Solved papers for J & K CET Engineering J and K - CET Engineering Solved Paper-2009
done J and K - CET Engineering Solved Paper-2009 Total Questions - 225
question_answer1) The quantities RC and \[\left( \frac{L}{R} \right)\] ( where R, L and C stand for resistance, inductance and capacitance respectively ) have the dimensions of
question_answer2) The correct vector relation between linear velocity \[\vec{v}\] and angular velocity \[\vec{\omega }\] in rigid body dynamics is ( where \[\vec{r}\] is the postion vector)
question_answer4) Magnitudes of four pairs of displacement vectors are given. Which pair of displacement vectors, under vector addition, fails to give a resultant vector of magnitude\[3\text{ }cm\]?
question_answer8) A cricket ball of mass \[0.5\text{ }kg\]strikes a cricket bat normally with a velocity of \[20\text{ }m{{s}^{-1}}\] and rebounds with velocity of \[10\text{ }m{{s}^{-1}}\]. The impulse of the force exerted by the ball on the bat is
question_answer11) A body, possessing kinetic energy T, moving on a rough horizontal surface, is stopped in a distance y. The frictional force exerted on the. body is
question_answer13) \[{{I}_{1}}\] and \[{{I}_{2}}\] are the moments of inertia of two circular discs about their central axes perpendicular to their surfaces. Their angular frequencies of rotation are \[{{\omega }_{1}}\] and \[{{\omega }_{2}}\] respectively. If they are brought into contact face to face with their axes of rotation coinciding with each other, the angular frequency of the composite disc will be
question_answer14) A child stands at one end of a boat moving with a speed v in still water. If the child starts running towards the other end of the boat with a speed u, the centre of mass of the system (boat and child) will move with a speed
question_answer17) A body is projected up from the surface of the earth with a velocity equal to \[\frac{3}{4}th\] of its escape velocity. If R be the radius of earth, the height it reaches is
question_answer20) Water flows through a pipe of varying cross-section. Then the ratio of the speeds of water at two points 1 and 2, where the radii of the pipe are \[{{r}_{1}}\] and \[{{r}_{2}}\] is
question_answer21) A piece of ice, with a stone embedded inside it, is floating in water contained in a vessel. When the ice melts completely, the level of water in vessel
A)
remains unchanged
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B)
rises
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C)
falls
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D)
falls in the beginning and rises to the same level later
question_answer23) Two small spheres of radii r and \[4r\] fall through a viscous liquid with the same 'terminal velocity. The ratio between the viscous forces acting on them is
question_answer24) A certain quantity of heat energy is given to a diatomic ideal gas which expands at constant pressure. The fraction of the heat energy that is converted into work is
question_answer26) Two monoatomic ideal gases A and B occupying the same volume V, are at the same temperature T and pressure p. If they are mixed, the resultant mixture has volume V and temperature T. The pressure of the mixture is
question_answer28) A Carnot's engine working between \[{{27}^{o}}C\] and \[{{127}^{o}}C\] has a work output of\[200\text{ }J/cycle\]. The energy supplied to the engine from the source in each cycle is
question_answer29) A particle is executing linear simple harmonic motion. The fraction of the total energy that is potential, when its displacement is \[\frac{1}{4}\] of the amplitude is
question_answer31) The third overtone of an open organ pipe is in resonance with the second overtone of a closed organ pipe. If the length of the open pipe is \[8\text{ }cm,\] then the length of closed pipe is
question_answer33) A sound wave with frequency \[256\text{ }Hz\]falls normally on a perfectly reflecting wall. The shortest distance from the wall at which the air particles will have maximum amplitude of vibrations is nearly ( velocity of sound in air is \[336\,m{{s}^{-1}}\])
question_answer34) When air medium in which two charges kept apart at a distance r is replaced by a dielectric medium of dielectric constant K, the force between the charges
question_answer36) Three charges \[-q,\] \[+Q\] and \[-q\] are placed in a straight line as shown. If the total potential energy of the system is zero, then the ratio \[\frac{q}{Q}\]is
question_answer37) Electric flux emanating through a surface element \[\overrightarrow{ds}=5\hat{i}\] placed in an electric field \[\vec{E}=4\hat{i}+4\hat{j}+4\hat{k}\] is
question_answer38) A parallel plate capacitor is charged to a potential of V volt. The battery is then disconnected and the distance between the plates of the capacitor is increased using an insulating handle. The potential difference between the plates of the capacitor will
question_answer39) Energy stored per unit volume of a parallel plate capacitor having plate area A and plate separation d when charged to a potential of V volts is (air space in between the plates)
question_answer40) The mutual electrostatic potential energy between two protons which are at a distance of \[9\times 10{{-}^{15}}\text{ }m,\] in \[_{92}{{U}^{235}}\] nucleus is
question_answer43) The tungsten filaments of two electric bulbs are of the same length. If one of them gives \[25\text{ }W\]power and the other \[60\text{ }W\]power, then
question_answer44) Heater coil A takes \[{{t}_{1}}\] second to boil certain quantity of water. Heater coil B takes 13 second to boil same quantity of water. If A and B are connected in series, the time taken to boil the same quantity of water by the combination is
question_answer46) A charge q coulomb makes n revolutions in one second in a circular orbit of radius r. The magnetic field at the centre of the orbit in \[N{{A}^{-1}}{{m}^{-1}}\]is
question_answer48) An electron travelling with velocity v, enters a region of space in which electric and magnetic fields exist. Then the electron goes uneffected for all values of fields
A)
if both electric and magnetic fields are normal to v
doneclear
B)
if the magnetic field alone in normal to v
doneclear
C)
if both electric and magnetic fields are parallel to v
question_answer52) Whenever there is a relative motion between a coil and a magnet, the magnitude of induced emf set up in the coil does not depend upon the
question_answer53) A uniformly wound coil of self-inductance \[1.2\times {{10}^{-4}}H\]and resistance \[3\Omega \]. is broken up into two identical coils. These coils are then connected parallel across a \[6V\]battery of negligible resistance. The time constant for the current in the circuit is (neglect mutual inductance)
question_answer56) The instantaneous values of current and voltage in an AC circuit are given by \[I=6\,\,\sin \,\left( 100\,\pi t+\frac{\pi }{4} \right),\] \[V=5\,\,\sin \,\left( 100\,\pi t-\frac{\pi }{4} \right),\] then
question_answer58) The relationship between phase difference \[\Delta \phi \] and the path difference \[\Delta x\] between two interfering waves is given by (\[\lambda \]= wavelength)
question_answer59) In Young's double slit experiment, the fringe width with light of wavelength \[6000\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,\]is\[3\text{ }mm\]. The fringe width, when the wavelength of light is changed to \[4000\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,\]is
question_answer62) If a transparent parallel plate of uniform thickness t and refractive index \[\mu ,\] is interposed perpendicularly in the path of a light beam, the optical path is
question_answer63) If the photoelectric work function for a metallic surface is \[4.125\text{ }eV,\]the cut-off wavelength for photoelectric phenomenon for the surface is
question_answer64) The masses of two particles having same kinetic energies are in the ratio\[1:2\]. Then their de-Broglie wavelengths are in the ratio
question_answer68) A radioactive isotope A with a half-life of \[1.25\times {{10}^{10}}\text{ }yr\]decays into B which is stable. A sample of rock from a planet is found to contain both A and B present in the ratio\[1:15\]. The age of the rock is (in years)
question_answer71) In a semiconducting material \[1/5th\]of the total current is carried by the holes and the remaining is carried by the electrons. The drift speed of electrons is twice that of holes at this temperature, the ratio between the -number densities of electrons and holes is
question_answer75) In a typical optical fibres, the difference between the refractive indices of core material and cladding material is of the order of
question_answer78) If the de-Broglie wavelength of a particle of mass m is 100 times its velocity then its value in terms of its mass\[(m)\] and Plants constant \[(h)\] is
question_answer80) The set of quantum numbers \[n=4,l=0\]and \[s=+\frac{1}{2}\] correspond to the most loosely bound, ground state electron of which one of the following atoms?
question_answer82) In the radioactive, decay, \[_{y}{{X}^{z}}\xrightarrow{(-8\alpha \,\text{and}\,\text{6}\beta )}{{\,}_{82}}P{{b}^{206}},x,y\]and \[z\]are
question_answer86) The solubility product of a sparingly soluble metal hydroxide \[\text{M(OH}{{\text{)}}_{\text{2}}}\]at 298 K is\[\text{5}\times \text{1}{{\text{0}}^{-16}}\,mo{{l}^{3}}\,d{{m}^{-9}}.\]The pH value of its aqueous and saturated solution is
question_answer87) In the synthesis of ammonia from nitrogen and hydrogen gases, if \[6\times {{10}^{-2}}\] moles of hydrogen disappears in 10 min, the number of moles of ammonia formed in 3 min is
question_answer88) In a reversible reaction, the enthalpy change and the, activation energy in the forward direction are respectively \[-x\,\text{kJ}\,\text{mo}{{\text{l}}^{-1}}\] and \[y\,kJ\,mo{{l}^{-1}},\]Therefore, the energy of activation in the backward direction in \[kJmo{{l}^{-1}},\]is
question_answer89) The rate constant for a first order reaction is \[6.909\,{{\min }^{-1}},\]Therefore, the time required, in minute, for the participation of 75% of the initial reactant is
question_answer91) At 300 K, two pure liquids A and B have vapour pressures respectively 150 mm Hg and 100 mm Hg, In an equimolar liquid mixture of A and\[B,\] the mole fraction of B in the vapour mixture at this temperature is
question_answer92) The molar mass of the solute sodium hydroxide obtained from the measurement of the osmotic pressure of its aqueous solution at \[\text{27}{{\,}^{\text{o}}}\text{C}\]is\[25\,\text{g}\,\text{mo}{{\text{l}}^{-1}}.\]Therefore, its ionization percentage in this solution is
question_answer93) 25 g of a solute of molar mass \[250\,g\,mo{{l}^{-1}}\] is dissolved in 10 mL of water to obtain a solution whose density is \[1.25\,g{{(mL)}^{-1}}.\] The molarity and molality of the solution are respectively
question_answer94) The standard enthalpies of formation of A \[A(N{{H}_{3}}),B(C{{O}_{2}}),C(HI)\]are respectively \[-\,46,19,-\text{ }393.4,+\,24,94\] and\[-296.9\,\text{kJmo}{{\text{l}}^{-1}},\]The increasing order of their stability is
question_answer95) When 400 mL of 0.2 N solution of a weak acid is neutralised by a dilute aqueous solution of sodium hydroxide under standard conditions, \[4.4\,kJ\]amount of heat is liberated. Therefore, the standard enthalpy bf neutralisation of this weak acid, in \[kJ\,\text{equi}{{\text{v}}^{-1}},\]is
question_answer98) The oxidation numbers of the sulphur atoms in peroxomonosulphuric acid\[({{H}_{2}}S{{O}_{5}})\]and peroxodisulphuric acid \[({{H}_{2}}{{S}_{2}}{{O}_{8}})\] are respectively
question_answer99) In the electrolysis of aqueous solution of \[\text{CuS}{{\text{O}}_{\text{4}}}\] using copper electrodes, the process taking place at the anode is
question_answer100) The correct expression in SI system relating the equivalent conductance\[({{\Lambda }_{c}}),\]specific conductance \[(\kappa )\]and equivalent concentration [C] is (where C is the number of gram-equivalents of the electrolyte in one litre of the solution)
question_answer101) The standard reduction electrode potentials of the three electrodes P, Q and R are respectively \[-1.76\text{ }V,0.34\text{ }V\]and 0.8 V, then
A)
metal Q will displace the cation of P from its aqueous solution and deposit the metal P
doneclear
B)
both metals Q-and R will displace the cation of P from its aqueous solution and deposit the metal P
doneclear
C)
metal R will displace the cation of P from its aqueous solution and deposit the metal P
doneclear
D)
metal P will displace the cation of R from its aqueous solution and deposit the metal R
question_answer103) The van der Waals' constants for four gases P Q, R and S are 4J7, 3.59, 6.71 and 3.8 atm\[{{L}^{2}}.mo{{l}^{-2}}.\] Therefore, the ascending order of their liquification is
question_answer104) The unit cell of a binary alloy composed of ,A and B metals, has a ccp structure with A atoms occupying the corners and B atoms occupying centres of each face of the cube. If during the crystallisation of this alloy, in the unit cell two A atoms are missed, the overall composition per unit cell is
question_answer105) When an excess and a very dilute aqueous solution of\[\text{KI}\]is added to a very dilute aqueous solution of silver nitrate, the colloidal particles of silver iodide are associated with the Helmholtz double layer
question_answer122) The coordination compound of which one of the following compositions will produce two equivalents of AgCl on reaction with aqueous silver nitrate solution?
question_answer129) The IUPAC name of the molecule \[C{{H}_{3}}-\overset{O}{\mathop{\overset{||}{\mathop{C}}\,}}\,-\underset{C{{H}_{3}}}{\mathop{\underset{|}{\mathop{C}}\,}}\,=\underset{C{{H}_{3}}}{\mathop{\underset{|}{\mathop{C}}\,}}\,-\overset{O}{\mathop{\overset{||}{\mathop{C}}\,}}\,-OH\]
question_answer130) The ascending order of stability of the \[\bar{C}{{H}_{3}}(P),{{C}_{6}}{{H}_{5}}\bar{C}{{H}_{2}}(Q),\] \[{{(C{{H}_{3}})}_{2}}-CH(R)\]and \[{{H}_{2}}\bar{C}-CH=C{{H}_{2}}(S)\]is
question_answer131) The descending order of stability, of the carbonium ions \[{{C}_{6}}{{H}_{5}}\overset{+}{\mathop{C}}\,{{H}_{2}}(I),p(C{{H}_{3}}O){{C}_{6}}{{H}_{4}}\overset{+}{\mathop{C}}\,{{H}_{2}}(II),p(N{{O}_{2}})\] \[{{C}_{6}}{{H}_{4}}\overset{+}{\mathop{C}}\,{{H}_{2}}(III)\]and \[p(C{{H}_{3}}){{C}_{6}}{{H}_{4}}\overset{+}{\mathop{C}}\,{{H}_{2}}(IV)\]
question_answer133) The total number of acyclic structural and optical isomers possible for a hydrocarbon of molecular formula \[{{C}_{7}}{{H}_{16}}\]is
question_answer155) If the equation \[(a+1){{x}^{2}}-(a+2)x+(a+3)=0\] has roots equal in magnitude but opposite in signs, then the roots of the equation are
question_answer156) If a and p are roots of the quadratic equation \[{{x}^{2}}+4x+3=0,\]then the equation whose roots are \[2\alpha \,\text{+}\,\beta \] and \[\alpha \,\text{+2}\,\beta \] is
question_answer157) If the sum to 2 n terms of the \[AP\text{ }2,\text{ }5,\text{ }8,11,...\]is equal to the sum to n terms of the \[AP\text{ }57,\text{ }59,\text{ }61,\text{ }63,\text{ }...\text{ },\]then n is equal to
question_answer160) \[\frac{^{8}{{C}_{0}}}{6}{{-}^{8}}{{C}_{1}}{{+}^{8}}{{C}_{2}}.6{{-}^{8}}{{C}_{3}}{{.6}^{2}}+....{{+}^{8}}{{C}_{8}}{{.6}^{7}}\] is equal to
question_answer164) If \[{{x}_{1}},{{x}_{2}},......{{x}_{18}}\] are observations such, that \[\sum\limits_{j=1}^{18}{({{x}_{j}}-8)=9}\] and \[\sum\limits_{j=1}^{18}{{{({{x}_{j}}-8)}^{2}}=45,}\] then the standard deviation of these observations is
question_answer165) If \[(3,\,\,3)\] is a vertex of a triangle and \[(-3,\,\,6)\] and \[(9,\,\,6)\] are the mid points of the two sides through this vertex, then the centroid of the triangle is
question_answer169) The equation of the circle passing through the point \[(1,\,\,1)\] and through the points of intersection of the circles \[{{x}^{2}}+{{y}^{2}}=6\] and \[{{x}^{2}}+\text{ }{{y}^{2}}-6y+8=0\]is
question_answer171) If in a hyperbola, the distance between the foci is 10 and the transverse axis has length 8, then the length of its latuserectum is
question_answer172) If \[\tan \theta =\frac{1}{\sqrt{7}},\]then \[\frac{(\text{cose}{{\text{c}}^{2}}\,\theta -{{\sec }^{2}}\theta )}{(\text{cose}{{\text{c}}^{2}}\,\theta +{{\sec }^{2}}\theta )}\] is equal to
question_answer176) In \[\Delta \,\,ABC,\]if \[s=\frac{a+b+c}{2},\]then \[\left( b\,\,{{\cos }^{2}}\,\frac{C}{2}+c\,\,{{\cos }^{2}}\,\frac{B}{2} \right)\] is equal to
question_answer177) The number of solutions of the equation \[\sin \,x\,\,\cos \,\,3x=\sin \,3x\,\,\cos \,5x\]in \[\left[ 0,\frac{\pi }{2} \right]\] is
question_answer182) If a, b, c are all distinct and if \[\left| \begin{matrix} 1-{{a}^{3}} & {{a}^{2}} & a \\ 1-{{b}^{3}} & {{b}^{2}} & b \\ 1-{{c}^{3}} & {{c}^{2}} & c \\ \end{matrix} \right|=0,\] then
question_answer184) If X and Y are \[2\times 2\] matrices such that \[2X+3Y=O\] and \[X+2Y=I,\]where \[O\] and \[I\] denote the \[2\times 2\] zero matrix and the \[2\times 2\] identity matrix, then X is equal to
question_answer187) A, B, C, D, E, F in that order, are the vertices of a regular hexagon with centre origin. If the position vectors of the vertices A and B are respectively, \[4\hat{i}+3\hat{j}-\hat{k}\]and \[-3\hat{i}+\hat{j}+\hat{k},\] then\[\overrightarrow{DE}\] is equal to
question_answer188) If the position vectors of the vertices of triangle ABC are \[3\hat{i}+\hat{j}+2\hat{k},\,\,\,\hat{i}-2\hat{j}+7\hat{k}\]and \[-2\hat{i}+3\hat{j}+5\hat{k},\] then the triangle ABC is
question_answer189) If \[4|\vec{a}|=12|\vec{b}|=3|\vec{c}|=12\] and \[\vec{a}+\vec{b}+\vec{c}=\vec{0},\] then \[\vec{a}\,\,.\,\,\vec{b}+\vec{b}\,.\,\,\vec{c}+\vec{c}\,.\,\,\vec{a}\] is equal to
question_answer190) If \[2\text{ }\vec{a}+3\text{ }\vec{b}+\vec{c}=0,\] then \[\vec{a}\times \vec{b}+\vec{b}\times \vec{c}+\vec{c}\times \vec{a}\]is equal to
question_answer191) If \[\hat{i}-\hat{k},\,\lambda \hat{i}+\hat{j}+(1-\lambda )\hat{k}\] and \[\mu \hat{i}+\lambda \hat{j}+(1+\lambda -\mu )\hat{k}\]are three coterminal edges of a parallelopiped, then its volume depends on
question_answer192) \[\vec{u}\] and \[\vec{v}\] are unit vectors such that \[\vec{u}\,\,.\vec{v}\]. If \[\vec{r}\]is any vector coplanar with \[\vec{u}\] and \[\vec{v}\] then the magnitude of the \[\vec{u}\] vector \[\vec{v},\] is
question_answer194) A line makes an obtuse angle with the positive x-axis and angles \[\frac{\pi }{4}\] and \[\frac{\pi }{3}\] with the positive y and z axes respectively. Its direction cosine are
question_answer195) The shortest distance between the straight line \[\frac{x-6}{1}=\frac{2-y}{2}=\frac{z-2}{2}\] and \[\frac{x+4}{3}-\frac{y}{-2}=\frac{1-z}{2}\] is
question_answer197) The equation of the plane passing through the point \[(1,1,1)\] and containing the line of intersection of the planes \[x+y+z=6\] and \[2x+3y+4z=12\] is
question_answer199) If \[\vec{a}\] is a constant vector and p is a real constant with \[|\vec{a}{{|}^{2}}>p,\] then the locus of a point with position vector \[|\vec{r}|\] such that \[|\vec{r}{{|}^{2}}-2\,\,\vec{r}.\,\vec{a}\,+\,\,p=O\]is
question_answer201) A drawer contains 5 brown socks and 4 blue socks well mixed. A man reaches the drawer and pulls out 2 socks at random. The probability that they match is
question_answer202) Events A, B, C are mutually exclusive events such that \[P(A)=\frac{(3x+1)}{3},\,\,P(B)=\frac{(1-x)}{4}\] and \[P(C)=\frac{(1-2x)}{2}\].The set of possible values of x are in the interval
question_answer205) The function \[f(x)\] is defined as \[f(x)=\frac{2x-{{\sin }^{-1}}x}{2x+{{\tan }^{-1}}x'}\], if \[x\ne 0\]. The value to be assigned to f at \[x=0\]so that the function is continuous there, is
question_answer206) The function \[f(x)=\left\{ \begin{matrix} |x-3|, & if & x\ge 1 \\ \frac{{{x}^{2}}}{4}-\frac{3x}{2}+\frac{13}{4}, & if & x<1 \\ \end{matrix} \right.\]is
A)
continuous and differentiable at \[x=3\]
doneclear
B)
continuous at \[x=3,\] but not differentiable at \[x=3\]
doneclear
C)
continuous and differentiable everywhere
doneclear
D)
continuous at \[x=1,\]but not differentiable at \[x=1,\]
question_answer212) Let \[f(x)={{x}^{3}}.\]. Use mean value theorem to write \[\frac{f(x+h)-f(x)}{h}=f'(x+\theta h)\] , with \[0<\theta <1\]. If \[x\ne 0,\]then \[\underset{h\to 0}{\mathop{\lim }}\,\,\,\theta \] is equal to
question_answer213) If \[f\,(x)=\underset{y\to x}{\mathop{lim}}\,\,\frac{{{\sin }^{2}}y-{{\sin }^{2}}x}{{{y}^{2}}-{{x}^{2}}},\]then \[\int{4x\,\,f(x)\,\,dx}\]is equal to
question_answer220) P and Q are two like parallel forces. If Q is moved parallel to itself through a distance x, then the resultant of P and Q moves through a distance
question_answer221) The greatest and the least magnitudes of the resultant of two forces of constant magnitudes are F and G. when the forces act at an angle \[2\alpha ,\] the magnitude of the resultant is equal to
question_answer222) The magnitude of moment of a couple in certain direction is G and in a direction orthogonal to this direction (anti-clockwise) is H. The magnitude of moment of couple in anti-clockwise direction at an angle \[\theta \] to the critical direction is given by
question_answer223) The amount of force that is needed to accelerate a truck of mass \[36000\,kg\]from rest to a velocity of \[60\,km/h\]in \[20\,s\] is
question_answer224) A body id falling freely under gravity starting from a point O.it passes through two points A and B. If \[OA=\,2AB,\] then the ratio of time takes by the body to cover the distance OA and AB is
question_answer225) A particle is projected from a point on the horizontal plane so as to just clear two walls each of height \[20\,m\]at distance \[30\,m\] and \[170\,m\] respectively from the point of projection. If \[\alpha \] is the angle projection then