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?
A) \[2.0\,\,m{{s}^{-2}}\]
B) \[2.5\,\,m{{s}^{-2}}\]
C) \[3.0\,\,m{{s}^{2}}\]
D) \[4.0\,\,m{{s}^{-2}}\]
View Answer play_arrowquestion_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\[g=10\,\,m{{s}^{-2}})\]
A) \[zero\]
B) \[1.25\,\,cm\]
C) \[2.5\,\,cm\]
D) \[5\,\,cm\]
View Answer play_arrowquestion_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
A) \[x=y{{z}^{2}}\]
B) \[x={{y}^{2}}z\]
C) \[{{y}^{2}}=xz\]
D) \[z={{x}^{2}}y\]
View Answer play_arrowquestion_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
A) \[\frac{6}{\sqrt{5}}\]
B) \[\frac{12}{\sqrt{5}}\]
C) \[\frac{16}{\sqrt{5}}\]
D) \[\frac{8}{\sqrt{5}}\]
View Answer play_arrowquestion_answer5) If the length of potentiometer wire is increased, then the length of the previously obtained balance point will
A) increase
B) decrease
C) remains unchanged
D) becomes two times
View Answer play_arrowquestion_answer6) If a steel wire of length I and magnetic moment \[M\] is bent into a semi-circular arc, then the new magnetic moment is
A) \[M\times l\]
B) \[\frac{M}{l}\]
C) \[\frac{2M}{\pi }\]
D) \[M\]
View Answer play_arrowquestion_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
A) \[\frac{\pi }{3}\]
B) \[\frac{\pi }{4}\]
C) \[\frac{\pi }{6}\]
D) \[\frac{5\pi }{12}\]
View Answer play_arrowquestion_answer8) If all of a sudden the radius of the earth decreases, then which one of the following statements will be true?
A) The angular momentum of the earth will become greater than that of the sun.
B) The periodic time of the earth will increase.
C) The energy and angular momentum will remain constant.
D) The angular velocity of the earth will increase
View Answer play_arrowquestion_answer9) If the external torque acting on a system is zero \[(i.e.,\,\,\tau =0)\], then
A) \[J=0\]
B) \[F=0\]
C) \[\omega =0\]
D) \[\alpha =0\]
View Answer play_arrowquestion_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
A) \[x=\sqrt{2}a\]
B) \[x=\frac{a}{\sqrt{2}}\]
C) \[x=\frac{\sqrt{2}a}{\sqrt{2}-1}\]
D) \[x=\frac{\sqrt{2a}}{\sqrt{2}+1}\]
View Answer play_arrowquestion_answer11) When the kinetic energy of an electron is increased, the wavelength of the associated wave will
A) decrease
B) increase
C) remains unchanged
D) None of these
View Answer play_arrowquestion_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
A) \[\infty \]
B) \[Zero\]
C) \[\frac{{{\mu }_{0}}}{4\pi }\frac{2i}{r}\]
D) \[\frac{{{\mu }_{0}}}{4\pi }\frac{2\pi i}{r}\]
View Answer play_arrowquestion_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
A) \[3:4\]
B) \[5:3\]
C) \[7:11\]
D) \[11:7\]
View Answer play_arrowquestion_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
A) \[67\]
B) \[81\]
C) \[89\]
D) \[90\]
View Answer play_arrowquestion_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
A) \[\left( \frac{n-1}{n} \right)f\]
B) \[\left( \frac{n+1}{n} \right)f\]
C) \[(n+1)f\]
D) \[(n-1)f\]
View Answer play_arrowquestion_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
A) \[2\]
B) \[4\]
C) \[5\]
D) None of these
View Answer play_arrowquestion_answer17) A diode is connected to \[220\,\,V(rms)AC\] in series with a capacitor as shown in figure. The voltage across the capacitor is
A) \[220\,\,V\]
B) \[110\,\,V\]
C) \[311.1\,\,V\]
D) \[\frac{220}{\sqrt{2}}V\]
View Answer play_arrowquestion_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
A) \[y=A\sin (\omega t+0.8\,\,kx)\]
B) \[y=-0.8\,\,A\sin (\omega t+kx)\]
C) \[y=A\sin (\omega t+kx)\]
D) \[y=0.8\,\,A\sin (\omega t+kx)\]
View Answer play_arrowquestion_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
A) \[10\,\,m/s\]
B) \[20\,\,m/s\]
C) \[30\,\,m/s\]
D) \[40\,\,m/s\]
View Answer play_arrowquestion_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
A) \[10\,\,J\]
B) \[20\,\,J\]
C) \[40\,\,J\]
D) \[50\,\,J\]
View Answer play_arrowquestion_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
A) \[2N,\,\,3N\]
B) \[5N,\,\,6N\]
C) \[10N,\,\,15N\]
D) \[20N,\,\,30N\]
View Answer play_arrowquestion_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
A) equilibrate the centripetal force
B) be vertical
C) be decreased
D) have a horizontal inward component
View Answer play_arrowquestion_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
B) the radius of moon is \[\frac{9}{\sqrt{6}}\] of the earth
C) moon is the satellite of the earth
D) None of the above
View Answer play_arrowquestion_answer24) Inertia is that property of a body by virtue of which the body is
A) unable to change by itself the state of uniform motion
B) unable to change by itself the state of rest and of uniform linear motion
C) unable to change by itself the state of rest
D) unable to change by itself the direction of motion
View Answer play_arrowquestion_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
A) equal on both
B) zero on both
C) on the surface of sphere\[A\]
D) on the surface of sphere\[B\]
View Answer play_arrowquestion_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
A) \[{{0}^{o}}C\]
B) \[-{{10}^{o}}C\]
C) \[{{10}^{o}}C\]
D) \[{{40}^{o}}C\]
View Answer play_arrowquestion_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
A) \[T\]
B) \[>T\]
C) \[<T\]
D) \[\ge T\]
View Answer play_arrowquestion_answer28) In the circuit shown, potential difference between \[x\] and \[y\] will be
A) \[Zero\]
B) \[120\,\,V\]
C) \[60\,\,V\]
D) \[20\,\,V\]
View Answer play_arrowquestion_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
A) \[1\,\,W\]
B) \[\frac{1}{3}\,\,W\]
C) \[\frac{1}{6}\,\,W\]
D) \[\frac{1}{12}\,\,W\]
View Answer play_arrowquestion_answer30) The transformation' ratio in the step-up transformer is
A) 1
B) greater than one
C) less than one
D) the ratio greater or less than one depends on the other factors.
View Answer play_arrowquestion_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
A) \[164\,\,cm\]
B) \[124\,\,cm\]
C) \[100\,\,cm\]
D) \[84\,\,cm\]
View Answer play_arrowquestion_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
A) \[15{}^\circ \]
B) \[35{}^\circ \]
C) \[55{}^\circ \]
D) \[75{}^\circ \]
View Answer play_arrowquestion_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\[E\]?
A) \[p\]
B) \[1.4p\]
C) \[\frac{7}{8}p\]
D) \[\frac{8}{7}p\]
View Answer play_arrowquestion_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
A) elasticity of wire \[P\] is maximum
B) elasticity of wire \[Q\] is maximum
C) elasticity of wire \[R\] is maximum
D) None of the above is true
View Answer play_arrowquestion_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
A) \[M\]
B) \[\frac{M(1-d/{{d}_{2}})}{(1-d/{{d}_{1}})}\]
C) \[M\left( 1-\frac{d}{{{d}_{2}}} \right)\]
D) \[M\left( 1-\frac{d}{{{d}_{1}}} \right)\]
View Answer play_arrowquestion_answer36) According to kinetic theory of gases, total energy of a gas is equal to
A) potential energy
B) kinetic energy
C) both [a] and [b]
D) None of the above
View Answer play_arrowquestion_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
A) \[\cos x\]
B) \[\frac{1}{\cos x}\]
C) \[\frac{1}{\sin x}\]
D) \[\frac{1}{\tan x}\]
View Answer play_arrowquestion_answer38) The \[rms\] current in a\[AC\] circuit is\[2A\]. If the watt less current be\[\sqrt{3}A\], what is the power factor of the circuit?
A) \[\frac{1}{2}\]
B) \[\frac{1}{3}\]
C) \[\frac{1}{\sqrt{3}}\]
D) \[\frac{1}{\sqrt{2}}\]
View Answer play_arrowquestion_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
A) \[100\Omega \]
B) \[50\Omega \]
C) \[20\Omega \]
D) \[10\Omega \]
View Answer play_arrowquestion_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
A) \[gx\]
B) \[\sqrt{gx}\]
C) \[gL\]
D) \[\sqrt{gL}\]
View Answer play_arrowquestion_answer41) Two equal masses each of 2 kg are suspended from a spring balance as shown in figure. The reading of the spring balance will be
A) Zero
B) 2 kg
C) 4 kg
D) between zero and 2 kg
View Answer play_arrowquestion_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
A) \[2\,\,m{{s}^{-1}}\]
B) \[0.5\,\,m{{s}^{-1}}\]
C) \[19.6\,\,m{{s}^{-1}}\]
D) \[4.43\,\,m{{s}^{-1}}\]
View Answer play_arrowquestion_answer43) For me circuit shown in figure,
A) resistance\[R=46\Omega \]
B) current through \[20\Omega \] resistance is\[0.1\,\,A\]
C) potential difference across the middle resistance is\[2V\]
D) All of the above are true
View Answer play_arrowquestion_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? \[\left( \frac{e}{m}\,\,for\,\,electron=1.8\times {{10}^{11}}C\,\,k{{g}^{-1}} \right)\]
A) \[0.1\]
B) \[0.2\]
C) \[0.3\]
D) \[1.0\]
View Answer play_arrowquestion_answer45) A water drop in air reflects the light rays as
A)
B)
C)
D)
View Answer play_arrowquestion_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?
A) \[{{l}_{1}}+{{l}_{2}}\]
B) \[\frac{{{l}_{1}}{{l}_{2}}}{{{l}_{1}}+{{l}_{2}}}\]
C) \[\frac{1}{{{l}_{1}}+{{l}_{2}}}\]
D) \[\frac{1}{{{l}_{1}}}+\frac{1}{{{l}_{2}}}\]
View Answer play_arrowquestion_answer47) An ideal thermometer should have
A) small heat capacity
B) large heat capacity
C) medium heat capacity
D) variable heat capacity
View Answer play_arrowquestion_answer48) For the circuit shown in figure, the impedance of the circuit will be
A) \[50\Omega \]
B) \[60\Omega \]
C) \[90\Omega \]
D) \[120\Omega \]
View Answer play_arrowquestion_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
A) \[1\times {{10}^{5}}\]
B) \[2.3\times {{10}^{10}}\]
C) \[1.15\times {{10}^{10}}\]
D) None of these
View Answer play_arrowquestion_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
A) \[X=0,\,\,Y=1\]
B) \[X=1,\,\,Y=1\]
C) \[X=1,\,\,Y=0\]
D) \[X=0,\,\,Y=0\]
View Answer play_arrowquestion_answer51) The reagent commonly used to determine hardness of water titrimetric ally is
A) oxalic acid
B) disodium salt of\[EDTA\]
C) sodium citrate
D) sodium thiosulphate
View Answer play_arrowquestion_answer52) In a solid lattice, the cation has left a lattice site and is located at an interstitial position. The lattice defect is
A) interstitial defect
B) vacancy defect
C) Frenkel defect
D) Schottky defect
View Answer play_arrowquestion_answer53) The molarity of a solution obtained by mixing \[800\,\,mL\] of \[0.5\,\,M\,\,HCl\] with \[200\,\,mL\] of \[1\,\,M\,\,HCl\] will be
A) \[0.8\,\,M\]
B) \[0.6\,\,M\]
C) \[0.4\,\,M\]
D) \[0.2\,\,M\]
View Answer play_arrowquestion_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\[=1.86\,\,K\,\,kg\,\,mo{{l}^{-1}})\]
A) \[-{{0.570}^{o}}C\]
B) \[-{{0.372}^{o}}C\]
C) \[-{{0.520}^{o}}C\]
D) \[+{{0.372}^{o}}C\]
View Answer play_arrowquestion_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
A) \[X>Y>Z\]
B) \[Y>Z>X\]
C) \[Y>X>Z\]
D) \[Z>X>Y\]
View Answer play_arrowquestion_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
A) \[2.3\]
B) \[4.6\]
C) \[9.2\]
D) \[18.4\]
View Answer play_arrowquestion_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\[90%\]?
A) \[300\,\,\min \]
B) \[360\,\,\min \]
C) \[398.8\,\,\min \]
D) \[400\,\,\min \]
View Answer play_arrowquestion_answer58) In the respect of the equation,\[k=A{{e}^{-Ea/RT}}\] in chemical kinetics, which one of the following statement is correct?
A) \[k\] is equilibrium constant
B) \[A\] is adsorption factor
C) \[{{E}_{a}}\] is activation energy
D) \[R\] is Rydberg constant
View Answer play_arrowquestion_answer59) What is the name of a phenomenon in which both adsorption and absorption takes places?
A) Chemisorption
B) Physisorption
C) Desorption
D) Sorption
View Answer play_arrowquestion_answer60) Colloidal solutions of gold, prepared by different methods are of different colours because of
A) variable valency of gold
B) different concentration of gold particles
C) impurities produced by different methods
D) different diameters of colloidal gold particles
View Answer play_arrowquestion_answer61) The most important ore of tin is
A) cassiterite
B) cryolite
C) cerussite
D) None of these
View Answer play_arrowquestion_answer62) Which process of purifications is represented by the following scheme? \[\underset{impure}{\mathop{Ti}}\,+2{{I}_{2}}\xrightarrow{{{250}^{o}}C}Ti{{I}_{4}}\xrightarrow{{{1400}^{o}}C}\underset{Pure}{\mathop{Ti}}\,+2{{I}_{2}}\]
A) Cupellation
B) Zone refining
C) van-Arkel process
D) Poling
View Answer play_arrowquestion_answer63) If the supply of oxygen is limited, \[{{H}_{2}}S\] reacts with \[{{O}_{2}}\] to form
A) \[{{H}_{2}}O+S{{O}_{3}}\]
B) \[{{H}_{2}}O+S\]
C) \[{{H}_{2}}S{{O}_{4}}+S\]
D) \[{{H}_{2}}O+S{{O}_{2}}\]
View Answer play_arrowquestion_answer64) Which two of the following salts are used for preparing iodised salt? \[(I)KI{{O}_{3}}\,\,(II)KI\,\,(III){{I}_{2}}\,\,(IV)HI\]
A) \[I,\,\,II\]
B) \[I,\,\,III\]
C) \[II,\,\,IV\]
D) \[III,\,\,IV\]
View Answer play_arrowquestion_answer65) Ammonia will not form complex with
A) \[A{{g}^{2+}}\]
B) \[P{{b}^{2+}}\]
C) \[C{{u}^{2+}}\]
D) \[C{{d}^{2+}}\]
View Answer play_arrowquestion_answer66) The magnetic moment of a transition metal ion is\[\sqrt{15}BM\]. Therefore, the number of unpaired electrons present in it is
A) \[4\]
B) \[1\]
C) \[2\]
D) \[3\]
View Answer play_arrowquestion_answer67) \[C{{e}^{4+}}\] is stable. This is because
A) half-filled \[d-\]orbitals
B) all paired electrons in \[d-\]orbitals
C) empty \[d-\]orbitals
D) fully filled \[d-\]orbitals
View Answer play_arrowquestion_answer68) \[[Co{{(N{{H}_{3}})}_{4}}C{{l}_{2}}]N{{O}_{2}}\]and\[[Co{{(N{{H}_{3}})}_{4}}ClN{{O}_{2}}]Cl\] exhibit which type is isomerism?
A) Geometrical
B) Optical
C) Linkage
D) lonisation
View Answer play_arrowquestion_answer69) The \[\pi -\]bonded organometallic compound which has ethene as one of its component is
A) Zeise's salt
B) ferrocene
C) dibenzene chromium
D) tetraethyltin
View Answer play_arrowquestion_answer70) Alcoholic \[KOH\] is used for
A) dehydration
B) dehydrogenation
C) dehydrohalogenation
D) dehalogenation
View Answer play_arrowquestion_answer71) Freon used as refrigerant is
A) \[C{{F}_{2}}=C{{F}_{2}}\]
B) \[C{{H}_{2}}{{F}_{2}}\]
C) \[CC{{l}_{2}}{{F}_{2}}\]
D) \[C{{F}_{4}}\]
View Answer play_arrowquestion_answer72) Which of the following reacts fastly with\[Na?\]
A) \[{{1}^{o}}\]alcohol
B) \[{{2}^{o}}\]alcohol
C) \[{{3}^{o}}\]alcohol
D) The reactivity of all is equal
View Answer play_arrowquestion_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
A) toluene
B) benzaldehyde
C) benzoic acid
D) benzene
View Answer play_arrowquestion_answer74) The formula of chloral is
A) \[CHC{{l}_{3}}\]
B) \[C{{H}_{2}}ClCHO\]
C) \[CC{{l}_{3}}CHO\]
D) \[CHC{{l}_{2}}CHO\]
View Answer play_arrowquestion_answer75) One of the following named reaction is an example of disproportionation reaction. Identify it
A) Birch reduction
B) Aldol condensation
C) Reimer-Tiemann reaction
D) Cannizaro reaction
View Answer play_arrowquestion_answer76) Calcium formate on dry heating yields
A) acetone
B) formaldehyde
C) acetic acid
D) acetaldehyde
View Answer play_arrowquestion_answer77) Which amongst the following is the most stable carbocation?
A) \[C{{H}_{3}}-\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\overset{+}{\mathop{C}}}\,-H\]
B) \[C{{H}_{3}}-\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\overset{\begin{smallmatrix} C{{H}_{3}} \\ | \end{smallmatrix}}{\mathop{{{C}^{+}}}}}\,\]
C) \[\overset{+}{\mathop{C}}\,{{H}_{3}}\]
D) \[C{{H}_{3}}\overset{+}{\mathop{C}}\,{{H}_{2}}\]
View Answer play_arrowquestion_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
A) \[2.0\times {{10}^{-6}}mol\,\,{{L}^{-1}}\]
B) \[1.0\times {{10}^{-5}}mol\,\,{{L}^{-1}}\]
C) \[1.0\times {{10}^{-6}}mol\,\,{{L}^{-1}}\]
D) \[1.0\times {{10}^{-7}}mol\,\,{{L}^{-1}}\]
View Answer play_arrowquestion_answer79) Which one of the following pairs represents stereoisomerism?
A) Chain isomerism and rotational isomerism,
B) Structural isomerism and geometric isomerism
C) Linkage isomerism and geometric isomerism
D) Optical isomerism and geometric isomerism
View Answer play_arrowquestion_answer80) Aniline in a set of reactions yielded a product\[D\]. The structure of the product D would be
A) \[{{C}_{6}}{{H}_{5}}C{{H}_{2}}N{{H}_{2}}\]
B) \[{{C}_{6}}{{H}_{5}}NHC{{H}_{2}}C{{H}_{3}}\]
C) \[{{C}_{6}}{{H}_{5}}NHOH\]
D) \[{{C}_{6}}{{H}_{5}}C{{H}_{2}}OH\]
View Answer play_arrowquestion_answer81) The correct order in which the \[O-O\] bond length increases in the following is
A) \[{{H}_{2}}{{O}_{2}}<{{O}_{2}}<{{O}_{3}}\]
B) \[{{O}_{3}}<{{H}_{2}}{{O}_{2}}<{{O}_{2}}\]
C) \[{{O}_{2}}<{{O}_{3}}<{{H}_{2}}{{O}_{2}}\]
D) \[{{O}_{2}}<{{H}_{2}}{{O}_{2}}<{{O}_{3}}\]
View Answer play_arrowquestion_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\[Al=27)\]
A) \[180\,\,kg\]
B) \[270\,\,kg\]
C) \[540\,\,kg\]
D) \[90\,\,kg\]
View Answer play_arrowquestion_answer83) The number of moles of \[KMn{{O}_{4}}\] reduced by one mole of \[KI\] in alkaline medium is
A) one fifth
B) five
C) one
D) two
View Answer play_arrowquestion_answer84) Which of the following molecules has trigonal planar geometry?
A) \[I{{F}_{3}}\]
B) \[PC{{l}_{3}}\]
C) \[N{{H}_{3}}\]
D) \[B{{F}_{3}}\]
View Answer play_arrowquestion_answer85) Which one of the following forms micelles in aqueous solution above certain concentration?
A) Urea
B) Dodecyl trimethyl ammonium chloride
C) Pyridinium chloride
D) Glucose
View Answer play_arrowquestion_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
A) group 14
B) group 16
C) group 4
D) group 6
View Answer play_arrowquestion_answer87) Which of the following pairs of a chemical reaction is certain to result in a spontaneous reaction?
A) Exothermic and decreasing disorder
B) Endothermic and increasing disorder
C) Exothermic and increasing disorder
D) Endothermic and decreasing disorder
View Answer play_arrowquestion_answer88) The monomer of the polymer
A)
B) \[{{(C{{H}_{3}})}_{2}}C=C{{(C{{H}_{3}})}_{2}}\]
C) \[C{{H}_{3}}CH=CH\cdot C{{H}_{3}}\]
D) \[C{{H}_{3}}CH=C{{H}_{2}}\]
View Answer play_arrowquestion_answer89) The correct sequence of increasing covalent character is represented by
A) \[LiCl<NaCl<BeC{{l}_{2}}\]
B) \[BeC{{l}_{2}}<NaCl<LiCl\]
C) \[NaCl<LiCI<BeC{{l}_{2}}\]
D) \[BeC{{l}_{2}}<LiCl<NaCl\]
View Answer play_arrowquestion_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
B) presence of \[HCl\] increases the sulphide ion concentration
C) solubility product of group II sulphides is more than that of group IV sulphides
D) sulphides of group IV cations are unstable in\[HCl\]
View Answer play_arrowquestion_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
A) \[-41\,\,kJ\,\,mo{{l}^{-1}}\]
B) \[-1312\,\,kJ\,\,mo{{l}^{-1}}\]
C) \[-164\,\,kJ\,\,mo{{l}^{-1}}\]
D) \[-82\,\,kJ\,\,mo{{l}^{-1}}\]
View Answer play_arrowquestion_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
A) \[{{K}_{2}}=\frac{1}{{{K}_{1}}}\]
B) \[{{K}_{2}}=K_{1}^{2}\]
C) \[{{K}_{2}}=\frac{{{K}_{1}}}{2}\]
D) \[{{K}_{2}}=\frac{1}{K_{1}^{2}}\]
View Answer play_arrowquestion_answer93) Names of some compounds are given. Which one is not correct in \[IUPAC\] system?
A) \[C{{H}_{3}}-\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{C}}\,H-\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\mathop{C}}\,H-C{{H}_{3}}\] 3-methyl-2-butanol
B) \[C{{H}_{3}}-C{{H}_{2}}\equiv C-CH{{(C{{H}_{3}})}_{2}}\] 4-methyl-2-pentyne
C) \[C{{H}_{3}}-C{{H}_{2}}-\underset{\begin{smallmatrix} || \\ C{{H}_{2}} \end{smallmatrix}}{\mathop{C}}\,-\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\mathop{C}}\,H-C{{H}_{3}}\] 2-ethyl-3-methyl-but-1-ene
D) \[C{{H}_{3}}-C{{H}_{2}}-C{{H}_{2}}-\underset{\begin{smallmatrix} | \\ C{{H}_{2}}C{{H}_{3}} \end{smallmatrix}}{\mathop{C}}\,H-\overset{\begin{smallmatrix} C{{H}_{3}} \\ | \end{smallmatrix}}{\mathop{C}}\,H-C{{H}_{2}}C{{H}_{3}}\] 3-methyl-4-ethyle heptane
View Answer play_arrowquestion_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
A) \[3\,\,mol\]
B) \[4\,\,mol\]
C) \[1\,\,mol\]
D) \[2\,\,mol\]
View Answer play_arrowquestion_answer95) Dominance of strong repulsive forces among the molecules of the gas \[(Z=\]compressibility factor)
A) depends on \[Z\] and indicated by\[Z=1\]
B) depends on \[Z\] and indicated by\[Z>1\]
C) depends on \[Z\] and indicated by\[Z<1\]
D) is independent of\[Z\]
View Answer play_arrowquestion_answer96) When glucose reacts with bromine water, the main product is
A) acetic acid
B) saccharic acid
C) glyceraldehyde
D) gluconic acid
View Answer play_arrowquestion_answer97) Protein present in hair is
A) albumin
B) globulin
C) keratin
D) chromoprotein
View Answer play_arrowquestion_answer98) The hydrolysis of 2-bromo-3-methyl butane by \[{{S}_{N}}1\] mechanism gives mainly
A) 3-methl-2-butanol
B) 2-methyl-2-butanol
C) 2, 2-dimethyl-l-propanol
D) 2 methyl-1-butanol
View Answer play_arrowquestion_answer99) The \[pH\] value of an acid is \[5\] and its concentration is\[1\,\,M\] . What is the value of \[{{K}_{a}}\] for the acid?
A) \[{{10}^{-7}}\]
B) \[{{10}^{-5}}\]
C) \[{{10}^{-10}}\]
D) \[{{10}^{-8}}\]
View Answer play_arrowquestion_answer100) If \[1\] mole of an ideal gas expands isothermally at \[{{37}^{o}}C\] from \[15\,\,L\] to\[25\,\,L\], the maximum work obtained is
A) \[12.87\,\,J\]
B) \[6.43\,\,J\]
C) \[8.57\,\,J\]
D) \[2.92\,\,J\]
View Answer play_arrowquestion_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
A) \[p{{x}^{2}}+2xy+p{{y}^{2}}=0\]
B) \[p{{x}^{2}}-2xy+p{{y}^{2}}=0\]
C) \[p{{x}^{2}}+2xy-p{{y}^{2}}=0\]
D) None of these
View Answer play_arrowquestion_answer102) If\[z=i{{\log }_{e}}(2-\sqrt{3})\], then find the value of\[\cos z\].
A) \[2\]
B) \[-2\]
C) \[2i\]
D) \[-2i\]
View Answer play_arrowquestion_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
A) \[AP\]
B) \[GP\]
C) \[HP\]
D) None of these
View Answer play_arrowquestion_answer104) Find the value of \[^{1}{{P}_{1}}+2{{\cdot }^{2}}{{P}_{2}}+3{{\cdot }^{3}}{{P}_{3}}+4{{\cdot }^{4}}{{P}_{4}}+...{{+}^{n}}{{P}_{n}}\]
A) \[^{n+1}{{P}_{n+1}}\]
B) \[^{n+1}{{P}_{n+1}}-1\]
C) \[^{n+1}{{P}_{n+1}}-2\]
D) \[^{n+1}{{P}_{n+1}}+1\]
View Answer play_arrowquestion_answer105) The eccentricity of an ellipse whose pair of a conjugate diameter are \[y=x\] and \[3y=-2x\] is
A) \[\frac{2}{3}\]
B) \[\frac{1}{3}\]
C) \[\frac{1}{\sqrt{3}}\]
D) None of these
View Answer play_arrowquestion_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
A) \[1\]
B) \[2\]
C) \[3\]
D) \[4\]
View Answer play_arrowquestion_answer107) Let \[u\] and \[v\] be two odd functions, then the function \[uov\] is
A) an even function
B) an odd function
C) neither even nor odd
D) a periodic function
View Answer play_arrowquestion_answer108) The period of the function \[f(x)=2\sin x+3\cos 2x\]is
A) \[\pi \]
B) \[2\pi \]
C) \[\frac{\pi }{2}\]
D) None of these
View Answer play_arrowquestion_answer109) If\[y=\frac{1}{{{t}^{2}}-t-6}\]and\[t=\frac{1}{x-2}\], then the values of \[x\]which make the function \[y\] discontinuous, are
A) \[2,\,\,\frac{2}{3},\,\,\frac{7}{3}\]
B) \[2,\,\,\frac{3}{2},\,\,\frac{7}{3}\]
C) \[2,\,\,\frac{3}{2},\,\,\frac{3}{7}\]
D) None of the above
View Answer play_arrowquestion_answer110) The sub tangent at any point of the curve\[{{x}^{m}}{{y}^{n}}={{a}^{m+n}}\]varies as
A) \[{{(abscissa)}^{2}}\]
B) \[{{(abscissa)}^{3}}\]
C) abscissa
D) ordinate
View Answer play_arrowquestion_answer111) \[f(x)=1+[\cos x]x,\]in\[0<x\le \frac{\pi }{2}\]
A) has a minimum value
B) has a maximum value\[2\]
C) is continuous in\[\left[ 0,\,\,\frac{\pi }{2} \right]\]
D) is not differentiable at\[x=\frac{\pi }{2}\]
View Answer play_arrowquestion_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
A) \[14\mathbf{i}-8\mathbf{j}+12\mathbf{k}\]
B) \[-14\mathbf{i}-8\mathbf{j}-12\mathbf{k}\]
C) \[7\mathbf{i}+9\mathbf{j}+2\mathbf{k}\]
D) \[7\mathbf{i}-9\mathbf{j}+2\mathbf{k}\]
View Answer play_arrowquestion_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\[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}+2abc\].
A) \[0\]
B) \[1\]
C) \[-1\]
D) \[\frac{1}{2}\]
View Answer play_arrowquestion_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
A) \[7\]
B) \[8\]
C) \[4\]
D) \[11\]
View Answer play_arrowquestion_answer115) Equation of the chord of the hyperbola \[25{{x}^{2}}-16{{y}^{2}}=400\] which is bisected at the point \[(6,\,\,2)\] is
A) \[16x-75y=418\]
B) \[75x-16y=418\]
C) \[25x-4y=400\]
D) None of these
View Answer play_arrowquestion_answer116) \[\int{\frac{1}{{{x}^{6}}+{{x}^{4}}}dx}\]is equal to
A) \[-\frac{1}{3{{x}^{3}}}+\frac{1}{x}+\cos \text{e}{{\text{c}}^{-1}}x+C\]
B) \[-\frac{1}{3{{x}^{3}}}+\frac{1}{x}+{{\cot }^{-1}}x+C\]
C) \[-\frac{1}{3{{x}^{3}}}+\frac{1}{x}+ta{{n}^{-1}}x+C\]
D) None of the above
View Answer play_arrowquestion_answer117) Find the sum of the series\[\frac{1}{2\cdot 3}+\frac{1}{4\cdot 5}+\frac{1}{6\cdot 7}+...\]
A) \[\log \frac{e}{2}\]
B) \[\log \frac{e}{4}\]
C) \[\log \frac{2}{3}\]
D) \[\log \frac{2}{4}\]
View Answer play_arrowquestion_answer118) The equation \[{{\tan }^{4}}x-2{{\sec }^{2}}x+{{a}^{2}}=0\] will have atleast one solution, if
A) \[|a|\,\,\le 4\]
B) \[|a|\,\,\le 2\]
C) \[|a|\,\,\le \sqrt{3}\]
D) \[|a|\,\,\le \sqrt{2}\]
View Answer play_arrowquestion_answer119) If\[\sin \theta +\cos \theta =\sqrt{2}\cos ({{90}^{o}}-\theta )\], then find the value of\[\cot \theta \]
A) \[\frac{1}{2}\]
B) \[0\]
C) \[-1\]
D) \[2\]
View Answer play_arrowquestion_answer120) If\[2-{{\cos }^{2}}\theta =3\sin \theta \cos \theta \],\[\sin \theta \ne cos\theta \], then find the value of\[\cot \theta \]
A) \[\frac{1}{2}\]
B) \[0\]
C) \[-1\]
D) \[2\]
View Answer play_arrowquestion_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
A) \[x\sqrt{2}\]
B) \[\frac{x}{\sqrt{2}}\]
C) \[\frac{x}{2\sqrt{2}}\]
D) \[\frac{x}{4}\]
View Answer play_arrowquestion_answer122) The coefficient of \[{{x}^{n}}\] in the expansion of\[{{(1-x)}^{-2}}\]is
A) \[\frac{{{2}^{n}}}{2!}\]
B) \[n+1\]
C) \[n+2\]
D) \[2n\]
View Answer play_arrowquestion_answer123) If \[f(x)\] is an even function, then\[\int_{0}^{x}{f(t)}\,\,dt\]
A) odd function
B) even function
C) neither even nor odd
D) None of the above
View Answer play_arrowquestion_answer124) Solve\[(xy-1)\frac{dy}{dx}+{{y}^{2}}=0\]
A) \[xy+\log x=C\]
B) \[xy+\log y=C\]
C) \[xy-\log y=C\]
D) \[xy-\log x=C\]
View Answer play_arrowquestion_answer125) Find the order and degree of the differential equation \[{{\left( \frac{{{d}^{4}}y}{d{{x}^{4}}} \right)}^{3/5}}-5\frac{{{d}^{3}}y}{d{{x}^{3}}}+6\frac{{{d}^{2}}y}{d{{x}^{2}}}-8\frac{dy}{dx}+5=0\]
A) \[4,\,\,3\]
B) \[3,\,\,4\]
C) \[4,\,\,5\]
D) \[5,\,\,4\]
View Answer play_arrowquestion_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
A) \[74\]
B) \[62\]
C) \[64\]
D) \[72\]
View Answer play_arrowquestion_answer127) The locus of the middle points of chords of the parabola \[{{y}^{2}}=8x\] drawn through the vertex is a parabola whose
A) focus is\[(2,\,\,0)\]
B) latusrectum\[=8\]
C) focus is\[(0,\,\,2)\]
D) latusrectum\[=4\]
View Answer play_arrowquestion_answer128) lf\[\sqrt{x}+\sqrt{y}=10\], find\[\frac{dx}{dy}\]at\[y=4\].
A) \[4\]
B) \[-3\]
C) \[-4\]
D) \[3\]
View Answer play_arrowquestion_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.
A) \[i\]
B) \[-i\]
C) \[1\]
D) \[-1\]
View Answer play_arrowquestion_answer130) The equation\[z\bar{z}+z+\bar{z}+10=0\], represents
A) a circle
B) a parabola
C) an ellipse
D) a hyperbola
View Answer play_arrowquestion_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.
A) \[12\,\,cm\]
B) \[6\,\,cm\]
C) \[18\,\,cm\]
D) \[3\,\,cm\]
View Answer play_arrowquestion_answer132) If\[\log (p+r)+\log (p+r-2q)=2\log (p-r)\], then \[p,\,\,\,q\] and \[r\] are in
A) \[AP\]
B) \[GP\]
C) \[HP\]
D) None of these
View Answer play_arrowquestion_answer133) Find the sum of the real roots of the equation\[{{x}^{2}}+5|x|+\,\,6=0\]
A) \[5\]
B) \[10\]
C) \[-5\]
D) None of these
View Answer play_arrowquestion_answer134) If\[A=\left[ \begin{matrix} 1 & 2 \\ 2 & 1 \\ \end{matrix} \right]\]and\[f(x)=\frac{1+x}{1-x}\], find the value of\[f(A)\].
A) \[\left[ \begin{matrix} 1 & 1 \\ 1 & 1 \\ \end{matrix} \right]\]
B) \[\left[ \begin{matrix} -1 & -1 \\ -1 & -1 \\ \end{matrix} \right]\]
C) \[\left[ \begin{matrix} 2 & 2 \\ 2 & 2 \\ \end{matrix} \right]\]
D) None of these
View Answer play_arrowquestion_answer135) A skew-symmetric matrix \[M\] satisfies the relation\[M+I=0\], where \[I\] is the unit matrix. Then, \[MM'\]is equal to
A) \[I\]
B) \[2I\]
C) \[-I\]
D) None of these
View Answer play_arrowquestion_answer136) Let \[X\] and \[Y\] be two random variables. The relationship \[E(XY)=E(X)\cdot E(Y)\] holds
A) always
B) if\[E(X+Y)=E(X)+E(Y)\]is true
C) if \[X\] and \[Y\] are independent
D) if \[X\] can be obtained from \[Y\] by a linear transformation
View Answer play_arrowquestion_answer137) Find the number of solutions of the equation\[\sin 2x+\cos 4x=2\].
A) \[0\]
B) \[1\]
C) \[2\]
D) infinite
View Answer play_arrowquestion_answer138) In any\[\Delta ABC\], find the least value of\[\frac{{{\sin }^{2}}A+\sin A+1}{\sin A}\].
A) \[3\]
B) \[\sqrt{3}\]
C) \[1\]
D) \[2\]
View Answer play_arrowquestion_answer139) Find the critical points of the function \[f(x)={{(x-2)}^{2/3}}(2x+1)\].
A) \[-1\]and\[2\]
B) \[1\]
C) \[1\]and\[-\frac{1}{2}\]
D) \[1\]and\[2\]
View Answer play_arrowquestion_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
A) \[2\]
B) \[4\]
C) \[6\]
D) \[8\]
View Answer play_arrowquestion_answer141) Find the angle between the straight lines \[\frac{x+1}{2}=\frac{y-2}{5}=\frac{z+3}{4}\]and \[\frac{x-1}{1}=\frac{y+2}{2}=\frac{z-3}{-3}\]
A) \[{{45}^{o}}\]
B) \[{{30}^{o}}\]
C) \[{{60}^{o}}\]
D) \[{{90}^{o}}\]
View Answer play_arrowquestion_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
A) \[2x+17y+9z=0\]
B) \[28x-17y+9z=0\]
C) \[2x+17y-9z=0\]
D) None of these
View Answer play_arrowquestion_answer143) The function defined by the equation \[xy-\log y=1\]satisfies\[x(yy''+y{{'}^{2}})-y''+kyy'=0\]. Find the value of\[k\].
A) \[-3\]
B) \[3\]
C) \[1\]
D) \[-1\]
View Answer play_arrowquestion_answer144) If\[f(x)={{[1-{{(x-3)}^{4}}]}^{1/7}}\], find\[{{f}^{-1}}(x)\].
A) \[3+{{(1-x)}^{7/4}}\]
B) \[3+{{(1-{{x}^{4}})}^{7}}\]
C) \[3+{{(1-{{x}^{7}})}^{1/4}}\]
D) \[3-{{(1-{{x}^{4}})}^{1/7}}\]
View Answer play_arrowquestion_answer145) Find the value of\[\underset{n\to \infty }{\mathop{\lim }}\,\frac{{{a}^{n}}+{{b}^{n}}}{{{a}^{n}}+{{d}^{n}}},\,\,a>b,\,\,d\].
A) \[-1\]
B) \[1\]
C) \[0\]
D) \[\frac{1}{2}\]
View Answer play_arrowquestion_answer146) The function \[y={{x}^{2}}+ax+b\] has a minimum at \[x=3\] and minimum value is\[5\]. Find\[a+b\].
A) \[-6\]
B) \[14\]
C) \[20\]
D) \[8\]
View Answer play_arrowquestion_answer147) The coefficient of \[{{x}^{n}}\] in the expansion of \[{{(1-9x+20{{x}^{2}})}^{-1}}\]
A) \[{{5}^{n}}-{{4}^{n}}\]
B) \[{{5}^{n+1}}-{{4}^{n+1}}\]
C) \[{{5}^{n-1}}-{{4}^{n-1}}\]
D) None of these
View Answer play_arrowquestion_answer148) The minimum value of\[f(x)=|x-1|+|x-2|+|x-3|\] is equal to
A) \[1\]
B) \[2\]
C) \[3\]
D) \[0\]
View Answer play_arrowquestion_answer149) \[\frac{{{d}^{20}}y}{d{{x}^{20}}}(2\cos x\cos 3x)\]is equal to
A) \[{{2}^{20}}(\cos 2x-{{2}^{20}}\cos 4x)\]
B) \[{{2}^{20}}(\cos 2x+{{2}^{20}}\cos 4x)\]
C) \[{{2}^{20}}(\sin 2x+{{2}^{20}}\sin 4x)\]
D) \[{{2}^{20}}(\sin 2x-{{2}^{20}}\sin 4x)\]
View Answer play_arrowquestion_answer150) The logically equivalent proposition of \[p\Leftrightarrow q\] is
A) \[(p\wedge q)\vee (p\wedge q)\]
B) \[(p\Rightarrow q)\wedge (q\Rightarrow p)\]
C) \[(p\wedge q)\vee (q\Rightarrow p)\]
D) \[(p\wedge q)\Rightarrow (q\vee p)\]
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