) (B) (A) (B) (B) (A) (D) (A) (A) (B) (C) (C)

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