Solved papers for VIT Engineering VIT Engineering Solved Paper-2009
done VIT Engineering Solved Paper-2009 Total Questions - 120
question_answer1) When a wave traverses a medium, the displacement of a particle located at\[x\] at a time \[t\] is given by \[y=a\text{ }sin\left( bt-\text{c}x \right)\], where \[a\],\[b\]and\[c\] are constants of the wave, which of the following is a quantity with dimensions?
question_answer2) A body is projected vertically upwards at time \[t=0\] and it is seen at a height \[H\]at timer, and \[{{t}_{1}}\] and \[{{t}_{2}}\] second during its flight. The maximum height attained is (g is acceleration due to gravity)
question_answer3) A particle is projected up from a point at an angle with the horizontal direction. At any time \[t\], if \[p\] is the linear momentum, \[y\] is the vertical displacement, \[x\] is horizontal displacement, the graph among the following which does not represent the variation of kinetic energy of the particle is
question_answer4) A motor of power \[{{P}_{0}}\] is used to deliver water at a certain rate through a given horizontal pipe. To increase the rate of flow of water through the same pipe \[n\] times, the power of the motor is increased top. The ratio of \[{{P}_{1}}\], to \[{{P}_{0}}\] is
question_answer5) A body of mass 5 kg makes an elastic collision with another body at rest and continues to move in the original direction after collision with a velocity equal to \[\frac{1}{10}th\] of its original velocity. Then the mass of the second body is
question_answer6) A particle of mass \[4m\] explodes into three pieces of masses\[m\], \[m\] and \[2m.\] the equal masses move along X-axis and V-axis with velocities \[4\text{ }m{{s}^{-1}}\] and \[6m{{s}^{-1}}\] respectively. The magnitude of the velocity of the heavier mass is
question_answer7) A body is projected vertically upwards from the surface of the earth with a velocity equal to half the escape velocity. If R is the radius of the earth, maximum height attained by the body from the surface of the earth is
question_answer8) The displacement of a particle executing SHM is given by \[y=\,5\,\sin \,\left( 4t+\frac{\pi }{3} \right)\] If T is the time period and the mass of the particle is 2g, the kinetic energy of the particle when \[t=\frac{T}{4}\] is given by
question_answer9) If the ratio of lengths, radii and Youngs modulus of steel and brass wires shown in the figure are a, b and c respectively, the ratio between the increase in lengths of brass and steel wires would be
question_answer10) A soap bubble of radius \[r\] is blown up to form a bubble of radius \[2r\] under isothermal conditions. If T is the surface tension of soap solution, the energy spent in the blowing
question_answer11) Eight spherical rain drops of the same mass and radius are falling down with a terminal speed of\[6\text{ }cm-{{s}^{-1}}\]. If they coalesce to form one big drop, what will be the terminal speed of bigger drop? (Neglect the buoyancy of the air)
question_answer12) A clock pendulum made of invar has a period of 0.5 s, at \[20{}^\circ C\]. If the clock is used in a climate where the temperature averages to\[30{}^\circ C\], how much time does the clock lose in each oscillation? \[(\text{For invar},\alpha =9\times {{10}^{-7}}{{/}^{0}}C,\,g=cons\tan t)\]
question_answer13) A piece of metal weighs \[45g\] in air and \[25g\] in a liquid of density \[1.5\times {{10}^{3}}kg-{{m}^{-3}}\] kept at \[30{}^\circ C\]. When the temperature of the liquid is raised to \[40{}^\circ C\], the metal piece weighs \[27g\]. The density of liquid at \[40{}^\circ C\] is \[1.25\times {{10}^{3}}kg-{{m}^{-3}}\]. The coefficient of linear expansion of metal is
question_answer14) An ideal gas is subjected to a cyclic process ABCD as depicted in the\[p-V\]diagram given below: Which of the following curves represents the equivalent cyclic process?
question_answer15) An ideal gas is subjected to cyclic process involving four thermodynamic states, the amounts of heat \[\left( Q \right)\] and work \[\left( W \right)\] involved in each of these states are \[{{Q}_{1}}~=\text{ }6000\text{ }J\], \[{{Q}_{2}}=-5500\text{ }J\]; \[{{Q}_{3}}=-3000\text{ }J\]; \[{{Q}_{4}}~=3500\text{ }J\] \[{{W}_{1}}=2500\text{ }J\]; \[{{W}_{2}}=-1000\text{ }J\]; \[{{W}_{3}}=-1200\text{ }J\]; \[{{W}_{4}}=x\text{ }J\]. The ratio of the net work done by the gas to the total heat absorbed by the gas is r). The values of x and n respectively are
question_answer16) Two cylinders A and B fitted with pistons contain equal number of moles of an ideal monoatomic gas at 400 K. The piston of A is free to move while that of B is held fixed. Same amount of heat energy is given to the gas in each cylinder. If the rise in temperature of the gas in A is 42 K, the rise in temperature of the gas in B is
question_answer17) Three rods of same dimensional have thermal conductivity 3 K, 2 K and K. They are arranged as shown in the figure below Then, the temperature of the junction in steady state is
question_answer18) Two sources A and B are sending notes of frequency 680 Hz. A listener moves from A and B with a constant velocity u. If the speed of sound in air is \[340\text{ }m{{s}^{-1}}\], what must be the value of us that he hears 10 beats per second?
question_answer19) Two identical piano wires have a fundamental frequency of 600 cycle per second when kept under the same tension. What fractional increase in the tension of one wires will lead to the occurrence of 6 beats per second when both wires vibrate simultaneously?
question_answer20) In the Youngs double slit experiment, the intensities at two points \[{{P}_{1}}\] and \[{{P}_{2}}\] on the screen are respectively \[{{I}_{1}}\] and \[{{I}_{2}}\]. If \[{{P}_{1}}\] is located at the centre of a bright fringe and \[{{P}_{2}}\] is located at a distance equal to a quarter of fringe width from \[{{P}_{1}}\], then \[\frac{{{I}_{1}}}{{{I}_{2}}}\] is
question_answer21) In Youngs double slit experiment, the 10th maximum of wavelength \[{{\lambda }_{1}}\]is at a distance of \[{{y}_{1}}\] from the central maximum- When the wavelength of the source is changed to \[{{\lambda }_{2}}\], 5th maximum is at a distance of \[{{y}_{2}}\] from its central maximum. The ratio \[\left( \frac{{{y}_{1}}}{{{y}_{2}}} \right)\] is
question_answer24) Two bar magnets A and Bare placed one over the other and are allowed to vibrate in a vibration magnetometer. They make 20 oscillations per minute when the similar poles of A and B are on the same side, while they make 15 oscillations per minute when their opposite poles lie on the same side. If \[{{\text{M}}_{\text{A}}}\] and \[{{\text{M}}_{\text{B}}}\]are the magnetic moments of A and B and if \[{{\text{M}}_{\text{A}}}\text{}{{\text{M}}_{\text{B}}}\], the ratio of \[{{\text{M}}_{\text{A}}}\] and \[{{\text{M}}_{\text{B}}}\]is
question_answer25) A bar magnet is 10 cm long is kept with its north (N)-pole pointing north. A neutral point is formed at a distance of 15 cm from each pole. Given the horizontal component of earths field is 0.4 Gauss, the pole strength of the magnet is
question_answer26) An infinitely long thin straight wire has uniform linear charge density of\[\frac{1}{3}C{{m}^{-1}}.\]. Then, the magnitude of the electric intensity at a point 18 cm away is \[(given\,{{\varepsilon }_{0}}=8.8\,\times \,{{10}^{-12}}\,{{C}^{2}}\,N{{m}^{-2}})\]
question_answer27) Two point charges \[-q\] and \[+q\] are located at points (0, 0, \[-a\]) and (0, 0, \[a\]) respectively. The electric potential at a point (0, 0, \[z\]), where \[z<a\] is
question_answer28) In the adjacent shown circuit, a voltmeter of internal resistance R, when connected across B and C reads \[\frac{100}{3}\]V. Neglecting the internal resistance of the battery, the value of R
question_answer29) A cell in secondary circuit gives null deflection for 2.5 m length of potentiometer having 10 m length of wire. If the length of the potentiometer wire is increased by 3 m without changing the cell in the primary, the position of the null point now is
question_answer30) The following series L-C-R circuit, when driven by an emf source of angular frequency 70 kilo-radians per second, the circuit effectively behaves like
question_answer31) A wire of length \[l\] is bent into a circular loop of radius R and carries a current\[I\]. The magnetic field at the centre of the loop is\[B\]. The same wire is now bent into a double loop of equal radii. If both loops carry the same current \[I\] and it is in the same direction, the magnetic field at the centre of the double loop will be
question_answer32) An infinitely long straight conductor is bent into the shape as shown below. It carries a current of I ampere and the radius of the circular loop is R metre. Then, the magnitude of magnetic induction at the centre of the circular loop is
question_answer33) The work function of a certain metal is \[3.31\times {{10}^{-19}}J\]. Then, the maximum kinetic energy of photoelectrons emitted by incident radiation of wavelength \[\text{5000 }\overset{\text{o}}{\mathop{\text{A}}}\,\] is (Given, \[h=6.62\times {{10}^{-34}}J-s\], \[c=3\times {{10}^{8}}m{{s}^{-1}}\],\[e=1.6\times {{10}^{-19}}C\])
question_answer34) A photon of energy E ejects a photoelectron from a metal surface whose work function is \[{{W}_{0}}\]. If this electron enters into a uniform magnetic field of induction B in a direction perpendicular to the field and describes a circular path of radius \[r\], then the radius \[r\] is given by, (in the usual notation)
question_answer35) Two radioactive materials \[{{X}_{1}}\] and \[{{X}_{2}}\] have decay constants \[10\lambda \] and \[\lambda \] respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of \[{{X}_{1}}\] to that of \[{{X}_{2}}\] will be \[1/e\]after a time
question_answer37) A bullet of mass 0.02 kg travelling horizontally with velocity \[250\text{ }m{{s}^{-1}}\]strikes a block of wood of mass 0.23 kg which rests on a rough horizontal surface. After the impact, the block and bullet move together and come to rest after travelling a distance of 40 m. The coefficient of sliding friction of the rough surface is \[\left( g=9.8\text{ }m{{s}^{-2}} \right)\]
question_answer38) Two persons A and B are located in X-Y plane at the points (0, 0) and (0, 10) respectively. (The distances are measured in MKS unit). At a time (\[t=0\], they start moving simultaneously with velocities \[{{\mathbf{\vec{v}}}_{A}}=2\mathbf{j}m{{s}^{-1}}\] and \[{{\mathbf{\vec{v}}}_{B}}=2\mathbf{\hat{i}}m{{s}^{-1}}\]respectively. The time after which\[A\]and\[B\]are at their closest distance is
question_answer39) A rod of length; is held vertically stationary with its lower end located at a point P, on the horizontal plane. When the rod is released to topple about P, the velocity of the upper end of the rod with which it hits the ground is
question_answer40) A wheel of radius 0.4 m can rotate freely about its axis as shown in the figure. \[A\]String is wrapped over its rim and a mass of 4 kg is hung. An angular acceleration of \[8\text{ }rad-{{s}^{-2}}\] is produced in it due to the torque. Then, moment of inertia of the wheel is \[(g=10m{{s}^{-2}})\]
question_answer41) Given that \[Alkyne\xrightarrow[Lindlars\,\,catalyst]{{{H}_{2}}}A\xrightarrow{Ozonolysis}\underset{only}{\mathop{B}}\,\], express the \[\xleftarrow[\Pr ocess]{Wac\ker }C{{H}_{2}}=C{{H}_{2}}\] bond energy in kcal/mol.
question_answer45) The number of \[52153\] pi bonds present in \[Alkyne\xrightarrow[Lindlars\,\,catalyst]{{{H}_{2}}}A\xrightarrow{Ozonolysis}\underset{only}{\mathop{B}}\,\]and \[\xleftarrow[\Pr ocess]{Wac\ker }C{{H}_{2}}=C{{H}_{2}}\] molecules, respectively are
question_answer46) The wavelengths of electron waves in two orbits is \[{{H}_{3}}C-C\equiv C-C{{H}_{3}}\]. The ratio of kinetic energy of electrons will be
question_answer48) Electrons with a kinetic energy of \[\underline{X}\]are evolved from the surface of a metal, when it is exposed to radiation of wavelength of 600 nm. The minimum amount of energy required to remove an electron from the metal atom is
question_answer51) In Gattermann reaction, a diazonium group is replaced by \[{{109}^{o}}28\] using \[\underline{X}\]. \[\underline{X}\] and \[\Delta {{H}_{f}}(H)=218kJ/mol\] are
question_answer53) Dipole moment of \[{{109}^{o}}28\] \[\underline{X}\]Bond length of \[\underline{X}\] and \[p\pi .d\pi \]. The ratio of fraction of electric charge, \[p\pi .d\pi \], existing on each atom in \[\Delta {{H}_{f}}(H)=218kJ/mol\] and \[H-H\] is
question_answer54) \[Alkyne\xrightarrow[Lindlars\,\,catalyst]{{{H}_{2}}}A\xrightarrow{Ozonolysis}\underset{only}{\mathop{B}}\,\] on hydrolysis forms X and \[\xleftarrow[\Pr ocess]{Wac\ker }C{{H}_{2}}=C{{H}_{2}}\]. Compound X loses water at \[{{H}_{3}}C-C\equiv C-C{{H}_{3}}\] and gives Y\ Compounds X and Y respectively are
question_answer56) Aluminium reacts with \[\underline{X}\] and forms compound X. If the coordination number of aluminium in X is 6, the correct formula of X is
question_answer58) Assertion [A] K, Rb and Cs form superoxides. Reason [R] The stability of the superoxides increases from K to Cs due to decrease in lattice energy. The correct answer is
A)
Both [A] and [R] are true and [R] is the correct explanation of [A]
doneclear
B)
Both [A] and [R] are true but [R] is not the correct explanation of [A]
question_answer59) How many \[\text{ }\!\!\!\!\text{ mL }\!\!\!\!\text{ }\] of perhydrol is required to produce sufficient oxygen which can be used to completely convert 2 L of \[{{H}_{3}}C-C\equiv C-C{{H}_{3}}\] gas to \[{{H}_{3}}C-C{{H}_{2}}-C\equiv CH\] gas?
question_answer60) \[\text{pH}\] of a buffer solution decreases by 0.02 units when 0.12 g of acetic acid is added to 250 mL of a buffer solution of acetic acid and potassium acetate at \[27{}^\circ \]. The buffer capacity of the solution is
question_answer63) What are X and Y in the following reaction sequence? \[Alkyne\xrightarrow[Lindlars\,\,catalyst]{{{H}_{2}}}A\xrightarrow{Ozonolysis}\underset{only}{\mathop{B}}\,\]
question_answer65) One per cent composition of an organic compound A is, carbon: 85.71% and hydrogen 14.29%. Its vapour density is 14. Consider the following reaction sequence \[{{H}_{3}}C-C{{H}_{2}}-C\equiv CH\] Identify , \[{{H}_{2}}C=CH-C\equiv CH\]
question_answer67) A codon has a sequence of \[{{107}^{o}}\], and specifies a particular B that is to be incorporated into a \[{{109}^{o}}28\]. What are \[\underline{X}\],\[\underline{X}\],\[p\pi .d\pi \]?
question_answer71) For the following cell reaction, \[911\] \[104\] \[52153\] \[Alkyne\xrightarrow[Lindlars\,\,catalyst]{{{H}_{2}}}A\xrightarrow{Ozonolysis}\underset{only}{\mathop{B}}\,\] \[\xleftarrow[\Pr ocess]{Wac\ker }C{{H}_{2}}=C{{H}_{2}}\] of the cell is
question_answer73) At \[HC\equiv C-C{{H}_{2}}-C\equiv CH\], the molar conductances at infinite dilution for the strong electrolytes \[NaOH\], \[{{104}^{o}}40\] and \[{{103}^{o}}\] are \[{{107}^{o}}\], \[{{109}^{o}}28\] and \[\underline{X}\]respectively, \[\underline{X}\] in \[p\pi .d\pi \] is
question_answer74) The cubic unit cell of a metal (molar mass \[\Delta {{H}_{f}}(H)=218kJ/mol\]) has an edge length of 362 pm. Its density is \[H-H\]. The type of unit cell is
question_answer75) The equilibrium constant for the given reaction is 100. \[52.15\] What is the equilibrium constant for the reaction given below? \[911\]
question_answer77) The concentration of an organic compound in chloroform is 6.15 g per 100 mL of solution. A portion of this solution in a 5 cm polarimeter tube causes an observed rotation of \[{{104}^{o}}40\]. What is the specific rotation of the compound?
question_answer78) 20 mL of 0.1 M acetic acid is mixed with 50 mL of potassium acetate. \[\underline{X}\] of acetic acid \[p\pi .d\pi \] at \[Xe{{O}_{3}}\]. Calculate concentration of potassium acetate if pH of the mixture is 4.8.
question_answer79) Calculate \[52.15\] for the reaction, \[911\] given the following : [A] \[104\] \[52153\] [B] \[Alkyne\xrightarrow[Lindlars\,\,catalyst]{{{H}_{2}}}A\xrightarrow{Ozonolysis}\underset{only}{\mathop{B}}\,\] \[\xleftarrow[\Pr ocess]{Wac\ker }C{{H}_{2}}=C{{H}_{2}}\] [C] \[{{H}_{3}}C-C\equiv C-C{{H}_{3}}\] \[{{H}_{3}}C-C{{H}_{2}}-C\equiv CH\]
question_answer84) If\[x\]is numerically so small so that\[{{x}^{2}}\]and higher powers of\[x\]can be neglected, then \[{{\left( 1+\frac{2x}{3} \right)}^{3/2}}\cdot {{(32+5x)}^{-1/5}}\] is approximately equal to
question_answer86) Let \[f(x)={{x}^{2}}+ax+b,\] where \[a,b\in R.\] If \[f(x)=0\] has all its roots imaginary, then the roots of \[f(x)+f(x)+f(x)=0\]are
question_answer88) If x, y, z are all positive and are the \[p\text{th},\] \[q\text{th}\]and \[r\text{th}\]terms of a geometric progression respectively, then the value of the determinant \[\left| \begin{matrix} \log x & p & 1 \\ \log y & q & 1 \\ \log z & r & 1 \\ \end{matrix} \right|\,\,\text{equals}\]
question_answer96) If \[{{m}_{1}},\] \[{{m}_{2}},\] \[{{m}_{3}}\]and \[{{m}_{4}}\] are respectively the magnitudes of the vectors \[{{\overrightarrow{a}}_{1}}=2\hat{i}-\hat{j}+\hat{k},\text{ }{{\overrightarrow{a}}_{2}}=3\hat{i}-4\hat{j}-4\hat{k},\] \[{{\overrightarrow{a}}_{3}}=\hat{i}+\hat{j}-\hat{k},\]and \[{{\overrightarrow{a}}_{4}}=-\hat{i}+3\hat{j}+\hat{k},\] then the correct order of \[{{m}_{1}},{{m}_{2}},{{m}_{3}}\]and \[{{m}_{4}}\]is
question_answer97) If X is a binomial variate with the range {0,1, 2, 3, 4, 5, 6} and \[P\left( X=2 \right)=4P\left( X=4 \right),\] then the parameter p of X is
question_answer98) The area (in square unit) of the circle which touches the lines \[4x\text{ }+\text{ }3y\text{ }=\text{ }15\] and \[4x\text{ }+\text{ }3y\text{ }=\text{ }5\] is
question_answer101) The equations of the circle which pass through the origin and makes intercepts of lengths 4 and 8 on the x and y-axes respectively are
question_answer102) The point\[\left( 3,\,-4 \right)\]lies on both the circles \[{{x}^{2}}+{{y}^{2}}-2x+8y+13=0\] and \[{{x}^{2}}+{{y}^{2}}-4x+6y+11=0\] Then, the angle between the circles is
question_answer103) The equation of the circle which passes through the origin and cuts orthogonally each of the circles \[{{x}^{2}}+{{y}^{2}}-6x+8=0\] and\[{{x}^{2}}+{{y}^{2}}-2x-2y=7\]is
question_answer105) If the circle \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\] intersects the hyperbola\[xy={{c}^{2}}\]in four points \[({{x}_{i}},\,{{y}_{i}}),\]for \[i=\] 1, 2, 3 and 4, then \[{{y}_{1}}+{{y}_{2}}+{{y}_{3}}+{{y}_{4}}\] equals
question_answer108) If a line in the space makes angle \[\alpha ,\]\[\beta \]and \[\gamma \] with the coordinate axes, then \[\cos 2\alpha +\cos 2\beta +\cos 2\gamma +{{\sin }^{2}}\alpha +{{\sin }^{2}}\beta \] \[+{{\sin }^{2}}\gamma \]equals
question_answer111) If \[f:R\to R\]is defined by \[f(x)=\left\{ \begin{matrix} \frac{2\sin x-\sin 2x}{2x\,\cos x}, & \text{if}\,x\ne 0 \\ a, & \text{if}\,x=0 \\ \end{matrix} \right.\] then the value of a so that\[f\]is continuous at 0 is
question_answer118) The line \[x=\frac{\pi }{4}\]divides the area of the region bounded by \[y=\text{sin }x,\] \[y=\text{cos }x\] and x-axis \[\left( 0\le x\le \frac{\pi }{2} \right)\] into two regions of areas \[{{A}_{1}}\] and \[{{A}_{2}}\]. Then\[{{A}_{1}}:{{A}_{2}}\]equals