Solved papers for BCECE Engineering BCECE Engineering Solved Paper-2015
done BCECE Engineering Solved Paper-2015 Total Questions - 150
question_answer1) A ball is thrown from the ground to clear a wall 3 m high at a distance of 6 m and falls 18m away from the wall, the angle of projection of ball is
question_answer2) Consider if the electric flux entering and leaving an enclosed surface respectively are \[{{\phi }_{1}}\] and \[{{\phi }_{2}}\], the electric charge inside the surface will be
question_answer3) If the escape speed of a projectile on Earth's surface is \[11.2km{{s}^{-1}}\] and a body is projected out with thrice this speed, then determine the speed of the body far away from the Earth.
question_answer4) Determine the potential drop between the points A and C in the following circuit. Resistances \[1\Omega \]and \[2\Omega \] are representing the internal resistances of the respective cells.
question_answer5) A tank is filled with a liquid up to a height H. A small hole is made at the bottom of this tank. Consider \[{{t}_{1}}\] be the time taken to empty first half of the tank and \[{{t}_{2}}\] be the time taken to empty rest half of the tank. Then, determine the ratio \[\frac{{{t}_{1}}}{{{t}_{2}}}.\]
question_answer6) An electron and a proton enter a magnetic field perpendicularly both have same kinetic energy. Which of the following statements are true?
question_answer7) The coefficient of volume expansion of glycerine is\[49\times {{10}^{-5}}{{K}^{-1}}\]. What is the fractional change in its density for a \[\text{3}0{}^\circ \text{ C}\] rise in temperature?
question_answer8) If a conducting rod of length \[4l\] is rotated about at point O in a uniform magnetic field B directed into the paper and \[DE=\text{ I},EA=3I,\]then
question_answer9) An open organ pipe has a fundamental frequency of\[\text{3}00\text{ Hz}\]. The first overtone of a closed organ pipe has the same frequency as the first overtone of organ pipe. How long is each pipe?
question_answer11) In a car race, car A takes a time t less than car B at the finish and passes the finishing point with speed v more than that of the car B. Assuming that both the cars starts from rest and travel with constant accelerations \[{{a}_{1}}\] and \[{{a}_{2}}\] respectively. So, the value of \[v\] will be
question_answer12) If an equiconvex lens is cut into two halves along (i) \[~XOX'\] and (ii) \[YOY'\]as shown in the figure. Let \[f,f',f''\] be the focal lengths of complete lens of each, in case (i) and of each half in case (ii) respectively. Chooses the correct statement form the following?
question_answer13) The bob of a pendulum is released from a horizontal position A as shown in the figure. If the length of the pendulum is\[\text{1}.\text{5 m}\], what is the speed with which the bob arrives at the lower most point B, given that it dissipated 5% of its initial energy against air resistance?
question_answer14) In a photo emissive cell with executing wavelength \[\lambda \], the fastest electron has speed \[v\]. If the exciting wavelength is changed to \[\frac{3\lambda }{4}\], the speed of fastest emitted electron will be
A)
greater than \[v{{\left( \frac{4}{3} \right)}^{1/2}}\]
doneclear
B)
\[v{{\left( \frac{3}{4} \right)}^{1/2}}\]
doneclear
C)
\[v{{\left( \frac{4}{3} \right)}^{1/2}}\]
doneclear
D)
less than \[v{{\left( \frac{4}{3} \right)}^{1/2}}\]
question_answer15) A ball of mass m moving at a speed \[v\] makes a head on collision with an identical ball at rest. The kinetic energy at the balls after the collision is \[\text{3}/\text{4th}\] of the original. What is the coefficient of restitution?
question_answer16) A radioactive material decays by simultaneous emission of two particles with half-lives \[\mathbf{1620}\text{ }\mathbf{yr}\] and \[\mathbf{810}\text{ }\mathbf{yr}\] respectively. The time in years after which one-fourth of material remains, is
question_answer17) A cylinder rolls up an inclined plane at an angle of\[\text{3}0{}^\circ \]. At the bottom of the inclined plane, the centre of mass of the cylinder has speed of\[\text{5 m}/\text{s}\]. How long will it take to return to the bottom?
question_answer18) The current gain in the common emitter amplifier mode of a transistor is 10. The input impedance is\[20k\Omega \], and load of resistance is \[100k\Omega \]. The power gain is
question_answer19) What will be the displacement equation of the simple harmonic motion obtained by combining the motions? \[{{x}_{}}_{1}=2\sin \omega t,\]\[{{x}_{}}_{2}=4\sin \left( \omega t+\frac{\pi }{6} \right)\]and \[{{x}_{3}}=6\sin \left( \omega t+\frac{\pi }{3} \right)\]
question_answer20) An ammeter A reads \[\text{2 A}\] and the voltmeter \[V\] reads\[\text{2}0\text{ V}\]. The value of resistance R is (assuming finite resistaneces of ammeter and voltmeter)
question_answer21) A stream of water flowing horizontally with the speed of \[15m{{s}^{-1}}\] gushes out of a tube of cross-sectional area \[{{10}^{-2}}{{m}^{-2}}\] and hits a vertical wall nearby. What is the force exerted on the wall by the impact or water? Assuming it does not rebound.
question_answer22) Two charges \[+6\mu C\]and \[-4\mu C\]are placed \[\text{15 cm}\] apart as shown. At what distances from A to its right, the electrostatic potential is zero?
question_answer23) A shell of mass \[0.0\text{2}0\text{ kg}\] is fired by a gun of mass\[\text{1}00\text{ kg}\]. If the muzzle speed of the shell is\[\text{8}0\text{m}{{\text{s}}^{\text{-1}}}\]. What is the recoil speed of the gun?
question_answer24) If\[E=100\sin (100t)\] volt and\[I=100\sin \left( 100t+\frac{\pi }{3} \right)mA\]are the instantaneous voltage and current, then the rms values of voltage and current are respectively;
question_answer25) If torques of equal magnitudes are applied to a hollow cylinder and a solid sphere both having the same mass and radius. The cylinder is free to rotate about its standard axis of symmetry and the sphere is free to rotate about an axis passing through its centre. Which of the two will acquire a greater angular speed after a given time?
question_answer26) The threshold frequency for certain metal is\[3.3\times {{10}^{14}}Hz.\] If light of \[8.2\times {{10}^{14}}Hz\]frequency is incident on the metal, then the cut-off voltage of the photoelectric current will be
question_answer27) If two simple pendulums first of bob mass \[{{M}_{1}}\] and length \[{{l}_{1}}\], second of bob mass \[{{M}_{2}}\] and length \[{{l}_{2}}\]. Given \[{{M}_{1}}={{M}_{2}}\] and. \[{{l}_{1}}=2{{l}_{2}}\] If the vibrational energies of both are same, then which of the following is correct?
question_answer28) A thin film of soap solution \[({{\mu }_{s}}=1.4)\] lies on the top of a glass plate\[({{\mu }_{g}}=1.5)\]. When visible light is incident almost normal to the plate, two adjacent reflection maxima are observed at two wavelengths \[\text{42}0\text{ nm}\] and \[\text{63}0\text{ nm}\]. The minimum thickness of the soap solution are
question_answer29) An air bubble starts rising from the bottom of a lake. Its diameter is \[\text{3}.\text{6 mm}\] at the bottom and \[\text{4 mm}\] at the surface. The depth of the lake is \[\text{25}0\text{ cm}\] and the temperature at surface is40°C. What is the temperature at the bottom of the lake? Given atmpospheric pressure \[=\text{76 cm}\] of Hg and \[\text{g}=\text{ 98}0\text{ cm}/{{\text{s}}^{\text{2}}}\].
question_answer31) A simple harmonic wave of amplitude 8 unit travels along positive x-axis. At any given instant of time, for a particle at a distance of \[\text{1}0\text{ cm}\] from the origin, the displacement is + 6 unit and for a particle at a distance of \[\text{25 cm}\] from the origin, the displacement is\[+\text{ 4 unit}\]. Calculate the wavelength.
question_answer32) When a battery of emf \[\text{8 V}\] with internal resistance \[0.5\Omega \], is charged by a \[\text{12}0\text{V}\] DC supply using a series resistance of\[15.5\Omega ,\], then the terminal voltage of the battery is
question_answer33) A rigid bar of mass \[\text{15 kg}\] is supported symmetrically by three wires each \[\text{2 m}\] long. Those at each end are of copper and the middle one is of iron. Determine the ratio of their diameters if each is to have the tension.
question_answer34) Figure given below shows a network of four capacitors of capacitance equal to \[{{C}_{1}}=C,{{C}_{2}}=2C,{{C}_{3}}\]\[=3C,{{C}_{4}}\]\[=4C\]are connected to a battery. The ratio of charges on \[{{C}_{2}}\]and \[{{C}_{4}}\] is
question_answer35) Two trains A and B of length \[\text{4}00\text{ m}\] each are moving on two parallel tracks with a uniform speed of \[\text{72 km}{{\text{h}}^{-1}}\] in the same direction, with A head of speed B. The driver of B decides to overtake A and accelerates by \[\text{1m}/{{\text{s}}^{\text{2}}}\]. if after\[\text{5}0\text{s}\], the guard of B just brushes past the driver of A, what was the original distance between them?
question_answer36) If a fully charged capacitor C with initial charge \[{{q}_{0}}\]is connected to a coil of self inductance L at \[t=\text{ }0\]. The time at which the energy is stored equally between the electric field and magnetic field is
question_answer37) A rocket is fired from the Earth towards the Sun. At what distance from the Earth's centre, the gravitational force on the rocket is zero? Mass of the Sun \[=2\times {{10}^{30}}kg\]and mass of the Earth \[=6\times {{10}^{24}}kg.\]
question_answer38) In the figure given below, for an angle of incidence \[\text{45}{}^\circ \] at the top surface, what is the minimum refractive index need to total internal reflection at vertical face?
question_answer39) A solid cylinder of mass \[\text{2}0\text{ kg}\] rotates about its axis with angular speed\[\text{100 rad }{{\text{s}}^{-1}}\]. The radius of the cylinder is\[0.\text{25 m}\]. What is the . kinetic energy associated with the rotation of cylinder? What is the magnitude of angular momentum of cylinder about its axis?
question_answer40) A change of \[\text{8}.0\text{ mA}\] in the emitter current brings a change of \[7.\text{9 mA}\] in the correct collector current. The values of \[\alpha \] and \[\beta \] are
question_answer41) A stone of mass \[0.\text{25 kg}\] tied to the end of a string is whirled round in a circle of radius 1.5m with speed 40 rev/min in a horizontal plane. What is the tension in the string and what is the maximum speed with which the stone can be whirled around, if the string can withstand a maximum tension of\[~\text{2}00\text{ N}\]?
A)
\[\text{6}.\text{6 N, 35m}{{\text{s}}^{\text{-1}}}\]
doneclear
B)
\[\text{6N},\text{37m}{{\text{s}}^{\text{-1}}}\]
doneclear
C)
\[~\text{7}.\text{5 N, 46 m}{{\text{s}}^{\text{-1}}}\]
question_answer42) A straight wire of mass 200 g and length \[\text{1}.\text{5 m}\] carries a current of 2 A. It is suspended in mid air by a uniform horizontal magnetic field B, The magnitude of B (in tesla) is
question_answer43) A U-shaped wire is dipped in a soap solution and removed. The thin soap film formed between the wire and light slider supports a weight of 1.5 x lO2]^. The length of the slider is 30 cm. What is the surface tension of the film?
question_answer44) At constant pressure, the ratio of increase in volume of an ideal gas per degree rise in kelvin temperature to its original volume is
question_answer45) The length of a magnet is large compared to its width and breadth. The time period of its oscillation in vibration magnetometer is\[\text{2 s}\]. The magnet is cut along its length into three equal parts and three parts are then palced on each other with their like poles together. The time period of this combination will be
question_answer46) A body of mass \[\text{1 kg}\] is moving in a vertical circular path of radius\[\text{1 m}\]. The difference between the kinetic energies at its highest and lowest positions is
question_answer47) If electrical force between two charges is \[\text{2}00\text{ N}\] and we increase \[\text{1}0%\] charge on one of the charges and decrease \[\text{1}0%\] charge on the other, then electrical force between them for the same distance becomes
question_answer48) The acceleration due to gravity on the planet is 9 times the acceleration due to gravity on planet B. A man jumps to a height of 2 m on the surface of A. What is the height of jump by the same on the planet B?
question_answer49) In hydrogen atom Spectrum, frequency of \[2.7\times {{10}^{15}}Hz\] of EM wave is emitted when transmission takes place from 2 to1. If it moves from 3 to 1, the frequency emitted will be
question_answer50) If a ray of light in a denser medium strikes a rarer medium at an angle of incidence\[i\] the angles of reflection and refraction are respectively r and r'. If the reflected and refracted rays are at right angles to each other, the critical angle for the given pair of media is
question_answer51) Consider the following reaction sequence of alkene \[C{{H}_{3}}CH=CHC{{H}_{3}}\xrightarrow{{{O}_{3}}}A\xrightarrow[Zn]{{{H}_{2}}O}B\] The product B is
question_answer53) The energy required to excite the electron in the atom from\[n=1\] to \[n=2,\], when the ionisation enthalpy of hydrogen atom is \[1.312\times {{10}^{6}}J\]/mol will be (in the unit of \[{{10}^{5}}\]).
question_answer56) The reactivity order of halogenations of alkianes is \[{{F}_{2}}>C{{l}_{2}}>B{{r}_{2}}>{{I}_{2}}.\] (i) Lower the activation energy for the chain initiation step, more reactive is the halogen. (ii) Lower the activation energy for the first chain o- propagation step, more reactive is the halogen. (iii) Lower the activation energy for the second chain propagation step, more reactive is the halogen. (iv) More negative is the overall heat of the reaction ( \[\Delta H_{r}^{\circ }\] of- halogenation of alkane) more reactive is the halogen.
question_answer61) If the dipole moment of \[\text{HBr}\]is \[2.60\times {{10}^{-30}}\text{Cm}\]and the interatomic spacing is \[1.41\overset{\text{o}}{\mathop{\text{A}}}\,,\]then the per cent ionic character of \[\text{HBr}\]is
question_answer62) Consider the following reaction, \[\text{CC}{{\text{l}}_{\text{3}}}\text{CH=C}{{\text{H}}_{\text{2}}}\xrightarrow[{{\text{H}}_{\text{2}}}{{\text{O}}_{\text{2}}}\text{/HOCl}]{\text{NaB}{{\text{O}}_{\text{4}}}}\]Product (P) P is
question_answer65) Beryllium gives a compound \[\text{X}\] with the following percentage composition: Be Molecular weight of \[-61%,\,N-37.8%,\,Cl-48%,\,H-8.1%\] \[\text{X}\] is \[\text{148 g mo}{{\text{l}}^{-}}^{\text{1}}\] and that of Be is \[\text{9 g mo}{{\text{l}}^{\text{-1}}}.\] The molecular formula of the compound is
question_answer67) Compound A undergoes following reactions to form B and C Black coloured solid (A) \[\xrightarrow{KN{{O}_{3}}+KOH}\] Green coloured solution (B) Green coloured \[\xrightarrow{C{{O}_{2}}}\] Pink solution \[\left( \text{C} \right)\text{ }+\text{ }\left( \text{A} \right)\] Solution (B) (C) decolourised by \[\text{F}{{\text{e}}^{\text{3}}}^{+}\]Identify A, B and C respectively
A)
\[\text{Mn}{{\text{O}}_{\text{2}}}\text{,KMn}{{\text{O}}_{\text{4}}}\text{ and }{{\text{K}}_{\text{2}}}\text{Mn}{{\text{O}}_{\text{4}}}\]
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B)
\[~\text{Mn}{{\text{O}}_{2}}\text{, }{{\text{K}}_{\text{2}}}\text{Mn}{{\text{O}}_{\text{4}}}\text{ and KMn}{{\text{O}}_{\text{4}}}\]
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C)
\[\text{KMn}{{\text{O}}_{\text{4}}},\text{ Mn}{{\text{O}}_{2}}\text{ and }{{\text{K}}_{\text{2}}}\text{Mn}{{\text{O}}_{\text{4}}}\]
doneclear
D)
\[\text{KMn}{{O}_{\text{4}}},\text{ }{{\text{K}}_{\text{2}}}\text{Mn}{{\text{O}}_{\text{4}}}\text{ and Mn}{{\text{O}}_{\text{2}}}\]
question_answer68) The reaction between nitric oxide \[\left( \text{NO} \right)\] and oxygen to form nitrogen dioxide \[\left( \text{N}{{\text{O}}_{2}} \right)\] is a key step in photochemical smog formation \[\text{2NO(g)+}{{\text{O}}_{\text{2}}}\text{(g)}\to \text{2N}{{\text{O}}_{\text{2}}}\text{(g)}\] The grams of \[\text{N}{{\text{O}}_{\text{2}}}\]are formed by complete by reaction of \[\text{1}.\text{2}0\text{ g}\] of NO is
question_answer69) \[2HC\equiv CH\xrightarrow[+N{{H}_{4}}Cl]{C{{H}_{2}}C{{l}_{2}}}A\xrightarrow[\text{HCl}]{\text{1mol}}B\]Identify the compounds A and B
question_answer70) At\[\text{8}0{}^\circ \text{ C}\], the vapour pressure of pure liquid A is 520 mm Hg and that of pure liquid B is 1000 mm Hg. If a mixture solution of A and B boils at \[\text{8}0{}^\circ \text{ C}\] and 1 atm pressure, the amount of A in the mixture is
question_answer72) Consider the following reaction,\[\text{ZnC}{{\text{l}}_{\text{2}}}\text{+NaOH}\to \underset{\text{White ppt}\text{.}}{\mathop{B}}\,\to \xrightarrow{NaOH}\underset{\text{soluble}}{\mathop{C}}\,\] Then, the final product C is
question_answer73) The vapour pressure of pure water is 23.5 mm Hg. Then, the vapour pressure of an aqueous solution which contains 5 mass percent of urea is (Molar mass of urea is 60).
question_answer75) Consider the following reactions, \[\text{C(s)+}{{\text{O}}_{\text{2}}}\text{(g)}\to \text{C}{{\text{O}}_{\text{2}}}\text{(g),}\Delta \text{H}=-94\text{kcal}\] \[\text{2CO(g)}+{{\text{O}}_{\text{2}}}\to \text{2C}{{\text{O}}_{\text{2}}}\text{(g),}\Delta \text{H}=-135.2\text{kcal}\] Then, the heat of formation of \[~\text{CO }\left( \text{g} \right)\] is
question_answer76) If the \[p{{K}_{a}}\] of a weak acid HA is 4.80 and the \[p{{K}_{b}}\] of a weak base BOH is 4.78. Then, the pH of an aqueous solution of the corresponding salt, BA will be
question_answer78) A nitrogenous substance A is treated with \[\text{HN}{{\text{O}}_{2}}\] and the product formed is further treated with \[\text{NaOH}\] solution which produces blue colouration. Then, A will be
question_answer79) Argon crystallises in fee arrangement and the density of solid and liquid at is \[\text{1}.\text{59 g}/\text{c}{{\text{m}}^{\text{3}}}\]and\[\text{1}.\text{42 g}/\text{c}{{\text{m}}^{\text{3}}},\], respectively. The percentage of empty space in liquid at is
question_answer81) When\[\text{4A}\] of current is passed through a 1.0 L, 0.10 M\[\text{F}{{\text{e}}^{3+}}(aq)\]) solution for 1 h, it is partly reduced to Fe(s) and partly of. \[F{{e}^{2+}}(aq)\]Identify the incorrect statement.
A)
0.10 mole of electrons are required to convert all \[F{{e}^{3+}}\] to \[F{{e}^{2+}}\]
doneclear
B)
0.025 mol of Fe(s) will be deposited
doneclear
C)
0.075 mol of iron remains as \[\text{F}{{\text{e}}^{2+}}\]
doneclear
D)
0.050 mol of iron remains as \[\text{F}{{\text{e}}^{2+}}\]
question_answer84) Give that, \[E_{F{{e}^{2+}}/Fe}^{\circ }=-0.44V,\]\[E_{F{{e}^{2+}}/F{{e}^{3+}}}^{\circ }=-0.77V.\] if \[F{{e}^{2+}},F{{e}^{3+}}\] and Fe solid are kept together, then
question_answer86) In terms of Arrhenius equation, \[k=A{{e}^{-{{E}_{a}}RT}}\]the temperature dependence of rate constant (k) of a chemical reaction is written. Then, the activation energy \[({{E}_{a}})\] of the reaction can be calculated by plotting.
question_answer87) Which one of the following electrolytes is most effective for the coagulation of \[\text{Fe}{{\left( \text{OH} \right)}_{\text{3}}}\]Sol?
question_answer88) \[PhC{{H}_{2}}C{{H}_{3}}\xrightarrow[(ii){{H}_{3}}{{O}^{+}}]{(i)Cr{{O}_{2}}C{{l}_{2}}/CC{{l}_{4}}}PhC{{H}_{2}}CHO\] The above reaction is an example of which name reaction?
question_answer93) Arrange the following compounds in the increasing order of their reactivity towards HCN. (i) Acetaldehyde (ii) Acetone (iii) Di ? tert ? butyl ketone (iv) Methyl ?tert ?butyl ketone
A)
\[~\text{III }<\text{ II }<\text{ IV }<\text{ I}\]
doneclear
B)
\[\text{II }<\text{ I }<\text{ IV }<\text{ II}\]
doneclear
C)
\[~\text{IV }<\text{ III }<\text{ II }<\text{ I}\]
doneclear
D)
\[~\text{II }<\text{ IV }<\text{ I }<\text{ III}\]
question_answer96) When 0.1 M \[\text{NaOH}\] is titrated with 0.1 M, 20 mL HA till the end point, \[{{K}_{a}}(HA)=6\times {{10}^{-6}}\] and degree of dissociation of HA is small as compared to unity. What is the pH of the resulting solution at the end point?
question_answer97) Arrange the following in the decreasing order of basic character. (i) p-toluidine (ii) N, N-dimethyl-p-toluidine (iii) p-nitroaniline (iv) Aniline
A)
\[~\text{II }>\text{ III }>\text{ I }>\text{ IV}\]
doneclear
B)
\[\text{I }>\text{ II }>\text{ III }>\text{ IV}\]
doneclear
C)
\[~\text{II }>\text{ I }>\text{ IV }>\text{ III}\]
doneclear
D)
\[~\text{IV }>\text{ III }>\text{ I }>\text{ II}\]
question_answer98) What is the enthalpy of the disproportionation of \[\text{MgCl}\] if the enthalpy of formation of hypothetical \[\text{MgCl}\] is \[-\text{125 kJ}/\text{mol}\] and the =\[MgC{{l}_{2}}\] is\[-\text{ 642 kJ}/\text{mol}\]?
question_answer99) The decreasing order of reactivity towards electrophilic addition of the following is (i) \[\text{CH }=\text{CH}\] (ii) \[\text{C}{{\text{H}}_{\text{2}}}=\text{C}{{\text{H}}_{\text{2}}}\] (iii) \[{{\text{H}}_{\text{2}}}\text{C}=\text{CH}\text{Cl}\] (iv) \[\text{H}\underset{\text{Cl}}{\mathop{\underset{|}{\mathop{\text{C}}}\,}}\,=\underset{\text{Cl}}{\mathop{\underset{|}{\mathop{\text{C}}}\,}}\,\text{H}\]
A)
\[\text{I }>\text{ II }>\text{ III }>\text{ IV}\]
doneclear
B)
\[~\text{II }>\text{ I }>\text{ III }>\text{ IV}\]
doneclear
C)
\[\text{IV }>\text{ 111 }>\text{ I }>\text{ II}\]
doneclear
D)
\[~\text{IV }>\text{ III }>\text{ II }>\text{ I}\]
question_answer100) Given the following bond dissociation enthalpies\[\left( \text{kJ mo}{{\text{l}}^{\text{-1}}} \right)\]. \[P\equiv P-490,P-P-209,\] \[N\equiv N-946,\] \[N-N-160\]Compare the enthalpy changes for the process (i) \[2{{P}_{2}}(g)\to {{P}_{4}}(g)\] (ii) \[2{{N}_{2}}(g)\to {{N}_{4}}(g)\] Choose the correct option.
A)
\[{{P}_{4}}\] is feasible but \[{{\text{N}}_{\text{4}}}\]is not feasible
doneclear
B)
\[{{P}_{4}}\] is not feasible but \[{{\text{N}}_{\text{4}}}\]is feasible
doneclear
C)
Both \[{{\text{P}}_{4}}\] and \[{{\text{N}}_{\text{4}}}\]are feasible
doneclear
D)
Both \[{{P}_{4}}\] and \[{{\text{N}}_{\text{4}}}\]are not feasible
question_answer102) Let \[f(x)\] be twice differentiable function such that \[f''(0)=2.\] Then,\[\underset{x\to 0}{\mathop{\lim }}\,\frac{2f(x)-3f(2x)+f(4x)}{{{x}^{2}}}\]is equal to
question_answer104) Let \[\alpha \]and \[\beta \]be the roots of \[{{x}^{2}}+bx+1=0\] Then, the equation whose roots are \[-\left( \alpha +\frac{1}{\beta } \right)\]and \[-\left( \beta +\frac{1}{\alpha } \right),\] is
question_answer111) A differentiable function \[f(x)\]has a relative minimum at \[x=0\], then the function\[y=f(x)+ax+b\]has a relative minimum at \[x=0\] for
question_answer112) The probability that atleast one of the events A and B occurs, is 0.6. If A and B occur simultaneously with probability 0.2, then \[p(\bar{A})+P(\bar{B})\] is equal to
question_answer114) From 50 students taking examinations in 1 Mathematics, Physics and Chemistry, 37 passed in Mathematics, 24 in Physics and 43 in Chemistry. Atmost 19 passed in Mathematics and Physics, atmost 29 passed in Mathematics and Chemistry and atmost 20 passed in Physics and Chemistry. The largest possible-number that could have passed all three examinations, is
question_answer115) The area bounded by the curves \[y=\cos x\]and \[y=\sin x\]between the ordinates \[x\text{ }=\text{ }0\]and \[x=\frac{3\pi }{2}\] is
question_answer121) 1f \[a=\hat{i}+\hat{j},b=2\hat{j}-\hat{k}\]and \[r\times a=b\times a,\] \[r\times b\] \[=a\times b,\] then a unit vector in the direction of r is
question_answer122) 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_answer123) From the bottom of a pole of height A, the angle of elevation of the top of a tower is \[\alpha \]. The pole subtends an angle \[\beta \] at the top of the tower. The height of the tower is
question_answer125) The equation of a straight line passing through the point of intersection of \[x-y+1=0\]and \[3x+y-5=0\] and perpendicular to one of them, is
question_answer128) The direction ratios of the normal to the n plane passing through the points (1,-2, 3), (-1, 2,-1) and parallel to the line \[\frac{x-2}{2}=\frac{y+1}{3}=\frac{z}{4}\] are proportional to
question_answer130) If the rate of change of area of a square plate is 13 equal to that of the rate of change of its perimeter, then length of the side is
question_answer135) If A is a square matrix such that \[{{\text{A}}^{\text{2}}}\text{ }=\text{ A}\] and \[\text{B }=\text{ I }-\text{ A,}\], then \[AB+BA+I-{{(I-A)}^{2}}\] is equal to
question_answer136) The radius of the circle passing through the foci of the ellipse \[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{9}=1\] and having its centre \[(0,3),\] is
question_answer137) Let \[f(x)={{({{x}^{3}}+2)}^{30}}\] .If \[{{f}^{n}}(x)\] is a polynomial of degree 20, where \[{{f}^{n}}(x)\] denotes the nth order derivative of \[f(x)\] with respect to x, then the value of n is
question_answer140) If \[{{z}_{1}}\] and \[{{z}_{2}}\] are two complex numbers such that \[\operatorname{Im}\] \[({{z}_{1}}+{{z}_{2}})=0,\]\[\operatorname{Im}\]\[({{z}_{1}}{{z}_{2}})=0,\], then
question_answer143) The degree of the differential equation\[x=1+\frac{dy}{dx}+\frac{1}{2!}{{\left( \frac{dy}{dx} \right)}^{2}}+\frac{1}{3!}{{\left( \frac{dy}{dx} \right)}^{3}}+...\]is