Solved papers for Manipal Engineering Manipal Engineering Solved Paper-2015
done Manipal Engineering Solved Paper-2015 Total Questions - 170
question_answer1) Two point charges 2q and 8q are placed at a distance r apart. Where should a third charge -q be placed between them, so that the electrical potential energy of the system is minimum?
question_answer2) If levels 1 and 2 are separated by an energy \[C\xrightarrow[{}]{{}}D;{{k}_{2}}={{10}^{12}}{{e}^{-24,606/T}}\] such that the corresponding transition frequency falls in the middle of the visible range, calculate the ratio of the populations of two levels in the thermal equilibrium at room temperature.
question_answer4) We have a galvanometer of resistance 25 \[C{{l}^{-}}\]. It is shunted by 2.5 \[9.2g{{N}_{2}}{{O}_{4}}\] wire. The part of the total current that flows through the galvanometer is given as
question_answer5) Two moles of helium are mixed with n moles of hydrogen. The root mean square (rms) speed of gas molecules in the mixture is \[-{{T}^{2}}{{\left[ \frac{\delta (G/T)}{\delta T} \right]}_{p}}\] times the speed of sound in the mixture. Then, the value of n is
question_answer6) A coil having n turns and resistance RQ, is connected with a galvanometer of resistance \[{{T}^{2}}{{\left[ \frac{\delta (G/T)}{\delta T} \right]}_{v}}\] This combination is moved in time second from a magnetic field \[-{{T}^{2}}{{\left[ \frac{\delta (G/T)}{\delta T} \right]}_{v}}\] weber to \[C{{l}_{2}}O,IC{{l}^{-}}_{2}\] weber. The induced current in the circuit is
question_answer7) A thin film of soap solution \[L{{i}^{+}}\]lies on the top of a glass plate (a =1.5). When incident light is almost normal to the plate, two adjacent reflection maxima are observed at two wavelengths 420 nm and 630 nm. The minimum thickness of the soap solution is (a)
question_answer8) A coil in the shape of an equilateral triangle of side l is suspended between the pole pieces of a permanent magnet such that B is in the plane of the coil. If due to current i in the triangle, a torque t acts on it. The side I of the triangle is
question_answer9) The two blocks of masses \[K{{l}_{2}}\] and \[{{l}^{-}}\]are kept on a smooth horizontal table as shown in the figure. Block of mass \[{{K}^{+}};{{l}^{-}}\] but not \[{{l}_{2}}\] is fastened to the spring. If now both the blocks are pushed to the left, so that the spring is compressed at a distance d. The amplitude of oscillation of block of mass \[l_{3}^{-}\] after the system released, is
question_answer10) A juggler keeps on moving four balls in air throwing the balls after regular intervals. When one ball leaves his hand (speed \[A\cap B\]), the position of other balls (height in metre) will be \[f(x)=\sqrt{{{x}^{2}}-4,}a=2\]
question_answer11) Two coils have mutual inductance 0.005 H. The current changes in the first coil according to equation \[\sqrt{5}\] where \[\sqrt{3}\] A and \[\sqrt{3}+1\]. The maximum value of emf in the second coil is
question_answer12) A ball is projected from the point O with velocity 20 m/s at an angle of 60° with horizontal as shown in the figure. At highest point of its trajectory, it strikes a smooth plane of inclination 30° at point A. The collision is perfectly inelastic. The maximum height from the ground attained by the ball is
question_answer13) In a nuclear reactor, \[f(x)=x{{e}^{x}}^{(1-x)},\] undergoes fission liberating 200 MeV of energy. The reactor has a 10% efficiency and produces 1000 MW power. If the reactor is to function for 10 yr, then find the total mass of uranium required.
question_answer14) A capacitor of capacitance \[(1+{{\omega }^{5}})...(1+{{\omega }^{3n}})\] is charged to potential 50 V with a battery. The battery is now disconnected and an additional charge \[{{2}^{3n}}\] is given to the positive plate of the capacitor. The potential difference across the capacitor will be
question_answer16) Under what conditions current passing through the resistance R can be increased by short circuiting the battery of emf \[{{2}^{2n}}\]? The internal resistances of the two batteries are\[{{2}^{n}}\] and \[{{x}^{2r}}\] respectively.
question_answer17) A rectangular glass slab ABCD of refractive index \[\frac{\pi }{6}\] is immersed in water of refractive index \[\frac{\pi }{2}\]A ray of light is incident at the surface AB of the slab as shown. The maximum value of the angle of incidence \[{{\cos }^{-1}}\frac{x}{2}+{{\cos }^{-1}}\frac{y}{3}=\theta ,\]such the ray comes out only from the another surface CD is given by
question_answer18) A sinusoidal wave travelling in the positive direction on stretched string has amplitude 20 cm, wavelength 1 m and wave velocity 5 m/s. At x = 0 and t = 0, it is given that y = 0 and \[\tan \left( {{\sec }^{-1}}x \right)=\sin \left( {{\cos }^{-1}}\frac{1}{\sqrt{5}} \right),\]Find the wave function y (x,t).
question_answer19) The length of a potentiometer wire is 7. A cell of emf E is balanced at length l/3 from the positive end of the wire. If the length of the wire is increased by l/2. Then, at what distance will the same cell give a balance point?
question_answer20) Find the inductance of a unit length of two parallel wires, each of radius a, whose centres are at distance d apart and carry equal currents in opposite directions. Neglect the flux within the wire.
question_answer21) Two wires of same lengths are shaped into a square and a circle. If they carry same current, then the ratio of their magnetic moments is
question_answer22) A circular coil of 100 turns has an effective radius of 0.05 m and carries a current of How much work is required to turn it in an external magnetic field of 1.5 Wb/m2 through 180° about its axis perpendicular to the magnetic field? The plane of the coil is initially perpendicular to the magnetic field.
question_answer25) The alternating voltage and current in an electric circuit are respectively given by \[\frac{{{d}^{2}}u}{d{{x}^{2}}}=2v\] The reactance of the circuit will be
question_answer26) The biological damage caused by 1 gray \[\frac{1}{8}\]radiation is compared with 1 gray \[\frac{1}{4}\]radiation in the same type of human tissue. The damage caused by the y-radiation is
A)
more serious as compared to the damage caused by the \[\text{ }\!\!\alpha\!\!\text{ -}\]radiation.
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B)
less serious as compared to the damage caused by the a-radiation
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C)
equally serious as the damage caused by the \[\frac{1}{2}\]radiation
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D)
incomparable with the damage caused by the \[\int_{{}}^{{}}{\frac{1-{{x}^{2}}}{(1+{{x}^{2}})\sqrt{1+{{x}^{4}}}}dx}\]radiation, because \[\sqrt{2}{{\sin }^{-1}}\left\{ \frac{\sqrt{2}x}{{{x}^{2}}+1} \right\}+C\]radiation are not particles.
question_answer27) Two identical coherent sources placed on a diameter of a circle of radius R at separation \[\frac{1}{\sqrt{2}}{{\sin }^{-1}}\left\{ \frac{\sqrt{2}x}{{{x}^{2}}+1} \right\}+C\] symmetrically about the centre of the circle. The sources emit identical wavelength X each. The number of points on the circle with maximum intensity is \[\frac{1}{2}{{\sin }^{-1}}\left\{ \frac{\sqrt{2}x}{{{x}^{2}}+1} \right\}+C\]
question_answer28) Two point masses 1 and 2 move with uniform velocities \[\Delta ABC,\left| \begin{matrix} 1 & a & b \\ 1 & c & a \\ 1 & b & c \\ \end{matrix} \right|=0,\] and \[{{\sin }^{2}}A+{{\sin }^{2}}B\text{ }+{{\sin }^{2}}C\] respectively. Their initial position vectors are \[\frac{3\sqrt{3}}{2}\] and \[\frac{9}{4}\] respectively. Which of the following should be satisfied for the collision of the point masses?
question_answer29) A neutron moving with a speed v makes a head on collision with a hydrogen atom in ground state kept at rest. The minimum kinetic energy of neutron for which inelastic collision will take place is
question_answer30) The specific heat at constant volume for the mono atomic argon is 0.075 kcal/kg-K, whereas its gram molecular specific heat is \[\frac{5}{2}\] cal/mol K. The mass of the carbon atom is
question_answer32) A block of mass m is lying on the edge having inclination angle \[{{x}^{2}}+{{y}^{2}}=9,\]Wedge is moving with a constant acceleration, a \[\left( \frac{3}{2},\frac{1}{2} \right)\] The minimum value of coefficient of friction \[\left( \frac{1}{2},\frac{3}{2} \right)\] so that m remains stationary with respect to wedge is
question_answer33) A small particle of mass m is released from rest from point A inside a smooth hemispherical bowl as shown in the figure. The ratio (x) of magnitude of centripetal force and normal reaction on the particle at any point B varies with 9 as
question_answer34) A solid cylinder is rolling down on an inclined plane of angle \[\frac{1}{4}\]. The coefficient of static friction between the plane and the cylinder is \[{{(y-2)}^{2}}=(x-1),\] The condition for the cylinder not to slip is
question_answer36) A large slab of mass 5 kg lies on a smooth horizontal surface, with a block of mass 4 kg lying on the top of it, the coefficient of friction between the block and the slab is 0.25. If the block is pulled horizontally by a force of F = 6N, the work done by the force of friction on the slab between the instants t = 2 s and t = 3 s is
question_answer37) Two unequal masses are connected on two sides of a light string passing over a light and smooth pulley as shown in the figure. The system is released from the rest. The larger mass is stoped for a moment, Is after the system is set into motion. The time elapsed before the string is tight again is
question_answer38) Figure shows an irregular block of material of refractive index \[f(x)=\left\{ \begin{matrix} \frac{\sin (\cos x)-\cos x}{{{(\pi -2x)}^{3}}}, & x\ne \frac{\pi }{2} \\ k, & x=\frac{\pi }{2} \\ \end{matrix} \right.\]A ray of light strikes the face AB as shown in figure. After refraction, it is incident on a spherical surface CD of radius of curvature 0.4 m and enters a medium of refractive index 1.514 to meet PQ at E. Find the distance OE up to two places of decimal.
question_answer39) The ratio of the energy required to raise a satellite upto a height h above the earth to the kinetic energy of the satellite into the orbit is
question_answer41) The frequency of son meter wire is f, but when the weights producing the tensions are completely immersed in water, the frequency becomes f/2 and on immersing the weights in a certain liquid, the frequency becomes f/3. The specific gravity of the liquid is
question_answer42) Find the frequency of light which ejects electron from a metal surface fully stopped by a retarding potential of 3V. The photoelectric effect begins in this metal at a frequency of \[f(x)=[x]+\left[ x+\frac{1}{2} \right]\]
question_answer43) Equations of a stationary and a travelling waves are as follows, \[f(x)=\min \{1,{{x}^{2}},{{x}^{3}}\},\]and \[{{x}_{n}}=\cos \frac{\pi }{{{3}^{n}}}+i\sin \frac{\pi }{{{3}^{n}}},\] The phase difference between two points \[{{x}_{1}}.{{x}_{2}}.{{x}_{3}}...\]and \[9{{x}^{2}}-18\text{ }\!\!|\!\!\text{ x }\!\!|\!\!\text{ }+5=0\] are \[{{\log }_{e}}\]and \[{{2}^{x}}+{{2}^{y}}={{2}^{x+y}}y,\] respectively for two waves. The ratio \[\frac{dy}{dx}\]is
question_answer45) A small block of wood of specific gravity 0.5 is submerged at a depth of 1.2 m in a vessel filled with the water. The vessel is accelerated upwards with an acceleration \[\frac{{{2}^{x}}+{{2}^{y}}}{{{2}^{x}}-{{2}^{y}}}\] Time taken by the block to reach the surface, if it is released with zero initial velocity is
question_answer46) An electron beam accelerated from rest through a potential 'difference of 5000 V in vacuum is allowed to impinge on a surface normally. The incident current is \[\frac{{{2}^{x}}+{{2}^{y}}}{1+{{2}^{x+y}}}\] and if the electron comes to rest on striking the surface, the force on it is
question_answer47) A uniform rod of length 2 m, specific gravity 0.5 and mass 2 kg is hinged at one end to the bottom of a tank of water (specific gravity =1.0) filled upto a height of 1 m as shown in the figure. Taking the case \[3x-y=0\]the force exerted by the hinge on the rod is
question_answer48) A projectile is thrown in upward direction making an angle of 60° with the horizontal direction with a velocity of 150 \[2x+y=0\] Then, the time after which its inclination with horizontal is 45°, is
question_answer50) In Young's double slit experiment, fringes of width \[{{m}^{3}}-3m+2n=0\] are produced on the screen kept at a distance of 1m from the slit. When the screen is moved away by \[{{m}^{3}}+3m+2n=0\]fringe width changes by \[\Delta ABC,\]The separation between the slits is \[a=4,b=3,\angle A=60{}^\circ .\] The wavelength of light used is..... .nm.
question_answer56) The enthalpy of combustion of carbon and carbon monoxide are - 393.5 and 283 kJ/mol respectively. The enthalpy of formation of carbon monoxide per mole is
question_answer57) Equivalent amounts of \[\frac{9n}{n+1}\] and \[\frac{12n}{n+1}\]are heated in a closed vessel till equilibrium is obtained. If 80% of the hydrogen can be converted to HI, the \[\frac{3n}{n+1}\]at this temperature is
question_answer58) Which of the following is false about \[\int_{\sqrt{\ln 2}}^{\sqrt{\ln 3}}{\frac{x\sin {{x}^{2}}}{\sin {{x}^{2}}+\sin (\ln 6-{{x}^{2}})}dx}\]?
question_answer68) The standard reduction potential E° for half reactions are, \[{{x}^{2}}-ax+b=0,\] \[{{\sin }^{2}}(A+B)\] The emf of the cell reaction; \[\frac{{{a}^{2}}}{{{a}^{2}}+{{(1-b)}^{2}}}\]is
question_answer69) \[\frac{{{a}^{2}}}{{{a}^{2}}+{{b}^{2}}}\] The activation energy for the forward reaction is 50 kcal. What is the activation energy for the back word reaction?
question_answer78) An organic compound of molecular formula \[\theta \]did not give a silver mirror with Tollen's reagent, but gave an oxime with hydroxylamine, it may be
question_answer88) For the two gaseous reactions, following data \[{{u}_{2}}\] \[\frac{13}{30}\]the temperature at which \[\frac{23}{30}\] becomes equal to \[\frac{19}{30}\]is
question_answer91) In CsCI type structure, the coordination number of \[{{D}_{k}}=\left| \begin{matrix} a & {{2}^{k}} & {{2}^{16}}-1 \\ b & 3({{4}^{k}}) & 2({{4}^{16}}-1) \\ c & 7({{8}^{k}}) & 4({{8}^{16}}-1) \\ \end{matrix} \right|,\] and \[\sum\limits_{k=1}^{16}{{{D}_{k}}}\]respectively are
question_answer92) \[{{x}^{2}}-4x+4{{y}^{2}}=12\]is heated in 1L vessel till equilibrium state is established.\[\frac{\sqrt{3}}{2}\] In equilibrium state, 50% \[\frac{2}{\sqrt{3}}\] was dissociated, equilibrium constant will be (molecular wt. of \[\sqrt{3}\])
question_answer103) If \[\frac{2}{3}\] and \[\frac{3}{2}\] then \[\frac{{{d}^{2}}y}{d{{x}^{2}}}={{\left\{ y+{{\left( \frac{dy}{dx} \right)}^{2}} \right\}}^{1/4}}\]contains
question_answer104) The value of c prescribed by Lagrange's mean value theorem, when \[1+\frac{2}{3}+\frac{6}{{{3}^{2}}}+\frac{10}{{{3}^{3}}}+\frac{14}{{{3}^{4}}}+...\] and b = 3, is
question_answer108) Let X denotes the number of times heads occur in n tosses of a fair coin. If P (X = 4), P (X = 5) and P (X = 6} are in AP, then the value of n is
question_answer116) If PQRS is a convex quadrilateral with 3, 4, 5 and 6 points marked on sides PQ, QR, RS and PS respectively. Then, the number of triangles with vertices on different sides is
question_answer119) If A is a square matrix such that \[{{v}_{sound}}=\sqrt{\frac{\gamma RT}{M}},\]and \[{{v}_{rms}}=2{{v}_{sound}}\] then \[\gamma =\frac{3}{2}=\] is equal to
question_answer120) The functions \[{{C}_{p}}=\frac{{{n}_{1}}{{C}_{{{p}_{1}}}}+{{n}_{2}}{{C}_{{{p}_{2}}}}}{{{n}_{1}}+{{n}_{2}}}\] and \[\therefore \]satisfy the equation
question_answer127) The centre of the circle passing through (0,0) and (1,0) and touching the circle \[2{{\left( \frac{\tau }{\sqrt{3}Bi} \right)}^{1/2}}\]is
question_answer129) The area of the region bounded by the parabola \[d\sqrt{\frac{{{m}_{1}}}{{{m}_{1}}+{{m}_{2}}}}\] the tangent to the parabola at the point (2,3J and the X-axis, is
question_answer131) Numbers 1,2,3,...,100 are written down on each of the cards A, B and C. One number is selected at random from each of the cards. The probability that the numbers so selected can be the measures (in cm) of three sides of a right angled triangle, is
question_answer136) The total number of natural numbers of 6 digits that can be made with digits 1, 2, 3, 4, if all digits are to appear in the same number at least once, is
question_answer137) The number of solutions of the equation \[{{r}_{2}}\]belonging to the domain of definition of \[{{E}_{2}}{{r}_{1}}>{{E}_{1}}(R+{{r}_{2}})\] {(x + 1) (x + 2)}, is
question_answer139) If 3x + y = 0 is a tangent to the circle with centre at the point (2, - 1), then the equation of the other tangent to the circle from the origin, is
question_answer145) The radius of the circle passing through the foci of the ellipse \[{{T}^{2}}{{\left[ \frac{\delta (G/T)}{\delta T} \right]}_{v}}\] and having its centre at (0,3), is
question_answer149) Let a.b and c be non-zero vectors such that no two are collinear and \[{{l}^{-}}\]a. If \[{{K}^{+}};{{l}^{-}}\] is the acute angle between the vectors b and c, then sin \[{{l}_{2}}\] equals
question_answer153) If an isosceles triangle of vertical angle 29 is inscribed in a circle of radius a. Then, area of the triangle is maximum, when \[\left[ -\frac{1}{2},1 \right]\] is equal to
question_answer158) Let.\[{{\cos }^{-1}}\frac{x}{2}+{{\cos }^{-1}}\frac{y}{3}=\theta ,\] and \[9{{x}^{2}}-12xy\cos 6+4{{y}^{2}}\]be two urns such that \[-36{{\sin }^{2}}\theta \]contains 3 white, 2 red balls and \[36{{\sin }^{2}}\theta \] contains only 1 white ball. A fair coin is tossed. If head appears, then 1 ball is drawn at random from urn \[36{{\cos }^{2}}\theta \] and put into \[\tan \left( {{\sec }^{-1}}x \right)=\sin \left( {{\cos }^{-1}}\frac{1}{\sqrt{5}} \right),\]. However, if tail appears, then 2 balls are drawn at random from \[\pm \frac{3}{\sqrt{5}}\] and put into \[\pm \frac{\sqrt{5}}{3}\]. Now, 1 ball is drawn at random from \[\pm \sqrt{\frac{3}{5}}\]. Then, probability of the drawn ball from \[y=(2x-1){{e}^{2(1-x)}}\] being white is
question_answer160) The eccentricity of the conic \[\underset{x\to -1}{\mathop{\lim }}\,\left( \frac{{{x}^{4}}+{{x}^{2}}=x+1}{{{x}^{2}}-x+1} \right)\frac{1-\cos (x+1)}{{{(x+1)}^{2}}}\]is
question_answer163) The equation of the plane through the intersection of the planes \[\frac{{{d}^{2}}u}{d{{x}^{2}}}=-2u\]and \[{{\tan }^{-1}}\left( \frac{\sqrt{1+{{x}^{2}}}-1}{x} \right)\]and parallel to -Y-axis, is
question_answer164) Let \[\int_{{}}^{{}}{\frac{1-{{x}^{2}}}{(1+{{x}^{2}})\sqrt{1+{{x}^{4}}}}dx}\]and \[\sqrt{2}{{\sin }^{-1}}\left\{ \frac{\sqrt{2}x}{{{x}^{2}}+1} \right\}+C\]vector such that \[\frac{1}{\sqrt{2}}{{\sin }^{-1}}\left\{ \frac{\sqrt{2}x}{{{x}^{2}}+1} \right\}+C\]and the angle between \[\frac{1}{2}{{\sin }^{-1}}\left\{ \frac{\sqrt{2}x}{{{x}^{2}}+1} \right\}+C\] and c is 30°. Then, \[\Delta ABC,\left| \begin{matrix} 1 & a & b \\ 1 & c & a \\ 1 & b & c \\ \end{matrix} \right|=0,\]is equal to
question_answer166) A cone whose height is always equal to its diameter, is increasing in volume at the rate of 40cm3/s. At what rate is the radius increasing when its circular base area is 1m2?
question_answer168) The equations of the straight lines passing through the point (4, 3) and making intercepts on the coordinate axes whose sum is -1, is