Solved papers for JCECE Engineering JCECE Engineering Solved Paper-2013
done JCECE Engineering Solved Paper-2013 Total Questions - 150
question_answer1) A boat can go across a lake and return in time \[{{T}_{0}}\] at a speed\[v\]. On a rough day there is a uniform current at speed \[{{v}_{1}}\] to help the onward journey and impede the return journey. If the time taken to go across and return on the same day be\[T\], then \[T/{{T}_{0}}\] will be
question_answer2) If a balloon of mass \[M\] is descending down with an acceleration\[a(<g)\], then what is the value of mass \[m\] (of its contents) that must be removed so that it starts moving up with an acceleration\[a\]?
question_answer3) If for a spherical mirror object distance, \[u=(50.1\pm 0.5)\] and image distance\[v=(20.1\pm 0.2)\], then focal length of the spherical mirror will be
question_answer5) If a current carrying circular loop is placed in a \[x-y\] plane as shown in adjoining figure and a magnetic field is applied along\[z-axis\], then the loop will
question_answer6) If the three vectors \[A,\,\,\,B\] and \[C\] satisfy the relation \[\mathbf{A}\bullet \mathbf{B}=0\] and \[\mathbf{A}\bullet \mathbf{C}=0\], then vector A is parallel to
question_answer7) A car weighing \[2\times {{10}^{3}}kg\] and moving at \[20\,\,m/s\] along a main road collides with a lorry of mass \[8\times {{10}^{3}}kg\] which emerges at \[5\,\,m/s\] from a cross road at right angle to the main road. If the two vehicles lock, what will be then velocity after the collision?
question_answer8) If a water particle of mass \[10\,\,mg\] and having a charge of \[1.5\times {{10}^{-6}}C\] stays suspended in a room, then the magnitude and direction of electric field in the room is
question_answer9) In the adjoining figure,\[E=5\,\,V,\,\,r=1\Omega \]\[,\]\[{{R}_{2}}=4\Omega ,\,\,{{R}_{1}}={{R}_{3}}=1\Omega \] and \[C=3\mu F\]. The numerical value of the charge on each plate of the capacitor is
question_answer11) A pure resistive circuit element \[X\] when connected to a \[AC\] supply of peak voltage \[200\,\,V\] gives a peak current of\[5\,\,A\]. \[A\] second current element \[Y\] when connected to same \[AC\] supply gives the same value of peak current but the current lags behind by\[{{90}^{o}}\]. If series combination of \[X\] and \[Y\] is connected to the same supply, what is the impedance of the circuit?
question_answer12) Two circular coils \[C\] and \[D\] have equal number of turns and carry equal currents in the same direction in the same sense and subtend same solid angle at point \[O\] as shown in figure. The smaller coil \[C\] is midway between \[O\] and\[D\]. If we represent magnetic field induction due to bigger coil and smaller coil \[C\] as \[{{B}_{D}}\] and \[{{B}_{C}}\] respectively, then By \[{{B}_{D}}/{{B}_{C}}\] is
question_answer13) Equal volume of two immiscible liquids of densities \[p\] and \[2p\] are filled in a vessel as shown in figure. Two small holes are made at depth \[\frac{h}{2}\] and \[\frac{3h}{2}\] from the surface of lighter liquid. If \[{{v}_{1}}\] and \[{{v}_{2}}\] are the velocities of efflux at these two holes, then \[{{v}_{1}}/{{v}_{2}}\] will be.
question_answer14) Three conducting rods of same material and cross-section are connected as shown in figure. Temperatures of \[A,\,\,\,D\] and \[C\] are maintained at\[{{20}^{o}}C\], \[{{90}^{o}}C\] and\[{{0}^{o}}C\]. If there is no flow of heat in\[AB\], then ratio of the lengths of \[BC\] and \[BD\] is
question_answer15) If two air columns of lengths \[100\,\,cm\] and \[101\,\,cm\] sounding in their fundamental note gave \[17\] beats in \[20\] seconds, then the velocity of sound will be
question_answer16) If two springs of spring constants \[{{k}_{1}}\] and \[{{k}_{2}}\] while executing \[SHM\] have equal highest velocities, then the ratio of their amplitudes will be (their masses are in ratio\[1:2)\]
question_answer19) The intensity of gamma radiation from a given source is\[I\]. If on passing through \[36\,\,mm\] of lead its intensity is reduced to\[\frac{I}{8}\], then what will be the thickness of lead which reduces its intensity to\[\frac{I}{2}\]?
question_answer20) An unpolarized beam of light is incident on a group of four polarizing sheets, which are arranged in such a way that the characteristic direction of each polarizing sheet makes an angle of \[{{30}^{o}}\] with that of the preceding sheet. The fraction of incident unpolarized light transmitted is
question_answer21) Two coherent sources of intensity ratio \[\beta \] interfere. Then, the value\[({{I}_{\max }}-{{I}_{\min }})/\]\[({{I}_{\max }}+{{I}_{\min }})\] is
question_answer22) A luminous object is placed at a distance of \[30\,\,cm\] from the convex lens of focal length\[20\,\,cm\]. On the other side of the lens, at what distance from the lens a convex mirror of radius of curvature \[10\,\,cm\] be placed in order to have an upright image of the object coincident with it?
question_answer23) If a charge \[-150\,\,nC\] is given to a concentric spherical shell and a charge \[+50\,\,nC\] is placed at its centre, then the charge on inner and outer surface of the shell is
question_answer25) In the adjoining figure, if \[10\] calorie heat is produced per second in \[5\Omega \] resistor due to the flow of current through it, then the heat produced in \[6\Omega \] resistor is
question_answer26) A rod of length \[L\] rotates about an axis passing through one of its ends and perpendicular to its plane. If the linear mass density of the rod varies as\[\rho =(A{{r}^{3}}+B)kg/m\], then the moment of inertia of the rod about the given axis of rotation is
question_answer28) A body is projected with velocity \[{{v}_{1}}\] from the point\[A\], another body at the same time is projected vertically upwards from \[B\] with velocity \[{{v}_{2}}\] as shown in adjoining figure. If the point \[B\] lies vertically below the highest point \[C\], then for both bodies to collide the ratio\[\frac{{{v}_{2}}}{{{v}_{1}}}\]should be
question_answer29) A police van moving on a highway with a speed of \[30\,\,km/h\] fires a bullet at a thief?s car speeding away in the same direction with a speed of\[192\,\,km/h\]. If the muzzle speed of the bullet is\[150\,\,km/h\], with what speed does the bullet hit the thief?s car?
question_answer30) A machine gun of mass \[10\,\,kg\] fires \[30\,\,g\] bullets at the rate of \[6\] bullets/s with a speed of\[400\,\,m/s\]. The force required to keep the gun in position will be
question_answer31) A body of mass \[0.1\,\,kg\] when rotated in a circular path of diameter \[1.0\,\,m\] on a frictionless horizontal plane by means of string, makes \[10\] revolutions in \[31.4\] seconds. The centripetal force acting on the body will be
question_answer32) A plane electromagnetic wave propagating in \[x\,\,(-)\]direction as a wave function (in \[SI\] units) is given as \[\psi (x,\,\,t)={{10}^{3}}\sin \pi (3\times {{10}^{6}}x-9\times {{10}^{14}}t)\] The speed of the wave is
question_answer33) A thin lens of focal length \[f\] and aperture diameter \[d\] forms an image of intensity\[I\]. If the central part of the aperture upto diameter\[d/2\] is blocked by an opaque paper, then the new focal length and intensity of image will be
question_answer34) Light of wavelength \[\lambda \] strikes a photo sensitive surface and electrons are ejected with kinetic energy\[E\]. If the kinetic energy is to be increased to\[2E\], then the wavelength must be changed to\[\lambda '\], where
question_answer35) In a photo electric effect experiment, the maximum kinetic energy of the emitted electrons is \[1\,\,eV\] for incoming radiation of frequency \[{{v}_{0}}\] and \[3\,\,eV\] for incoming radiation of frequency\[3{{v}_{0}}/2\]. What is the maximum kinetic energy of the electrons emitted for incoming radiations of frequency\[9{{v}_{0}}/4\]?
question_answer36) If the energy of hydrogen atom in the ground state is \[-13.6\,\,eV\], then energy of \[H{{e}^{+}}\] ion in first excited state will be
question_answer38) For a transistor in common base, the current gain is\[~0.95\]. If the load resistance is \[400\,\,k\Omega \] and input resistance is \[200\,\,k\Omega \], then the voltage gain and power gain will be
question_answer41) Let a beam of wavelength \[\lambda \] falls on parallel reflecting planes with separation\[d\], then the angle \[\theta \] that the beam should make with the planes so that reflected beams from successive planes may interfere constructively should be (where,\[n=1,\,\,2,\,\,...)\]
question_answer43) A weight \[mg\] is suspended from the middle of a rope whose ends are at same level. If the rope is no longer horizontal, the minimum tension required to completely straighten the rope will be
question_answer44) Two triodes having amplification factors \[30\] \[\text{and}\] \[21\] and plate resistances \[5k\Omega \] and \[4k\Omega \] respectively are connected in parallel. The composite amplification factor of the system is
question_answer46) If a magnet is dropped along the axial line of a horizontally held copper ring, then the acceleration of the magnet while it passing through the ring will
question_answer47) A clock which keeps correct time at\[{{20}^{o}}C\], is subjected to\[{{40}^{o}}C\]. If coefficient of linear expansion of the pendulum is\[12\times {{10}^{-6}}{{/}^{o}}C\], then how much will it gain or loss in time?
question_answer48) The resistance of a resistance thermometer have values \[2.71\] and \[3.70\] ohms at \[{{10}^{o}}C\] and \[{{100}^{o}}C\] respectively. The temperature at which the resistance is \[3.26\,\,ohm\] is
question_answer50) A coil is wound on a transformer of rectangular cross-section. If all the linear dimensions of the transformer are increased by a factor 2 and the number of turns per unit length of the coil remains the same, the self-inductance increases by a factor of
question_answer51) A drop of water is about\[0.05\,\,mL\]. The density of water at room temperature is about\[1.0\,\,m{{L}^{-1}}\]. The number of water molecules present in a drop of water are
question_answer54) A black compound of manganese reacts with a halogen acid to give greenish yellow gas. When excess of this gas reacts with \[N{{H}_{3}}\]an unstable trihalide is formed. In this process, the oxidation state of nitrogen changes from
question_answer56) Bond dissociation enthalpy of \[E-H(E=\] element) bonds is given below. Which of the compounds will act as strongest reducing agent? Compound \[=\]\[N{{H}_{3}}\] \[P{{H}_{3}}\] \[As{{H}_{3}}\] \[Sb{{H}_{3}}\] \[{{\Delta }_{diss(E-H)(kJmo{{l}^{-1}})}}=\]\[389\] \[322\] \[297\] \[255\]
question_answer57) The electronic configuration of a transition element \['X'\] in \[+3\] oxidation state is\[[Ar]3{{d}^{5}}\]. What is its atomic number?
question_answer60) When\[0.1\,\,mol\,\,CoC{{l}_{3}}\], \[{{(N{{H}_{3}})}_{5}}\] is treated with excess of \[AgN{{O}_{3}},\,\,0.2\,\,mole\] of \[AgCl\] are obtained. The conductivity of solution will correspond to
question_answer65) A beaker contains a solution of substance\['A'\]. On dissolving substance \['A'\] in small amount in this solution, precipitation of substance \['A'\] takes place. The solution is
question_answer66) \[4L\] of \[0.02\,\,M\] aqueous solution of \[NaCl\] was diluted by adding \[1\,\,L\] of water. The molality of the resultant solution is
question_answer69) Consider the reaction \[A\xrightarrow{{}}B\,\,;\]the concentration of both the reactants and the products varies exponentially with time. Which of the following figures correctly describes the change in concentration of reactants and products with time?
question_answer78) Which is the most suitable reagent for the following conversion? \[C{{H}_{3}}-CH=CH-C{{H}_{2}}-\overset{\begin{smallmatrix} O \\ || \end{smallmatrix}}{\mathop{C}}\,-C{{H}_{3}}\to \]\[C{{H}_{3}}-CH=CH-C{{H}_{2}}-\overset{\begin{smallmatrix} O \\ || \end{smallmatrix}}{\mathop{C}}\,-OH\]
question_answer79) \[C{{H}_{3}}-C\equiv CH\xrightarrow[1%HgS{{O}_{4}}]{40%{{H}_{2}}S{{O}_{4}}}a\xrightarrow{Isomerisation}\] Structure of \[A\] and the type of isomerism in the above reaction are respectively.
question_answer83) The order of reactivity of following alcohols with halogen acids is \[I.C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}OH\] \[II.C{{H}_{3}}C{{H}_{2}}-\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{C}}\,H-C{{H}_{3}}\] \[III.C{{H}_{3}}C{{H}_{2}}-\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\overset{\begin{smallmatrix} C{{H}_{3}} \\ | \end{smallmatrix}}{\mathop{C}}}\,-OH\]
question_answer89) An alkene\['A'\]contains three\[C-C\], eight\[C-H\]\[\sigma -\]bonds and one\[C-C-\pi \]bond.\['A'\]on ozonolysis gives two moles of an aldehyde of molar mass\[44\,\,u\]. \[IUPAC\]name of \[A\]is
question_answer97) For the reaction,\[{{C}_{3}}{{H}_{8}}(g)+5{{O}_{2}}(g)\xrightarrow{{}}3C{{O}_{2}}(g)+4{{H}_{2}}O(l)\]at constant temperature, \[\Delta H-\Delta E\] is
question_answer99) On adding\[0.1\,\,M\]solution each of\[[A{{g}^{+}}],\,\,[B{{a}^{2+}}],\,\,(C{{a}^{2+}}]\]in \[N{{a}_{2}}S{{O}_{4}}\]solution, species first precipitated is \[[{{K}_{sp}}BaS{{O}_{4}}={{10}^{-11}},\,\,{{K}_{sp}}CaS{{O}_{4}}={{10}^{-6}}\]and\[{{K}_{sp}}A{{g}_{2}}S{{O}_{4}}={{10}^{-5}}]\]
question_answer100) Heat of neutralisation of \[HF\] (a weak acid) with strong base is\[-16.4\,\,kcal\]. Calculate heat of ionisation of \[HF\] in water.
question_answer101) If the slope of one of the lines represented by the equation \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0\] be square of the other, then the value of\[\frac{a+b}{h}+\frac{8{{h}^{2}}}{ab}\]is
question_answer102) If \[\theta \] is real and \[{{z}_{1}},\,\,{{z}_{2}}\] are connected by \[z_{1}^{2}+z_{2}^{2}+2{{z}_{1}}{{z}_{2}}\cos \theta =0\], then triangle with vertices \[0,\,\,{{z}_{1}}\] and \[{{z}_{2}}\] is
question_answer103) Total number of values of\['a'\], so that \[{{x}^{2}}-x-a=0\] has integral roots, where \[a\in N\] and\[6\le a\le 100\], is equal to
question_answer105) If any tangent to the ellipse\[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] intercepts equal lengths 'I' on the axes, then\[l\]is equal to
question_answer110) The value of \['p'\] such that the length of subtangent and subnormal is equal for the curve \[y={{e}^{px}}+px\] at the point \[(0,\,\,1)\] is
question_answer111) If the function \[f(x)=2{{x}^{3}}-9a{{x}^{2}}+12{{a}^{2}}x+1\], where \[a>0\] attains its maximum and minimum at \[p\] and \[q\] respectively, such that \[{{p}^{2}}=q\], then a equals to
question_answer112) If\[\mathbf{a}=x\mathbf{i}+(x-1)\mathbf{j}+\mathbf{k}\]and\[\mathbf{b}=(x+1)\mathbf{i}+\mathbf{j}+a\mathbf{k}\] always make an acute angle with each other for every value of\[x\in R\], then
question_answer114) A variable plane passes through the fixed point \[(a,\,\,b,\,\,c)\] and meets the axes at\[A,\,\,B,\,\,C\]. The locus of the point of intersection of the planes through \[A,\,\,B,\,\,C\] and parallel to the coordinates planes is
question_answer115) If \[PQ\] is a double of the .hyperbola\[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\] such that \[OPQ\] is an equilateral triangle, \[O\] being the centre of the hyperbola, then the eccentricity \['e'\] of the hyperbola satisfies
question_answer117) In a geometric series, the first term \[=a,\] common ratio\[=r\]. If \[{{S}_{n}}\] denotes the sum of the \[n\] terms and\[{{U}_{n}}=\sum\limits_{n=1}^{n}{{{S}_{n}}}\], then\[r{{S}_{n}}+(1-r){{U}_{n}}\] equals to
question_answer118) If \[{{x}_{1}}\] and \[{{x}_{2}}\] are two distinct roots of the equation\[a\cos x+b\sin x=c\], then\[\tan \frac{{{x}_{1}}+{{x}_{2}}}{2}\] is equal to
question_answer121) A vertical pole \[PS\] has two marks at \[Q\] and \[R\] such that the portions \[PQ,\,\,\,PR\] and \[PS\] subtend angles \[\alpha ,\,\,\,\beta \] and \[\gamma \] at a point on the ground distance \[x\] from the bottom of pole. If \[PQ=a,\,\,PR=b,\,\,PS=c\]and\[\alpha +\beta +\gamma ={{180}^{o}}\], then \[{{x}^{2}}\] is equal to
question_answer124) The degree of the differential equation \[{{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{3}}+{{\left( \frac{dy}{dx} \right)}^{2}}+\sin \left( \frac{dy}{dx} \right)+1=0\]is
question_answer126) The range of\[\alpha \], for which the point \[(\alpha ,\,\,\alpha )\] lies inside the region bounded by the curves \[y=\sqrt{1-{{x}^{2}}}\]and \[x+y=1\] is
question_answer127) Find the length of the line segment joining the vertex of the parabola \[{{y}^{2}}=4ax\] and a point on the parabola where the line segment makes an angle \['\theta '\] to the x-axis.
question_answer129) If\[{{a}_{1}},\,\,{{a}_{2}},...,\,\,{{a}_{n-1}}\]are the nth roots of unity, then the value of\[(1-{{a}_{1}})(1-{{a}_{2}})...(1-{{a}_{n-1}})\] is equal to
question_answer131) A person writes a letter to four of his friends. He asks each one of them, to copy the letter and mail to four different persons with instructions that they move the chain similarly. Assuming that the chain is not broken and that it costs \[50\,\,paise\] to mail one letter. When the 8th set of letter is mailed, then the amount on postage will be
question_answer132) If \['a'\] be the \[AM\] between \[b\] and \[c\] and \[GM's\]are \[{{G}_{{}}}\] and\[{{G}_{2}}\], then \[G_{1}^{3}+G_{2}^{3}\] is equal to
question_answer136) If \[{{x}_{1}},\,\,{{x}_{2}},...,\,\,{{x}_{n}}\] be n observations such that \[\Sigma x_{i}^{2}=400\] and\[\Sigma {{x}_{i}}=80\]. Then, a possible value of \[n\] among the following is
question_answer139) The value of \['a'\] for which the function \[f(x)=(4a-3)(x+\log 5)+2(a-7)\] \[\cot \frac{x}{2}\cdot {{\sin }^{2}}\frac{x}{2}\]does not possess critical points is
question_answer140) \[\mathbf{a}\]and \[\mathbf{c}\] are unit vectors and\[|\mathbf{b}|\,\,=4\]. If angle between \[\mathbf{b}\] and \[\mathbf{c}\] is and \[{{\cos }^{-1}}\left( \frac{1}{4} \right)\]\[\text{and}\]\[\mathbf{a}\times \mathbf{b}=2\mathbf{a}\times \mathbf{c}\], then\[\mathbf{b}=\lambda \mathbf{a}+2\mathbf{c}\], where\[\lambda \]is equal to
question_answer141) If the planes\[x-cy-bz=0\], \[cx-y+az=0\]and\[bx+ay-z=0\] pass through a straight line, then the value of \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}+2abc\]is
question_answer142) The plane \[ax+by=0\] is rotated through an angle \[\alpha \] about its line of intersection with the plane\[z=0\], then the equation to the plane in new position is
question_answer147) If\[{{(1+x-2{{x}^{2}})}^{6}}=1+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+...+{{a}_{12}}{{x}^{12}}\], then the expression\[{{a}_{2}}+{{a}_{4}}+{{a}_{6}}+...+{{a}_{12}}\]has the value
question_answer148) If \[f:\left[ 0,\,\,\frac{\pi }{2} \right]\to [0,\,\,\infty ]\] be a function defined by \[y=\sin \left( \frac{x}{2} \right)\], then \[f\] is
question_answer149) If the function \[f(x)\] is defined by \[f(x)=a+bx\] and \[{{f}^{r}}=fff...\] (repeated \[r\] times), then\[\frac{d}{dx}\{{{f}^{r}}(x)\}\]is equal to