KEAM (All Unit) Past Paper PDF 14-05-2024
Document Details
Uploaded by WillingOrientalism
null
2024
CEE KERALA
null
Tags
Related
Summary
This is a past paper for a physics exam. The paper is from CEE KERALA 2024 and covers questions on various topics in physics, including electrostatics, capacitance, magnetism, and current electricity.
Full Transcript
Date: 14-05-2024 Batch: ENGG. 2024 Version Brilliant E1 STUDY CENTRE CEE KERALA ENGG. MODEL EXAM - ALL UNIT Puliyannoor P.O., PALA...
Date: 14-05-2024 Batch: ENGG. 2024 Version Brilliant E1 STUDY CENTRE CEE KERALA ENGG. MODEL EXAM - ALL UNIT Puliyannoor P.O., PALA TEST ID 211 Ph - 04822 206416, 206516, 206459 www.brilliantpala.org [PHYSICS + CHEMISTRY + MATHEMATICS] PHYSICS 1. In the basic CsCl crystal structure Cs+ and Cl– ions are arranged in a bcc configuration as shown in figure. The net electrostatic force exerted by the eight Cs+ ions on the Cl– ion is: 1 4e2 1 16e2 A) B) 4 a 2 40 3a 2 0 1 16e2 1 8e 2 C) 4 3a 2 D) zero E) 4 3a 2 0 0 2. A conducting sphere is placed in air of dielectric strength 3 × 106 V/m. What is the minimum radius of the sphere that can be raised to a potential of 9 million volts? A) 3m B) 9m C) 12m D) 1.5m E) 4.5m 3. A capacitor of 2F is charged as shown in the diagram. When the switch S is turned to position 2, the percentage of its stored energy dissipated is: A) 0% B) 20% C) 60% D) 75% E) 80% 4. What is the equivalent resistance between points A and B in the networks shown in the figure? (R1 = R2 = R3 = R4 = R) A) R B) R 2 C) R 4 D) 2 3 R E) 4 3 R 5. In India electricity is supplied for domestic use at 220V. It is supplied at 110V in USA. If the resistance of a 60W bulb for use in India is R, the resistance of a 60W bulb for use in USA will be: A) 2R B) R/4 C) R/2 D) R E) R/3 FT24A/KEAM-MOD/P+C+M[E1] 2 Brilliant STUDY CENTRE 6. In a potentiometer experiment the balancing length with a cell is at length 240cm. On shunting the cell with a resistance 2 the balancing length becomes 120cm. The internal resistance of the cell is: A) 1 B) 0.5 C) 4 D) 2 E) 5 7. The resistance of an ammeter is 13 and its scale is graduated for a current upto 100A. After an additional shunt has been connected to this ammeter it becomes possible to measure currents upto 750A by this meter. The value of shunt resistance is: A) 20 B) 0.2 C) 10 D) 200 E) 2 8. A short magnet of moment 6.75 A.m produces a neutral point on its axis. If the horizontal component of 2 earth’s field is 5 × 10–5 wb/m2, the distance of the neutral point should be: A) 10cm B) 20 cm C) 30 cm D) 40 cm E) 50 cm 9. A bar magnet is hung by a thin cotton thread in a uniform horizontal magnetic field and is in the equilibrium state. The energy required to rotate it by 60o is W. Now the torque required to keep the magnet in this new position is: 3W 2W W A) B) C) D) 3W E) W 2 3 3 10. A horizontal overhead power line is at a height 4m from the ground and carries a current of 100A from east to west. The magnetic field directly below it on the ground is 0 4 10 7 TmA 1 . A) 2.5 × 10–7 T northword B) 2.5 × 10–7 T southword C) 5 × 10–6 T northword D) 5 × 10–6 T southword E) 7.5 × 10–6 T northword 11. A and B are two wire carrying a current I in the same direction. x and y are two electron beams moving in the same direction. There will be: A) Attraction between A and B, repulson between x and y B) Repulsion between A and B, attraction between x and y C) Attraction between A and B and x and y D) Repulsion between A and B and x and y E) can’t predict 12. An electron moving in a circular orbit of radius r makes n rotations per second. The magnetic field produced at the centre has magnitude 0 n2e 0 ne 0 ne 0 ne2 A) zero B) C) D) E) r 2r 2r 2r 13. A conducting circular loop is placed in a uniform magnetic field 0.04T with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at 2mm/s. The induced e.m.f. in the loop when the radius is 2cm is: A) 1.6 V B) 3.2 V C) 4.8 V D) 0.8 V E) 5.6 V 14. A transformer having efficiency of 90% is working on 200V and 3 KW power supply. If the current in the secondary coil is 6A, the voltage across the secondary coil and the current in the primary coil respectively are: A) 300V, 15A B) 450V, 13.5A C) 600V, 15A D) 600V, 13.5A E) 450V, 15A FT24A/KEAM-MOD/P+C+M[E1] 3 Brilliant STUDY CENTRE 15. In the given circuit the potential difference across resistance is 54V and power consumed it is 16W. If AC frequency is 60Hz. Find the value of L A) 1H B) 2H C) 5H D) 4H E) 6H 16. A source of sound of frequency 500 Hz is moving towards on observer with velocity 30 m/s. The speed of sound is 330 m/s. The frequency heard by the observer will be A) 545 Hz B) 550 Hz C) 500 Hz D) 560 Hz E) 600 Hz 17. A particle of mass m1 makes an elastic, one dimensional collision with a stationary particle of mass m2. What fraction of the kinetic energy of m1 is carried away by m2? m1 m2 2m1m2 m1m2 4m1m2 A) m B) m C) m m 2 D) m m 2 E) m m 2 2 1 1 2 1 2 1 2 18. A train of length 200m switches on its headlight when it starts moving with acceleration 0.5 m/s2. Some time later, its tail light is switched on. An observer on the ground notices that the two events occur at the same place. The time interval between the two events is: A) 10 2 S B) 20 S C) 20 2 S D) 40 S E) 60 S 19. A car starts from the rest and moves on a surface on which the coefficient of friction between the road and the tyres increases linearly with distance x. The car moves with the maximum possible acceleration. The kinetic energy E of the car will be proportional to: A) x–2 B) x–1 C) x D) x2 E) x3 20. A uniform heavy chain is placed on a table with a part of it hanging over the edge. It just begins to slide when this part is one-third of its length. The coefficient of friction between the table and the chain is: A) 12 B) 13 C) 2 3 D) 3 4 E) 1 4 21. The escape velocity for a planet is V. A tunnel is dug along its diameter and a particle is dropped into the tunnel. At the centre of the planet, the speed of the particle will be: V V A) V B) V 2 C) 2 D) 2 2 E) 2V 22. The average translational kinetic energy of O2 (molar mass 32) at a particular temperature is 0.048 eV. The average translational kinetic energy of N2 (molar mass 28) molecules in eV at the same temperature is: A) 0.0015 B) 0.003 C) 0.048 D) 0.768 E) 0.096 23. Equal masses of three liquids A, B and C have temperatures 10oC, 25oC and 40oC respectively. If A and B are mixed, the mixture has a temperature of 15oC. If B and C are mixed, the mixture has a temperature of 30oC. If A and C are mixed, the mixture will have a temperature of: A) 16oC B) 20oC C) 25oC D) 29oC E) 35oC 24. A body cools from 50oC to 40oC in 5 minutes. The surrounding temperature is 20oC. In what further time in (minutes) will it cool to 30oC ? 15 25 A) 5 B) C) D) 10 E) 15 2 3 FT24A/KEAM-MOD/P+C+M[E1] 4 Brilliant STUDY CENTRE 25. A string A has double the length, double the tension, double the diameter and double the density as another nA string B. Their fundamental frequencies of vibration are nA and nB respectively. The ratio nB is equal to: A) 13 B) 12 C) 2 D) 4 E) 1 4 26. Water drops fall at regular intervals from a tap 5m above the ground.Third drop is leaving the tap at the instant, the first drop touches the ground. How far above the ground is the second drop at that instant? A) 1.25 m B) 2.50 m C) 3.75 m D) 4m E) 6 m 27. A planet has a mass of eight times the mass of earth and density is also equal to eight times the average density of the earth. If g is the acceleration due to earth’s gravity on its surface, then acceleration due to gravity on planet’s surface is A) 16 g B) 8 g C) 4 g D) 2 g E) 12 g 28. A block of mass 2 kg hangs from the rim of a wheel of radius 0.5 m.On releasing from rest the block falls through 5m height in 2 sec. The moment of inertia of the wheel will be A) 2.5 kgm2 B) 1.5 kgm2 C) 1 kgm2 D) 3.2 kgm2 E) 3 kgm2 29. A wire of length L and cross sectional area A is made of material of Young’s modulus Y. The workdone in strectching the wire by an amount x is given by YAx 2 YAx 2 YAL2 YAL2 YAx A) B) C) D) E) L 2L x 2x L 30. A fluid is flowing through a tube of length L. The radius of the tube is r and the velocity of fluid is v. If the radius of the tube is increased to 2r. Then what will be the new velocity ? v v A) B)4 v C) 2v D) E) 3v 4 2 31. Calculate the change in internal energy when 5 gram of air is heated from 00C to 40C. The specific heat of air at constant volume is 0.172 calg-1 0C-1 A) 8J B) 5.5 J C) 14.4 J D) 4 J E) 7J 32. Focal length of a convex lens of refractive index 1.5 is 2 cm. Focal length of lens when immersed in a liquid of refractive index of 1.25 will be A) 10 cm B) 2.5 cm C) 5cm D) 7.5 cm E) 12cm 33. Monochromatic green light of wavelength 5 ×10-7 m illuminates a pair of slits 1 mm apart. The separation of bright lines on the interference pattern formed on a screen 2m away is A) 0.25 m B) 0.1 mm C) 1mm D) 0.01mm E) 0.8 m 34. A photon of energy 6eV are incident on a potassium surface of work function 2.1eV. What is the stopping potential? A) -6V B) -2.1V C) -3.9V D) -8.1V E) -5.4 V FT24A/KEAM-MOD/P+C+M[E1] 5 Brilliant STUDY CENTRE 35. A semiconductor has the electron concentration 0.45×1012 m-3 and hole concentration 5×1020 m-3.Find its conductivity if electron mobility = 0.135 m2v-1s-1 and hole mobility = 0.48m2v-1s-1. A ) 38.4 1m 1 B) 19.2 1m 1 C) 47.3 1m 1 D) 38.4×10-7 1m 1 E) None of these 36. Two satellites are orbiting around the earth in circular orbits of the same radius. One of them is 100 times greater in mass than the other. Their period of revolution are in the ratio A) 1 : 1 B) 10 : 1 C) 100 : 1 D) 1 : 100 E) 1 : 10 37. If h is the Planks constant, e is the electric charge the dimensional formula of h/e is same as that of : A) magnetic flux B) electric flux C) intensity of magnetic field D) electric field E) Boltzmans constant 38. An electron and proton with equal momentum enter perpendicularly in to a uniform magnetic field A) The path of proton shall be move curved than that of electron B) The path of proton shall be less curved than that of electron C) Both are equally curved D) Path of both will be straight line E) Cannot be predicted 39. There are two identical small holes on the opposite sides of a tank containing a liquid. The tank is open at the top. The difference in height between the two holes is h. As the liquid comes out of the two holes, the tank will experience a net horizontal force proportional to A) h B) h C) h3 2 D) h2 E) h3 40. For the given combination of gates, if the logic states of inputs A,B,C are as follows A = B = C = 0 and A = B = 1, C = 0 then the logic states of output D are A) 0, 0 B) 0, 1 C) 1, 0 D) 1,1 E) None of these 41. Magnetic induction B at the centre of a circular coil is given by: 0 NIR 2 0 NI 0 NI 0 NI 0 NI A) B) R 2 x 2 C) D) E) 2 R e j 3/ 2 2R 2 R 2R 42. Electromagnetic waves travel in a medium at a speed of 2 10 8 m s 1. If the relative permeability of the medium is 1.0, then then realtive permittivity is A) 1.5 B) 2.5 C) 2.25 D) 4.5 E) 4.25 43. Ionisation potential of hydrogen atom is 13.6 eV. Hydrogen atoms in the ground state are excited by monochromatic radiation of photon energy 12.1 eV. The spectral lines emitted by hydrogen atoms according to Bohr’s theory will be A) 1 B) 2 C) 3 D) 4 E) 5 FT24A/KEAM-MOD/P+C+M[E1] 6 Brilliant STUDY CENTRE 44. In an experiment to measure the height of a bridge by dropping stone into water underneath, if the error in measurement of time is 0.1 s at the end of 2s, then the error in estimation of height of bridge will be A) 0.49 m B) 0.98 m C) 1.96 m D) 2.12 m E) 2.26 m 45. Two second after projection, a projectile is travelling in a direction inclined at 30° to the horizontal. After 1 more second it is travelling horizontally then velocity of projection (g = 10 m/s2) A) 10 3 m/s B) 20 3 m/s C) 24 m/s D) 30 m/s E) 40 m/s CHEMISTRY 46. The mass of magnesium oxide formed by the complete combustion of 1.2 g Mg will be A) 2.0 g B) 1.0 g C) 4.0 g D) 4.8 g E) 2.4 g 47. De Broglie wavelength of an electron travelling at the speed of light would be: o o A) 9.1 nm B) 2.21 pm C) 2.43 pm D) 2.43 A E) 2.21 A 48. The IUPAC symbol of an element with atomic number 107 is A) Unh B) Uuh C) Uus D) Uns E) Unp 49. The correct order of electronegativity is: A) H Cl O S F B) H O Cl S F C) H S O Cl F D) H S Cl O F E) H Cl S O F 50. The hybridisation of the third carbon of the following molecule will be CH 3 CH C CH CH 3 A) sp 2 B) sp3 C) sp3d D) sp3d 2 E) sp 51. The enthalpies of combustion of C, H2 and ethanol are –393.5, –286 and –1368 kJ respectively. The enthalpy of formation of ethanol is: A) 2047 kJ B) 688.5 kJ C) –277 kJ D) –2047 kJ E) –688.5 kJ 52. For a homogeneous gaseous reaction 2C 3D at 300 K, the K = 0.605 atm. The K for the reaction at 300 K is very close to 2A B p C A) 1 10 2 B) 2 103 C) 1 10 3 D) 1 10 4 E) 2 104 53. The oxidation state of Cr in CrO5 is: A) +10 B) +6 C) +3 D) +2 E) None of these 54. The hybridization of C in diamond is A) sp2 B) sp C) sp3d D) sp3d2 E) sp3 NO2 CHO 55. The IUPAC name of the compound Cl A) 1–Nitro –2– Chlorocyclohexan–2–al B) 1–Chloro–3–Nitro cyclohexan–2–al C) 2–Chloro–6–Nitro cyclohexanal D) 2–Chloro–6–Nitro cyclohexane carbaldehyde E) 2–Nitro–6–Chlorocyclohexane carbaldehyde FT24A/KEAM-MOD/P+C+M[E1] 7 Brilliant STUDY CENTRE o 56. The C2 C3 bond length in propene is less than 1.54 A due to A) Resonance B) Inductive effect C) Hyper conjugation D) Electromeric effect E) Mesomeric effect o 57. Assertion (A) : All C–C bond lengths in benzene are equal to 1.34 A Reason (R) : All the bond lengths in benzene are equal due to resonance A) Both assertion and reason are true and reason is the correct explanation of assertion B) Both assertion and reason are true but reason is not the correct explanation of assertion C) Assertion is false but reason is true D) Both assertion and reason are false E) Assertion is true but reason is false 58. In the estimation of nitrogen by Duma’s method the nitrometer contains A) aq. KOH B) aq. HCl C) aq. NaHCO3 D) aq. CuSO4 E) None of these 59. During the thin layer chromatography, a component travelled a distance of 4.6 cm from the baseline while at the same time the solvent travelled a distance of 9.2 cm from the baseline. The Rf value of the component would be A) 0.46 B) 0.92 C) 0.5 D) 2 E) None of these 60. Identify the major product (c) formed in the following reaction sequences: A B C CH 3 CH 2 CH 2 I NaCN OH Partial hydrolysis NaOH Br2 major A) Propylamine B) Butylamine C) Butanamide D) Bromobutanoic acid E) Bromobutane 61. 0.008 M aqueous solution of Na2SO4 is isotonic with 0.02 M aqueous solution of glucose. The Van’t Hoff factor of Na2SO4 is A) 5 B) 2.5 C) 1.25 D) 1.125 E) None of these 62. Nernst equation for the electrode reaction: M g at 298 K M naq n e RT 1 A) E M n /M E M n / M nF ln M n o 2.303RT 1 B) E Mn / M E M n / M o log nF M n 0.0591 Reduced form C) E Mn / M E M n / M o log n Oxidised form 0.0591 Oxidised form D) E Mn / M E M n / M o log n Reduced form E) All of these FT24A/KEAM-MOD/P+C+M[E1] 8 Brilliant STUDY CENTRE 63. The activation energy for the reaction A B C D 120 kJ is 150 kJ. The activation energy for the C D A B will be: A) 30 kJ B) 270 kJ C) 135 kJ D) 15 kJ E) None of these 64. A radioactive element gets spilled over the floor of a room, its half life period is 30 days. If the initial activity is ten time the permissible value, after how many days will it be safe to enter the room? A) 100 days B) 1000 days C) 300 days D) 10 days E) 150 days 65. The oxidation state of O in OF2 and O2F2 is A) –2 and –1 B) +2 and +1 C) –2 and +1 D) +2 and –1 E) –2 and +2 66. Which of the following has no f electron in the zero oxidation state get it is an f–block element? A) Pa B) Np C) Th D) U E) Am 67. Maximum no. of geometrical isomers possible for the complex Pt NH 3 2 Cl2 is: A) 2 B) 3 C) 4 D) 5 E) 6 2 68. The hybridisation of Ni CN 4 is A) sp3 B) sp3d C) dsp3 D) dsp 2 E) sp 2 d 69. Which of the following is most reactive towards SN' mechanism? CH3 CH3 CH 3 C I CH 3 C Br A) CH 3 I B) C) CH3 CH3 D) CH 3 Br E) CH 3 CH 2 I 70. An organic compound on reaction with con.HCl and anhy. ZnCl2 developed an immdediate turbidity. The organic compound could be: CH 3 CH CH 2 OH A) CH 3OH B) CH 3 CH 2 OH C) CH3 CH3 CH3 CH OH CH 3 C OH D) E) CH3 CH3 71. Assertion : Phenol gives a violet coloured complex with neutral FeCl3 Reason : Phenol is less acidic and is an aliphatic alcohol A) Both assertion and reason are true and reason is the correct explanation of assertion B) Both assertion and reason are true but reason is not the correct explanation of assertion C) Assertion is true but Reason is false D) Both assertion and reason are false E) Assertion is false but Reason is true FT24A/KEAM-MOD/P+C+M[E1] 9 Brilliant STUDY CENTRE 72. The product ‘X’ in the following Reaction is: CH 3 CH CH CH 2 CH 3 i) O3 ii) Zn /H 2 O CH 3CHO X A) CH 3CHO B) CH 2O C) CH 3 CH 2CHO D) CH 3COOH E) CH 3CH 2 COOH 73. Which of the following gives a positive iodoform test? A) Acetaldehyde B) Acetone C) Acetophenone D) Ethanol E) All of these 74. Which of the following amines cannot be prepare by Gabriel phthalimide synthesis? A) CH 3 NH 2 B) CH 3CH 2 NH 2 C) CH3 CH CH 2 NH 2 CH3 NH2 CH2NH2 D) E) 75. Total no. of tripeptides than can be prepared using 3 different aminoacids (All tripeptides should contain this 3 amino acids) A) 6 B) 5 C) 4 D) 3 E) 2 MATHEMATICS 5 5 5 5 76. If nth term of the geometric progression 5, , ,..........is , the value of n is 2 4 8 1024 A) 12 B) 5 C) 6 D) 10 E) 11 r 77. Let a1, a2.......a100 be an arithmatic progression with a1 = 3, Sr a i ,1 r 100. For any integer n, with i 1 Sm 1 n 20 and m = 5n. Let Sn be independent of n. Then value of the common difference is A) 9 B) 6 C) 3 D) 5 E) 2 78. An AP consists of 23 terms. If the sum of the middle three terms is 141 and the sum of the last three terms is 261, then the first term is A) 2 B) 3 C) 4 D) 5 E) 6 79. If the sum of the first n terms of the AP. 2,4,6....is 240, then the value of n is A) 14 B) 15 C) 16 D) 17 E) 18 The least integer k which makes the roots of x 5x k 0 imaginary is 2 80. A) 4 B) 5 C) 6 D) 7 E) 8 6 1 81. Term independent of x in the expansion of x 2 is x A) 20 B) 15 C) 13 D) 12 E) 6 FT24A/KEAM-MOD/P+C+M[E1] 10 Brilliant STUDY CENTRE 2 5 82. Value of sec cosec is 3 6 A) -2 B) 2 C) 0 D) 4 E) -4 83. Value of tan 1 3 tan 1 1 is 2 3 1 5 1 2 1 1 1 5 1 1 A) tan B) tan C) tan D) tan E) tan 2 3 3 3 3 3 2 x 2 y2 84. The line y=mx+c touches the ellipse 1 if a 2 b2 A) c a 2 m 2 b 2 B) c 2 a 2 m 2 b 2 C) c 2 a 2 m 2 b 2 D) c a 2 m 2 b 2 E) c 2 a 2 1 m 2 85. The point which divides the line joining (1,3,4) and (4,3,1) internally in the ratio 2 : 1 is A) (2,-3,3) B) (2,3,5) C) (3,3,2) D) (-3,3,2) E) (3,-3,2) If a 5 , b 6 and a.b 86. 25 , then a b is A) 5 11 B) 6 11 C) 11 5 D) 11 6 E) 25 x y z 0 y z 5 87. If , then x + y + z = z 3 A) 4 B) 2 C) 0 D) -2 E) 8 88. If two numbers p and q are chosen randomly with replacement from {1,2,3,4}, then the probability that p 2 4q is 3 5 7 9 11 A) B) C) D) E) 16 16 16 16 16 1 lim 89. x 0 1 is 3 2 x 1 1 1 A) 0 B) 1 C) D) E) 2 3 4 2 2 90. If y 2 sin , x 2 1 cos , then value of d y2 at x dx 3 1 2 4 A) 3 B) C) D) E) 0 3 3 3 91. Slope of the normal to the curve y3 - xy - 8 = 0 at (0,2) is 1 1 A) B) -6 C) 3 D) E) 1 6 3 FT24A/KEAM-MOD/P+C+M[E1] 11 Brilliant STUDY CENTRE 92. A plane intersects the co-ordinate axes at A,B, C such that the centroid of triangle ABC is (3,2,1). Equa- tion of the plane is A) x 2y 3z 9 B) 2x 3y 6z 18 C) 2x 3y 6z 18 D) 2x y 6z 18 E) 2x 3y 6z 9 x 1 y 1 z x y 2 z 1 93. Equation of the plane containing and is 2 1 3 2 1 3 A) x y z 6 0 B) 8x y 5z 7 C) x 8y 3z 6 0 D) 8x y 5z 8 E) x 8y 3z 6 If the circles x 7 y 3 36 and x 5 y 2 49 touch each other externally, then the 2 2 2 2 94. point of contact is 19 19 17 9 19 9 17 9 19 9 A) , B) , C) , D) , E) , 13 13 13 13 13 13 13 13 13 13 x 5 x 4 x 6 dx 4 95. 1 1 x 5 5 x 5 6 C x 5 5 x 5 7 C 4 2 5 2 A) B) 30 35 1 1 x 5 6 x 5 7 C x 5 5 x 5 6 C 6 5 2 C) D) 42 30 1 x 5 5 x 5 7 C 5 2 E) 35 z z 96. If z r cos i sin , then z z A) 2 cos 2 B) cos 2 C) 2cos D) 2sin E) 2sin 2 cos x x sin x 97. x 2 x cos x dx equals x cos x x A) n C B) n C x x cos x x x C) n C D) n C x sin x x cos x x E) n C x sin x x y 98. The line 1 cuts the x-axis at P. Equation of the line passing through P and perpendicular to the given a b line is A) ax by a 2 B) ax by a 2 C) bx ay a 2 D) ax by b 2 E) bx ay ab FT24A/KEAM-MOD/P+C+M[E1] 12 Brilliant STUDY CENTRE 1 x 99. xe x dx equals A) n 1 xe x C B) n x e x C C) n x e x C D) n 1 xe x C 1 C E) x e x 2 100. If 43 C r 6 43 C3r 1 , value of r is A) 6 B) 8 C) 10 D) 12 E) 14 1 a 1 1 1 1 b 1 101. Value of is 1 1 1 c A) ab + bc + ca B) abc 1 1 1 C) a+b+c D) abc a b c 1 1 1 E) abc 1 a b c 102. A die is rolled three times. The probability that the sum of the three member is 15 is 5 5 11 6 7 A) B) C) D) E) 108 216 216 108 108 103. Value of cos sin 2 3 1 is 5 5 3 5 5 A) B) C) D) E) 3 3 5 3 3 1 1 104. If tan 2x tan 3x , then the value x is 2 1 1 1 1 1 A) B) C) D) E) 6 6 3 3 5 x 7 y3 z 2x z5 y 105. Angle between the lines and is 1 5 3 7 1 2 A) B) C) D) E) 0 2 3 4 6 dy 106. If y = 5 sinx, then at x is dx 2 1 1 A) log 5 B) 2 log5 C) log 5 D) log 5 E) 0 2 3 FT24A/KEAM-MOD/P+C+M[E1] 13 Brilliant STUDY CENTRE 107. If the scalar product of ˆi ˆj 2kˆ with the unit vector along piˆ 2ˆj 3kˆ is 2, then the value of p is A) 3 B) 4 C) 5 D) 6 E) 7 108. If a 2iˆ 2ˆj kˆ , b ˆi ˆj 2kˆ and a b a b , then is A) -1 B) 1 C) 0 D) 2 E) -2 6 109. x 3dx is 0 A) 18 B) 9 C) 6 D) 12 E) 0 3 sin x 110. dx sin x cos x is euqal to 6 A) B) C) D) E) 4 6 12 10 3 1 t2 111. If tan t , then 2 1 t2 A) sin B) cos C) tan D) cos 2 E) sin 2 17 112. If the length of the major axis of an ellipse is times that of the minor axis, the eccentricity is 8 13 8 2 2 15 9 A) B) C) D) E) 17 17 17 17 17 113. a 1 , b 3 and a b 7 , then angle between a and b is A) 0 B) C) D) E) 6 4 3 2 114. Average weight of 35 students is 40 kgms. If the weight of the teacher is included, the average increases by 1 kgms. The weight of the teacher is 2 A) 52 B) 54 C) 55 D) 58 E) 60 115. The eccentricity of a hyperbola is 2 and distance between the foci is 16. The equation is A) x2 - y2 = 4 B) x2 - y2 = 16 C) x2 - y2 = 32 D) x2 - y2 = 48 E) x2 - y2 = 64 116. One of the points on the parabola y2 = 12 x whose focal distance is 12, is A) 1, 12 B) 8, 4 6 C) 7, 2 21 D) 9, 6 3 E) (3,6) 117. Principal solution of 3 sec x 2 is 5 7 A) B) C) D) E) 6 6 6 6 3 118. The angle of elevation of the top of a tower from a point at a distance 500 metres from the foot is 300. Height of the tower is 500 250 A) 500 3 B) 3 C) 250 D) 250 3 E) 3 3 3 FT24A/KEAM-MOD/P+C+M[E1] 14 Brilliant STUDY CENTRE 119. Equation of the chord of the circle x2 + y2 = 81 which is bisected at (-2,3) is A) 3x - 3y = 13 B) 2x - 3y + 13 = 0 C) 2x - 3y = 13 D) 3x-y = -9 E) 3x - 4y +18 = 0 a cot x a cos x lim 120. x cot x cos x is equal to 2 A) log a B) log 2 C) a D) log x E) none of these 9 x2 2 121. The coefficient of x in the expansion of is 9 2 x A) 512 B) –512 C) 521 D) 251 E) 522 122. The area of a parallelogram with diagonals as a 3iˆ ˆj 2kˆ and b ˆi 3jˆ 4kˆ is 10 5 A) 10 3 B) C) 5 3 D) E) 3 3 3 x 1 y 2 z 3 x 2 y4 z5 123. The shortest distance between the lines and is 2 3 4 3 4 5 1 1 1 1 A) B) C) D) E) 6 6 6 3 3 dy 124. If x y e x y , then is equal to dx log x log x log x y log x 1 log x A) 1 log x B) 1 log x C) 1 log x 2 D) x 1 log x E) log x 4 4 2 125. If f x dx 4and 1 2 3 f x dx 7 , then the value of f x dx 1 A) –2 B) 3 C) 5 D) 8 E) –1 zi 126. If 1 , then the locus of z is zi A) x = 0 B) y =0 C) x=1 D) y = 1 E) none of these 12 22 32 22 32 42 127. The value of is 32 42 52 A) 8 B) –8 C) 400 D) 1 E) 0 2x 1 128. Let the function f be defined by f x . Then f 1 x is 1 3x x 1 3x 1 x 1 2x 1 1 3x A) B) C) D) E) 3x 2 x 1 3x 2 1 3x 2x 1 129. The value of a. b c a b c is equal to A) 0 B) a b c C) 2a D) a E) none of these FT24A/KEAM-MOD/P+C+M[E1] 15 Brilliant STUDY CENTRE a ab a 2b a 2b a ab 130. If value of is equal to ab a 2b a A) 9a 2 a b B) 9b2 a b C) a 2 a b D) b 2 a b E) 9b2 a b 131. The value of sin12 sin 48 sin 54 is equal to 2 1 1 1 A) B) C) D) E) 3 3 2 8 3 132. The point of contact of the line x y 2 0 with the parabola y 2 8x 0 is A) 2, 4 B) 2, 4 C) 2, 4 D) 2, 2 E) 6,8 133. The general solution of e x cos y dx e x sin y dy 0 is A) e x sin y cos y c B) e x sin y c C) e x c cos y D) e x c sin y E) e x cos y c 134. tan 1 x tan 1 y c is general solution of the differential equation dy 1 y 2 dy 1 x 2 A) B) C) 1 x 2 dy 1 y 2 dx 0 dx 1 x 2 dx 1 y 2 dy 1 y2 D) E) 1 x 2 dx 1 y dy 0 dx 1 x 2 1 2x 1 135. The domain of sin is 3 A) 2, 1 B) 2,1 C) R D) 1,1 E) 2,0 136. The sm of the series 1 2.2 3.2 2 4.23 5.24 ..... 100.299 is A) 99.2100 B) 100.2100 C) 99.2100 1 D) 1000.2100 E) 100.2100 1 1 1 0 137. For the matrix A 1 2 1 , which is correct 2 1 0 A) A 3 3A 2 I 0 B) A 3 3A 2 I 0 C) A 3 2A 2 I 0 D) A 3 A 2 I 0 E) A 3 A 2 I 0 i 0 i i i P 0 i i Q 0 0 138. If and then PQ is equal to i i 0 i i 2 2 2 2 1 0 0 1 1 1 1 2 2 0 1 0 1 0 A) B) C) D) E) 1 1 1 1 1 1 0 0 1 0 1 FT24A/KEAM-MOD/P+C+M[E1] 16 Brilliant STUDY CENTRE a 2 139. The value of a for which the matrix A is singular 2 4 A) a 1 B) a 1 C) a = 0 D) a = –1 E) none of these 140. Two cards are drawn successively with replacement from a well-shuffled pack of 52 cards. The probabil- ity of drawing two aces is 1 1 1 1 1 1 4 1 1 A) B) C) D) E) 13 13 17 52 51 13 51 13 13 26 26 1 3 1 3 141. The value of is 2 2 A) –1 B) 1 C) 0 D) 2 E) none of these 142. The number of ways in which 21 objects can be grouped into three groups of 8,7 and 6 objects is 20! 2 1! 2 1! 21! A) B) C) D) E) none of these 8! 7! 6! 8!7 ! 8 !7 !6 ! 8! 7!6! 143. If A 2 A I 0 , then the inverse of A is A) A 2 B) A 1 C) I A D) A I E) A 144. The area of the triangle whose vertices are (1,2,3), (2,5,–1) and (–1,1,2) is 155 155 165 A) 150 sq. units B) 145 sq. units C) sq.units D) sq.units E) sq.units 2 2 2 145. If n and r are two positive integers such that n r, then n C r 1 n C r is equal to n 1 n 1 n 1 A) n C n r B) n C r C) Cr D) Cr E) C r 1 146. If and are roots of the equation 4x 2 2x 1 0 then the value of 2 2 is 3 1 1 A) 2 B) C) 3 D) E) 4 4 2 xy dy 147. If sec a, then is xy dx x y x A) B) C) y D) x E) y x a 148. If f x y f x .f y , f 3 3, f 0 11 , then f 3 is equal to A) 11.e33 B) 33 C) 11 D) log 33 E) none of these 1 x 1 x 99 149. The value of dx is equal to 0 1 11 1 11 1 A) B) C) D) E) 10100 10100 10010 11100 1010 dy 150. If y = x tan y, then is equal to dx tan y y tan y tan x tan y A) B) C) D) E) x x 2 y2 xx y 2 2 yx x y2 x x 2 y2 Date: 14-05-2024 Batch: ENGG. 2024 Version Brilliant E1 STUDY CENTRE CEE KERALA ENGG. MODEL EXAM - ALL UNIT Puliyannoor P.O., PALA TEST ID 211 Ph - 04822 206416, 206516, 206459 www.brilliantpala.org [PHYSICS + CHEMISTRY + MATHEMATICS] PHYSICS 1. D By symmetry net force = 0 V r V 9 10 6 KQ KQ 2. A E ; V ; E ; min E r2 r r max 3 106 3. E Initial energy Ui 12 2V 2 V 2 ; Final voltage after switch 2 is 0N C1V1 2V Vf 0.2V C1 C2 10 2 2V Final energy in both the capacitor = 12 C1 C2 Vf 12 10 0.2V 2 2 10 4. E V2 5. B P so R V 2 R 6. D 7. E 2km 2 107 6.75 27 3 8. C BH r 3 5 ;r 30cm r 3 5 10 1000 10 3 9. D MBsin 60o ; w MB 1 cos 60 ; o 2 w 3 w 1 2 10. D 11. A FT24A/KEAM-MOD/P+C+M[E1] 2 Brilliant STUDY CENTRE 0 NI q e B ; I ne B 0 ne 12. C 2r T 1 ; (Here N = 1 as e– makes only one loop) n 2r d d dr 13. B e B r2 2rB 2 2 102 2 103 0.04 3.2V dt dt dt VSIS V 6 3000 14. E 0.9 S 3 ; VS 450V ; As VP IP 3000 so IP A 15A VP IP 3 10 200 15. A VR2 VL2 1202 ; VL 1202 542 107V VR i P ; i2fL VL ; 16 2 60L 107 ; L 0.96H 1H 54 uv 330 500 16. B V V Vs 330 30 17. E m1u m1v1 m2 v 2 and v 2 v1 1 u m2 v 22 1 2 Find v2 in terms of u. The required fraction is 1 m u2 2 1 18. C The train has covered a distance of 200m in the time interval 200m in the time interval 2 200m 0 1 0.5m /s 2 2 19. D Coefficient of friction = cx, c = constant Maximum acceleration = y cx y ; V 2 0 2 cgx x ; V2 x2; K.E. x 2 20. A mg T F F 2mg ; 1 2 GM 3GM 21. C Gravitational P. E. at the surface = and at the centre R 2R GM 3 GM 1 GMm 1 P.E. m = 2 R 2 mV ; 2 R 2 R GM V2 V2 Rg R 2 22. C m1s11 m2s 22 ..... 23. A m1s1 m2s 2 .... 10s1 25s2 For A + B 15 5s1 10s 2 ; s1 2s2 s1 s2 25s 2 40s 3 For B + C 30 ; s3 0.5s2 s2 s 3 10s1 40s 3 10 2s 2 40 0.5 s 2 40 For A + C 16 s1 s 3 2s 2 0.5s 2 2.5 FT24A/KEAM-MOD/P+C+M[E1] 3 Brilliant STUDY CENTRE 24. C If a body cools from temperature Q1 to Q2 in time t, when the surrounding temperature is 0 Q1 Q2 Q Q2 by Newton’s law of cooling C 1 0 t 2 25. E 26. C 1 4 3 3M 3 27. B M = R ; R 3 4 2 GM 4 3 g 2 GM ; 1 g M 3 2 3 R 3M 1 2 g planet 8M 3 8 3 1 2 = 8; g M 3 3 g planet 8 g 1 2h 28. B h at 2 ;a T = mg-ma 2 t2 RT R 2 T R 2m g a T = I RT I a a 29. B 30. A A1V1 = A2V2 31. C du = dQ - dW = mq T P v 32. C 33. C 34. C 35. A 2r 2r 36. A T= v 0 GM / r Which is independent of mass of satellite, hence both the satellites have same time period of revolution. 37. A 38. C FT24A/KEAM-MOD/P+C+M[E1] 4 Brilliant STUDY CENTRE 39. B 40. D 41. E C 42. C V 0 r 13.6 13.6 43. C Energy in excited state = –13.6 + 12.1 = –1.5 eV; 2 1.5 n 3 n 1.5 n n 1 3 3 1 No. of spectral lines = 3 2 2 h t .1 1 44. C h = ut 12at 19.6m; 2 2 2 ; h h h t 2 10 10 2u y 45. B T = 6 second = g ; u y 30m / s V y u y gt 30 20 tan 30° = V Vx ux ; ux = 10 3 m/s; u = u 2x u 2y x CHEMISTRY 46. A 47. C 48. D FT24A/KEAM-MOD/P+C+M[E1] 5 Brilliant STUDY CENTRE 49. D 50. E 51. C 52. C 53. B 54. E 55. D 56. C 57. C 58. A 59. C 60. A CH 3 CH 2 CH 2 I NaCN CH 3 CH 2 CH 2 CN CH 3 CH 2 CH 2 CONH 2 CH 3 CH 2 CH 2 NH 2 61. B 1 2 i M1 RT M 2 RT i M1 M 2 0.02 2 20 i 0.008 0.02 ; i 0.008 0.8 8 2.5 62. E 63. A 64. A 65. B 66. C 67. A 68. D 69. B 70. E 71. C 72. C 73. E 74. D 75. A FT24A/KEAM-MOD/P+C+M[E1] 6 Brilliant STUDY CENTRE MATHEMATICS 76. E 77. B 78. B 79. B 80. D 81. B 82. C 83. D 84. B 85. C 86. A 87. B 88. C 89. D FT24A/KEAM-MOD/P+C+M[E1] 7 Brilliant STUDY CENTRE 90. C 91. A 92. C 93. B 94. C 95. B 96. A 97. B 98. B 99. A 100. D 101. E 102. A FT24A/KEAM-MOD/P+C+M[E1] 8 Brilliant STUDY CENTRE 103. E 104. B 105. A 106. E 107. D 108. B 109. B 110. C 111. B 112. D 113. D 114. D 115. C 116. D 117. A 118. B FT24A/KEAM-MOD/P+C+M[E1] 9 Brilliant STUDY CENTRE 119. B 120. A a cot x cos x 1 Lt log a cot x cos x x 2 121. B 122. C FT24A/KEAM-MOD/P+C+M[E1] 10 Brilliant STUDY CENTRE 123. B x dy log x 124. C y log x x y ; y 1 log x x ; y ; 1 log x dx 1 log x 2 125. C 126. B FT24A/KEAM-MOD/P+C+M[E1] 11 Brilliant STUDY CENTRE 127. B 128. A 129. A 130. B FT24A/KEAM-MOD/P+C+M[E1] 12 Brilliant STUDY CENTRE 131. C 132. A 133. E 134. C 135. B FT24A/KEAM-MOD/P+C+M[E1] 13 Brilliant STUDY CENTRE 136. C 2 3 1 7 9 3 A 5 6 2 , A A , A 15 19 6 2 3 2 137. B 3 4 1 9 12 4 Hence A 3 3A 2 I 0 138. B 139. B 140. E 141. A 142. C FT24A/KEAM-MOD/P+C+M[E1] 14 Brilliant STUDY CENTRE 143. C 144. C 145. D 146. B 147. B 148. B FT24A/KEAM-MOD/P+C+M[E1] 15 Brilliant STUDY CENTRE 149. A 150. B
