question_answer1) Four equal point charges Q each are placed in the xy plane at\[\left( 0,\text{ }2 \right),\text{ }\left( 4,\text{ }2 \right),\text{ }\left( 4,\,-2 \right)\text{ }and\text{ }\left( 0,-\,2 \right)\]. The work required to put a fifth charge Q at the origin of the coordinate system will be-
A) \[\frac{{{Q}^{2}}}{4\pi {{\varepsilon }_{0}}}\] done clear
B) \[\frac{{{Q}^{2}}}{2\sqrt{2}\pi {{\varepsilon }_{0}}}\] done clear
C) \[\frac{{{Q}^{2}}}{4\pi {{\varepsilon }_{0}}}\left( 1+\frac{1}{\sqrt{3}} \right)\] done clear
D) \[\frac{{{Q}^{2}}}{4\pi {{\varepsilon }_{0}}}\left( 1+\frac{1}{\sqrt{5}} \right)\] done clear
View Answer play_arrowquestion_answer2) A rigid massless rod of length 3l has two masses attached at each end as shown in the figure. The rod is pivoted at point P on the horizontal axis (see figure). When released from initial horizontal position, its instantaneous angular acceleration will be-
A) \[\frac{g}{13l}\] done clear
B) \[\frac{g}{2l}\] done clear
C) \[\frac{g}{3l}\] done clear
D) \[\frac{7g}{3l}\] done clear
View Answer play_arrowquestion_answer3) A closed organ pipe has a fundamental frequency of 1.5 kHz. The number of overtones that can be distinctly heard by a person with this organ pipe will be (Assume that the highest frequency a person can hear is 20,000 Hz)
A) 4 done clear
B) 7 done clear
C) 6 done clear
D) 5 done clear
View Answer play_arrowquestion_answer4) Consider the nuclear fission \[N{{e}^{20}}\to 2H{{e}^{4}}+{{C}^{\text{12}}}\] Given that the binding energy/nucleon of\[N{{e}^{20}}\], \[H{{e}^{4}}\] and \[{{C}^{12}}\] are respectively, 8.03 MeV, 7.07 MeV and 7.86 MeV, identify the correct statement-
A) 8.3 MeV energy will be released done clear
B) energy of 11.9 MeV has to be supplied done clear
C) energy of 12.4 MeV will be supplied done clear
D) energy of 3.6 MeV will be released done clear
View Answer play_arrowquestion_answer5) A metal plate of area \[1\times {{10}^{-}}^{4}\,{{m}^{2}}\] is illuminated by a radiation of intensity\[16\text{ }mW/{{m}^{2}}\]. The work function of the metal is 5 eV. The energy of the incident photons is 10 eV and only \[10%\] of it produces photo electrons. The number of emitted photoelectrons per second and their maximum energy, respectively, will be-
A) \[{{10}^{14}}\] and 10 eV done clear
B) \[{{10}^{12}}\] and 5 Ev done clear
C) \[{{10}^{11}}\] and 5 eV done clear
D) \[{{10}^{10}}\]and 5 eV done clear
View Answer play_arrowquestion_answer6) For the circuit shown below, the current through the Zener diode is-
A) 5 mA done clear
B) zero done clear
C) 14 mA done clear
D) 9 mA done clear
View Answer play_arrowquestion_answer7) Two vectors \[\overrightarrow{A}\text{ }and\text{ }\overrightarrow{B}\] have equal magnitudes. The magnitude of \[\left( \overrightarrow{A}+\text{ }\overrightarrow{B} \right)\] is 'n' times the magnitude of\[\left( \overrightarrow{A}-\overrightarrow{B} \right)\]. The angle between \[\overrightarrow{A}\] and \[\overrightarrow{B}\] is-
A) \[{{\sin }^{-1}}\,\left[ \frac{n-1}{n+1} \right]\] done clear
B) \[{{\sin }^{-1}}\,\left[ \frac{{{n}^{2}}-1}{{{n}^{2}}+1} \right]\] done clear
C) \[{{\cos }^{-1}}\,\left[ \frac{{{n}^{2}}-1}{{{n}^{2}}+1} \right]\] done clear
D) \[{{\cos }^{-1}}\,\left[ \frac{n-1}{n+1} \right]\] done clear
View Answer play_arrowquestion_answer8) The diameter and height of a cylinder are measured by a meter scale to be \[12.6\,\,\pm \,\,0.1\] cm and \[34.2\,\,\pm \,0.1\] cm, respectively. What will be the value of its volume in appropriate significant figures?
A) \[4264.4\,\,\pm \,\,81.0\text{ }c{{m}^{3}}\] done clear
B) \[4264\,\,\pm \,\,81c{{m}^{3}}\] done clear
C) \[4300\,\,\pm \,\,80\text{ }c{{m}^{3}}\] done clear
D) \[4260\,\,\pm \,\,80\text{ }c{{m}^{3}}\] done clear
View Answer play_arrowquestion_answer9) A current of 2 mA was passed through an unknown resistor which dissipated a power of 4.4 W. Dissipated power when an ideal power supply of 11 V is connected across it is-
A) \[11\times {{10}^{-5}}\text{ }W\] done clear
B) \[11\times {{10}^{-3}}\text{ }W\] done clear
C) \[11\times {{10}^{5}}\text{ }W\] done clear
D) \[11\times {{10}^{-}}^{4}W\] done clear
View Answer play_arrowquestion_answer10) Two stars of masses \[3\times {{10}^{31}}\] kg each, and at distance \[2\times {{10}^{11}}\] m rotate in a plane about their common centre of mass 0. A meteorite passes through 0 moving perpendicular to the star/s rotation plane. In order to escape from the gravitational field of this double star, the minimum speed that meteorite should have at 0 is- (Take Gravitational constant; \[G=6.67\times {{10}^{-11}}\,N{{m}^{2}}k{{g}^{-}}^{2})\]
A) \[2.4\times {{10}^{4}}m/s\] done clear
B) \[1.4\times {{10}^{5}}m/s\] done clear
C) \[3.8\times {{10}^{4}}m/s\] done clear
D) \[2.8\times {{10}^{5}}m/s\] done clear
View Answer play_arrowquestion_answer11) Consider a Young's double slit experiment as shown in figure. What should be the slit separation d in terms of wavelength \[\lambda \] such that the first minima occurs directly in front of the slit\[\left( {{S}_{1}} \right)\]?
A) \[\frac{\lambda }{2(5-\sqrt{2})}\] done clear
B) \[\frac{\lambda }{2(\sqrt{5}-2)}\] done clear
C) \[\frac{\lambda }{(5-\sqrt{2})}\] done clear
D) \[\frac{\lambda }{(\sqrt{5}-2)}\] done clear
View Answer play_arrowquestion_answer12) At some location on earth the horizontal component of earth's magnetic field\[18\times {{10}^{-}}^{6}T\]. At this location, magnetic needle of length 0.12 m and pole strength 1.8 Am is suspended from its mid-point using a thread, it makes \[45{}^\circ \] angle with horizontal in equilibrium. To keep this needle horizontal, the vertical force that should be applied at one of its ends is-
A) \[3.6\times {{10}^{-5}}\,N\] done clear
B) \[1.8\times {{10}^{-5}}\text{ }N\] done clear
C) \[1.3\times {{10}^{-5}}\,N\] done clear
D) \[6.5\times {{10}^{-5}}\,N\] done clear
View Answer play_arrowquestion_answer13) Charges -q and +q located at A and B. respectively, constitute an electric dipole. Distance \[AB=2a\], 0 is the mid-point of the dipole and OP is perpendicular to AB. A charge Q is placed at P where \[OP=y\] and \[y\,\,>\,\,>\,\,2a\]. The charge Q experiences an electrostatic force F. If Q is now moved along the equatorial line to P? such that \[OP'=\left( \frac{y}{3} \right)\], the force on Q will be close to- \[\left( \frac{y}{3}>>2a \right)\]
A) 9F done clear
B) 3F done clear
C) F/3 done clear
D) 27F done clear
View Answer play_arrowquestion_answer14) The self-induced emf of a coil is 25 volts. When the current in it is changed at uniform rate from 10 A to 25 A in 1s, the change in the energy of the inductance is-
A) 740 J done clear
B) 637.5 J done clear
C) 540 J done clear
D) 437.5 J done clear
View Answer play_arrowquestion_answer15) Half mole of an ideal monoatomic gas is heated at constant pressure of 1 atm from\[20{}^\circ C\text{ }to\text{ }90{}^\circ C\]. Work done by gas is close to -(Gas constant \[R=8.31\text{ }J\] /mol. K)
A) 581 J done clear
B) 73 J done clear
C) 146 J done clear
D) 291 J done clear
View Answer play_arrowquestion_answer16) Two kg of a monoatomic gas is at a pressure of \[4\times {{10}^{4}}N/{{m}^{2}}\]. The density of the gas is \[8\text{ }kg/{{m}^{3}}\]. What is the order of energy of the gas due to its thermal motion?
A) \[{{10}^{4}}\] J done clear
B) \[{{10}^{3}}J\] done clear
C) \[{{10}^{5}}\text{ }J\] done clear
D) \[{{10}^{6}}J\] done clear
View Answer play_arrowquestion_answer17) The modulation frequency of an AM radio station is 250 kHz, which is 10% of the carrier wave. If another AM station approaches you for license what broadcast frequency will you allot?
A) 2900 kHz done clear
B) 2750 kHz done clear
C) 2250 kHz done clear
D) 2000 kz done clear
View Answer play_arrowquestion_answer18) The electric field of a plane polarized electromagnetic wave in free space at time \[t=0\] is given by an expression \[\overrightarrow{E}\left( x,y \right)=10\widehat{j}\text{ }cos\left[ \left( 6x+8z \right) \right]\]. The magnetic field \[\overrightarrow{B}\left( x,\text{ }z,\text{ }t \right)\] is given by - (c is the velocity of light)
A) \[\frac{1}{c}(6\widehat{k}+8\widehat{i})\,cos[(6x+8z-10ct)]\] done clear
B) \[\frac{1}{c}(6\widehat{k}-8\widehat{i})\,cos[(6x+8z-10ct)]\] done clear
C) \[\frac{1}{c}(6\widehat{k}+8\widehat{i})\,cos[(6x-8z+10ct)]\] done clear
D) \[\frac{1}{c}(6\widehat{k}-8\widehat{i})\,cos[(6x+8z+10ct)]\] done clear
View Answer play_arrowquestion_answer19) A particle starts from the origin at time \[t=0\] and moves along the positive x-axis. The graph of velocity with respect to time is shown in figure. What is the position of the particle at time\[t=5s\]?
A) 3 m done clear
B) 9 m done clear
C) 10 m done clear
D) 6 m done clear
View Answer play_arrowquestion_answer20) Two forces P and Q, of magnitude 2F and 3F, respectively; are at an angle 9 with each other. If the force Q is doubled, then their resultant also gets doubled. Then, the angle \[\theta \] is-
A) \[90{}^\circ \] done clear
B) \[60{}^\circ ~\] done clear
C) \[30{}^\circ ~~\] done clear
D) \[120{}^\circ \] done clear
View Answer play_arrowquestion_answer21) The eye can be regarded as a single refracting surface. The radius of curvature of this surface is equal to that of cornea (7.8 mm). This surface separateds two media of refractive indices 1 and 1.34. Calculate the distance from the refracting surface at which a parallel beam of light will come to focus-
A) 2 cm done clear
B) 3.1 cm done clear
C) 4.0 cm done clear
D) 1 cm done clear
View Answer play_arrowquestion_answer22) A cylindrical plastic bottle of negligible mass is filled with 310 ml of water and left floating in a pond with still water. If pressed downward slightly and released, it starts performing simple harmonic motion at angular frequency co. If the radius of the bottle is 2.5 cm then co is close to - (density of water\[={{10}^{3}}kg/{{m}^{3}}\]).
A) \[2.50\text{ }rad\text{ }{{s}^{-}}^{1}\] done clear
B) \[3.75\text{ }rad\text{ }{{s}^{-1}}\] done clear
C) \[5.00\text{ }rad\text{ }{{s}^{-1}}\] done clear
D) \[1.25\text{ }rad\text{ }{{s}^{-1}}\] done clear
E) None of these done clear
View Answer play_arrowquestion_answer23) A hope and a solid cylinder of same mass and radius are made of a permanent magnetic material with their magnetic moment parallel to their respective axes. But the magnetic moment of hoop is twice of solid cylinder. They are placed in a uniform magnetic field in such a manner angle with the field. If the oscillation periods of hoop and cylinder are \[{{T}_{h}}\text{ }and\text{ }{{T}_{c}}\] respectively, then-
A) \[{{T}_{h}}=1.5\text{ }{{T}_{c}}\] done clear
B) \[{{T}_{h}}={{T}_{c}}\] done clear
C) \[{{T}_{h}}=2{{T}_{c}}\] done clear
D) \[{{T}_{h}}=0.5{{T}_{c}}\] done clear
View Answer play_arrowquestion_answer24) The Wheatstone bridge shown in figure, here, gets balanced when the carbon resistor used as \[{{R}_{1}}\] has the colour code (Orange, Red, Brown). he resistors \[{{R}_{2}}\text{ }and\text{ }{{R}_{4}}\text{ }are\text{ }80\Omega \,\,and\text{ }40\Omega \] , respectively. Assuming that the colour code for the carbon resistors gives their accurate values, the colour code for the carbon resistor, used as Rs, would be-
A) Brown, Blue, Brown done clear
B) Grey, Black, Brown done clear
C) Red, Green, Brown done clear
D) Brown, Blue, Black done clear
View Answer play_arrowquestion_answer25) The actual value of resistance R, shown in the figure is \[30\,\Omega \]. This is measured in an experiment as shown using the standard formula \[R=\frac{V}{I}\] where V and I are the readings of the voltmeter and ammeter, respectively. If the measured value of R is \[5%\] less, then the internal resistance of the voltmeter is-
A) 570 \[\Omega \] done clear
B) 600 \[\Omega \] done clear
C) 350 \[\Omega \] done clear
D) 35 \[\Omega \] done clear
View Answer play_arrowquestion_answer26) An unknown metal of mass 192 g heated to a temperature of \[100{}^\circ C\] was immersed into a brass calorimeter of mass 128 g containing 240 g of water at a temperature of \[8.4{}^\circ \,C\]. Calculate the specific heat of the unknown metal if water temperature stabilizes at \[21.5{}^\circ C\]. (Specific heat of brass is \[394\text{ }J\text{ }k{{g}^{-1}}{{K}^{-1}}\])
A) 458 J \[394\text{ }J\text{ }k{{g}^{-1}}{{K}^{-1}}\] done clear
B) 1232 J \[394\text{ }J\text{ }k{{g}^{-1}}{{K}^{-1}}\] done clear
C) 654 J \[394\text{ }J\text{ }k{{g}^{-1}}{{K}^{-1}}\] done clear
D) 916 J \[394\text{ }J\text{ }k{{g}^{-1}}{{K}^{-1}}\] done clear
View Answer play_arrowquestion_answer27) A particle which is experiencing a force, given by \[\overrightarrow{F}=3\overrightarrow{i}-12\overrightarrow{j}\], undergoes a displacement of \[\overrightarrow{d}=4\overrightarrow{i}\] . If particle had a kinetic energy of 3 J at the beginning of the displacement what is its kinetic energy at the end of the displacement?
A) 9 J done clear
B) 10 J done clear
C) 12 J done clear
D) 15 J done clear
View Answer play_arrowquestion_answer28) A particle executes simple harmonic motion with an amplitude of 5 cm. When the particle is at 4 cm from the mean position, the magnitude of its velocity in SI units is equal to that of its acceleration. Then, its periodic time in seconds is-
A) \[\frac{4\pi }{3}\] done clear
B) \[\frac{3\,}{8}\pi \] done clear
C) \[\frac{7\,}{3}\pi \] done clear
D) \[\frac{8\,\pi }{3}\] done clear
View Answer play_arrowquestion_answer29) Two identical spherical balls of mass M and radius R each are stuck on two ends of a rod of length 2R and mass M (see figure). The moment of inertia of the system about the axis passing perpendicularly through the centre of the rod is:
A) \[\frac{17}{15}M{{R}^{2}}\] done clear
B) \[\frac{137}{15}M{{R}^{2}}\] done clear
C) \[\frac{209}{15}M{{R}^{2}}\] done clear
D) \[\frac{152}{15}M{{R}^{2}}\] done clear
View Answer play_arrowquestion_answer30) A parallel plate capacitor having capacitance 12 pF is charged by a battery to a potential difference of 10 V between its plates. The charging battery is now disconnected and a porcelain slab of dielectric constant 6.5 is slipped between the plates. The work done by the capacitor on the slab is:
A) 508 pJ done clear
B) 692 pJ done clear
C) 560 pJ done clear
D) 600 pJ done clear
View Answer play_arrowquestion_answer31) A reaction of cobalt (III) chloride and ethylenediamine in a 1 : 2 mole ratio generates two isomeric products A (violet coloured) and B (green coloured). A can show optical activity, but B is optically inactive. What type of isomers does A and B represent?
A) Ionisation isomers done clear
B) Linkage isomers done clear
C) Coordination isomers done clear
D) Geometrical isomers done clear
View Answer play_arrowquestion_answer32) The pair that contains two \[P-H\] bonds in each of the oxoacids is:
A) \[{{H}_{3}}P{{O}_{2}}\text{ }and\text{ }{{H}_{4}}{{P}_{2}}{{O}_{5}}\] done clear
B) \[{{H}_{4}}{{P}_{2}}{{O}_{5}}\text{ }and\text{ }{{H}_{4}}{{P}_{2}}{{O}_{6}}\] done clear
C) \[{{H}_{4}}{{P}_{2}}{{O}_{5}}\,and\,{{H}_{3}}P{{O}_{3}}\] done clear
D) \[{{H}_{3}}P{{O}_{3}}\] and \[{{H}_{3}}P{{O}_{2}}\] done clear
View Answer play_arrowquestion_answer33) In the reaction of oxalate with permanganate in acidic medium, the number of electrons involved in producing one molecule of \[C{{O}_{2}}\] is:
A) 10 done clear
B) 2 done clear
C) 1 done clear
D) 5 done clear
View Answer play_arrowquestion_answer34) The reaction that is NOT involved in the ozone layer depletion mechanism in the stratosphere is:
A) \[Cl\overset{\bullet }{\mathop{O}}\,(g)+O(g)\,\,\to \,\,\overset{\bullet }{\mathop{Cl}}\,(g)+{{O}_{2}}(g)\] done clear
B) \[C{{F}_{2}}C{{l}_{2}}(g)\,\,\,\xrightarrow{uv}\,\,\overset{\bullet }{\mathop{Cl}}\,(g)+\overset{\bullet }{\mathop{C}}\,{{F}_{2}}Cl(g)\] done clear
C) \[\,C{{H}_{4}}+2{{O}_{3}}\to 3C{{H}_{2}}=O+3\,\,{{H}_{2}}O\] done clear
D) \[HOCl(g)\xrightarrow{hv}\,\,\overset{\bullet }{\mathop{OH}}\,\,(g)+\overset{\bullet }{\mathop{Cl\,}}\,(g)\] done clear
View Answer play_arrowquestion_answer35) An aromatic compound 'A' having molecular formula \[{{C}_{7}}{{H}_{6}}{{O}_{2}}\] on treating with aqueous ammonia and heating forms compound 'B'. The compound 'B' on reaction with molecular bromine and potassium hydroxide provides compound 'C' having molecular formula\[{{C}_{6}}{{H}_{7}}N\]. The structure of 'A' is:
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer36) For an elementary chemical reaction; \[{{A}_{2}}\,\,2{{A}_{1}}\], the expression for \[\frac{d[A]}{dt}\] is
A) \[2{{K}_{1}}\left[ {{A}_{2}} \right]-{{K}_{-1}}{{[A]}^{2}}\] done clear
B) \[{{K}_{1}}\left[ {{A}_{2}} \right]-{{K}_{-1}}{{[A]}^{2}}\] done clear
C) \[{{K}_{1}}\left[ {{A}_{2}} \right]+{{K}_{-1}}{{[A]}^{2}}\] done clear
D) \[2{{K}_{1}}\left[ {{A}_{2}} \right]-2{{K}_{-1}}{{[A]}^{2}}\] done clear
View Answer play_arrowquestion_answer37) The electrolytes usually used in the electroplating of gold and silver, respectively are:
A) \[{{\left[ Au{{\left( CN \right)}_{2}} \right]}^{-}}and\text{ }{{\left[ Ag{{\left( CN \right)}_{2}} \right]}^{-}}\] done clear
B) \[{{\left[ Au{{\left( CN \right)}_{2}} \right]}^{-}}and\text{ }{{\left[ Ag{{\left( Cl \right)}_{2}} \right]}^{-}}\] done clear
C) \[{{\left[ Au{{\left( OH \right)}_{4}} \right]}^{-}}and\text{ }{{\left[ Ag{{\left( OH \right)}_{2}} \right]}^{-}}\] done clear
D) \[{{[Au{{(N{{H}_{3}})}_{2}}]}^{+}}\,and\,\,{{[Ag{{(CN)}_{2}}]}^{-}}\] done clear
View Answer play_arrowquestion_answer38) Among the following reactions of hydrogen with halogens, the one that requires a catalyst is
A) \[{{H}_{2}}+B{{r}_{2}}\to 2HBr\] done clear
B) \[{{H}_{2}}+C{{l}_{2}}\to 2HCl\] done clear
C) \[{{H}_{2}}+{{F}_{2}}\to 2HF\] done clear
D) \[{{H}_{2}}+{{I}_{2}}\to 2HI\] done clear
View Answer play_arrowquestion_answer39) The major product of the following reaction is
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer40) What is the IUPAC name of the following compound?
A) 4-Bromo-3-methylpent-2-ene done clear
B) 3-Bromo 1, 2-dimethylbut-1-ene done clear
C) 3-Bromo-3-methyl-1, 2-dimethylprop-1-ene done clear
D) 2-Bromo-3-methylpent-3-ene done clear
View Answer play_arrowquestion_answer41) A compound of formula \[{{A}_{2}}{{B}_{3}}\] has the hcp lattice. Which atom forms the hcp lattice and what fraction of tetrahedral voids is occupied by the other atoms:
A) hcp lattice - A, \[\frac{1}{3}\] Tetrahedral voids - B done clear
B) hcp lattice - B, \[\frac{1}{3}\] Tetrahedral voids - A done clear
C) hcp lattice - A, \[\frac{2}{3}\] Tetrahedral voids - B done clear
D) hcp lattice -B, \[\frac{2}{3}\] Tetrahedral voids - A done clear
View Answer play_arrowquestion_answer42) Sodium metal on dissolution in liquid ammonia gives a deep blue solution due to the formation of:
A) ammoniated electrons done clear
B) sodamide done clear
C) sodium-ammonia complex done clear
D) sodium ion-ammonia complex done clear
View Answer play_arrowquestion_answer43) Which of the following- test cannot be used for identifying amino acids?
A) Ninhydrin test done clear
B) Barfoed lest done clear
C) Xanthoproteic test done clear
D) Biuret test done clear
View Answer play_arrowquestion_answer44) What will be the major product in the following mononitration reaction?
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer45) The difference in the number of unpaired electrons of a metal ion in its high spin and low-spin octahedral complexes is two. The metal ion is
A) \[M{{n}^{2+}}\] done clear
B) \[N{{i}^{2}}^{+}\] done clear
C) \[C{{o}^{2+}}\] done clear
D) \[F{{e}^{2}}^{+}\] done clear
View Answer play_arrowquestion_answer46) The ground state energy of hydrogen atom is- 13.6 eV. The energy of second excited state of \[H{{e}^{+}}\] ion in eV is:
A) - 6.04 done clear
B) - 54.4 done clear
C) - 27.2 done clear
D) - 3.4 done clear
View Answer play_arrowquestion_answer47) The 71st electron of an element X with an atomic number of 71 enters into the orbital;
A) 4f done clear
B) 6s done clear
C) 6p done clear
D) 5d done clear
View Answer play_arrowquestion_answer48) The major product of the following reaction
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer49) The major product obtained in the following reaction is:
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer50) In the cell \[Pt\left| \,\left( s \right)\, \right|{{H}_{2}}\](g, 1 bar) \[\left| \text{ }HCl\left( aq \right)\text{ } \right|\] \[AgCl\left| \,\left( s \right)\, \right|\,Ag\left( s \right)|Pt\left( s \right)\] the cell potential is 0.92 V when a \[{{10}^{-}}^{6}\] molal HCl solution is used. The standard electrode potential of \[\left( AgCl/Ag,C{{l}^{-}} \right)\] electrode is: {Given, \[\frac{2.303RT}{F}\,=\,0.06V\,at\,\,298\,K\]
A) 0.94 V done clear
B) 0.40V done clear
C) 0.76 V done clear
D) 0.20 V done clear
View Answer play_arrowquestion_answer51) Which is the most suitable reagent for the following transformation?
A) alkaline\[KMn{{O}_{4}}\] done clear
B) Tollen's neagent done clear
C) \[{{I}_{2}}/NaOH\] done clear
D) \[Cr{{O}_{2}}C{{l}_{2}}/C{{S}_{2}}\] done clear
View Answer play_arrowquestion_answer52) The process with negative entropy change is
A) Dissociation of\[CaS{{O}_{4}}\], (s) to CaO(s) and \[S{{O}_{3}}\](g) done clear
B) Dissolution of iodine in water done clear
C) Synthesis of ammonia from N2 and H2 done clear
D) Sublimation of dry ice done clear
View Answer play_arrowquestion_answer53) Elevation in the boiling point for 1 molar solution of glucose is 2 K. The depression in the freezing point for 2 molar solution of glucose in the same solvent is 2 K. The relation between \[{{K}_{b}}\] and \[{{K}_{f}}\] is:
A) \[{{K}_{b}}={{K}_{f}}\] done clear
B) \[{{K}_{b}}\,=0.5\,\,{{K}_{f}}\] done clear
C) \[{{K}_{b}}\,=\,1.5\,{{K}_{f}}\] done clear
D) \[{{K}_{b}}=2\,\,{{K}_{f}}\] done clear
View Answer play_arrowquestion_answer54) The amount of sugar \[\left( {{C}_{12}}{{H}_{22}}{{O}_{11}} \right)\] required to prepare 2L of its 0.1 M aqueous solution is:
A) 17.1 g done clear
B) 34.2 g done clear
C) 68.4 g done clear
D) 136.8 g done clear
View Answer play_arrowquestion_answer55) The correct match between item - I and item - II is:
Item - I (compound) | Item - II (reagent) |
(A) Lysine | (P) 1-naphthol |
(B) Furfural | (Q) ninhydrin |
(C) Benzylalcohol | (R) \[KMn{{O}_{4}}\] |
(D) Styrene | (S) Ceric ammonium nitate |
A) [A] \[\to \] (Q); [B] \[\to \] (R); [C] \[\to \] (S); [D] \[\to \] (P) done clear
B) [A] \[\to \] (Q); [B] \[\to \] (P); [C] \[\to \] (S); [D] \[\to \] (R) done clear
C) [A] \[\to \] (R); [B] \[\to \] (P); [C] \[\to \] (Q); [D] \[\to \] (S) done clear
D) [A] \[\to \] (Q); [B] \[\to \] (P); [C] \[\to \] (R); [D] \[\to \] (S) done clear
View Answer play_arrowquestion_answer56) An ideal gas undergoes isothermal compression from \[5{{m}^{3}}\] to \[1\text{ }{{m}^{3}}\] against a constant external pressure of \[4\text{ }N{{m}^{-}}^{2}\]. Heat released in this process is used to increase the temperature of 1 mole of Al. If molar heat capacity of Al is 24 J \[mo{{l}^{-1}}\text{ }{{K}^{-1}}\], the temperature of Al increases by:
A) \[\frac{2}{3}\]K done clear
B) \[\frac{3}{2}\]K done clear
C) 1 K done clear
D) 2 K done clear
View Answer play_arrowquestion_answer57) The major product of the following reaction is:
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer58) The number of 2-centre-2-electron and 3- centre -2-electron bonds in \[{{B}_{2}}{{H}_{6}}\], respectively are:
A) 2 and 2 done clear
B) 2 and 1 done clear
C) 2 and 4 done clear
D) 4 and 2 done clear
View Answer play_arrowquestion_answer59) Haemoglobin and gold sol are examples of:
A) positively charged sols done clear
B) negatively charged sols done clear
C) Positively and negatively charged sols, respectively done clear
D) negatively and positively charged sols, respectively done clear
View Answer play_arrowquestion_answer60) 5.1 g \[N{{H}_{4}}SH\] is introduced in 3.0 L evacuated flask at \[327{}^\circ C\]. 30% of the solid \[N{{H}_{4}}SH\] decomposed to \[N{{H}_{3}}\] and \[{{H}_{2}}S\] as gases. The \[{{K}_{p}}\] of the reaction at \[327{}^\circ C\] is (\[R=0.082\] L atm \[mo{{l}^{-1}}\text{ }{{K}^{-}}^{1}\], Molar mass of \[S=32\] g \[mo{{l}^{-}}^{1}\] molar mass of \[N=14\,g\text{ }mo{{l}^{-1}}\])
A) \[0.242\times {{10}^{-4}}\text{ }at{{m}^{2}}\] done clear
B) \[1\times {{10}^{-4}}\text{ }at{{m}^{2}}\] done clear
C) \[4.9\times {{10}^{-3}}\text{ }at{{m}^{2}}\] done clear
D) \[0.242\text{ }at{{m}^{2}}\] done clear
View Answer play_arrowquestion_answer61) The length of the chord of the parabola \[{{x}^{2}}=4y\] having equation \[x-\sqrt{2}y+4\sqrt{2}=0\] is-
A) \[8\sqrt{2}\] done clear
B) \[6\sqrt{3}\] done clear
C) \[3\sqrt{2}\] done clear
D) \[2\sqrt{11}\] done clear
View Answer play_arrowquestion_answer62) Let N be the set of natural numbers and two functions f and g be defined as \[f,\text{ }g\text{ }:\text{ }N\to N\] such that \[f(n)\,=\,\left\{ \begin{matrix} \frac{n+1}{2} \\ \frac{n}{2} \\ \end{matrix} \right.\,\,\,\begin{matrix} ;\,\,\,\,if\,\,n\,\,is\,\,odd \\ ;\,\,if\,\,n\,\,is\,\,given \\ \end{matrix}\,\,\,\,;\,\,and\]\[g\left( n \right)=n-{{\left( -1 \right)}^{n}}\] . Then fog is
A) neither one-one nor onto done clear
B) onto but not one-one done clear
C) both one-one and onto done clear
D) one-one but not onto done clear
View Answer play_arrowquestion_answer63) Two sides of a parallelogram are along the lines,\[x+y=3\,\,\,\And \,\,x-y+3=0\]. If its diagonals intersect at (2, 4), then one of its vertex is-
A) (2, 1) done clear
B) (2, 6) done clear
C) (3, 5) done clear
D) (3, 6) done clear
View Answer play_arrowquestion_answer64) If mean and standard deviation of 5 observations \[{{x}_{1}},\text{ }{{x}_{2}},\text{ }{{x}_{3}},\text{ }{{x}_{4}},\text{ }{{x}_{5}}\] are 10 and 3 respectively, then the variance of 6 observations \[{{x}_{1}},\text{ }{{x}_{2}},\text{ }......\text{ }{{x}_{5}}\] and - 50 is equal to
A) 582.5 done clear
B) 507.5 done clear
C) 586.5 done clear
D) 509.5 done clear
View Answer play_arrowquestion_answer65) The value of cot \[\left( \sum\limits_{n\,=\,1}^{19}{{{\cot }^{-1}}}\left( 1+\sum\limits_{p\,=\,1}^{n}{2\,p} \right) \right)\]is -
A) \[\frac{22}{23}\] done clear
B) \[\frac{23}{22}\] done clear
C) \[\frac{21}{19}\] done clear
D) \[\frac{19}{21}\] done clear
View Answer play_arrowquestion_answer66) The value of\[cos\frac{\pi }{{{2}^{2}}}.\,cos\frac{\pi }{{{2}^{3}}}\,\,......\,cos\,\frac{\pi }{{{2}^{10}}}.\,sin\,\frac{\pi }{{{2}^{10}}}\] is-
A) \[\frac{1}{256}\] done clear
B) \[\frac{1}{2}\] done clear
C) \[\frac{1}{1024}\] done clear
D) \[\frac{1}{512}\] done clear
View Answer play_arrowquestion_answer67) If \[\sum\limits_{r\,=\,0}^{25}{{{\{}^{50}}{{C}_{r}}{{.}^{50\,-\,r}}{{C}_{25\,-\,r}}\}\,=\,K{{(}^{50}}{{C}_{25}})}\] then K is equal to
A) \[{{2}^{24}}\] done clear
B) \[{{2}^{25}}-1\] done clear
C) \[{{2}^{25}}\] done clear
D) \[{{\left( 25 \right)}^{2}}\] done clear
View Answer play_arrowquestion_answer68) Let \[{{a}_{1}},\text{ }{{a}_{2}},{{a}_{3}},.....\text{ }{{a}_{10}}\] be in G.P. with \[{{a}_{i}}>0\] for \[i=1,\text{ }2,\text{ }......10\] and S be the set of pairs (r, k), r, k e N (the set of natural numbers) for which
\[\left| \begin{matrix} {{\log }_{e}}\,{{a}_{1}}{{\,}^{r}}{{a}_{2}}^{k} & {{\log }_{e}}\,{{a}_{2}}{{\,}^{r}}{{a}_{3}}^{k} & {{\log }_{e}}\,{{a}_{3}}{{\,}^{r}}{{a}_{4}}^{k} \\ {{\log }_{e}}\,{{a}_{4}}{{\,}^{r}}{{a}_{5}}^{k} & {{\log }_{e}}\,{{a}_{5}}{{\,}^{r}}{{a}_{6}}^{k} & {{\log }_{e}}\,{{a}_{6}}{{\,}^{r}}{{a}_{7}}^{k} \\ {{\log }_{e}}\,{{a}_{7}}{{\,}^{r}}{{a}_{8}}^{k} & {{\log }_{e}}\,{{a}_{8}}{{\,}^{r}}{{a}_{9}}^{k} & {{\log }_{e}}\,{{a}_{9}}{{\,}^{r}}{{a}_{10}}^{k} \\ \end{matrix} \right|=0\] |
Then the number of elements in S, is - |
A) 10 done clear
B) 4 done clear
C) 2 done clear
D) infinitely many done clear
View Answer play_arrowquestion_answer69) Two vertices of a triangle are (0, 2) and (4, 3). If its orthocenter is at the origin, then its third vertex lies in which quadrant-
A) third done clear
B) fourth done clear
C) second done clear
D) first done clear
View Answer play_arrowquestion_answer70) If the probability of hitting a target by a shooter, in any shot, is \[\frac{1}{3}\], then the minimum number of independent shots at the target required by him so that the probability of hitting the target at least once is greater than \[\frac{5}{6}\], is-
A) 4 done clear
B) 6 done clear
C) 5 done clear
D) 3 done clear
View Answer play_arrowquestion_answer71) The tangent to the curve, \[y=x{{e}^{{{x}^{2}}}}\]passing through the point (1, e) also passes through the point
A) \[\left( \frac{4}{3},\,\,\,2e \right)\] done clear
B) \[\left( 3,\,\,\,6e \right)\] done clear
C) \[\left( 2,\,\,3e \right)\] done clear
D) \[\left( \frac{5}{3},\,\,2e \right)\] done clear
View Answer play_arrowquestion_answer72) The value of \[\int\limits_{-\pi /2}^{\pi /2}{\frac{dx}{[x]+[sin\,x]+4}}\] where [t] denotes the greatest integer less than or equal to t, is-
A) \[\frac{1}{12}(7\pi -5)\] done clear
B) \[\frac{1}{12}(7\pi +5)\] done clear
C) \[\frac{3}{10}(4\pi -3)\] done clear
D) \[\frac{3}{20}(4\pi -3)\] done clear
View Answer play_arrowquestion_answer73) Let \[S=\,\left\{ (x,\,\,y)\,\in \,\,{{R}^{2}}:\frac{{{y}^{2}}}{1+r}-\frac{{{x}^{2}}}{1-r}=1 \right\};\,r\ne \pm 1\]Then S represents
A) an ellipse whose eccentricity is \[\frac{1}{\sqrt{r}+1}\] where \[r>1\] done clear
B) a hyperbola whose eccentricity is \[\frac{2}{\sqrt{r+1}}\], when \[0<r<1\] done clear
C) a hyperbola whose eccentricity is \[\frac{2}{\sqrt{1-r}}\]when \[0<r<1\] done clear
D) an ellipse whose eccentricity is \[\sqrt{\frac{2}{r+1}}\] when \[r>1\] done clear
View Answer play_arrowquestion_answer74) If \[\int\limits_{0}^{x}{f(t)\,dt\,\,=\,\,{{x}^{2}}+}\int\limits_{x}^{1}{{{t}^{2}}f(t)\,\,dt\,\,then\,\,f\,\,'\left( \frac{1}{2} \right)}\] is-
A) \[\frac{18}{25}\] done clear
B) \[\frac{6}{25}\] done clear
C) \[\frac{24}{25}\] done clear
D) \[\frac{4}{5}\] done clear
View Answer play_arrowquestion_answer75) Let \[A=\left[ \begin{matrix} 2 & b & 1 \\ b & {{b}^{2}}+1 & b \\ 1 & b & 2 \\ \end{matrix} \right]\] where\[b>0\]. Then the minimum value of \[\frac{\det (A)}{b}\]is-
A) \[\sqrt{3}\] done clear
B) \[-2\sqrt{3}\] done clear
C) \[-\sqrt{3}\] done clear
D) \[2\sqrt{3}\] done clear
View Answer play_arrowquestion_answer76) With the usual notation, in \[\Delta \,ABC\], if \[\angle A+\angle B=120{}^\circ \], \[a=\sqrt{3}+1\,\,and\,\,b=\sqrt{3}-1\], then the ratio \[\angle A:\angle B\], is-
A) 9 : 7 done clear
B) 7 : 1 done clear
C) 5 : 3 done clear
D) 3 : 1 done clear
View Answer play_arrowquestion_answer77) The value of \[\lambda \]. such that sum of the squares of the roots of the quadratic equation, \[{{x}^{2}}+(3-\lambda )x+2=\lambda \] has the least value is-
A) 1 done clear
B) 2 done clear
C) \[\frac{15}{8}\] done clear
D) \[\frac{4}{9}\] done clear
View Answer play_arrowquestion_answer78) On which of the following lines lies the point of intersection of the line, \[\frac{x-4}{2}=\frac{y-5}{2}=\frac{z-3}{1}\] and the plane,\[x+y+z=2\]?
A) \[\frac{x-4}{1}=\frac{y-5}{1}=\frac{z-5}{-1}\] done clear
B) \[\frac{x-2}{2}=\frac{y-3}{2}=\frac{z+3}{3}\] done clear
C) \[\frac{x-1}{1}=\frac{y-3}{2}=\frac{z+4}{-5}\] done clear
D) \[\frac{x+3}{3}=\frac{4-y}{3}=\frac{z+1}{-\,2}\] done clear
View Answer play_arrowquestion_answer79) The positive value of \[\lambda \] for which the co-efficient of \[{{x}^{2}}\] in the expression \[{{x}^{2}}{{\left( \sqrt{x}+\frac{\lambda }{{{x}^{2}}} \right)}^{10}}\]is 720, is-
A) 4 done clear
B) \[2\sqrt{2}\] done clear
C) 3 done clear
D) \[\sqrt{5}\] done clear
View Answer play_arrowquestion_answer80) Let \[z={{\left( \frac{\sqrt{3}}{2}+\frac{i}{2} \right)}^{5}}\,+\,{{\left( \frac{\sqrt{3}}{2}-\frac{i}{2} \right)}^{5}}\]. If R(z) and I(z) respectively denote the real and imaginary parts of z, then-
A) \[R\left( z \right)=-3\] done clear
B) \[R\left( z \right)<0\text{ }and\text{ }I\left( z \right)>0\] done clear
C) \[I\left( z \right)=0\] done clear
D) \[R\left( z \right)>0\text{ }and\text{ }I\left( z \right)>0\] done clear
View Answer play_arrowquestion_answer81) The number of values of \[\theta \,\in (0,\,\,\,\pi )\] for which the system of linear equations
\[x+3y+7z=0\] \[-x+4y+7z=0\] \[\left( sin3\theta \right)x+\left( cos2\theta \right)y+2z=0\] |
has a non-trivial solution, is- |
A) two done clear
B) one done clear
C) four done clear
D) three done clear
View Answer play_arrowquestion_answer82) The curve amongst the family of curves represented by the differential equation, \[({{x}^{2}}-{{y}^{2}})dx+2xy\,\,\,dy=0\] which passes through (1, 1) is
A) a circle with centre on the y-axis done clear
B) an ellipse with major axis along the y-axis done clear
C) a circle with centre on the x-axis done clear
D) a hyperbola with transverse axis along the x-axis done clear
View Answer play_arrowquestion_answer83) Let \[f:\left( -1,\text{ }\,1 \right)\to R\] be a function defined by\[f(x)=max\left\{ -|x|-\sqrt{1-{{x}^{2}}} \right\}\]. If K be the set of all points at which f is not differentiable then K has exactly-
A) one element done clear
B) three elements done clear
C) five elements done clear
D) two elements done clear
View Answer play_arrowquestion_answer84) Consider the following three statements:
P : 5 is a prime number |
Q : 7 is a factor of 192 |
R : L.C.M. of 5 and 7 is 35 |
A) \[(P\wedge Q)\vee (\sim R)\] done clear
B) \[P\vee (\sim Q\wedge R)\] done clear
C) \[(\sim P)\wedge (\sim Q\wedge R)\] done clear
D) \[\left( \sim P \right)\vee \left( Q\wedge R \right)\] done clear
View Answer play_arrowquestion_answer85) Let f be a differentiable function such that \[f'(x)\,=\,7-\frac{3}{4}\,\frac{f(x)}{x},\,\,(x>0)\] and\[f(1)\,\ne \,4\]. Then \[\underset{x\to {{0}^{+}}}{\mathop{\lim }}\,\,xf\left( \frac{1}{x} \right)\,\]
A) does not exist done clear
B) exists and equals \[\frac{4}{7}\] done clear
C) exists and equals 4 done clear
D) exists and equals 0 done clear
View Answer play_arrowquestion_answer86) If \[\overrightarrow{\alpha }=(\lambda -2)\overrightarrow{a}+\overrightarrow{b}\,\,and\,\,\overrightarrow{\beta }=(4\lambda -2)\overrightarrow{a}+3\overrightarrow{b}\] be two given vectors where vectors \[\overrightarrow{a}\] and \[\overrightarrow{b}\] are non-collinear. The value of \[\lambda \] which vectors \[\overrightarrow{a}\] and \[\overrightarrow{b}\] are collinear, is-
A) 4 done clear
B) 3 done clear
C) - 3 done clear
D) - 4 done clear
View Answer play_arrowquestion_answer87) The plane which bisects the line segment joining the points (-3, -3, 4) and (3, 7, 6) at right angles, passes through which one of the following points?
A) (2, 1, 3) done clear
B) (4, -1, 2) done clear
C) (4, 1, -2) done clear
D) (-2, 3, 5) done clear
View Answer play_arrowquestion_answer88) If the area of an equilateral triangle inscribed in the circle \[{{x}^{2}}+{{y}^{2}}+10x+12y+c=0\] is \[27\sqrt{3}\] sq units then c is equal to
A) 20 done clear
B) 25 done clear
C) -25 done clear
D) 13 done clear
View Answer play_arrowquestion_answer89) If \[\int{{{x}^{5}}.\,{{e}^{-}}^{4{{x}^{3}}}dx=\frac{1}{48}{{e}^{-4{{x}^{3}}}}\,f(x)+C}\], where C is a constant of integration, then f(x) is equal to-
A) \[-2{{x}^{3}}-1\] done clear
B) \[-\text{ }2{{x}^{3}}+1\] done clear
C) \[4{{x}^{3}}+1\] done clear
D) \[-\,4{{x}^{3}}-1\] done clear
View Answer play_arrowquestion_answer90) A helicopter is flying along the curve given by\[y-{{x}^{3/2}}\,=7,\,\,(x\ge 0)\,\]. A soldier positioned at the point \[\left( \frac{1}{2},\,\,7 \right)\]wants to shoot down the helicopter when it is nearest to him. Then this nearest distance is:
A) \[\frac{1}{6}\,\sqrt{\frac{7}{3}}\] done clear
B) \[\frac{\sqrt{5}}{6}\] done clear
C) \[\frac{1}{2}\] done clear
D) \[\frac{1}{3}\,\sqrt{\frac{7}{3}}\] done clear
View Answer play_arrow
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