KEAM (ENGINEERING) ANSWER KEY 2018

Transcription

1 PGE: M.O: Kunnumpuram, yurveda College Jn., Trivandrum-, (: , Website: KOCHI KOLLM BRNCHES Puthussery Building, Kaloor Sivajyothi Comple, Polayathode (: (: KEM (ENGINEERING) KEY 08 QUESTIONS & S PPER I PHYSICS & CHEMISTRY. The one-dimensional motion of a point particle is shown in the figure. Select the correct statement () The total distance travelled by the particle is zero (B) The total displacement of the particle is zero (C) The maimum acceleration of the particle is ½ ms (D) The total distance travelled by the particle at the end of 0s is 00 m (E) t the 5 th second, the acceleration of the particle is ms. The period of oscillation of a simple pendulum is given by T = π L, where L is the g length of the pendulum and g is the acceleration due to gravity. The length is measured using a meter scale which has 000 divisions. If the measured value L is 50 cm, the accuracy in the determination of g is.% and the time taken for 00 oscillations is 00 seconds, what should be the resolution of the clock (in milliseconds) () (B) (C) 5 (D) 0.5 (E) From a circular card board of uniform thickness and mass M, a square disc of maimum possible area is cut. If the moment of inertia of the square with the ais of rotation at the Ma centre and perpendicular to the plane of the disc is, the radius of the circular card 6 board is a () a (B) (C) a (D) (E) a a B

2 PGE: 4. The length is measured using a vernier system whose main scale is 30 cm long with 600 divisions. If 9 divisions of the main scale coincide with 0 divisions of the vernier scale, then its least count is () 0.5 cm (B) 0.05 cm (C) 0.5 mm (D) 0.05 mm (E) mm D k λ 5. particle of mass m is moving along the -ais under the potential V( ) = +, where k and λ are positive constants of appropriate dimensions. The particle is slightly displaced from its equilibrium position. The particle oscillates with the angular frequency ω given by () 3 k (B) 3 m k (C) (D) 3 m (E) 3 k m k m k m C 6. Two particles of mass m and m have their position vectors as a function of time as r ur () t = ti $ t 3 $ j + t k $ and r ur () t = ti $ t 3 $ j t k $ respectively (where t is the time). Which one of the following graphs represents the path of the centre of mass E 7. Two planets and B have the same average density. Their radii R and R B are such that R : R B = 3 :. If g and g B are the acceleration due to gravity at the surfaces of the planets, the g : g B equals () 3 : (B) : 3 (C) 9 : (D) : 9 (E) 3: 8. The magnetic induction field has the dimensions of () Force (B) Force constant (C) Surface tension Surface tension (D) Current (E) Force constant current D

3 PGE: 3 9. Einstein was awarded the Nobel Prize for his work on () Photoelectric effect (B) Special theory of relativity (C) Brownian motion (D) General theory of relativity (E) Quantum theory 0. thin circular ring of mass m and radius R is rotating about its ais perpendicular to the plane of the ring with a constant angular velocity ω. Two point particles each of mass M are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity ω/. Then, the ratio m/m is () (B) (C) (D) (E) B. body of mass m = kg is moving in a medium and eperiences a fractions force F = kv, where v is the speed of the body. The initial speed is v 0 = 0 ms and after 0s, its energy becomes half of initial energy. Then, the value of k is () 0ln (B) ln (C) ln (D) 0 ln (E) ln 0. r The position vector of the particle is rt () = acosωti $ + a sin ωtj $, where a and ω are real constants of suitable dimensions. The acceleration is () perpendicular to the velocity (B) parallel to the velocity (C) directed away from the origin (D) perpendicular to the position vector (E) always along the direction of $ i 3. Some of the following equations are kinetic equations, where the symbols have their usual meaning. The work-energy theorem is represented by () v = u + at (B) s = ut (C) s = ut + at u (D) v = + as (E) v = u + as E 4. If, v and a denote the displacement, the velocity and the acceleration of a particle eecuting simple harmonic motion of time period T, then which of the following do not change with time? () at/v (B) at + πv (C) a T + 4π v (D) at (E) vt 5. rubber cord of density d, Young s modulus Y and length L is suspended vertically. If the cord etends by a length 0.5L under its own weight, then L is Y () (B) Y (C) Y dg (D) (E) dg dg dg dg Y Y B

4 PGE: 4 6. Which of the following graphs represents the speed v of a projectile as a function of time t B 7. body P floats in water with half its volume immersed. nother body Q floats in a liquid of density 3/4 th of the density of water with two-third of the volume immersed. The ratio of density of P to that of Q is () : (B) : (C) : (D) : 3 (E) 3 : 4 B 8. pipe of m length is closed at one end. Taking the speed of sound in air as 30 ms, the air column in the pipe cannot resonate for the frequency (in Hz) () 80 (B) 60 (C) 40 (D) 560 (E) 70 B 5 9. wave pulse in a string is described by the equation y = and another wave (3 4) t + 5 pulse in the same string is described by y = (3 + 4t 6) +. The values of y, y and are in meters and t in seconds. Which of the following statement is correct? () y travels along -direction and y along + -direction (B) both y and y travel along -direction (C) both y and y travel along + -direction (D) at = m, y and y always cancel (E) at time t = s, y and y eactly cancel everywhere D

5 PGE: 5 0. The maimum transverse velocity and maimum transverse acceleration of a harmonic wave in a one-dimensional string are ms and ms respectively. The phase velocity if the wave is ms. The waveform is () sin( t) (B) sin( t) (C) sin( t) (D) sin(/ t) (E) sin ( t/). Two particles and B of same mass have their de Broglie wavelengths in the ratio λ : λ B = k :. Their potential energies U : U B = : k. The ratio of their total energies E : E B is () k : (B) : k (C) k : (D) : k (E) :. particle is moving along the -ais such that its acceleration is proportional to the displacement from the equilibrium position and they are in the same direction. The displacement (t) is given by () sin ωt, ω > 0 (B) sin ωt + cos ωt, ω > 0 (C) e ωt, ω > 0 (D) e ωt + sin ωt, ω > 0 (E) e ωt + e ωt, ω and ω > 0 3. block of mass kg is free to move along the -ais. It is at rest and from time t = 0 onwards it is subjected to a time-dependent force F(t) in the -direction. The force F(t) varies with t as shown in figure. The kinetic energy of the block at t = 4 s is () J (B) J (C) 3 J (D) 0 J (E) 4 J D 4. Consider a wire with density ρ and stress σ. For the same density, if the stress increases times, the speed of the transverse waves along the wire changes by () (B) (C) (D) (E) 4 5. Two soap bubbles of radii 3 mm and 4 mm confined in vacuum coalesce isothermally to form a new bubble. The radius of the bubble formed (in mm) is () 3 (B) 3.5 (C) 4 (D) 5 (E) 7 D

6 PGE: 6 6. n oscillator circuit contains an inductor 0.05 H and a capacitor of capacity 80 µf. When the maimum voltage across the capacitor is 00 V, the maimum current (in amperes) in the circuit is () (B) 4 (C) 8 (D) 0 (E) 6 7. The displacement y of a particle if given by y = 4cos (t/) sin (000 t). This epression may be considered to be a result of the superposition of how many simple harmonic motions? () 4 (B) 3 (C) (D) 5 (E) 6 8. cylindrical tube, open at both the ends has fundamental frequency n. If one of the ends is closed, the fundamental frequency will become n () (B) n (C) n (D) 4n (E) 3n 9. uniform bar of mass m is supported by a pivot at its top about which the bar can swing like a pendulum. If a force F is applied perpendicular to the lower end of the bar as shown in figure, what is the value of F in order to hold the bar in equilibrium at an angle θ from the vertical () mg sinθ (B) mg sin θ (C) mg cos θ mg (D) sin mg θ (E) cos E 30. particle of rest mass m 0 is travelling so that its total energy is twice its rest mass energy. It collides with another stationary particle of rest mass m 0 to form a new particle. What is the rest mass of the new particle? () 6m 0 (B) m 0 (C) 3m 0 (D) 3m 0 (E) 3m 0 E 3. The dimensions of ε 0 (permittivity in free space) is () ML T 4 (B) ML 3 T (C)M L 3 T 4 (D) ML 3 T (E) M L 3 T 4 E 3. The displacement of a wave is represented by y = sin (500 t 0.05) where all the quantities are in their proper units. The maimum particle velocity (in ms ) of the medium is () 0.5 (B) 0.03 (C) 0.50 (D) 0.75 (E) 0.3 E θ

7 PGE: The electric field of certain radiation is given by the equation E = 00 {sin (4π 0 0 ) t + sin (4π 0 5 )t} falls in a metal surface having work function.0 ev. The maimum kinetic energy (in ev) of the photo electrons is (use Planck s constant (h) = Js and electron charge (E) = C) () 3.3 (B) 4.3 (C) 5.3 (D) 6.3 (E) 7.3 D 34. The de Broglie wavelength λ n of the electron in the n th orbit of hydrogen atom is () inversely proportional to n (B) proportional to n (C) proportional to n (D) inversely proportional to n (E) inversely proportional to radius of the orbit in the n th state 35. In a thermodynamic system, Q represents the energy transferred to or from a system by heat and W represents the energy transferred to or from a system by work I. Q > 0 and W = 0 II. Q < 0 and W = 0 III. W > 0 and Q = 0 IV. W < 0 and Q = 0 Which of the above will lead to an increase in the internal energy of the system () I only (B) II only (C) I and IV only (D) II and III only (E) II and IV only 36. cylinder closed at both ends is separated into two equal parts (45 cm each) by a piston impermeable to heat. Both the parts contain the same masses of gas at a temperature of 300 K and a pressure of atm. How much the gas should be heated in one part of the cylinder to shift the piston by 5 cm and the pressure of the gas after shifting the piston () T = 365 K and P =.5 atm (B) T = 350 K and P =.5 atm (C) T = 375 K and P =.5 atm (D) T = 350 K and P =.5 atm (E) T = 375 K and P =.5 atm E 37. Five moles of an ideal moatomic gas with an initial temperature of 50 o C epand and in the process absorb 500 J of heat and does 500 J of work. The final temperature of the gas in o C is (Ideal gas constant R = 8.34 JK mol ) () 34 (B) 6 (C) 44 (D) 66 (E) The temperature of an ideal gas is increased from 00 K to 400 K. If the rms speed of the gas molecule is v at 00 K then at 400 K it becomes () v (B) 4v (C) 0.5 v (D) 0.5 v (E) v

8 PGE: uniform copper rod of 50 cm length is insulated on the sides, and has its ends eposed to ice and steam respectively. If there is a layer of water mm thick at each end, the temperature gradient (in o C m ) in the bar is (ssume that the thermal conductivity of copper is 400 Wm K and water is 0.4 Wm K ) () 60 (B) 40 (C) 50 (D) 55 (E) Carnot engine whose low temperature reservoir is at 350 K has an efficiency of 50%. It is desired to increase this to 60%. If the temperature of the low temperature reservoir remains constant, then the temperature of high temperature reservoir must be increased by how many degrees () 5 (B) 75 (C) 00 (D) 50 (E) 0 4. Two identical systems, with heat capacity at constant volume that varies as C v = bt 3 (where b is a constant) are thermally isolated. Initially, one system is at a temperature 00 K and the other is at 00 K. The systems are then brought into thermal contact and the combined system is allowed to reach thermal equilibrium. The final temperature (in K) of the combined system will be () 7 (B) 4 (C) 50 (D) 80 (E) 5 4. Water flows steadily through a horizontal pipe of a variable cross section. If the pressure of the water is p at a point where the speed of the flow is v, what is the pressure at another point where the speed of the flow is v; let the density of water be ρ () p + (3/)ρv (B) p ρv (C) p + ρv (D) p 3 ρv (E) p (3/)ρv E 43. soap bubble of radius r is blown up to form a bubble of radius r under isothermal conditions. If σ is the surface tension of soap solution, the energy spent in doing so is () 6πσr (B) 3πσr (C) 4πσr (D) πσr (E) 9πσr C 44. The mean momentum of a nucleon in a nucleus with mass number varies as () 3 (B) (C) /3 (D) /3 (E) /3 E 45. decay chain of the nucleus 38 9 U involves eight α-decays and si β-dacays. The final nucleus at the end of the process will be () Z = 76; = 00 (B) Z = 84; = 06 (C) Z = 84; = 4 (D) Z = 8; = 06 (E) Z = 8; = 00 D

9 PGE: flat mirror revolves at a constant angular velocity making n = 0.4 revolutions per second. With what velocity (in ms - ) will a light spot move along a spherical screen with a radius of 5 meters, if the mirror is at the centre of curvature of the screen () 37.7 (B) 60.3 (C) 68.7 (D) 75.4 (E) 90.4 D 47. parallel beam of light of wavelength 4000 Å passes through a slit of width M. The angular spread of the central maima in the diffraction pattern is () rad (B) rad (C). 0 3 rad (D) rad (E) rad 48. wire made of aluminium having resistivity ρ = Ω m with a circular cross section and has a radius of 0 3 m. current of 5 flows through the wire. If the voltage difference between the ends is V, what is the length of the wire in meters () 50 (B) 60 (C) 90 (D) 0 (E) When two capacitors are connected in parallel the resulting combination has capacitance 0 µf. The same capacitors when connected in series results in a capacitance 0.5 µf. The respective values of individual capacitors are ().9 µf and 0. µf (B) (8 + 5) µf and ( 5) µf (C) (5 + 5) µf and (5 5) µf (D) µf and.7 µf (E) 5 µf and µf 50. rectangular conducting loop of length 4 m and breadth 4 m carrying a current of 5 in the anti-clockwise direction is placed in the y-plane. The magnitude of the magnetic induction field vector B at the intersection of the diagonals is (Use µ 0 = 4π 0 7 N ) (). 0 6 T (B). 0 5 T (C) T (D) T (E). 0 7 T

10 PGE: 0 5. Three point charges 4q, Q and q are placed in a straight line of length L at points 0, L/ and L respectively. The net force on charge q is zero. The value of Q is () 4q (B) q (C) 0.5q (D) q (E) 3q r 5. particle of charge Q moves with a velocity v = ai ur in a magnetic field B = bj + ck, where a, b and c are constants. The magnitude of the force eperienced by the particle is () Q (b + c) (B) Zero (C) Qa Qa ( b + c ) (D) Qa ( b c ) (E) Qa(b c) C 53. point charge +Q is held at rest at a point P. nother point charge q, whose mass is m, moves at a constant velocity v in a circular orbit of radius R around P. The work required to increase the radius of revolution of q from R to another orbit R is (R > R ) Qq Qq () (B) (C) Qq R R R R R R (D) Qq (E) Qq R R R R D 54. voltage V PQ = V 0 cos ωt (where V 0 is a real amplitude) is applied between the points P and Q in the network shown in the figure. The values of capacitance and inductance are R 3 C = and L = ωr 3 ω Then, the total impedance between P and Q is ().5 R (B) R (C) 3R (D) 4R (E).5 R 55. Two particles and B of same mass have their total energies E and E B in the ratio E : E B = :. Their potential energies U and U B are in the ratio U : U B = :. If λ and λ B are their de Broglie wavelengths, then λ : λ B is () : (B) : (C) : (D) : (E) : D

11 PGE: 56. The electrical conductivity of a metal is () directly proportional to the mean free path (B) directly proportional to the mass of electron (C) inversely proportional to the relaation time (D) inversely proportional to the mean free path (E) directly proportional to the average speed of free electrons 57. MeV neutron is emitted in a fission reactor. If it looses half of its kinetic energy in each collision with a moderator atom, how many collisions must it undergo to achieve thermal energy of ev () 0 (B) 6 (C) 30 (D) 4 (E) The 6 V Zener diode is shown in figure has negligible resistance and a knee current of 5 m. The minimum value of R (in Ω) so that the voltage across it does not fall below 6 V is () 40 (B) 60 (C) 7 (D) 80 (E) 0 D 59. n electron is moving with a velocity 0 6 m/s along positive -direction in the uniform electric field of V/m applied along positive y-direction. The magnitude and direction of a uniform magnetic field (in Tesla) that will cause the electrons to move undeviated along its original path is () 40 in ve z-direction (B) 40 in +ve z-direction (C) 4 in +ve z-direction (D) 4 in ve z-direction (E) 8 in +ve z-direction 60. What is the minimum thickness (in nm) of a soap film (n =.3) that results in constructive interference in reflected light if the film is illuminated with light whose wavelength in free space is 60 nm () 00 (B) 0 (C) 60 (D) 40 (E) Three variable Boolean epression PQ + PQR + P Q + PQ R can be written as () Q + P R (B) P + Q R (C) Q + PR (D) Q + P R (E) P + QR

12 PGE: 6. prism is made up of material of refractive inde. The angle of the prism is. If the angle of minimum deviation is equal to the angle of the prism, the value of is () 30 o (B) 45 o (C) 60 o (D) 75 o (E) 90 o E 63. Consider a cylindrical conductor of Length L and area of cross section. The specific L conductivity varies as σ( ) = σ0 where is the distance along the ais of the cylinder from one of its ends. The resistance of the system along the cylindrical ais is L 3 L L L 4 L () (B) (C) (D) (E) 3σ σ 3σ σ 3σ If the emission rate of blackbody at 0 o C is R then, the rate of emission at 73 o C is () R (B) 4R (C) 8R (D) 6R (E) 3R D 65. For any material, if R, T and represent the reflection coefficient, transparent coefficient and absorption coefficient respectively, then, for a blackbody which one of the following is true () R =, T = 0, = 0 (B) R =, T =, = 0 (C) R = 0, T =, = (D) R = 0, T = 0, = (E) R = 0, T =, = 0 D 66. In the given circuit P and Q form the inputs. The output Y is () Y = P (B) Y = PQ (C) Y = P + Q (D) Y = Q D (E) Y = P + Q 67. radio transmitter sends out 60 W of radiation. ssuming that the radiation is uniform on a sphere with the transmitter at its centre, the intensity (in W/m ) of the wave at a distance km is () (B) (C). 0-8 (D) (E) E

13 PGE: Consider a system of gas of a diatomic molecule in which the speed of sound at 0 0 C is 60 ms -. Then, the molecular weight of the gas is (Given the gas constant R is 8.34 J/mol.K) () g (B) mg (C) 4 g (D) 0 g (E) 0 g 69. satellite is orbiting the earth in a circular orbit of radius R. Which one of the following statements is true? () angular momentum varies as R (B) linear momentum varies as R (C) frequency of revolution varies as R (D) kinetic energy varies as R (E) potential energy varies as R D 70. The magnitude of a magnetic field at the centre of a circular coil of radius R, having N turns and carrying a current I can be doubled by changing () I to I and N to N keeping R unchanged (B) N to N/ and keeping I and R unchanged (C) N to N and R to R keeping I unchanged (D) R to R and I to I keeping N unchanged (E) I to I and keeping N and R unchanged E 7. n alternating voltage V = V 0 sin ωt is applied across a circuit and as a result, a current π I = I 0 sin ωt + flows in it. The power consumed per cycle is () I 0 V 0 (B) 0.5 I 0 V0 (C) 0.7 I 0 V 0 (D).4I 0 V 0 (E) zero E 7. n electromagnetic wave of intensity I is incident on a non-reflecting surface. If C is the speed of light in free space, then, the ratio I/C is same as () momentum (B) force (C) pressure (D) pressure per unit area (E) force area 73. Which element has the highest first ionization potential? () N (B) Ne (C) He (D) H (E) Li 74. Which statement(s) is (are) false for the periodic classification of elements? () The properties of the elements are the periodic functions of their atomic numbers (B) Non-metallic elements are lesser in number than the metallic elements (C) The first ionization energies of the elements along a period do not vary in a regular manner with increase in atomic number (D) For transition elements, the d-electrons are filled monotonically with increase in atomic number (E) Both (C) and (D) D

14 PGE: The electronegativities of N, C, Si and P are in the order () P < Si < C < N (B) Si < P < N < C (C) Si < P < C < N (D) P < Si < N < C (E) Difficult to predict 76. Gd(64) has unpaired electrons with sum of spin () 7, 3.5 (B) 8, 3 (C) 6, 3 (D) 8, 4 (E) 9, 3.5 D 77. When SO gas is passed into aqueous Na CO 3 the product(s) formed is (are) () NaHSO 4 (B) Na SO 4 (C) NaHSO 3 (D) Na SO 3 and NaHSO (E) NaHSO 4 and Na SO Portland cement does not contain () CaSiO 4 (B) CaSiO 3 (C) Ca 3 l O 6 (D) Ca 3 (PO 4 ) (E) Both (C) and (D) D 79. l (SO 4 ) 3 is used in the following but not () s a coagulant in treating drinking water and sewage (B) In plastics industry (C) s a mordant in dyeing (D) In paper industry (E) Both (C) and (D) 80. Maimum number of covalent bonds formed by N and P are () 3, 5 (B) 3, 6 (C) 3, 4, 5 (D) 3, 4, 6 (E) None of the above E 8. Consider the following statements concerning N H 4. It is an eothermic compound. It burns in air with the evolution of heat 3. It has kinetic stability 4. In reduces Fe 3+ to Fe + in acidic medium Which of the following combination is correct? () and 3 are correct (B) and are correct (C) ll are correct (D) 3 and 4 are correct (E), 3 and 4 are correct 8. Consider the following species. [O ]. [CO] + 3. [O ] + mong these sigma bond alone is present in () alone (B) alone (C) 3 alone (D) and (E), and 3

15 PGE: Select the correct option(s) for the following statements. Cl O and ClO are used as bleaching agents. OCl salts are used as detergents 3. OCl disproportionates in alkaline medium 4. BrO 3 is oidized in acidic medium (),, 3 correct (B), 3, 4 correct (C),, 4 correct (D), 3, 4 correct (E) ll are correct 84. When H O is added to an acidified K Cr O 7 solution () green colour solution is obtained (B) yellow solution is obtained (C) blue-violet solution is obtained (D) green precipitate is formed (E) yellow precipitate is formed 85. Consider the following compounds. (NH 4 ) Cr O 7. NH 4 NO 3. NH 4 VO 3 4. NH 4 NO 3 Which compound(s) yield nitrogen gas upon heating? () and (B) and 3 (C) 3 and 4 (D) and 4 (E) ll 86. How many peroy linkages are present in CrO 5? () (B) (C) 3 (D) 4 (E) More than four bonds are made by how many elements in carbon family? () (B) (C) 3 (D) 4 (E) 5 E 88. The effective nuclear charge of an element with three valence electrons is.60. What is the atomic number of the element? () (B) (C) 3 (D) 4 (E) 5 E 89. The elution sequence of a miture of compounds containing chlorobenzene, anthracene and p-cresol developed of an alumina column using a solvent system of progressively increasing polarity is () anthracene chlorobenzene p-cresol (B) anthracene p-cresol chlorobenzene (C) chlorobenzene p-cresol anthracene (D) chlorobenzene anthracene p-cresol (E) p-cresol anthracene chlorobenzene 90. Number of constitutional isomers of alkane with formula C 6 H 4 is () 3 (B) (C) 5 (D) 0 (E) 8

16 PGE: 6 9. Phenylacetylene on treatment with HgSO 4 /H SO 4, H O produces () acetophenone (B) Phenylacetaldehyde (C) Phenylacetic acid (D) -phenylethanol (E) -phenylethanol 9. Which of the following compounds are aromatic? N + H B C D (), B (B), B, C (C) B, C (D) B, C, D (E), B, D 93. romatic electrophilic substitution reaction that is reversible is () Nitration (B) Chlorination (C) Sulphonation (D) lkylation (E) cylation 94. Which one of the following statements is false? () R and S configurations correspond to the enantiomers of an optically active compound (B) The process of converting an optically active compound into a racemate is called racemization (C) molecule containing a plane of symmetry can be optically active (D) Optical isomers that are not enantiomers are called diastereoisomers (E) ll chiral objects are asymmetric 95. Neopentyl bromide undergoes dehydrohalogenation to give alkenes even though it has no β- hydrogen. This is due to () E mechanism (B) E mechanism (C) Rearrangement of carbocations by E mechanism (D) EcB mechanism (E) Ei mechanism 96. The compound which does not lead to nitrile by substitution with NaCN/DMSO is () Benzyl chloride (B) Ethyl chloride (C) Isopropyl chloride (D) Chlorobenzene (E) Isobutyl chloride D 97. Oidation of alcohols to aldehydes is very successful for the alcohols like () pent--yn--ol (B) -heanol (C) n-propyl alcohol (D) -pentanol (E) -octanol

17 PGE: The compound that does not undergo haloform reaction is () cetaldehyde (B) Ethanol (C) cetone (D) cetophenone (E) Propiophenone E 99. The halogen compound which will not react with phenol to give ethers is () Ethyl chloride (B) Methyl chloride (C) Benzyl chloride (D) Vinyl chloride (E) llyl chloride D 00. The weakest among the following acids is () Peroyacetic acid (B) cetic acid (C) Chloroacetic acid (D) Trichloroacetic acid (E) Propanoic acid 0. The nitrosation of N, N-dimethylaniline takes place through the attack of electrophile () Nitronium ion (B) Protonated nitrous acid (C) Nitrous acid (D) Nitrite ion (E) Nitrosonium ion E 0. The nitrogenous base present only in RN is () Guanine (B) denine (C) Cytosine (D) Uracil (E) Thymine D 03. Green fuel is the fuel obtained from () Bio-waste (B) Metal waste (C) Plastic waste (D) Chemical waste (E) Electronic waste 04. Barbiturates are potent () Hypnotics (B) ntimicrobials (C) ntacids (D) ntiseptics (E) ntiallergics 05. mole of FeSO 4 (atomic weight of Fe is g mol ) is oidized to Fe (SO 4 ) 3. Calculate the equivalent weight of ferrous ion () (B) 7.9 (C) 8.6 (D).68 (E) Mass % of carbon in ethanol is () 5 (B) 3 (C) 34 (D) 90 (E) 80

18 PGE: One mole of ethanol is produced reacting graphite, H and O together. The standard enthalpy of formation is 77.7 kj mol. Calculate the standard enthalpy of the reaction when 4 moles of graphite is involved () 77.7 (B) (C) (D) 69.4 (E) Which of the following process best describes atomization of CH 4 (g)? () Eothermic (B) Endothermic (C) Non-spontaneous (D) Spontaneous (E) Both (B) and (C) E 09. Consider the equilibrium X + Y? P. Find the stoichiometric coefficient of the P using the data given in the following table X / mol L Y / mol L P / mol L () (B) (C) 3 (D) 0.5 (E) 4 0. Which of the following can help predict the rate of a reaction if the standard Gibbs free energy of reaction ( r G ) is known? () Equilibrium constant (B) r H (C) r U (D) Heat liberated during the course of reaction in calorimeter (E) Both (B) and (). Calculate the molarity of a solution containing 5g of NaOH dissolved in the product of a H O fuel cell operated at current for 595. hours. (ssume F = C / mol of electrons and molecular weight of NaOH as 49 g mol ) () 0.05 M (B) 0.05 M (C) 0. M (D) M (E) M *. If mole of NaCl solute is dissolved into the kg of water, at what temperature will water boil at.03 bar? (K b of water is 0.5 K kg mol ) () K (B) K (C) K (D) K (E) 375 K 3. Consider the electrochemical reaction between g(s) and Cl (g) electrodes in litre of 0. M KCl aqueous solution. Solubility product of gcl is and F = C/mol. t µ current, calculate the time required to start observing the gcl precipitation in the galvanic cell () 73 s (B) 346 s (C) s (D) s (E) 0 s

19 PGE: 9 4. The voltage of the cell consisting of Li (s) and F (g) electrodes is 5.9 V at standard condition at 98 K. What is the voltage if the electrolyte consists of M LiF. (ln = 0.693, R = 8.34 J K mol and F = C mol ) () 5.90 V (B) V (C) 5.88 V (D) 4.9 V (E) 4.8 V 5. Consider the galvanic cell, Pt(s) H ( bar) HCl (aq) (M) Cl ( bar) Pt(s). fter running the cell for sometime, the concentration of the electrolyte is automatically raised to 3M HCl. Molar conductivity of the 3M HCl is about 40 S cm mol and limiting molar conductivity of HCl is about 40 S cm mol. If K b of water is 0.5 K kg mol, calculate the boiling point of the electrolyte at the end of the eperiment () K (B) K (C) 378. K (D) K (E) 38.6 K 6. The data given below are for the reaction of and D to form product at 95 K. Find the correct rate epression for this reaction D / mol L / mol L Initial rate / mol L s () k [D ] [] (B) k [D ] [] (C) k [D ] [] (D) k [D ] [] (E) k [D ] [] 0 7. Find the unit of the rate constant of a reaction represented with a rate equation, rate = k [] / [B] 3/ () mol L s (B) s (C) mol L s (D) mol L s (E) mol 3 L 3 s 8. Under what condition the order of the reaction,, catalyst HI H (g) + I (g), is zero () t high temperature (B) t high partial pressure of HI (C) t low partial pressure of HI (D) t high partial pressure of H (E) t high partial pressure of I 9. Which of the following statement is true about the adsorption? () H < 0 and S < 0 (B) H > 0 and S < 0 (C) H < 0 and S > 0 (D) H = 0 and S < 0 (E) H = 0 and S > 0 0. In NH 3 synthesis by Haber s process, what is the effect on the rate of the reaction with the addition of Mo and CO, respectively? () Increases and decreases (B) Decreases and decreases (C) Decreases and increases (D) Both Mo and CO increases the rate (E) Both Mo and CO does not affect the rate

20 MTHEMTICS KEM KEY 08 PGE: M.O: Kunnumpuram, yurveda College Jn., Trivandrum-, (: , Website: KOCHI KOLLM BRNCHES Puthussery Building, Kaloor Sivajyothi Comple, Polayathode (: (: KEM (ENGINEERING) KEY 08 PPER II MTHEMTICS QUESTIONS & S o o (cos75 + i sin75 ). The value of is o o 0.(cos30 + i sin30 ) 5 () ( + i ) (B) 0 ( + i) (C) 0 ( i) 5 (D) ( i ) (E) ( + i ) B. If the conjugate of a comple number z is, then z is i () (B) (C) i i + i D (D) i + (E) i 3. The value of i () + i + i is equal to (B) + i (C) i (D) i (E) i 4. The modulus of + i i i + i is E () (B) (C) 4 (D) 8 (E) 0 5. If z i 4 /3 = e π, then ( z 9 z 94 ) 3 + is equal to () (B) (C) i (D) i (E) 0

21 MTHEMTICS KEM KEY 08 PGE: 6. If a and b are real numbers and (a + ib) = + 3i, then (b + ia) is equal to () i + 3 (B) + 3i (C) 3i (D) 0 (E) i 3 E 7. If α βα, = 5α 3, β = 5β 3, then the equation having α β and β α as its roots is () 3 9 3= 0 (B) = 0 (C) (D) 3 9 9= 0 (E) = 0 E = 0 8. The focus of the parabola 3 (), 4 3 (B), 4 D y y 4 + 3= 0 is 3 (C), 4 9. If f : R (0, ) is an increasing function and if, f( ) lim f ( ) is equal to 08 3 (D), 4 f(3 ) lim f ( ) =, then 08 (E), 3 4 () 3 (B) 3 (C) (D) 3 (E) E 0. f() f( ) If f is differentiable at =, then lim is () f '() (B) f() f '() (C) f () f '() (D) f () + f '() (E) f() + f '(). Eccentricity of the ellipse () 3 (B) y 8 4y = is 3 (C) (D) 3 8 (E) 3 6. The focus of the parabola ( y + ) = 8( +) is () ( 4, ) (B) (, 4) (C) (, 4) (D) (4, ) (E) (, 4) 3. Which of the following is the equation of a hyperbola? () 4 + 6y + 7 = 0 (B) 4 + 4y 6 + 4y 60 = 0 (C) (E) y y = 0 (D) y = 0 D y y = 0

22 MTHEMTICS KEM KEY 08 PGE: 3 4. Let f( ) = p + q + r, where p, q, r are constants and p 0. If f(5) = 3 f() and f ( 4) = 0, then the other root of f is () 3 (B) 7 (C) (D) (E) 6 5. Let f : f = R R satisfy f ( ) f( y) = f ( y) for all real numbers and y. If f () = 4, then () 0 (B) 4 (C) (D) (E) B 6. Sum of last 30 coefficients in the binomial epansion of ( + ) 59 is () 9 (B) 59 (C) 58 (D) 59 9 (E) ( 3 + ) ( 3 ) = () 0 6 (B) 30 6 (C) 5 0 (D) 40 6 (E) 0 6 D 8. Three players, B and C play a game. The probability that, B and C will finish the game are respectively, 3 and. The probability that the game is finished is 4 () 8 (B) (C) 4 (D) 3 4 (E) D z + z + 9. If z = i and z = + i, then is z z + i () (B) (C) 3 (D) 3 (E) N sin 0. If f( ) = + cos, then lim f( ) is equal to () (B) (C) (D) 0 (E)

23 MTHEMTICS KEM KEY 08 PGE: 4. The value of sin 3 3 π is () 3 (B) (C) 3 (D) (E). The sum of odd integers from to 00 is () () (B) (0) (C) 3. If (D) (0) (E) (0) C sin cos y = + + cot + tan, then y'( ) is equal to (00) () cos (B) cos 3 (C) cos (D) cos (E) 3 cos 4. The foci of the hyperbola 6 9y y 90 = 0 are 4± 5 45 ± 5 45 (), (B), (C) ± 5 45 ± 5 45 (D), (E), 4± 5 45, 5. 5 If the sum of the coefficients in the epansions of ( a a + ) is zero, then a is equal to () 0 (B) (C) (D) (E) 6. The mean deviation of the data,9,9,3,6,9,4 from the mean is ().3 (B) 3.3 (C).57 (D) 3.57 (E) The mean and variance of a binomial distribution are 8 and 4 respectively. What is (X = )? () (B) (C) (D) (E) 5 8. The number of diagonals of a polygon with 5 sides is () 90 (B) 45 (C) 60 (D) 70 (E) 0

24 MTHEMTICS KEM KEY 08 PGE: 5 9. In a class, 40% of students study maths and science and 60% of students study maths. What is the probability of a student studying science given the student is already studying maths? () 3 (B) 6 (C) 3 (D) 5 (E) 4 C 30. The eccentricity of the conic + y + 3y+ = 0 is () 0 (B) (C) (D) (E) 3. If the mean of a set of observations,,. 0 is 0, then the mean of + 4, + 8, 3+..., is () 34 (B) 3 (C) 4 (D) 38 (E) letter is taken at random from the word GTTISTICS and another letter is taken at random from the word SSISTNT. The probability that they are same letters is () 45 C (B) 3 90 (C) 9 90 (D) If sin α and cos α are the roots of the equation a + b+ c = 0, then () a b + ac = 0 (B) ( a c) = b + c (C) a + b ac = 0 (D) a + b + ac = 0 (E) a + b + c = 0 (E) If the sides of a triangle are 4, 5 and 6 cms. Then the area of triangle is..sq.cms. π π () (B) 7 (C) 4 (D) 4 7 (D) E 35. In a group of 6 boys and 4 girls, a team consisting of four children is formed such that the team has atleast one boy. The number of ways of forming a team like this is () 59 (B) 09 (C) 00 (D) 40 (E) 36. password is set with 3 distinct letters from the word LOGRITHMS. How many such passwords can be formed? () 90 (B) 70 (C) 80 (D) 7 (E) 0

25 MTHEMTICS KEM KEY 08 PGE: If 5 97 is divided by 5, the remainder obtained is () 3 (B) 5 (C) 4 (D) 0 (E) 38. quadratic equation a + b+ c= 0, with distinct coefficients is formed. If a, b, c are chosen from the numbers, 3, 5, then the probability that the equation has real roots is () 3 (B) 5 (C) 4 (D) 5 (E) lim () (B) 9 D is equal to (C) 9 (D) 3 4 (E) The minimum value of f ( ) = ma{, +, } is () (B) 3 (C) (D) 0 (E) B 4. The equations of the asymptotes of the hyperbola y + 3 y 0= 0 are () =, y = 3 (B) =, y = 3 (C) =, y = 3 (D) = 4, y = 3 (E) = 3, y = 4 B 4. If f() = 6 + 6, then f () is equal to () (B) + 4 (C) log (6) (D) (E) 6 C 43. The standard deviation of the data 6, 5, 9, 3,, 8, 0 is 5 () (B) 5 53 (C) N (D) 53 7 (E) 6 cos m 44. lim 0 cos n = m () n (B) n m (C) (D) (E) 0

26 MTHEMTICS KEM KEY lim 0 = () 0 (B) (C) D (D) PGE: 7 (E) 46. Let f and g be differentiable functions such that f(3) = 5, g(3) = 7, f (3) = 3, g (3) = 6, f (7) = and g (7) = 0. If h() = (fog) (), then h (3) = () 4 (B) (C) 6 (D) 0 (E) = o o sin(0 ) cos(0 ) () (B) D (C) (D) 4 (E) poison variate X satisfies P(X = ) = P( = ). P(X = 6) is equal to 4 () 45 e (B) 45 e (C) 9 e (D) 4 e (E) 45 e 49. Let a and b be consecutive integers selected from the first 0 natural numbers. The probability that () 9 9 a + b + ab is an odd positive integer is D (B) 0 9 (C) 3 9 (D) (E) n ellipse of eccentricity is inscribed in a circle. point is chosen inside the circle at 3 random. The probability that the point lies outside the ellipse is () 3 (B) 3 (C) 9 (D) 9 (E) 7 B 5. If the vectors 4i + j + mk, 7i + j + 6k and i + 5 j + 4k are coplanar, then m is equal to () 38 (B) 0 (C) 0 (D) 0 (E) 5

27 MTHEMTICS KEM KEY 08 r r r 5. Let a = i + j + k, b = i + 3 j + 5k and c = 7i + 9 j + k. Then the area of the r r r r parallelogram with diagonals a + b and b + c is () 4 6 (B) (C) 6 (D) 6 (E) PGE: r r r r r r rr rr rr If a = 3, b =, c = 4 and a + b + c = 0, then the value of ab. + bc. + ca. is equal to () 3 (B) 6 (C) 9 (D) 3 (E) 6 D r r r r 54. IF a b = a = b =, then the angle between a r and b r is equal to π () (B) 3 π π (C) (D) (E) π 55. r r If the vectors a = i j + k, b = i + 4 j + k r and c = λ i + 9 j + µ k are mutually orthogonal, then λ + µ is equal to () 5 (B) 9 (C) (D) 0 (E) The solutions of = 0 are (), 04 (B), 04 (C), 03 (D) 04, (E),03 D 57. If the equations + a + = 0and a = 0 have a real common root b, then the value of b is equal to () 0 (B) (C) (D) (E) If sin θ cos θ =, then the value of sin 3 θ cos 3 θ is equal to () (B) (C) 0 (D) (E) 59. Two dice of different colours are thrown at a time. The probability that the sum is either 7 or is () 7 36 (B) 9 (C) 3 (D) 5 9 (E) 6 7

28 MTHEMTICS KEM KEY 08 PGE: is equal to 9! 3!7! 5!5! 7!3! 9! 9 0 () (B) (C) 0! 8! 9! (D) 0 7! (E) 8 9! 6. The order and degree of the differential equation ( y"') ( y") ( y') + y = 0 is () 3 and (B) and (C) and 3 (D) and 4 (E) 3 and 5 6. d is equal to () 0 (B) (C) (D) 4 (E) D d + + is equal to π () 0 (B) 4 (C) π 4 (D) π (E) π 64. If 4 f ( d ) = 4 and 4 (3 f ( )) d = 7, then f ( d ) is () (B) (C) 3 (D) 4 (E) 5 E e 65. d = ( + ) e () + e (D) + c + + c e (B) c + e + e (E) + c + (C) e c + e The remainder when 000 is divided by 7 is () (B) (C) 8 (D) (E) 4

29 MTHEMTICS KEM KEY 08 PGE: The coefficient of 5 in the epansion of ( + 3) 8 is () 54 (B) 5 (C) 5 (D) (E) 4 π 68. The maimum value of 5 cos θ + 3 cos θ is 3 () 5 (B) (C) 0 (D) (E) 69. The area of the triangle in the comple plane formed by z, iz and z + iz is () z (B) z (C) z (D) z + iz (E) z + iz 70. Let f : C be a differentiable function. If f is even, then f (0) is equal to () (B) (C) 0 (D) (E) C 7. The coordinate of the point dividing internally the line joining the points (4, ) and (8, 6) in the ratio 7 : 5 is () (6, 8) (B) (8, 6) (C), (D), (E) (7, 3) C 7. The area of the triangle formed by the points (a, b + c), (b, c + a), (c, a + b) is (a) abc (B) a + b + c (C) ab + bc + ca (D) 0 (E) a(ab + bc + ca) D 73. If (, y) is equidistant from (a + b, b a) and (a b, a + b), then () a + by = 0 (B) a by = 0 (C) b + ay = 0 (D) b ay = 0 (E) = y D y 74. The equation of the line passing through (a, b) and parallel to the line + = is a b y y y () + = 3 (B) + = (C) + = 0 a b a b a b y y (D) + + = 0 (E) + = 4 a b a b

30 MTHEMTICS KEM KEY 08 PGE: 75. If the points (a, a), (a, a) and (a, a) enclose a triangle of area 8 square units, then the centroid of the triangle is equal to () (4, 4) (B) (8, 8) (C) ( 4, 4) (D) ( 4,4 ) (E) (6, 6) B 76. The area of a triangle is 5 sq. units. Two of its vertices are (, ) and (3, ). The third verte lies on y = + 3. The coordinates of the third verte can be (), (B), (C), (D), (E), 4 4 C 77. If + y + g + fy + = 0 represents a pair of straight lines, then f + g is equal to () 0 (B) (C) (D) 4 (E) If θ is the angle between the pair of straight lines 5y + 4y = 0, then tan θ is equal to () 9 (B) 6 (C) 9 (D) (E) If 3i + j 5k = i j + k + y i + 3 j k + z i + j 3k, then () =, y =, z = 3 (B) =, y = 3, z = (C) = 3, y =, z = (D) =, y = 3, z = (E) =, y =, z = 3 S80. sin 5 o = 3 () (B) 3 + (C) 3 (D) + 3 (E) (+ 3) 8. If a r r and b = 3i + 6 j + 6k () 3 i + j + k r r are collinear and ab=. 7, then a r is equal to (D) i + 3 j + 3k (E) i 3 j + k B (B) i + j + k (C) i + j + k

31 MTHEMTICS KEM KEY 08 r 8. If a = 3 r, b = 5 r r and ab=. 30 r r, then a b is equal to PGE: () 30 (B) E (C) (D) (E) If 56 P r + 6 : 54 P r + 3 = :, then r is equal to () 69 (B) 4 (C) 5 (D) 6 (E) Distance between two parallel lines y = + 4 and y = is () 5 (B) 5 5 (C) 5 (D) 5 (E) ( 7 C C ) + ( 7 C + 7 C 3 ) ( 7 C C 7 ) = () 8 (B) 7 (C) 7 (D) 8 (E) The coefficient of in the epansion of ( ) ( ) 6 is () 7 (B) 9 (C) 7 (D) 9 (E) 0 D 87. The equation of the circle with centre (, ) which passes through (4, 5) is () + y 4 + 4y 77 = 0 (B) + y 4 4y 5 = 0 (C) + y + + y 59 = 0 (D) + y y 3 = 0 (E) + y + 4 y 6 = The point in the y-plane which is equidistant from (, 0, 3), (0, 3, ) and (0, 0, ) is () (,, 3) (B) ( 3,, 0) (C) (3,, 0) (D) (3,, 0) (E) (3,, ) D 89. Let f : be such that f() = and f ( + y) = f() f(y) for all natural numbers and y. n If f ( a+ k) = 6 ( n ), then a is equal to k = () 3 (B) 4 (C) 5 (D) 6 (E) If n C r = 36, n C r = 84 and n C r + = 6, then n = () 3 (B) 4 (C) 8 (D) 9 (E) 0 D

32 MTHEMTICS KEM KEY 08 PGE: 3 9. Let f : (-, ) (-, ) be continuous, f() = f( ) for all (, ) and f (0) =, then the value of 4 f 4 is () (B) (C) 3 (D) 4 (E) 5 9. lim θ + = () (B) (C) 0 (D) (E) If f is differentiable at = and lim h 0 f ( + h) = 5, then f '() = h () 0 (B) (C) 3 (D) 4 (E) 5 E 94. The maimum value of the function is attained at () 0 (B) 3 (C) 4 (D) (E) 5 D π 95. If f( )cos d = { f ( )} + c, then f is π () c (B) + c (C) c + (D) π + c (E) c + C 96. d = /4 + sin 3 π /4 π () π ( ) (B) π ( + ) (C) π ( ) π (D) π ( + ) (E), E π 0 + sin sin cos d = () (B) π (C) 4 π (D) π (E) 0 C

33 MTHEMTICS KEM KEY 08 PGE: lim sin tdt 0 0 = () 3 (B) 9 (C) 3 (D) 0 (E) 6 D 99. The area bounded by y = sin, = and = π is π π π () (B) (C) 4 8 π (D) 6 (E) π B 00. The differential equation of the family of curves y = e ( cos+ Bsin ). where and B are arbitrary constants is () y'' y' + y = 0 (B) y'' + y' y = 0 (C) (D) y'' + y' y = 0 (E) y'' y' y = 0 y y y '' + ' + = 0 0. The real part of ( i 3) 3 is () 0 (B) (C) (D) (E) 0 N + e 0. lim 0 () = B (B) (C) (D) (E) 0 (sin+ cos )( sin ) 03. d = sin () sin + cos sin cos + c (B) + c (C) sin sin sin (D) sin cos + c (E) sin cos sin + cos + c sin sin + cos + c

34 MTHEMTICS KEM KEY 08 PGE: plane is at a distance of 5 units from the origin; and perpendicular to the vector $ i + $ j + k$ r. The equation of the plane is r () r.$ $ $ ( i + j k ) = 5 (B) r.$ $ $ ( i + j k ) = 5 r r (C) r.$ $ $ ( i + j + k ) = 5 (D) r. $ $ ( $ i + j + k ) = 5 r (E) r.$ i $ j + k$ = 5 ( ) 05. sin sin B is equal to cos+ cos B + B () sin B (D) tan D B (B) tan( + B) (C) cot (E) cot( + B) 06. If sin4,then d = cos 4t + B t dt = () (B) 6 (C) 5 (D) 6 (E) 5 n n n n 07. The arithmetic mean of Co, C, C,..., Cn is () n n + (B) n n (C) n n + (D) n n (E) n n The variance of first 0 natural numbers is () 399 (B) 379 D (C) 33 (D) 33 4 (E) If S is a set with 0 elements and = {( y, ): y, S, y}, then the number of elements in is () 00 (B) 90 (C) 80 (D) 50 (E) 45

35 MTHEMTICS KEM KEY 08 PGE: 6 0. coin is tossed and a die is rolled. The probability that the coin shows head and the die shows 3 is () (B) (C) (D) (E) If = 3, then the sum of all the diagonal entries of is 3 () (B) 3 (C) 3 (D) 4 (E) 4 E. Let 3 7 f( ) =. If = 9 is a root of f( ) = 0, then the other root are 7 6 () and 7 (B) 3 and 6 (C) 7 and 3 (D) 6 and (E) 6 and 7 3. If [ 3 ] 5 = 0 5 3, then can be () (B) (C) 4 (D) 4 (E) 0, D 0 4. If = and = 0 =, then = () (B) (C) (D) 3 (E) 0 B 5. If 4 3 a b c d e 6 6 = , then 5a + 4b + 3c + d + e is equal to () (B) (C) (D) (E) 3

36 MTHEMTICS KEM KEY 08 PGE: 7 6. a b + c b c + a = c a + b () (B) 0 (C) ( a)( b)( c) (D) a + b + c (E) ( a + b + c) 7. If 8. If f( ) = 3( ) ( )( ) ( ), then f (50) = () 0 (B) (C) 4 (D) (E) 3 cos cos ( ) = + sin cos + sin cos, then () sin sin (B) π / 0 ( d ) = (C) (D) (E) 0 9. The equation of the plane passing through the points (,,3), (, 4, ) and (3,,) is () 5 + y + z 3 = 0 (B) 5 + 6y + z= 3 (C) 5 + 6y + z= 3 (D) + y + z = 3 (E) + 6y + 5z = 7 B 0. In an arithmetic progression, if the k th term is 5k +, then the sum of first 00 terms is () 50(507) (B) 5(506) (C) 50(506) (D) 5(507) (E) 5(506)