question_answer1) Two beams of light will not give rise to an interference pattern, if
A) they are coherent done clear
B) they have the same wavelength done clear
C) they are linearly polarized perpendicular to each other done clear
D) they are not monochromatic done clear
View Answer play_arrowquestion_answer2) A slit of width a is illuminated with a monochromatic light of wavelength \[\lambda \] from a distant source and the diffraction pattern is observed on a screen placed at a distance D from the slit. To increase the width of the central maximum one should
A) decrease D done clear
B) decrease \[\alpha \] done clear
C) decrease \[\lambda \] done clear
D) The width cannot be changed done clear
View Answer play_arrowquestion_answer3) A thin film of soap solution (n = 1.4) lies on the top of a glass plate (n = 1.5). When visible light is incident almost normal to the plate, two adjacent reflection maxima are observed at two wavelengths 400 and 630 nm. The minimum thickness of the soap solution is
A) 420 nm done clear
B) 450 nm done clear
C) 630 nm done clear
D) 1260 nm done clear
View Answer play_arrowquestion_answer4) If the speed of a wave doubles as it passes from shallow water into deeper water, its wavelength will be
A) unchanged done clear
B) halved done clear
C) doubled done clear
D) quadrupled done clear
View Answer play_arrowquestion_answer5) A light whose frequency is equal to 6 x 1014 Hz is incident on a metal whose work function is \[2eV\left[ h=6.63\,\times \,{{10}^{-34}}\,Js,1eV=1.6\,\times \,{{10}^{-19}}J \right]\] The maximum energy of the electrons emitted will be
A) 2.49 eV done clear
B) 4.49 eV done clear
C) 0.49 eV done clear
D) 5.49 eV done clear
View Answer play_arrowquestion_answer6) An electron microscope is used to probe the atomic arrangements to a resolution of 5 A. What should be the electric potential to which the electrons need to be accelerated?
A) 2.5V done clear
B) 5V done clear
C) 2.5 kV done clear
D) 5kV done clear
View Answer play_arrowquestion_answer7) Which phenomenon best supports the theory that matter has a wave nature?
A) Electron momentum done clear
B) Electron diffraction done clear
C) Photon momentum done clear
D) Photon diffraction done clear
View Answer play_arrowquestion_answer8) The radioactivity of a certain material drops to \[\frac{1}{16}\]of the initial value in 2 h. The half-life of this radio nuclide is
A) 10 min done clear
B) 20 min done clear
C) 30 min done clear
D) 40 min done clear
View Answer play_arrowquestion_answer9) An observer A sees an asteroid with a radioactive element moving by at a speed \[=0.3c\] and measures the radioactivity decay time to be\[{{T}_{A}}\]. Another observer B is moving with the asteroid and measures its decay time as\[{{T}_{B}}\]. Then \[{{T}_{A}}\] and \[{{T}_{B}}\] are related as
A) \[{{T}_{B}}<\text{ }{{T}_{A}}\] done clear
B) \[{{T}_{A}}={{T}_{B}}\] done clear
C) \[{{T}_{B~}}>{{T}_{A}}\] done clear
D) Either [A] or [C] depending on whether the asteroid is approaching or moving away from A done clear
View Answer play_arrowquestion_answer10) \[^{234}U\]has 92 protons and 234 nucleons total in its nucleus. It decays by emitting an alpha particle. After the decay it becomes
A) \[^{232}U\] done clear
B) \[^{232}Pa\] done clear
C) \[^{230}Th\] done clear
D) \[^{230}Ra\] done clear
View Answer play_arrowquestion_answer11) \[{{K}_{\alpha }}\,and\,{{K}_{\beta \,}}X-rays\] are emitted when there is a transition of electron between the levels
A) \[n=2\] to \[n=1\] and \[n=3\] to \[n=1\] respectively done clear
B) \[n=2\] to \[n=1\] and \[n=3\] to \[n=2\]respectively done clear
C) \[n=3\] to \[n=2\] and \[n=4\] to \[n=2\]respectively done clear
D) \[n=3\] to \[n=2\] and \[n=4\] to \[n=3\]respectively done clear
View Answer play_arrowquestion_answer12) A certain radioactive material \[_{Z}{{X}^{A}}\]starts emitting \[\alpha \] and \[\beta \] panicles successively such that the end product is \[_{Z-3}{{Y}^{A-8}}.\]. The number of \[\alpha \]and \[\beta \] particles emitted are
A) 4 and 3 respectively done clear
B) 2 and 1 respectively done clear
C) 3 and 4 respectively done clear
D) 3 and 8 respectively done clear
View Answer play_arrowquestion_answer13) In the circuit shown above, an input of 1 V is fed into the inverting input of an ideal Op-amp A. The output signal \[{{\text{V}}_{\text{out}}}\] will be
A) + 10 V done clear
B) -10 V done clear
C) 0 V done clear
D) infinity done clear
View Answer play_arrowquestion_answer14) When a solid with a band gap has a donor level just below its empty energy band, the solid is
A) an insulator done clear
B) a conductor done clear
C) p-type semiconductor done clear
D) n-type semiconductor done clear
View Answer play_arrowquestion_answer15) A \[p-n\] junction has acceptor impurity concentration of \[{{10}^{17}}\]\[c{{m}^{-3}}\]in the \[P\] side and donor impurity concentration of \[{{10}^{16}}c{{m}^{-3}}\]in the \[N\] side. What is the contact potential at the junction? (\[kT=\]thermal energy, intrinsic carrier concentration \[{{n}_{i}}1.4\times {{10}^{10}}c{{m}^{-3}}\])
A) \[\text{(}kT/e)\text{ }In\text{ }(4\times {{10}^{12}})\] done clear
B) \[\text{(}kT/e)\text{ }In\text{ }(2.5\times {{10}^{23}})\] done clear
C) \[(kT/e)\text{ }ln\text{ }({{10}^{23}})\] done clear
D) \[(kT/e)\text{ }ln\text{ }({{10}^{9}})\] done clear
View Answer play_arrowquestion_answer16) A Zener diode has a contact potential of 1 V in the absence of biasing. It undergoes Zener breakdown for an electric field of \[{{10}^{6}}\,\,V/m\] at the depletion region of \[p-n\] junction. If the width of the depletion region is 2.5 \[\mu \]m, what should be the reverse biased potential for the Zener breakdown to occur?
A) 3.5 V done clear
B) 2.5 V done clear
C) 1.5 V done clear
D) 0.5 V done clear
View Answer play_arrowquestion_answer17) In Colpitt oscillator the feedback network consists of
A) two inductors and a capacitor done clear
B) two capacitors and an inductor done clear
C) three pairs of RC circuit done clear
D) three pairs of RL circuit done clear
View Answer play_arrowquestion_answer18) The reverse saturation of\[p-n\]diode
A) depends on doping concentrations done clear
B) depends on diffusion lengths of carriers done clear
C) depends on the doping concentrations and diffusion lengths done clear
D) depends on the doping concentrations, diffusion length and device temperature done clear
View Answer play_arrowquestion_answer19) A radio station has two channels. One is AM at \[\text{1020 kHz}\]and the other FM at 89.5 MHz. For good results you will use
A) longer antenna for the AM channel and shorter for the FM done clear
B) shorter antenna for the AM channel and longer for the FM done clear
C) Same length antenna will work for both done clear
D) Information given is not enough to say which one to use for which done clear
View Answer play_arrowquestion_answer20) The communication using optical fibres is based on the principle of
A) total internal reflection done clear
B) Brewster angle done clear
C) polarization done clear
D) resonance done clear
View Answer play_arrowquestion_answer21) In nature, the electric charge of any system is always equal to
A) half integral multiple of the least amount of charge done clear
B) zero done clear
C) square of the least amount of charge done clear
D) integral multiple of the least amount of charge. done clear
View Answer play_arrowquestion_answer22) The energy stored in the capacitor as shown in Fig. [a] is \[\text{4}\text{.5}\times \text{1}{{\text{0}}^{\text{-6}}}\text{J}\]. If the battery is replaced by another capacitor of 900 pF as shown in Fig. [b], then the total energy of system is
A) \[4.5\times {{10}^{-6}}J\] done clear
B) \[\text{2}\text{.25}\times \text{1}{{\text{0}}^{\text{-6}}}\text{J}\] done clear
C) zero done clear
D) \[\text{9}\times \text{1}{{\text{0}}^{\text{-6}}}\text{J}\] done clear
View Answer play_arrowquestion_answer23) Equal amounts of a metal are converted into cylindrical wires of different lengths L and cross-sectional area A. The wire with the maximum resistance is the one, which has
A) length \[=\text{ }L\] and area \[=\text{ }A\] done clear
B) length = \[\frac{L}{2}\] and area \[=\text{ }2A\] done clear
C) length \[=\text{ }2L\] and area = \[\frac{A}{2}\] done clear
D) All have the same resistance, as the amount of the metal is the same done clear
View Answer play_arrowquestion_answer24) If the force exerted by an electric dipole on a charge \[q\] at a distance of 1 m is \[F\], the force at a point 2 m away in the same direction will be
A) \[\frac{F}{2}\] done clear
B) \[\frac{F}{4}\] done clear
C) \[\frac{F}{6}\] done clear
D) \[\frac{F}{8}\] done clear
View Answer play_arrowquestion_answer25) A solid sphere of radius\[{{R}_{1}}\] and volume charge density \[\rho =\frac{{{\rho }_{0}}}{r}\]is enclosed by a hollow sphere of radius \[{{R}_{2}}\]with negative surface charge density \[\alpha \], such that the total charge in the system is zero, \[{{\rho }_{0}}\]is a positive constant and \[r\] is the distance from the centre of the sphere. The ratio \[\frac{{{R}_{2}}}{{{R}_{1}}}\]is
A) \[\frac{\sigma }{{{\rho }_{0}}}\] done clear
B) \[\sqrt{2\sigma /{{\rho }_{0}}}\] done clear
C) \[\sqrt{{{\rho }_{0}}/(2\sigma )}\] done clear
D) \[\frac{{{\rho }_{0}}}{\sigma }\] done clear
View Answer play_arrowquestion_answer26) A solid spherical conductor of radius R has a spherical cavity of radius \[a\left( a<R \right)\] at its centre. A charge \[+Q\] is kept at the centre. The charge at the inner surface, outer surface and at a position \[r\left( a<r<R \right)\] are respectively
A) \[+Q\],\[-Q\], \[0\] done clear
B) \[Q\], \[+Q\], \[0\] done clear
C) \[0\],\[-Q\], \[0\] done clear
D) \[+Q\], \[0\], \[0\] done clear
View Answer play_arrowquestion_answer27) A cylindrical capacitor has charge Q and length L. If both the charge and length of the capacitors are doubled, by keeping other parameters fixed, the energy stored in the capacitor
A) remains same done clear
B) increases two times done clear
C) decreases two times done clear
D) increases four times done clear
View Answer play_arrowquestion_answer28) Three resistances of 4\[\Omega \] each are connected as shown in figure. If the point D divides the resistance into two equal halves, the resistance between point A and D will be
A) \[12\Omega \] done clear
B) \[6\Omega \] done clear
C) \[3\Omega \] done clear
D) \[\frac{1}{3}\Omega \] done clear
View Answer play_arrowquestion_answer29) The resistance of a metal increases with increasing temperature because
A) the collisions of the conducting electrons with the electrons increase done clear
B) the collisions of the conducting electrons with the lattice consisting of the ions of the metal increase done clear
C) the number of conduction electrons decrease done clear
D) the number of conduction electrons increase done clear
View Answer play_arrowquestion_answer30) In the absence of applied potential, the electric current flowing through a metallic wire is zero because
A) the electrons remain stationary done clear
B) the electrons are drifted in random direction with a speed of the order of \[{{10}^{-2}}cm/s\] done clear
C) the electrons move in random direction with a speed of the order close to that of velocity of light done clear
D) electrons and ions move in opposite direction done clear
View Answer play_arrowquestion_answer31) A meter bridge is used to determine the resistance of an unknown wire by measuring the balance point length l. If the wire is replaced by another wire of same material but with double the length and half the thickness, the balancing point is expected to be
A) \[\frac{1}{8l}\] done clear
B) \[\frac{1}{4l}\] done clear
C) \[8l\] done clear
D) \[16l\] done clear
View Answer play_arrowquestion_answer32) Identify the incorrect statement regarding a superconducting wire
A) transport current flows through its surface done clear
B) transport current flows through the entire area of cross-section of the wire done clear
C) it exhibits zero electrical resistivity and expels applied magnetic field done clear
D) it is used to produce large magnetic field done clear
View Answer play_arrowquestion_answer33) A sample of \[\text{HCl}\] gas is placed in an electric field of \[3\times {{10}^{4}}\text{N}{{\text{C}}^{\text{-1}}}\]. The dipole moment of each\[\text{HCl}\]molecule is \[6\times {{10}^{-30}}\text{Cm}\]. The maximum torque that can act on a molecule is
A) \[2\times {{10}^{-34}}{{\text{C}}^{\text{2}}}\text{m}{{\text{N}}^{\text{-1}}}\] done clear
B) \[2\times {{10}^{-34}}\text{Nm}\] done clear
C) \[18\times {{10}^{-34}}\text{Nm}\] done clear
D) \[0.5\times {{10}^{34}}{{\text{C}}^{\text{-2}}}\text{N}{{\text{m}}^{\text{-1}}}\] done clear
View Answer play_arrowquestion_answer34) When a metallic plate swings between the poles of a magnet
A) no effect on the plate done clear
B) eddy currents are set up inside the plate and the direction of the current is alone the motion of the plate done clear
C) eddy currents are set up inside the plate and the direction of the current oppose the motion of the plate done clear
D) eddy currents are set up inside the plate done clear
View Answer play_arrowquestion_answer35) When an electrical appliance is switched on, it responds almost immediately, because
A) the electrons in the connecting wires move with the speed of light done clear
B) the electrical signal is carried by electromagnetic waves moving with the speed of light done clear
C) the electrons move with the speed which is close to but less than speed of light done clear
D) the electrons are stagnant done clear
View Answer play_arrowquestion_answer36) Two identical incandescent light bulbs are connected as shown in the figure. When the circuit is an AC voltage source of frequency \[f\], which of the following observations will be correct?
A) Both bulbs will glow alternatively done clear
B) Both bulbs will glow with same brightness provided frequency \[f=\frac{1}{2\pi }\sqrt{1/LC}\] done clear
C) Bulb \[{{b}_{1}}\]will light up initially and goes off, bulbs \[{{b}_{2}}\]will be constantly done clear
D) Bulb \[{{b}_{1}}\] will blink and bulb \[{{b}_{2}}\] will be ON constantly done clear
View Answer play_arrowquestion_answer37) A transformer rated at 10 kW is used to connect a 5 kV transmission line to a 240 V circuit. The ratio of turns in the windings of the transformer is
A) 5 done clear
B) 20.8 done clear
C) 104 done clear
D) 40 done clear
View Answer play_arrowquestion_answer38) Three solenoid coils of same dimension, same number of turns and same number of layers of winding are taken. Coil 1 with inductance \[{{L}_{1}}\] was wound using a Mn wire of resistance 11\[\Omega /m;\]Coil 3 with inductance \[{{L}_{3}}\] was wound using the similar wire but the direction of winding was reversed in each layer; Coil 3 with inductance \[{{L}_{3}}\] was wound using a superconducting wire. The self-inductance of the coils \[{{L}_{1}}\], \[{{L}_{2}}\], \[{{L}_{3}}\] are
A) \[{{L}_{1}}={{L}_{2}}={{L}_{3}}\] done clear
B) \[{{L}_{1}}={{L}_{2}};{{L}_{3}}=0\] done clear
C) \[{{L}_{1}}={{L}^{3}};{{L}^{2}}=0~\] done clear
D) \[{{L}_{1}}>{{L}_{2}}>{{L}_{3}}\] done clear
View Answer play_arrowquestion_answer39) Light travels with a speed of \[2\times {{10}^{8}}\,m/s\] in crown glass of refractive index 1.5. What is the speed of light in dense flint glass of refractive index 1.8?
A) \[1.33\times {{10}^{8}}m/s\] done clear
B) \[1.67\times {{10}^{8}}m/s\] done clear
C) \[2.0\times {{10}^{8}}m/s\] done clear
D) \[3.0\times {{10}^{8}}m/s\] done clear
View Answer play_arrowquestion_answer40) A parallel beam of fast moving electrons is incident normally on a narrow slit. A screen is placed at a large distance from the slit. If the speed of the electrons is increased, which of the following statement is correct?
A) Diffraction pattern is not observed on the screen in the case of electrons done clear
B) The angular width of the central maximum of the diffraction pattern will increase done clear
C) The angular width of the central maximum will decrease done clear
D) The angular width of the central maximum will remains the same done clear
View Answer play_arrowquestion_answer41) \[C{{H}_{3}}C{{H}_{3}}+HN{{O}_{3}}\xrightarrow{675K}\]?
A) \[C{{H}_{3}}C{{H}_{2}}N{{O}_{2}}\] done clear
B) \[C{{H}_{3}}C{{H}_{2}}N{{O}_{2}}+C{{H}_{3}}N{{O}_{2}}\] done clear
C) \[2C{{H}_{3}}N{{O}_{2}}\] done clear
D) \[C{{H}_{2}}=C{{H}_{2}}\] done clear
View Answer play_arrowquestion_answer42) When acetamide is hydrolysed by boiling with acid, the product obtained is
A) acetic acid done clear
B) ethyl amine done clear
C) ethanol done clear
D) acetamide done clear
View Answer play_arrowquestion_answer43) Which will not go for diazotisation?
A) \[{{C}_{6}}{{H}_{5}}N{{H}_{2}}\] done clear
B) \[{{C}_{6}}{{H}_{5}}C{{H}_{2}}N{{H}_{2}}\] done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer44) Secondary nitroaikanes can be converted into ketones by using Y. Identify Y from the following
A) aqueous \[HCl\] done clear
B) aqueous \[NaOH\] done clear
C) \[KMn{{O}_{4}}\] done clear
D) \[CO\] done clear
View Answer play_arrowquestion_answer45) Alkyi cyanides undergo Stephen reduction to produce
A) aldehyde done clear
B) secondary amine done clear
C) primary amine done clear
D) amide done clear
View Answer play_arrowquestion_answer46) The continuous phase contains the dispersed phase throughout, example is
A) water in milk done clear
B) fat in milk done clear
C) water droplets in mist done clear
D) Oil in water done clear
View Answer play_arrowquestion_answer47) The number of hydrogen atoms present in 25.6 g of \[({{C}_{12}}{{H}_{22}}{{O}_{11}})\]which has a molar mass of 342.3 g is
A) \[342.3g\] done clear
B) \[9.91\times {{10}^{23}}\] done clear
C) \[11\times {{10}^{23}}\] done clear
D) \[44\times {{10}^{23}}H\]atoms done clear
View Answer play_arrowquestion_answer48) Milk changes after digestion into
A) cellulose done clear
B) fructose done clear
C) glucose done clear
D) lactose done clear
View Answer play_arrowquestion_answer49) Which of the following set consists only of essential amino acids?
A) Alanihe, tyrosine, cystme done clear
B) Leucine, lysme,tryptophane done clear
C) Alanine, glutamine, lycine done clear
D) leucine, proline, glycine done clear
View Answer play_arrowquestion_answer50) Which of the following is a ketohexose?
A) Glucose done clear
B) Sucrose done clear
C) Fructose done clear
D) Ribose:- done clear
View Answer play_arrowquestion_answer51) The oxidation number .of oxygen in \[K{{O}_{3}},N{{a}_{2}}{{O}_{2}}\]is
A) \[3,2\] done clear
B) \[1,0\] done clear
C) \[0,1\] done clear
D) \[-0.33,-1\] done clear
View Answer play_arrowquestion_answer52) Reaction of \[PC{{l}_{3}}\] and PhMgBr would give
A) bromobenzene done clear
B) chlorobenzene done clear
C) triphenylphosphine done clear
D) dichlorobenzene done clear
View Answer play_arrowquestion_answer53) Which of the following is not a characteristic of transition elements?
A) Variable oxidation states done clear
B) Formation of coloured compounds done clear
C) Formation of interstitial compounds done clear
D) Natural radioactivity done clear
View Answer play_arrowquestion_answer54) \[Cl-P-Cl\] bond angles in PCIs molecule are
A) \[{{120}^{o}}\] and \[{{90}^{o}}\] done clear
B) \[{{60}^{o}}\] and \[{{90}^{o}}\] done clear
C) \[{{60}^{o}}\] and \[{{120}^{o}}\] done clear
D) \[{{120}^{o}}\] and \[{{30}^{o}}\] done clear
View Answer play_arrowquestion_answer55) The magnetic moment of a salt containing \[Z{{n}^{2+}}\] ion is
A) \[0\] done clear
B) \[1.87\] done clear
C) \[5.92\] done clear
D) \[2\] done clear
View Answer play_arrowquestion_answer56) The number of formula, units of calcium fluoride, \[Ca{{F}_{2}}\] present in 146.4 g of \[Ca{{F}_{2}}\] (the molar mass of \[Ca{{F}_{2}}\] is 78.08 g/mol) is
A) \[1.129\times {{10}^{24}}Ca{{F}_{2}}\] done clear
B) \[1.146\times {{10}^{24}}Ca{{F}_{2}}\] done clear
C) \[7.808\times {{10}^{24}}Ca{{F}_{2}}\] done clear
D) \[1.877\times {{10}^{24}}Ca{{F}_{2}}\] done clear
View Answer play_arrowquestion_answer57) The IUPAC name of the given compound \[[Co{{(N{{H}_{3}})}_{5}}Cl]C{{l}_{2}}\]is
A) penta amino cobalt chloride chlorate done clear
B) cobalt penta ammine chloro chloride done clear
C) pentamine chloro cobalt (III) chloride done clear
D) penta, amino cobalt (III) chlorate done clear
View Answer play_arrowquestion_answer58) When \[SC{{N}^{-}}\] is added to an aqueous solution containing \[Fe{{(N{{O}_{3}})}_{3}},\]the complex ion produced is
A) \[{{[Fe{{(O{{H}_{2}})}_{2}}(SCN)]}^{2+}}\] done clear
B) \[{{[Fe{{(O{{H}_{2}})}_{5}}(SCN)]}^{2+}}\] done clear
C) \[{{[Fe{{(O{{H}_{2}})}_{8}}(SCN)]}^{2+}}\] done clear
D) \[{{[Fe(O{{H}_{2}})(SCN)]}^{6+}}\] done clear
View Answer play_arrowquestion_answer59) Hair dyes contain
A) copper nitrate done clear
B) gold chloride done clear
C) silver nitrate done clear
D) copper sulphate done clear
View Answer play_arrowquestion_answer60) Schottky defects occurs mainly in electrovalent compounds where
A) positive ions and negative ions are of different size done clear
B) positive ions and negative ions are of same size done clear
C) positive ions are small and negative ions are big done clear
D) positive ions are big and negative ions are Small done clear
View Answer play_arrowquestion_answer61) The number of unpaired electrons calculated in \[{{[Co{{(N{{H}_{3}})}_{6}}]}^{3+}}\]and \[{{[Co({{F}_{6}})]}^{3-}}\] are
A) 4 and 4 done clear
B) 0 and 2 done clear
C) 2 and 4 done clear
D) 0 and 4 done clear
View Answer play_arrowquestion_answer62) The standard free energy change of a reaction is \[\Delta {{G}^{o}}=-115kJ\] at 298 K. Calculate the equilibrium constant \[{{K}_{P}}\] in \[\log {{K}_{P}}\] \[(R=8.314\,\,J{{K}^{-1}}mo{{l}^{-1}}).\]
A) \[20.16\] done clear
B) \[2.303\] done clear
C) \[2.016\] done clear
D) \[13.83\] done clear
View Answer play_arrowquestion_answer63) If an endothermic reaction occurs spontaneously at constant temperature (T) and pressure (p), then which of the following is true?
A) \[\Delta G>0\] done clear
B) \[\Delta H<0\] done clear
C) \[\Delta S>0\] done clear
D) \[\Delta S<0\] done clear
View Answer play_arrowquestion_answer64) If a plot of \[{{\log }_{10}}C\] versus t gives a straight line for a given reaction, then the reaction is
A) zero order done clear
B) first order done clear
C) second order done clear
D) third order done clear
View Answer play_arrowquestion_answer65) A spontaneous process is one in which the system suffers
A) no energy change done clear
B) a lowering of free energy done clear
C) a lowering of entropy done clear
D) an increase in internal energy done clear
View Answer play_arrowquestion_answer66) The half-life period of a first order reaction is 1 min 40 s. Calculate its rate constant.
A) \[6.93\times {{10}^{-3}}{{\min }^{-1}}\] done clear
B) \[6.93\times {{10}^{-3}}{{s}^{-1}}\] done clear
C) \[6.93\times {{10}^{-3}}s\] done clear
D) \[6.93\times {{10}^{3}}s\] done clear
View Answer play_arrowquestion_answer67) The molar conductivities of \[KCl,Nacl\] and \[KN{{O}_{3}}\] are 152, 128 and \[111\,\,S\,\,\,c{{m}^{2}}\,\,mo{{l}^{-1}}\] respectively. What is the molar conductivity of \[NaN{{O}_{3}}\]?
A) \[101\,\,S\,c{{m}^{2}}mo{{l}^{-1}}\] done clear
B) \[87S\,c{{m}^{2}}\,mo{{l}^{-1}}\] done clear
C) \[-101S\,c{{m}^{2}}\,mo{{l}^{-1}}\] done clear
D) \[-391\,\,S\,c{{m}^{2}}\,mo{{l}^{-1}}\] done clear
View Answer play_arrowquestion_answer68) The electrochemical cell stops working after sometime because
A) electrode potential of both the electrodes becomes zero done clear
B) electrode potent : of both the electrodes becomes equal done clear
C) one of the electrodes is eaten away done clear
D) the cell reaction gets reversed done clear
View Answer play_arrowquestion_answer69) The amount of electricity required to produce one mole of copper from copper sulphate solution will be
A) 1 F done clear
B) 2.33 F done clear
C) 2 F done clear
D) 1.33 F done clear
View Answer play_arrowquestion_answer70) Dipping iron article into a strongly alkaline solution of sodium phosphate
A) does not affect the article done clear
B) forms \[F{{e}_{2}}{{O}_{3}}.x{{H}_{2}}O\] on the surface done clear
C) forms iron phosphate film done clear
D) forms ferric hydroxide done clear
View Answer play_arrowquestion_answer71) Hydro oration oxidation of 4-methyl octene would give
A) 4-methyl octanol done clear
B) 2-methyl decane done clear
C) 4-methyl heptanol done clear
D) 4-mediyL2-octanone done clear
View Answer play_arrowquestion_answer72) When ethyl alcohol is heated with cone. \[{{H}_{2}}S{{O}_{4}}\], the product obtained is
A) \[C{{H}_{3}}COO{{C}_{2}}{{H}_{5}}\] done clear
B) \[{{C}_{2}}{{H}_{2}}\] done clear
C) \[{{C}_{2}}{{H}_{6}}\] done clear
D) \[{{C}_{2}}{{H}_{4}}\] done clear
View Answer play_arrowquestion_answer73) Anisole is the product obtained from phenol by the reaction known as
A) coupling done clear
B) etherification done clear
C) oxidation done clear
D) esterification done clear
View Answer play_arrowquestion_answer74) Ethylene glycol gives oxalic acid on oxidation with:
A) acidified \[{{K}_{2}}C{{r}_{2}}{{O}_{7}}\] done clear
B) acidified \[KMn{{O}_{4}}\] done clear
C) alkaline \[KMn{{O}_{4}}\] done clear
D) periodic acid done clear
View Answer play_arrowquestion_answer75) Diamond is hard because
A) all the four valence electrons are bonded to each carbon atoms by covalent bonds done clear
B) it is a giant molecule done clear
C) it is made up of carbon atoms done clear
D) it cannot be burnt done clear
View Answer play_arrowquestion_answer76) A Wittig reaction with an aldehyde gives
A) ketone compound - done clear
B) a long chain fatty acid done clear
C) olefin compound done clear
D) epoxide done clear
View Answer play_arrowquestion_answer77) Cannizaro reaction is given by
A) \[HCHO\] done clear
B) done clear
C) done clear
D) \[C{{H}_{3}}C{{H}_{2}}OH\] done clear
View Answer play_arrowquestion_answer78) Identify the reactant.
A) \[{{H}_{2}}O\] done clear
B) \[HCHO\] done clear
C) \[CO\] done clear
D) \[C{{H}_{3}}CHO\] done clear
View Answer play_arrowquestion_answer79) Maleic acid and fumaric acid are
A) position isomers done clear
B) geometric isomers done clear
C) enantiomers done clear
D) functional isomers done clear
View Answer play_arrowquestion_answer80) The gas evolved on heating alkali formate with soda-lime is
A) \[CO\] done clear
B) \[C{{O}_{2}}\] done clear
C) hydrogen done clear
D) water vapour done clear
View Answer play_arrowquestion_answer81) If \[\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}\] be three unit vectors such that \[\overrightarrow{a}\times (\overrightarrow{b}\times \overrightarrow{c})=\frac{1}{2}\overrightarrow{b},\]\[\overrightarrow{b}\] and \[\overrightarrow{c}\] being non-parallel. If \[{{\theta }_{1}}\] is the angle between \[\overrightarrow{a}\] and \[\overrightarrow{b}\] and \[{{\theta }_{2}}\] is the angle between \[\overrightarrow{a}\] and \[\overrightarrow{c}\], then
A) \[{{\theta }_{1}}=\frac{\pi }{6},{{\theta }_{2}}=\frac{\pi }{3}\] done clear
B) \[{{\theta }_{1}}=\frac{\pi }{3},{{\theta }_{2}}=\frac{\pi }{6}\] done clear
C) \[{{\theta }_{1}}=\frac{\pi }{2},{{\theta }_{2}}=\frac{\pi }{3}\] done clear
D) \[{{\theta }_{1}}=\frac{\pi }{3},{{\theta }_{2}}=\frac{\pi }{2}\] done clear
View Answer play_arrowquestion_answer82) The\[{{\vec{r}}^{2}}-\vec{r}\cdot \vec{c}+h=0,\] \[|\vec{c}|>\sqrt{h},\] represents
A) circle done clear
B) ellipse done clear
C) cone done clear
D) sphere done clear
View Answer play_arrowquestion_answer83) The simplified expression of \[\sin \,(ta{{n}^{-1}}x),\] for any real number x is given by
A) \[\frac{1}{\sqrt{1+{{x}^{2}}}}\] done clear
B) \[\frac{x}{\sqrt{1+{{x}^{2}}}}\] done clear
C) \[-\frac{1}{\sqrt{1+{{x}^{2}}}}\] done clear
D) \[-\frac{x}{\sqrt{1+{{x}^{2}}}}\] done clear
View Answer play_arrowquestion_answer84) If \[\left| \frac{z-25}{z-1} \right|=5,\]find the value of\[|z|\].
A) 3 done clear
B) 4 done clear
C) 5 done clear
D) 6 done clear
View Answer play_arrowquestion_answer85) Argument of the complex number\[\left( \frac{-1-3i}{2+i} \right)\]is
A) \[45{}^\circ \] done clear
B) \[135{}^\circ \] done clear
C) \[225{}^\circ \] done clear
D) \[240{}^\circ \] done clear
View Answer play_arrowquestion_answer86) In a triangle ABC, the sides b and c are the roots of the equation \[{{x}^{2}}-61x+820=0\] and\[A={{\tan }^{-1}}\left( \frac{4}{3} \right)\] then \[{{a}^{2}}\] is equal to
A) 1098 done clear
B) 1096 done clear
C) 1097 done clear
D) 1095 done clear
View Answer play_arrowquestion_answer87) The shortest distance between the straight lines through the points \[{{A}_{1}}=(6,\,2,\,2)\] and \[{{A}_{2}}=(-4,\,0,\,-1),\]in the directions of \[(1,\,-2,\,\,2)\] and\[(3,\,-2,-\,2)\]is
A) 6 done clear
B) 8 done clear
C) 12 done clear
D) 9 done clear
View Answer play_arrowquestion_answer88) The centre and radius of the sphere\[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}+3x-4z+1=0\]are
A) \[\left( -\frac{3}{2},\,0,\,-2 \right);\frac{\sqrt{21}}{2}\] done clear
B) \[\left( \frac{3}{2},\,0,\,2 \right);\sqrt{21}\] done clear
C) \[\left( -\frac{3}{2},\,0,\,2 \right);\frac{\sqrt{21}}{2}\] done clear
D) \[\left( -\frac{3}{2},\,2,\,0 \right);\frac{21}{2}\] done clear
View Answer play_arrowquestion_answer89) Let A and B are two fixed points in a plane, then locus of another point C on the same plane such that CA + CB = constant, (> AB) is
A) circle done clear
B) ellipse done clear
C) parabola done clear
D) hyperbola done clear
View Answer play_arrowquestion_answer90) The directrix of the parabola\[{{y}^{2}}+4x+3=0\]is
A) \[x-\frac{4}{3}=0\] done clear
B) \[x+\frac{1}{4}=0\] done clear
C) \[x-\frac{3}{4}=0\] done clear
D) \[x-\frac{1}{4}=0\] done clear
View Answer play_arrowquestion_answer91) If \[g(x)\] is a polynomial satisfying \[g(x)g(y)=g(x)+g(y)+g(xy)-2\] for all real \[x\] and \[y\] and \[g(2)=5,\] then \[\underset{x\to 3}{\mathop{\lim }}\,g(x)\] is
A) 9 done clear
B) 10 done clear
C) 25 done clear
D) 20 done clear
View Answer play_arrowquestion_answer92) The value of \[f(0)\] so that \[\frac{(-{{e}^{x}}+{{2}^{x}})}{x}\]may be continuous at\[x=0\]is
A) \[\log \left( \frac{1}{2} \right)\] done clear
B) 0 done clear
C) 4 done clear
D) \[-1+\log 2\] done clear
View Answer play_arrowquestion_answer93) Let [ ] denotes the greatest integer function and\[f(x)=[{{\tan }^{2}}x]\]. Then,
A) \[\underset{x\to 0}{\mathop{\lim }}\,f(x)\] does not exist done clear
B) \[f(x)\]is continuous at \[x=0\] done clear
C) \[f(x)\] is not differentiable at \[x=0\] done clear
D) \[f(x)=1\] done clear
View Answer play_arrowquestion_answer94) A spherical balloon is expanding. If the radius is increasing at the rate of 2 cm/min, the rate at which the volume increases (in cubic centimetres per minute) when the radius is 5 cm, is
A) \[10\,\pi \] done clear
B) \[100\,\pi \] done clear
C) \[200\,\pi \] done clear
D) \[50\,\pi \] done clear
View Answer play_arrowquestion_answer95) The length of the parabola \[{{y}^{2}}=12x\] cut off by the latusrectum is
A) \[6\,[\sqrt{2}+\log (1+\sqrt{2})]\] done clear
B) \[3\,[\sqrt{2}+\log (1+\sqrt{2})]\] done clear
C) \[6\,[\sqrt{2}-\log (1+\sqrt{2})]\] done clear
D) \[3\,[\sqrt{2}-\log (1+\sqrt{2})]\] done clear
View Answer play_arrowquestion_answer96) If \[I=\int{\frac{{{x}^{5}}}{\sqrt{1+{{x}^{3}}}}}\,dx,\] then \[I\] is equal to
A) \[\frac{2}{9}{{(1+{{x}^{3}})}^{\frac{5}{2}}}+\frac{2}{3}{{(1+{{x}^{3}})}^{\frac{3}{2}}}+c\] done clear
B) \[\log |\sqrt{x}+\sqrt{1+{{x}^{3}}}|+\,c\] done clear
C) \[\log |\sqrt{x}-\sqrt{1+{{x}^{3}}}|+\,c\] done clear
D) \[\frac{2}{9}{{(1+{{x}^{3}})}^{\frac{3}{2}}}-\frac{2}{3}{{(1+{{x}^{3}})}^{\frac{1}{2}}}+c\] done clear
View Answer play_arrowquestion_answer97) Area enclosed by the curve\[\pi \,[4{{(x-\sqrt{2})}^{2}}+{{y}^{2}}]=8\] is
A) \[\pi \] sq unit done clear
B) \[2\] sq unit done clear
C) \[3\pi \] sq unit done clear
D) \[4\]sq unit done clear
View Answer play_arrowquestion_answer98) The value of \[\int_{0}^{a}{\sqrt{\frac{a-x}{x}}}dx\] is
A) \[\frac{a}{2}\] done clear
B) \[\frac{a}{4}\] done clear
C) \[\frac{\pi a}{2}\] done clear
D) \[\frac{\pi a}{4}\] done clear
View Answer play_arrowquestion_answer99) Let y be the number of people in a village at rime\[t\]. Assume that the rate of change of the population is proportional to the number of people in the village at any time and further assume that the population never increases in time. Then, the population of the village at any fixed time\[t\]is given by
A) \[y={{e}^{kt}}+c,\] for some constant \[c\le 0\] and \[k\ge 0\] done clear
B) \[y=c{{e}^{kt}},\] for some constants \[c\ge 0\] and \[k\le 0\] done clear
C) \[y={{e}^{ct}}+k,\] for some constants \[c\le 0\] and \[k\ge 0\] done clear
D) \[y=k{{e}^{ct}},\] for some constants \[c\ge 0\] and \[k\le 0\] done clear
View Answer play_arrowquestion_answer100) The differential equation of all straight lines touching the circle\[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]is
A) \[{{\left( y-\frac{dy}{dx} \right)}^{2}}={{a}^{2}}\left[ 1+{{\left( \frac{dy}{dx} \right)}^{2}} \right]\] done clear
B) \[{{\left( y-x\frac{dy}{dx} \right)}^{2}}={{a}^{2}}\left[ 1+{{\left( \frac{dy}{dx} \right)}^{2}} \right]\] done clear
C) \[\left( y-x\frac{dy}{dx} \right)={{a}^{2}}\left[ 1+\frac{dy}{dx} \right]\] done clear
D) \[\left( y-\frac{dy}{dx} \right)={{a}^{2}}\left[ 1-\frac{dy}{dx} \right]\] done clear
View Answer play_arrowquestion_answer101) The differential equation \[\left| \frac{dy}{dx} \right|+|y|+3=0\] admits
A) infinite number of solutions done clear
B) no solutions done clear
C) a unique solution done clear
D) many solutions done clear
View Answer play_arrowquestion_answer102) Solution of the differential equation \[xdy-ydx-\sqrt{{{x}^{2}}+{{y}^{2}}}dx=0\]is
A) \[y-\sqrt{{{x}^{2}}+{{y}^{2}}}=c\,{{x}^{2}}\] done clear
B) \[y+\sqrt{{{x}^{2}}+{{y}^{2}}}=c\,{{x}^{2}}\] done clear
C) \[y+\sqrt{{{x}^{2}}+{{y}^{2}}}=c\,{{y}^{2}}\] done clear
D) \[x-\sqrt{{{x}^{2}}+{{y}^{2}}}=c\,{{y}^{2}}\] done clear
View Answer play_arrowquestion_answer103) Let p, q, r and s be statements and suppose that \[p\to q\to r\to p.\]If \[\tilde{\ }s\to r,\]then
A) \[s\to \,\tilde{\ }q\] done clear
B) \[\tilde{\ }q\to s\] done clear
C) \[\tilde{\ }s\to \,\tilde{\ }q\] done clear
D) \[q\to \,\tilde{\ }s\] done clear
View Answer play_arrowquestion_answer104) In how many number of ways can 10 students be divided into three teams, one containing four students and the other three?
A) 400 done clear
B) 700 done clear
C) 1050 done clear
D) 2100 done clear
View Answer play_arrowquestion_answer105) If R be a relation denned as \[aRb\] iff \[|a-b|\,>0,\] then the relation is
A) reflexive done clear
B) symmetric done clear
C) transitive done clear
D) symmetric and transitive done clear
View Answer play_arrowquestion_answer106) Let S be a finite set containing n elements. Then the total number of commutative binary operation on S is
A) \[{{n}^{\left[ \frac{n(n+1)}{2} \right]}}\] done clear
B) \[{{n}^{\left[ \frac{n(n-1)}{2} \right]}}\] done clear
C) \[{{n}^{({{n}^{2}})}}\] done clear
D) \[{{2}^{({{n}^{2}})}}\] done clear
View Answer play_arrowquestion_answer107) A manufacturer of cotter pins knows that 5% of his product is defective. He sells pins in boxes of 100 and guarantees that not more than one pin will be defective in a box. In order to find the probability that a box will fail to meet the guaranteed quality, the probability distribution one has to employ is
A) binomial done clear
B) poisson done clear
C) normal done clear
D) exponential done clear
View Answer play_arrowquestion_answer108) The probability that a certain kind of component will survive a given shock test is\[\frac{3}{4}.\]The probability that exactly 2 of the next 4 components tested survive is
A) \[\frac{9}{41}\] done clear
B) \[\frac{25}{128}\] done clear
C) \[\frac{1}{5}\] done clear
D) \[\frac{27}{128}\] done clear
View Answer play_arrowquestion_answer109) Mean and standard deviation from the following observations of marks of 5 students of a tutorial group (marks out of 25) 8 12 13 15 22 are
A) 14, 4.604 done clear
B) 15, 4.604 done clear
C) 14, 5.604 done clear
D) None of these done clear
View Answer play_arrowquestion_answer110) A random variable X follows binomial distribution with mean \[\alpha \] and variance\[\beta \]. Then
A) \[0<\alpha <\beta \] done clear
B) \[0<\beta <\alpha \] done clear
C) \[\alpha <0<\beta \] done clear
D) \[\beta <0<\alpha \] done clear
View Answer play_arrowquestion_answer111) The system of equations \[x+y+z=0\] \[2x+3y+z=0\] and \[x+2y=0\] has
A) a unique solution; \[x=0,y=0,z=0\] done clear
B) infinite solutions done clear
C) no solution done clear
D) finite number of non-zero solutions done clear
View Answer play_arrowquestion_answer112) \[{{\left[ \begin{matrix} 0 & a \\ b & 0 \\ \end{matrix} \right]}^{4}}=I,\]then
A) \[a=1=2b\] done clear
B) \[a=b\] done clear
C) \[a={{b}^{2}}\] done clear
D) \[ab=1\] done clear
View Answer play_arrowquestion_answer113) If \[D=\] diag \[({{d}_{1}},{{d}_{2}},\,......\,{{d}_{n}}),\]where \[{{d}_{i}}\ne 0,\]for\[i=1,\,2,\,.....\,n,\]then \[{{D}^{-1}}\]is equal to
A) \[{{D}^{T}}\] done clear
B) \[D\] done clear
C) \[\text{adj}\,(D)\] done clear
D) \[\text{diag}\,(d_{1}^{-1},\,d_{2}^{-1},\,....\,d_{n}^{-1})\] done clear
View Answer play_arrowquestion_answer114) If x, y, z are different from zero and\[\Delta =\left| \begin{matrix} a & b-y & c-z \\ a-x & b & c-z \\ a-x & b-y & c \\ \end{matrix} \right|=0,\] then the value of the expression \[\frac{a}{x}+\frac{b}{y}+\frac{c}{z}\] is
A) 0 done clear
B) -1 done clear
C) 1 done clear
D) 2 done clear
View Answer play_arrowquestion_answer115) Probability of getting positive integral roots of the equation \[{{x}^{2}}-n=0\] for the integer n, \[1\le n\le 40\] is
A) \[\frac{1}{5}\] done clear
B) \[\frac{1}{10}\] done clear
C) \[\frac{3}{20}\] done clear
D) \[\frac{1}{20}\] done clear
View Answer play_arrowquestion_answer116) The number of real roots of the equation \[{{x}^{4}}+\sqrt{{{x}^{4}}+20}=22\]is
A) 4 done clear
B) 2 done clear
C) 0 done clear
D) 1 done clear
View Answer play_arrowquestion_answer117) Let \[\alpha ,\beta \] be the roots of the equation \[{{x}^{2}}-ax+b=0\] and \[{{A}_{n}}={{\alpha }^{n}}+{{\beta }^{n}}.\] Then, \[{{A}_{n+1}}-a{{A}_{n}}+b{{A}_{n-1}}\] is equal to
A) \[-a\] done clear
B) \[b\] done clear
C) 0 done clear
D) \[a-b\] done clear
View Answer play_arrowquestion_answer118) If the sides of a right angle triangle form an AP, the sin of the acute angles are
A) \[\left( \frac{3}{5},\,\frac{4}{5} \right)\] done clear
B) \[\left( \sqrt{3},\frac{1}{\sqrt{3}} \right)\] done clear
C) \[\left( \sqrt{\frac{\sqrt{5}-1}{2}},\sqrt{\frac{\sqrt{5}-1}{2}} \right)\] done clear
D) \[\left( \sqrt{\frac{\sqrt{3}-1}{2}},\sqrt{\frac{\sqrt{3}-1}{2}} \right)\] done clear
View Answer play_arrowquestion_answer119) The plane through the point \[\left( -1,\,\,-1,\,\,-1 \right)\] and containing the line of intersection of the planes\[\vec{r}\cdot (\hat{i}+3\hat{j}-\hat{k})=0\]and \[\vec{r}\cdot (\hat{j}+2\hat{k})=0\] is
A) \[\vec{r}\cdot (\hat{i}+2\hat{j}-3\hat{k})=0\] done clear
B) \[\vec{r}\cdot (\hat{i}+4\hat{j}+\hat{k})=0\] done clear
C) \[\vec{r}\cdot (\hat{i}+5\hat{j}-5\hat{k})=0\] done clear
D) \[\vec{r}\cdot (\hat{i}+\hat{j}+3\hat{k})=0\] done clear
View Answer play_arrowquestion_answer120) \[\vec{a}=\hat{i}-\hat{j}+\hat{k}\] and \[\vec{b}=2\hat{i}+4\hat{j}+3\hat{k}\] are one of the sides and medians respectively, of a triangle through the same vertex, then area of the triangle is
A) \[\frac{1}{2}\sqrt{83}\] done clear
B) \[\sqrt{83}\] done clear
C) \[\frac{1}{2}\sqrt{85}\] done clear
D) \[\sqrt{86}\] done clear
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