Solved papers for JCECE Engineering JCECE Engineering Solved Paper-2012
done JCECE Engineering Solved Paper-2012 Total Questions - 150
question_answer1) A monkey of \[25\,\,kg\] is holding a vertical rope. The rope does not break if a body of mass \[30\,\,kg\] is suspended from it, but the rope breaks if the mass of body suspended with the rope exceeds\[30\,\,kg\]. What will be the maximum acceleration with which the monkey can climb up along the rope?
question_answer2) A mass of \[10\,\,g\] moving horizontally with a velocity of \[100\,\,cm{{s}^{-1}}\] strikes a pendulum bob of same mass. The two masses after collision stick together. What will be the maximum height reached by the system now? (Take\[g=10\,\,m{{s}^{-2}})\]
question_answer3) The three physical quantities \[x,\,\,\,y\] and \[z\] have units \[g\,\,c{{m}^{2}},\,\,g\,\,{{s}^{-1}}\] and \[cm{{s}^{-2}}\] respectively. The relation between \[x,\,\,\,y\] and \[z\] is
question_answer4) If a vector \[\mathbf{A}\] having a magnitude of \[8\] is added to a vector \[\mathbf{B}\] which lies along\[x-axis\], then the resultant of two vectors lies along \[y-axis\] and has magnitude twice that of\[B\]. The magnitude of \[\mathbf{B}\] is
question_answer7) The amplitude and the periodic time of \[\text{a}\] \[SHM\] are \[5\,\,cm\] and \[6\,\,s\] respectively. At a distance of \[2.5\,\,cm\] away from the mean position, the phase will be
question_answer10) Two point charges \[-q\] and \[+q/2\] are situated at the origin and the point \[(a,\,\,0,\,\,0)\] respectively. The point along the\[x-axis\], where the electric field vanishes is
question_answer12) A current \[i\] ampere flows along the inner conductor of a coaxial cable and returns along the outer conductor of the cable, then the magnetic induction at any point outside the conductor at a distance \[r\] metre from the axis is
question_answer13) Two parallel long wires carry currents \[{{i}_{1}}\] and \[{{i}_{2}}\] with\[{{i}_{1}}>{{i}_{2}}\]. When the currents are in the same direction, the magnetic field midway between the wires is\[10\,\,\mu T\]. When the direction of \[{{i}_{2}}\] is reversed, it becomes\[40\,\,\mu T\]. Then, ratio of \[{{i}_{1}}/{{i}_{2}}\]is
question_answer14) The two coherent sources of equal intensity produce maximum intensity of \[100\] units at a point. If the intensity of one of the sources is reduced by \[36%\] \[\text{by}\] reducing its width then the intensity of light at the same point will be
question_answer15) A convex mirror of focal length \[f\] forms an image which is \[\frac{1}{n}\] times the object. The distance of the object from the mirror is
question_answer16) Consider a hydrogen like atom whose energy in nth excited state is given by\[{{E}_{n}}=\frac{13.6\,\,{{Z}^{2}}}{{{n}^{2}}}\], when this excited atom makes a transition from excited state to ground state, most energetic photons have energy \[{{E}_{\max }}=52.224\,\,eV\] and least energetic photons have energy\[{{E}_{\min }}=1.224\,\,eV\]. The atomic number of atom is
question_answer18) A wave travelling along positive \[x-axis\] is given by\[y=A\sin (\omega t-kx)\]. If it is reflected from a rigid boundary such that \[80%\] amplitude is reflected, then equation of reflected wave is
question_answer19) An engine approaches a hill with a constant speed. When it is at a distance of\[0.9\,\,km\], it blows a whistle, whose echo is heard by the driver after\[5\,\,s\]. If speed of sound in air is \[330\,\,m/s\], the speed of engine is
question_answer20) The graph between the resistive force \[F\] acting on a body and the distance covered by the body is shown in the figure. The mass of the body is \[25\,\,kg\] and initial velocity is\[2\,\,m/s\]. When the distance covered by the body is \[4\,\,m,\] its kinetic energy would be
question_answer21) A body of weight \[50\,\,N\] placed on a horizontal surface is just moved by a force of\[28.2\,\,N\]. The frictional force and normal reaction are
question_answer22) On a railway curve, the outside rail is laid higher than the inside one so that resultant force exerted on the wheels of the rail car by the tops of the rails will
question_answer23) The mass of the moon is \[\frac{1}{81}\] of the earth but the gravitational pull is \[\frac{1}{6}\] of the earth. It is due to the fact that
A)
the radius of earth is \[\frac{1}{6}\] of the moon
doneclear
B)
the radius of moon is \[\frac{9}{\sqrt{6}}\] of the earth
question_answer25) The radius of two metallic spheres \[A\] and \[B\] are \[{{r}_{1}}\] and \[{{r}_{2}}\] respectively\[({{r}_{1}}>{{r}_{2}})\]. They are connected by a thin wire and the system is given a certain charge. The charge will be greater
question_answer26) The temperature gradient in a rod of \[0.5\,\,m\] long is\[{{80}^{o}}C/m\]. If the temperature of hotter end of the rod is\[{{30}^{o}}C\], then the temperature of the cooler end is
question_answer27) Time period of a block suspended from the upper plate of a parallel plate capacitor by a spring of stiffness \[K\] is \[T\], when block is uncharged. If a charge \[q\] is given to the block then, die new time period of oscillation will be
question_answer29) A wire of length \[1\,\,m\] is moving at a speed of \[2\,\,m{{s}^{-1}}\]perpendicular to its length in a homogeneous magnetic field of\[0.5\,\,T\]. If the ends of the wire are joined to a circuit of resistance\[6\Omega \], then the rate at which work is being done to keep the wire moving at constant speed is
question_answer31) The focal length of the objective of a terrestrial telescope is \[80\,\,cm\] and it is adjusted for parallel rays, then its power is\[20\]. If the focal length of erecting lens is \[20\,\,cm\], then full length of the telescope will be
question_answer32) Un polarized light falls on two polarizing sheets placed one on top of the other. What must be the angle between the characteristic directions of the sheets if the intensity of the final transmitted light is one-third the maximum intensity of the first transmitted beam
question_answer33) The ratio of two specific heats of gas \[{{C}_{p}}/{{C}_{V}}\] for argon is \[1.6\] and for hydrogen is\[1.4\]. If adiabatic elasticity of argon at pressure \[p\] is \[E,\] then at what pressure the adiabatic elasticity of hydrogen will also be equal to\[E\]?
question_answer34) The stress-strain curves for three wires of different materials are shown in figure, where \[P,\,\,\,Q\] and \[R\] are the elastic limits of the wires. The figure shows that
question_answer35) A body of density \[{{d}_{1}}\] is counterpoised by \[Mg\]of weights of density \[{{d}_{2}}\] in air of density\[d\]. Then, the true mass of the body is
question_answer37) A dip needle lies, initially in the magnetic meridian when it shows an angle of dip \[\theta \] at a place. The dip circle is rotated through an angle \[x\] in the horizontal plane and then it shows an angle of dip\[\theta '\]. Then,\[\frac{\tan \theta '}{\tan \theta }\]will be
question_answer39) An electric bulb rated as \[500\,\,W-100\,\,V\] is used in a circuit having \[200\,\,V\] supply. The resistance \[R\] that must be put in series with the bulb, so that the bulb draws \[500\,\,W\] is
question_answer40) A string of length L and mass M hangs freely from a fixed point. Then, the velocity of transverse waves along the string at a distance\[x\] from the free end is
question_answer42) A body of mass \[2\,\,kg\] slides down a curved track which is quadrant of a circle of radius \[1\,\,m\] as shown in figure. All the surfaces are frictionless. If the body starts from. rest, its speed at the bottom of the track is
question_answer44) If \[10000\,\,V\] is applied across an X-ray tube, what will be the ratio of de-Broglie wavelength of the incident electrons to the shortest wavelength X-ray produced? \[\left( \frac{e}{m}\,\,for\,\,electron=1.8\times {{10}^{11}}C\,\,k{{g}^{-1}} \right)\]
question_answer46) Two capillary tubes of same radius \[r\] but of lengths \[{{l}_{1}}\] and \[{{l}_{2}}\] are fitted in parallel to the bottom of a vessel. The pressure head is\[p\]. What should be the length of a single tube that can replace the two tubes so that the rate of flow is same as before?
question_answer49) An optical fibre communication system works on a wavelength of\[1.3\mu m\]. The number of subscribers it can feed if a channel requires \[20\,\,kHz\] are
question_answer50) A system of logic gates is shown in the figure. From the study of truth table it can be found that to produce a high output \[(1)\] at\[R\], we must have
question_answer54) A solution of sucrose (molar mass\[~=342gmo{{l}^{-1}})\] has been prepared by dissolving \[68.5\,\,g\] of sucrose in \[1000\,\,g\] of water. The freezing point of solution obtained will be (\[{{K}_{f}}\]for water\[=1.86\,\,K\,\,kg\,\,mo{{l}^{-1}})\]
question_answer55) The standard electrode potential of three metals \[X,\,\,\,Y\] and \[Z\] are \[-1.2\,\,V,\,\,+0.5\,\,V\] and \[-\,\,3.0\,\,V\] respectively. The reducing power of these metals will be
question_answer56) The resistance of \[1\,\,N\] solution of acetic acid is\[250\,\Omega \], when measured in a cell having a cell constant of\[1.15\,\,c{{m}^{-1}}\]. The equivalent conductance (in\[{{\Omega }^{-1}}c{{m}^{2}}equi{{v}^{-1}})\] of \[1\,\,N\] acetic acid is
question_answer57) The thermal decomposition of a molecule shows first order kinetics. The molecule decomposes \[50%\] in\[120\,\,\min \]. How much time it will take to decompose\[90%\]?
question_answer62) Which process of purifications is represented by the following scheme? \[\underset{impure}{\mathop{Ti}}\,+2{{I}_{2}}\xrightarrow{{{250}^{o}}C}Ti{{I}_{4}}\xrightarrow{{{1400}^{o}}C}\underset{Pure}{\mathop{Ti}}\,+2{{I}_{2}}\]
question_answer73) Consider the following reaction\[Phenol\xrightarrow{Zn\,\,dust}X\xrightarrow[anhy\,\,AlC{{l}_{3}}]{C{{H}_{3}}Cl}Y\]\[\xrightarrow{alk\,\,KMn{{O}_{4}}}Z\] The product \[Z\] is
question_answer78) At\[{{25}^{o}}C\], the dissociation constant of a base,\[BOH\] is\[1.0\times {{10}^{-12}}\]. The concentration of hydroxyl ions in 0.01 M aqueous solution of the base would be
question_answer82) The mass of carbon anode consumed (giving only carbon dioxide) in the production of \[270\,\,kg\] of aluminium metal from bauxite by the Hall process is (Atomic mass\[Al=27)\]
question_answer86) A nuclide of an alkaline earth metal undergoes radioactive decay by emission of three \[\alpha -\]particles in succession. The group of the periodic table to which the resulting daughter element would belong is
question_answer90) \[{{H}_{2}}S\] gas when passed through a solution of cations containing HC1 precipitates the cations of second group of qualitative analysis but not those belonging to the fourth group. It is because
A)
presence of \[HCl\] decreases the sulphide ion concentration
doneclear
B)
presence of \[HCl\] increases the sulphide ion concentration
doneclear
C)
solubility product of group II sulphides is more than that of group IV sulphides
doneclear
D)
sulphides of group IV cations are unstable in\[HCl\]
question_answer91) The energy of second Bohr orbit of the hydrogen atom is \[-328\,\,kJ\,\,mo{{l}^{-1}}\]; hence the energy of fourth Bohr orbit would be
question_answer92) Equilibrium constants \[{{K}_{1}}\] and \[{{K}_{2}}\] for the following equilibria\[NO(g)+\frac{1}{2}{{O}_{2}}N{{O}_{2}}(g)\]and\[2N{{O}_{2}}(g)2NO(g)+{{O}_{2}}(g)\]are related as
question_answer94) \[10\,\,g\] of hydrogen and \[64\,\,g\] of oxygen were filled in a steel vessel and exploded. Amount to water produced in this reaction will be
question_answer101) If the lines represented by \[{{x}^{2}}-2pxy-{{y}^{2}}\] are rotated about the origin through an angle\[\theta \], one in clockwise direction and other in anti-clockwise direction. Then, die equation of bisectors of the angles between the lines in the new position is
question_answer103) The sum of the roots of quadratic equation \[a{{x}^{2}}+bx+c=0(a,\,\,b,\,\,c\ne 0)\] is equal to the sum of squares of their reciprocals, then \[\frac{a}{c},\,\,\frac{b}{a}\] and \[\frac{c}{b}\]are in
question_answer104) Find the value of \[^{1}{{P}_{1}}+2{{\cdot }^{2}}{{P}_{2}}+3{{\cdot }^{3}}{{P}_{3}}+4{{\cdot }^{4}}{{P}_{4}}+...{{+}^{n}}{{P}_{n}}\]
question_answer106) If the shortest distance between the lines \[\frac{x-3}{3}=\frac{y-8}{-1}=\frac{z-3}{1}\] and\[\frac{x+3}{-3}=\frac{y+7}{2}=\frac{z-6}{4}\] is\[\lambda \sqrt{30}\]units, then the value of\[\lambda \]is
question_answer112) If the force represented by \[\mathbf{i}+\mathbf{j}+\mathbf{k}\] is acting through the point \[5\mathbf{i}+4\mathbf{j}-3\mathbf{k}\], then its moment about the point\[(1,\,\,2,\,\,2)\]is
question_answer113) If the planes\[x-cy-bz=0\], \[ex-y+az=0\] and\[bx+ay-z=0\], pass through a line, then find the value of\[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}+2abc\].
question_answer114) A parallelepiped is formed by planes drawn through the points \[(2,\,\,3,\,\,5)\] and \[(5,\,\,9,\,\,7)\] parallel to the coordinate planes. The length of the diagonal of the parallelepiped is
question_answer121) Two posts are \[x\] metres apart and the height of one is double that of the other. If from the mid-point of the line joining their feet, an observer finds the angular elevations of their tops to be complementary, then the height (in metres) of the shorter post is
question_answer125) Find the order and degree of the differential equation \[{{\left( \frac{{{d}^{4}}y}{d{{x}^{4}}} \right)}^{3/5}}-5\frac{{{d}^{3}}y}{d{{x}^{3}}}+6\frac{{{d}^{2}}y}{d{{x}^{2}}}-8\frac{dy}{dx}+5=0\]
question_answer126) If the circle\[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\] touches by the line \[y=x\] at the point \[P\] such that \[OP=6\sqrt{2}\], where \[O\] is the origin, then the value of \[c\] is equal to
question_answer129) Find the value of\[{{e}^{iA}}.{{e}^{iB}}.{{e}^{iC}}.{{e}^{iD}}\], where \[A,\,\,\,B,\,\,\,C\] and \[D\] are the angles of a quadrilateral.
question_answer131) The lengths of three unequal edges of a rectangular solid block are in\[GP\]. The volume and total surface area of the block are \[216\,\,c{{m}^{3}}\] and\[252\,\,c{{m}^{2}}\], respectively. Find the shortest edge of the block.
question_answer140) If\[\mathbf{a}=2\mathbf{i}+2\mathbf{j}+3\mathbf{k}\],\[\mathbf{b}=-\mathbf{i}+2\mathbf{j}+\mathbf{k}\]and\[\mathbf{c}=3\mathbf{i}+\mathbf{j}\], then \[\mathbf{a}+t\mathbf{b}\] is perpendicular to \[\mathbf{c};\] if\[t\] is equal to
question_answer141) Find the angle between the straight lines \[\frac{x+1}{2}=\frac{y-2}{5}=\frac{z+3}{4}\]and \[\frac{x-1}{1}=\frac{y+2}{2}=\frac{z-3}{-3}\]
question_answer142) The equation of the plane passing through the line of intersection of the planes \[2x-y=0\] and \[3z-y=0\] and perpendicular to the plane \[4x+5y-3z=8\] is