question_answer1) A glass rod rubbed with silk is used to change a gold leaf electroscope and the leaves are observed to diverge. The electroscope thus charged is exposed to X-rays for a short r period. Then
A) the divergence of leave will not affected
B) the leaves will diverge further
C) the leaves will collapse
D) the leaves will melt
View Answer play_arrowquestion_answer2) An infinite number of charge, each of charge 1 \[\mu \]C are placed on the x-axis with coordinates \[x=1,\text{ }2,\text{ }4,\text{ }8,\,\,...\infty .\]If a charge of 1 C is kept at the origin, then what is the net force acting on 1C charge?
A) 9000 N
B) 12000 N
C) 24000 N
D) 36000 N
View Answer play_arrowquestion_answer3) A cube of side \[l\] is placed in a uniform field E, where \[E={{E}_{i}}\]. The net electric flux through the cube is
A) zero
B) \[{{l}^{2}}E\]
C) \[4{{l}^{2}}E\]
D) \[6{{l}^{2}}E\]
View Answer play_arrowquestion_answer4) The capacity of a capacitor is \[4\times {{10}^{-6}}F\] and its potential is 100 V. The energy released on discharging it fully will be
A) 0.02 J
B) 0.04 J
C) 0.025 J
D) 0.05 J
View Answer play_arrowquestion_answer5) Dimensions of a block are \[1\,cm\times 1\text{ }cm\times 100\,cm\]. If specific resistance of its material is \[3\times {{10}^{-7}}\Omega m\], then the resistance between the opposite rectangular faces is
A) \[3\times {{10}^{-7}}\Omega \]
B) \[3\times {{10}^{-9}}\Omega \]
C) \[3\times {{10}^{-5}}\Omega \]
D) \[3\times {{10}^{-3}}\Omega \]
View Answer play_arrowquestion_answer6) The magnitude and direction of the current in the circuit shown will be
A) 7/3 A from a to b through e
B) 7/3 A from b to a through e
C) 1 A from b to a through e
D) 1 A from a to b through e
View Answer play_arrowquestion_answer7) An electric bulb of 100 W is connected to a supply of electricity of 220 V. Resistance of the filament is
A) \[484\Omega \]
B) \[100\Omega \]
C) \[22000\Omega \]
D) \[242\Omega \]
View Answer play_arrowquestion_answer8) Pick out the wrong statement.
A) In a simple battery circuit, the point of lowest potential is the negative terminal of the battery.
B) The resistance of an incandescent lamp is greater when the lamp is switched off.
C) An ordinary 100 W lamp has less resistance than a 60 W lamp.
D) At constant voltage, the heat developed in a uniform wire varies inversely as the length of the wire used.
View Answer play_arrowquestion_answer9) The electrochemical equivalent of magnesium is 0.126 mg/C. A current of 5 A is passed in a suitable solution for 1 h. The mass of magnesium deposited will be
A) 0.0378 g
B) 0.227 g
C) 0.378 g
D) 2.27g
View Answer play_arrowquestion_answer10) In producing chlorine through electrolysis 100 W power at 125 V is being consumed. How much chlorine per minute is liberated? ECE of chlorine is \[0.367\times {{10}^{-6}}kg/C\].
A) 24.3 mg
B) 16.6 mg
C) 17.6 mg
D) 21.3 mg
View Answer play_arrowquestion_answer11) A particle carrying a charge equal to 100 times the charge on an electron is rotating per second in a circular path of radius 0.8 m. The value of the magnetic field produced at the centre will be (\[{{\mu }_{0}}\]= permeability for vacuum)
A) \[\frac{{{10}^{-7}}}{{{\mu }_{0}}}\]
B) \[{{10}^{-17}}{{\mu }_{0}}\]
C) \[{{10}^{-6}}{{\mu }_{0}}\]
D) \[{{10}^{-7}}{{\mu }_{0}}\]
View Answer play_arrowquestion_answer12) A rectangular loop carrying a current \[i\] is placed in a uniform magnetic field\[B\]. The area enclosed by the loop is \[A\]. If there are \[n\] turns in the loop, the torque acting on the loop is given by
A) \[ni\,\mathbf{A}\times \mathbf{B}\]
B) \[ni\,\,\mathbf{A}\cdot \mathbf{B}\]
C) \[\frac{1}{n}\left( i\mathbf{A}\times \mathbf{B} \right)\]
D) \[\frac{1}{n}(i\mathbf{A\times B})\]
View Answer play_arrowquestion_answer13) In a magnetic field of 0.05 T, area of a coil changes from \[101\text{ }c{{m}^{2}}\]to \[100\,\,c{{m}^{2}}\] without changing the resistance which is\[2\Omega \]. The amount of charge that flow during this period is
A) \[2.5\times {{10}^{-6}}C\]
B) \[2\times {{10}^{-6}}C\]
C) \[{{10}^{-6}}C\]
D) \[8\times {{10}^{-6}}C\]
View Answer play_arrowquestion_answer14) A solenoid has 2000 turns wound over a length of 0.30 m. The area of its cross-section is \[1.2\times {{10}^{-3}}{{m}^{2}}\]. Around its central section, a coil of 300 turn is wound. If an initial current of 2 A in the solenoid is reversed in 0.25 s, then the emf induced in the coil is
A) \[6\times {{10}^{-4}}V\]
B) \[4.8\times {{10}^{-3}}V\]
C) \[6\times {{10}^{-2}}V\]
D) \[48mV\]
View Answer play_arrowquestion_answer15) An inductive circuit contains a resistance of \[10\Omega \] and an inductance of 2.0 H. If an AC voltage of 120 V and frequency of 60 Hz is applied to this circuit, the current in the circuit would be nearly
A) 0.32 A
B) 0.16 A
C) 0.43 A
D) 0.80 A
View Answer play_arrowquestion_answer16) In a Millikans oil drop experiment the charge on an oil drop is calculated to be\[6.35\times {{10}^{-19}}C\]. The number of excess electrons on the drop is
A) 3.2
B) 4
C) 4.2
D) 6
View Answer play_arrowquestion_answer17) The values \[+\frac{1}{2}\] and \[-\frac{1}{2}\] of spin quantum number show
A) rotation of electron clockwise and anti-clockwise directions respectively
B) rotation of electron anti-clockwise and clockwise directions respectively
C) rotation in any direction according to convention
D) None of the above
View Answer play_arrowquestion_answer18) The frequency of incident light falling on a photosensitive metal plate is doubled, the kinetic energy of the emitted photoelectrons is
A) double the earlier value
B) unchanged
C) more than doubled
D) less than doubled
View Answer play_arrowquestion_answer19) Light of two different frequencies whose photons have energies 1 eV and 2.5 eV, respectively, successively illuminate a metal whose work function is 0,5 eV. The ratio of the maximum speed of the emitted electrons will be
A) 1 : 5
B) 1 : 4
C) 1 : 2
D) 1 : 1
View Answer play_arrowquestion_answer20) An electron accelerated under a potential difference \[V\] volt has a certain wavelength \[\lambda \] Mass of proton is some 2000 times of the mass of the electron. If the proton has to have the same wavelength \[\lambda \] , then it will have to be accelerated under a potential difference of
A) \[V\text{ }volt\]
B) \[2000\text{ }V\text{ }volt\]
C) \[\frac{V}{2000}\] volt
D) \[\sqrt{\text{2}000}\,V\,volt\]
View Answer play_arrowquestion_answer21) The ratio of momentum of an electron and \[\alpha \]-particle which are accelerated from rest by a potential difference of 100 V is
A) 1
B) \[\sqrt{(\text{2}{{\text{m}}_{\text{e}}}/{{\text{m}}_{\alpha }})}\]
C) \[\sqrt{({{\text{m}}_{\text{e}}}/{{\text{m}}_{\alpha }})}\]
D) \[\sqrt{(\text{m},/\text{2}{{\text{m}}_{\alpha }})}\]
View Answer play_arrowquestion_answer22) Sky wave propagation is used in
A) radio communication
B) satellite communication
C) T V communication
D) Both T V and satellite communication
View Answer play_arrowquestion_answer23) The frequency of an FM transmitter without signal input is called
A) the centre frequency
B) modulation
C) the frequency deviation
D) the carrier sweing
View Answer play_arrowquestion_answer24) What is the age of an ancient wooden piece if it is known that the specific activity of \[{{C}^{14}}\] nuclide in its amounts is 3/5 of that in freshly grown trees? Given the half of C nuclide is 5570 yr.
A) 1000 yr
B) 2000 yr
C) 3000 yr
D) 4000 yr
View Answer play_arrowquestion_answer25) A thin metallic spherical shell contains a charge Q on it. A point charge q is placed at the centre of the shell and another charge q is placed outside it as shown in the figure. All the three charges are positive. The force on the charge at the centre is
A) towards left
B) towards right
C) upward
D) zero
View Answer play_arrowquestion_answer26) As shown in the figure, charges \[+q\] and \[-q\] are placed at the vertices B and C of an isosceles triangle. The potential at the vertex A is
A) \[\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{2a}{\sqrt{{{a}^{2}}+{{b}^{2}}}}\]
B) zero
C) \[\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{q}{\sqrt{{{a}^{2}}+{{b}^{2}}}}\]
D) \[\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{\left( -q \right)}{\sqrt{{{a}^{2}}+{{b}^{2}}}}\]
View Answer play_arrowquestion_answer27) On moving a charge of 20 C by 2 cm, 2 J of work is done, then the potential difference between the points is
A) \[0.1\text{ }V\]
B) \[8\text{ }V\]
C) \[2\text{ }V\]
D) \[0.5\text{ }V\]
View Answer play_arrowquestion_answer28) The insulation property of air breaks down at\[3\times {{10}^{6}}V/m\]. The maximum charge that can be given to a sphere of diameter 5 m is nearly
A) \[2\times {{10}^{-2}}C~\]
B) \[2\times {{10}^{-3}}C\]
C) \[2\times {{10}^{-4}}C\]
D) \[2\times {{10}^{-5}}C\]
View Answer play_arrowquestion_answer29) Two capacitors of capacities C and 2C are connected in parallel and then connected in series with a third capacitor of capacity 3C. The combination is charged with V volt. The charge on capacitor of capacity C is
A) \[2\text{ }CV\]
B) \[CV\]
C) \[2\text{ }CV\]
D) \[\frac{3}{2}CV\]
View Answer play_arrowquestion_answer30) Five resistances are connected as shown in the figure. The effective resistance between points A and B is
A) \[\frac{10}{3}\Omega \]
B) \[\frac{10}{17}\Omega \]
C) \[40\Omega \]
D) \[45\Omega \]
View Answer play_arrowquestion_answer31) A potentiometer is connected across A and B and a balance is obtained at 64.0 cm. When potentiometer lead to B is moved to C, a balance is found at 8.0 cm. If the potentiometer is now connected across B and C, a balance will be found at
A) 8.0 cm
B) 56.0 cm
C) 64.0 cm
D) 72.0 cm
View Answer play_arrowquestion_answer32) In an electromagnetic wave, the average energy density associated with magnetic field is
A) \[L{{i}_{0}}^{2}/2\]
B) \[{{B}^{2}}/2{{\mu }_{0}}\]
C) \[{{\mu }_{0}}{{B}^{2}}/2\]
D) \[{{\mu }_{0}}/2{{B}^{2}}\]
View Answer play_arrowquestion_answer33) An electromagnetic wave going through vacuum is described by \[E={{E}_{0}}\sin (kx-\omega t)\] Which of the following is/are independent of the wavelength?
A) \[k\]
B) \[{{\omega }^{2}}\]
C) \[k/\omega \]
D) \[k{{\omega }^{2}}\]
View Answer play_arrowquestion_answer34) An ammeter reads up to 1 A. Its internal resistance is \[0.81\Omega \]. To increase the range to 10 A, the value of the required shunt is
A) \[0.09\Omega \]
B) \[0.03\Omega \]
C) \[0.3\Omega \]
D) \[0.9\Omega \]
View Answer play_arrowquestion_answer35) A coil of resistance \[10\Omega \] and inductance 5 H is connected to a 100 V battery. Then the energy stored in the coil is
A) 250 J
B) 250 erg
C) 125 J
D) 125 erg
View Answer play_arrowquestion_answer36) A nucleus \[_{Z}^{A}X\] emits an \[\alpha -particle\]. The resultant nucleus emits a\[{{\beta }^{+}}-particle\].The respective atomic and mass number of final nucleus will be
A) \[Z-3,A-4\]
B) \[Z-1,A-4\]
C) \[Z-2,A-4\]
D) \[Z,A-2\]
View Answer play_arrowquestion_answer37) In Youngs double slit experiment, the intensity of light at a point on the screen where the path difference is\[\lambda =1\]. The intensity of light at a point where the path difference becomes \[\lambda /3\] is
A) \[\frac{l}{4}\]
B) \[\frac{l}{3}\]
C) \[\frac{l}{2}\]
D) \[I\]
View Answer play_arrowquestion_answer38) Polarising angle for water is \[53{}^\circ 4\]. If light is incident at this angle on the surface of water and reflected the angle of refraction is
A) \[53{}^\circ 4\]
B) \[126{}^\circ 56\]
C) \[36{}^\circ 56\]
D) \[30{}^\circ 4\]
View Answer play_arrowquestion_answer39) A 2 V battery, a \[15\Omega \] resistor and a potentiometer of 100 cm length, all are connected in series. If the resistance of potentiometer wire is \[5\Omega \], then the potential gradient of the potentiometer wire is
A) 0.0005 V/cm
B) 0.05 V/cm
C) 0.02V/cm
D) 0.2 V/cm
View Answer play_arrowquestion_answer40) The output voltage of a transformer connected to 220 V line is 1100 V at 2 A current. Its efficiency is 100%. The current coming from the line is
A) 20 A
B) 10 A
C) 11 A
D) 22 A
View Answer play_arrowquestion_answer41) An alkene having molecular formula \[{{C}_{8}}{{H}_{12}}\] on ozonolysis yields glyoxal and 2, 2-dimethyl butane-1, 4-dial. The structure of alkene is
A)
B)
C)
D)
View Answer play_arrowquestion_answer42) Amongst \[Ni{{(CO)}_{4}},{{[Ni{{(CN)}_{4}}]}^{2-}}\]and \[[NiCl_{4}^{2-}]\]
A) \[Ni{{(CO)}_{4}}\] and \[NiCl_{4}^{2-}\] are diamagnetic but \[{{[Ni{{(CN)}_{4}}]}^{2-}}\] is paramagnetic
B) \[Ni{{(CO)}_{4}}\]and \[{{[Ni{{(CN)}_{4}}]}^{2-}}\] are diamagnetic but \[NiCl_{4}^{2-}\]is paramagnetic
C) \[NiCl_{4}^{2-}\] and \[{{[Ni{{(CN)}_{4}}]}^{2-}}\]are diamagnetic but \[Ni{{(CO)}_{4}}\] is paramagnetic
D) \[Ni{{(CO)}_{4}}\] is diamagnetic but \[NiCl_{4}^{2-}\] and \[{{[Ni{{(CN)}_{4}}]}^{2-}}\] is paramagnetic
View Answer play_arrowquestion_answer43) The equivalent conductances of two ions at infinite dilution in water at \[{{25}^{o}}C\] are given below \[\wedge _{B{{a}^{2+}}}^{o}=127.00\,Sc{{m}^{2}}/equiv\] \[\wedge _{C{{l}^{-}}}^{o}=76.00\,Sc{{m}^{2}}/equiv\] The equivalent conductance (in \[S\,c{{m}^{2}}\]/equiv) of \[BaC{{l}_{2}}\] at infinite dilution will be
A) \[203\]
B) \[279\]
C) \[205.5\]
D) \[139.5\]
View Answer play_arrowquestion_answer44) The product formed when phthalimide is treated with a mixture of \[B{{r}_{2}}\] and strong \[NaOH\] solution is
A) aniline
B) phthalamide
C) phthalic acid
D) anthranilic acid
View Answer play_arrowquestion_answer45) In a set of reactions acetic acid yielded a product D. \[C{{H}_{3}}COOH\xrightarrow{SOC{{l}_{2}}}A\xrightarrow[anly.\,\,AlC{{l}_{3}}]{Benzene}B\xrightarrow{HCN}\] \[C\xrightarrow{{{H}_{2}}O}D\] The structure of D would be
A)
B)
C)
D)
View Answer play_arrowquestion_answer46) The alcohol having molecular formula \[{{C}_{4}}{{H}_{9}}OH\], when shaken with a mixture of anhydrous \[ZnC{{l}_{2}}\] and cone. \[HCl\] gives an oily layer product after five minutes. The alcohol is
A) \[{{H}_{3}}C-{{(C{{H}_{2}})}_{3}}-OH\]
B) \[{{(C{{H}_{3}})}_{2}}CH-C{{H}_{2}}OH\]
C) \[{{(C{{H}_{3}})}_{3}}C-OH\]
D) \[{{H}_{3}}C-CH(OH)C{{H}_{2}}-C{{H}_{3}}\]
View Answer play_arrowquestion_answer47) p-toluidine and benzyl amine can be distinguished by
A) Sandmeyers reaction
B) Dye test
C) Molisch test
D) Gattermann reaction
View Answer play_arrowquestion_answer48) \[C{{H}_{3}}C{{H}_{2}}Br\] undergoes Wurtz reaction. We may expect some of the following product
\[A:C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}C{{H}_{3}}\] |
\[B:C{{H}_{2}}=C{{H}_{2}}\] |
\[C:C{{H}_{3}}-C{{H}_{3}}\] |
A) Only A
B) A and B
C) A, B and C
D) A and C
View Answer play_arrowquestion_answer49) Sometimes explosion occurs while distilling ethers. It is due to the presence of
A) peroxides
B) oxides
C) ketones
D) aldehydes
View Answer play_arrowquestion_answer50) Glycerine is used as a preservative for fruits and eatables because
A) it makes them sweet
B) it acts as an insecticide
C) it keeps the food moist
D) All of the above
View Answer play_arrowquestion_answer51) This reaction is called
A) Reimer-Tiemann reaction
B) Lederer-Manasse reaction
C) Sandmeyer reaction
D) Kolbes reaction
View Answer play_arrowquestion_answer52) \[C{{H}_{3}}-C-C{{H}_{3}}\xrightarrow{Se{{O}_{2}}}X+Se+{{H}_{2}}O;X\] is
A) \[\overset{OO}{\mathop{\overset{||||}{\mathop{C{{H}_{3}}-C-C-H}}\,}}\,\]
B) \[\overset{O}{\mathop{\overset{||}{\mathop{C{{H}_{3}}-C-OC{{H}_{3}}}}\,}}\,\]
C) \[\overset{O}{\mathop{\overset{||}{\mathop{C{{H}_{3}}-C-C{{H}_{2}}OH}}\,}}\,\]
D) None of the above
View Answer play_arrowquestion_answer53) Which of the following will give Cannizzaro reaction?
A) \[C{{H}_{3}}CHO\]
B) \[C{{H}_{3}}COC{{H}_{3}}\]
C) \[{{(C{{H}_{3}})}_{3}}C-CHO\]
D) \[C{{H}_{3}}C{{H}_{2}}CHO\]
View Answer play_arrowquestion_answer54) The secondary structure of a protein refers to:
A) \[\alpha \]-helical backbone
B) hydrophobic interactions
C) sequence of \[\alpha \]-amino acids
D) fixed configuration of the polypeptide backbone
View Answer play_arrowquestion_answer55) Self condensation of two moles of ethyl acetate in the presence of sodium ethoxide after acidification yields
A) acetic acid
B) acetoacetic ester
C) ethyl propionate
D) ethyl butyrate
View Answer play_arrowquestion_answer56) Which one of the following will be most basic?
A) Aniline
B) p-methoxyaniline
C) p-methyl aniline
D) Benzylamine
View Answer play_arrowquestion_answer57) \[M{{n}_{2}}{{O}_{7}}\] dissolves in water to give an acid. The colour of the acid is
A) green
B) blue
C) purple
D) red
View Answer play_arrowquestion_answer58) 925 fine silver means an alloy of
A) \[7.5%\text{ }Ag\] and \[92.5%\text{ }Cu\]
B) \[92.5%\text{ }Ag\] and \[7.5%\text{ }Cu\]
C) \[80%\text{ }Ag\] and \[20%\text{ }Cu\]
D) \[90%\text{ }Ag\] and \[10%\text{ }Cu\]
View Answer play_arrowquestion_answer59) In which of the following octahedral complexes of \[Co\] (At. no. 27), will the magnitude of \[{{\Delta }_{o}}\] be the highest?
A) \[{{[Co{{(CN)}_{6}}]}^{3-}}\]
B) \[{{[Co{{({{C}_{2}}{{O}_{4}})}_{3}}]}^{3-}}\]
C) \[{{[Co{{({{H}_{2}}O)}_{6}}]}^{3+}}\]
D) \[{{[Co{{(N{{H}_{3}})}_{6}}]}^{3+}}\]
View Answer play_arrowquestion_answer60) Assertion [A] \[C{{u}^{2+}}\] and \[C{{d}^{2+}}\] are separated by first adding \[KCN\] solution and then passing \[{{H}_{2}}S\] gas. Reason [R] \[KCN\] reduces \[C{{u}^{2+}}\] to \[C{{u}^{+}}\] and forms a complex with it. The correct answer is
A) Both [A] and [R] are true and [R] is the correct explanation of [A]
B) Both [A] and [R] are true but [R] is not the correct explanation of [A]
C) [A] is true but [R] is not true
D) [A] is not true but [R] is true
View Answer play_arrowquestion_answer61) The effective atomic number of cobalt in the complex \[{{[Co{{(N{{H}_{3}})}_{6}}]}^{3+}}\] is
A) 36
B) 24
C) 33
D) 30
View Answer play_arrowquestion_answer62) The IUPAC name for the complex \[[Co(N{{O}_{2}}){{(N{{H}_{3}})}_{5}}]C{{l}_{2}}\]is
A) nitrito-N-pentammine cobalt (III) chloride
B) nitrito-N-pentammine cobalt (II) chloride
C) pentaminenitrito-N-cobalt (II) chloride
D) pentaminenitrito-N-cobalt (III) chloride
View Answer play_arrowquestion_answer63) The radio-isotope used for treatment of thyroid disorders is
A) \[Na-24\]
B) \[P-32\]
C) \[Co-60\]
D) \[I-131\]
View Answer play_arrowquestion_answer64) Tetragonal crystal system has the following unit cell dimensions
A) \[a=b=c,\alpha =\beta =\gamma ={{90}^{o}}\]
B) \[a=b\ne c,\alpha =\beta =\gamma ={{90}^{o}}\]
C) \[a\ne b\ne c,\alpha =\beta =\gamma ={{120}^{o}}\]
D) \[a=b\ne c,\alpha =\beta ={{90}^{o}},\gamma ={{120}^{o}}\]
View Answer play_arrowquestion_answer65) A crystalline solid
A) changes rapidly from solid to liquid
B) has no definite melting point
C) undergoes deformation of its geometry easily
D) soften easily
View Answer play_arrowquestion_answer66) Two glass bulbs A and B are connected by a very small tube having a stop-cock. Bulb A has a volume of 100 cm3 and contained the gas while bulb B was empty. On opening stop-clock, the pressure fell down to 40%. The volume of the bulb B must be
A) \[75c{{m}^{3}}\]
B) \[125c{{m}^{3}}\]
C) \[150c{{m}^{3}}\]
D) \[250c{{m}^{3}}\]
View Answer play_arrowquestion_answer67) 20 mL of 0.2 M \[NaOH\] is added to 50 mL of 0.2 M acetic acid. The pH of this solution after mixing is \[({{K}_{a}}=1.8\times {{10}^{-5}})\]
A) \[4.5\]
B) \[2.3\]
C) \[3.8\]
D) \[4\]
View Answer play_arrowquestion_answer68) Consider the following equation, which represents a reaction in the extraction of chromium from its ore \[2F{{e}_{2}}{{O}_{3}}.C{{r}_{2}}{{O}_{3}}+4N{{a}_{2}}C{{O}_{3}}+3{{O}_{2}}\] \[\xrightarrow{{}}2F{{e}_{2}}{{O}_{3}}+4N{{a}_{2}}Cr{{O}_{4}}+4C{{O}_{2}}\] Which one of the following statements about the oxidation states of the substances is correct?
A) The iron has been reduced from \[+3\] to \[+2\] state.
B) The chromium has been oxidised from \[+3\] to \[+6\] state.
C) The carbon has been oxidised from \[+2\] to \[+4\] state.
D) There is no change in the oxidation state of the substances in the reaction.
View Answer play_arrowquestion_answer69) The freezing point of a solution composed of 10.0 g of \[KCl\] in 100 g of water is \[{{4.5}^{o}}C\]. Calculate the vant Hoff factor, i for this solution.
A) \[2.50\]
B) \[1.8\]
C) \[1.2\]
D) \[1.3\]
View Answer play_arrowquestion_answer70) In the reversible reaction, \[2N{{O}_{2}}{{N}_{2}}{{O}_{4}}\] the rate of disappearance of \[N{{O}_{2}}\] is equal to
A) \[\frac{2{{k}_{1}}}{{{k}_{2}}}{{[N{{O}_{2}}]}^{2}}\]
B) \[2{{k}_{1}}{{[N{{O}_{2}}]}^{2}}-2{{k}_{2}}[{{N}_{2}}{{O}_{4}}]\]
C) \[2{{k}_{1}}{{[N{{O}_{2}}]}^{2}}-{{k}_{2}}[{{N}_{2}}{{O}_{4}}]\]
D) \[(2{{k}_{1}}-{{k}_{2}})[N{{O}_{2}}]\]
View Answer play_arrowquestion_answer71) A chemical reaction was carried out at 300 K and 280 K. The rate constants were found to be \[{{k}_{1}}\] and \[{{k}_{2}}\] respectively. Then
A) \[{{k}_{2}}=4{{k}_{1}}\]
B) \[{{k}_{2}}=2{{k}_{1}}\]
C) \[{{k}_{2}}=0.25{{k}_{1}}\]
D) \[{{k}_{2}}=0.5{{k}_{1}}\]
View Answer play_arrowquestion_answer72) The rate constant of a reaction at temperature 200 K is 10 times less than the rate constant at 400 K. What is the activation energy of the reaction?
A) \[1842.4\text{ }R\]
B) \[460.6\text{ }R\]
C) \[230.3\text{ }R\]
D) \[921.2\text{ }R\]
View Answer play_arrowquestion_answer73) A vessel at 1000 K contains \[C{{O}_{2}}\] with a pressure of 0.5 atm. Some of the \[C{{O}_{2}}\] is converted into \[CO\] on the addition of graphite. The value of K if the total pressure at equilibrium is 0.8 atm, is
A) \[1.8atm\]
B) \[3atm\]
C) \[0.3atm\]
D) \[0.18atm\]
View Answer play_arrowquestion_answer74) For the reaction \[2A+BC,\] \[\Delta H=x\,cal\], which one of the following conditions would favour the yield of C on the basis of Le-Chatelier principle?
A) High pressure, high temperature
B) Only low temperature
C) High pressure, low temperature
D) Only low pressure
View Answer play_arrowquestion_answer75) The EMF of the cell, \[Mg|M{{g}^{2+}}(0.01M)||S{{n}^{2+}}(0.1M)|Sn\]at 298 K is \[(E_{M{{g}^{2+}}/Mg}^{o}=-2.34V,\,E_{S{{n}^{2+}}/Sn}^{o}=-0.14V)\]
A) \[2.17V\]
B) \[2.23V\]
C) \[2.51V\]
D) \[2.45V\]
View Answer play_arrowquestion_answer76) Heat of formation, \[\Delta H_{f}^{o}\] of an explosive compound like \[NC{{l}_{3}}\] is
A) positive
B) negative
C) zero
D) positive or negative
View Answer play_arrowquestion_answer77) For the reaction, \[{{C}_{3}}{{H}_{8}}(g)+5{{O}_{2}}(g)\xrightarrow{{}}3C{{O}_{2}}(g)+4{{H}_{2}}O)(l)\] at constant temperature, \[\Delta H-\Delta E\] is
A) \[RT\]
B) \[-3RT\]
C) \[3RT\]
D) \[-RT\]
View Answer play_arrowquestion_answer78) The favourable conditions for a spontaneous reaction are
A) \[T\,\,\Delta S>\Delta H,\,\Delta H=+ve,\,\Delta S=+ve\]
B) \[T\,\,\Delta S>\Delta H,\,\Delta H=+ve,\,\Delta S=-ve\]
C) \[T\,\,\Delta S>\Delta H,\,\Delta H=-ve,\,\Delta S=-ve\]
D) \[T\,\,\Delta S>\Delta H,\,\Delta H=+ve,\,\Delta S=+ve\]
View Answer play_arrowquestion_answer79) Compound A and B are treated with dil. \[HCl\] separately. The gases liberated are Y and Z respectively. Y turns acidified dichromate paper green while Z turns lead acetate paper black. The compound A and B are respectively.
A) \[N{{a}_{2}}C{{O}_{3}}\] and \[NaCl\]
B) \[N{{a}_{2}}S{{O}_{3}}\] and \[N{{a}_{2}}S\]
C) \[N{{a}_{2}}S\] and \[N{{a}_{2}}S{{O}_{3}}\]
D) \[N{{a}_{2}}S{{O}_{3}}\] and \[N{{a}_{2}}S{{O}_{4}}\]
View Answer play_arrowquestion_answer80) Which of the following is correct comparison of the stability of the molecules?
A) \[CN>O_{2}^{+}\]
B) \[CN={{N}_{2}}\]
C) \[{{N}_{2}}<{{O}_{2}}\]
D) \[H_{2}^{+}>He_{2}^{+}\]
View Answer play_arrowquestion_answer81) To the lines \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0,\] the lines \[{{a}^{2}}{{x}^{2}}+2h(a+b)\,xy+{{b}^{2}}{{y}^{2}}=0\]are
A) equally inclined
B) perpendicular
C) bisector of the angle
D) None of these
View Answer play_arrowquestion_answer82) If \[R\] be a relation from \[A=\{1,\,\,2,\,\,3,\,\,4\}\] to \[B=\{1,\,3,\,5\}\] such that \[(a,\,b)\in \,R\Leftrightarrow a<b,\]then \[RO{{R}^{-1}}\]is
A) \[\{(1,\,3),\,(1,\,5),\,(2,\,3),\,(2,\,5),\,(3,\,5),\,(4,\,5)\}\]
B) \[\{(3,\,1),\,(5,\,1),\,(3,\,2),\,(5,\,2),\,(5,\,3),\,(5,\,4)\}\]
C) \[\{(3,\,3),\,(3,\,5),\,(5,\,3),\,(5,\,5)\}\]
D) \[\{(3,\,3),\,(3,\,4),\,(3,\,4),\,(4,\,5)\}\]
View Answer play_arrowquestion_answer83) If \[x+iy={{(1-i\sqrt{3})}^{100}},\]then find\[(x,y).\]
A) \[({{2}^{99}},\,{{2}^{99}}\sqrt{3})\]
B) \[({{2}^{99}},\,-{{2}^{99}}\sqrt{3})\]
C) \[(-{{2}^{99}},\,{{2}^{99}}\sqrt{3})\]
D) None of these
View Answer play_arrowquestion_answer84) For a GP, \[{{a}_{n}}=3({{2}^{n}}),\] \[\forall \]\[n\in N.\] Find the common ratio.
A) \[2\]
B) \[3\]
C) \[\frac{1}{2}\]
D) \[\frac{1}{3}\]
View Answer play_arrowquestion_answer85) If \[a,\,b,\,c\]are in HP, then \[\frac{a}{b+c},\frac{b}{c+a},\frac{c}{a+b}\]will be in
A) AP
B) GP
C) HP
D) None of these
View Answer play_arrowquestion_answer86) If \[\frac{{{x}^{2}}+2x+7}{2x+3}<6,\]\[x\in R,\]then
A) \[x>11\]or\[x<-\frac{3}{2}\]
B) \[x>11\]or \[x<-1\]
C) \[-\frac{3}{2}<x<-1\]
D) \[-1<x<11\]or \[x<-\frac{3}{2}\]
View Answer play_arrowquestion_answer87) The number of ways of painting the faces of a cube of six different colours is
A) 1
B) 6
C) 6!
D) 36
View Answer play_arrowquestion_answer88) A line passes through (2, 2) and is perpendicular to the line \[3x+y=3.\] What is its y-intercept?
A) \[\frac{1}{3}\]
B) \[\frac{2}{3}\]
C) \[1\]
D) \[\frac{4}{3}\]
View Answer play_arrowquestion_answer89) The number of common tangents to the circles\[{{x}^{2}}+{{y}^{2}}=4\]and \[{{x}^{2}}+{{y}^{2}}-6x-8y=24\]is
A) 0
B) 1
C) 2
D) 4
View Answer play_arrowquestion_answer90) If \[D\]is the set of the \[x\] such that \[1-{{e}^{(1/x)-1}}\] is positive, then \[D\] is equal to
A) \[(-\,\infty ,\,1)\]
B) \[(-\,\infty ,\,0)\]
C) \[(1,\,\infty )\]
D) \[(-\,\infty ,\,0)\cup (1,\,\infty )\]
View Answer play_arrowquestion_answer91) Find the value of the limit \[\underset{x\to 0}{\mathop{\lim }}\,\frac{\sqrt{1-\cos x}}{x}\,\,.\]
A) 0
B) 1
C) \[\sqrt{2}\]
D) does not exist
View Answer play_arrowquestion_answer92) Evaluate\[\int{\frac{{{x}^{2}}+4}{{{x}^{4}}+16}dx.}\]
A) \[\frac{1}{2\sqrt{2}}{{\tan }^{-1}}\left( \frac{{{x}^{2}}-4}{2x\sqrt{2}} \right)+C\]
B) \[\frac{1}{2\sqrt{2}}{{\tan }^{-1}}\left( \frac{{{x}^{2}}-4}{2\sqrt{2}} \right)+C\]
C) \[\frac{1}{2\sqrt{2}}{{\tan }^{-1}}\left( \frac{{{x}^{2}}-4}{x\sqrt{2}} \right)+C\]
D) None of these
View Answer play_arrowquestion_answer93) Evaluate \[\int_{\pi /4}^{3\pi /4}{\frac{1}{1+\cos x}}dx\]
A) \[2\]
B) \[-2\]
C) \[\frac{1}{2}\]
D) \[-\frac{1}{2}\]
View Answer play_arrowquestion_answer94) If one AM A and two GM p and q are inserted between two given numbers, then find the value of \[\frac{{{p}^{2}}}{q}+\frac{{{q}^{2}}}{p}.\]
A) A
B) 2A
C) 3A
D) 4A
View Answer play_arrowquestion_answer95) If the roots of the equations \[{{x}^{2}}+ax+b=0\]are c and d, then one of the roots of the equation\[{{x}^{2}}+(2c+a)x+{{c}^{2}}+ac+b=0\]is
A) \[c\]
B) \[d-c\]
C) \[2d\]
D) \[2c\]
View Answer play_arrowquestion_answer96) The sum of the coefficients of\[{{(6a-5b)}^{n}},\]where n is positive integer, is
A) \[1\]
B) \[-1\]
C) \[{{2}^{n}}\]
D) \[{{2}^{n-1}}\]
View Answer play_arrowquestion_answer97) Find the value of \[{{(7.995)}^{1/3}}\]correct to four decimal places.
A) 1.9995
B) 1.9996
C) 1.9990
D) 1.9991
View Answer play_arrowquestion_answer98) The values of constants a and b so that \[\underset{x\to \infty }{\mathop{\lim }}\,\left( \frac{{{x}^{2}}+1}{x+1}-ax-b \right)=0\]
A) \[a=0,\,\,b=0\]
B) \[a=1,\,\,b=-1\]
C) \[a=-1,\,\,b=1\]
D) \[a=2,\,\,b=-1\]
View Answer play_arrowquestion_answer99) The projection of the vector \[i-2j+k\]on the vector \[4i-4j+7k\]is
A) \[\frac{5\sqrt{6}}{10}\]
B) \[\frac{19}{9}\]
C) \[\frac{9}{19}\]
D) \[\frac{\sqrt{6}}{19}\]
View Answer play_arrowquestion_answer100) If \[a,\,\,b,\,\,c\]are three non-zero vectors such that \[a+b+c=0\] and \[m=a\cdot b+b\cdot c+c\cdot a,\]then
A) \[m<0\]
B) \[m>0\]
C) \[m=0\]
D) \[m=3\]
View Answer play_arrowquestion_answer101) A line making angles \[45{}^\circ \] and \[60{}^\circ \] with the positive directions of the axes of x and y makes with the positive directions of z-axis, an angle of
A) \[60{}^\circ \]
B) \[120{}^\circ \]
C) \[60{}^\circ \,\,\text{or}\,\,120{}^\circ \]
D) None of these
View Answer play_arrowquestion_answer102) If \[I=\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right],\] \[J=\left[ \begin{matrix} 0 & 1 \\ -1 & 0 \\ \end{matrix} \right]\] and \[B=\left[ \begin{matrix} \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \\ \end{matrix} \right],\] then B is equal to
A) \[I\cos \theta +J\sin \theta \]
B) \[I\,\sin \theta +J\,\cos \theta \]
C) \[I\cos \theta -J\sin \theta \]
D) \[-I\cos \theta +J\sin \theta \]
View Answer play_arrowquestion_answer103) Which of the following is correct?
A) Determinant is a square matrix
B) Determinant is a number associated to matrix
C) Determinant is a number associated to a square matrix
D) All of the above
View Answer play_arrowquestion_answer104) If \[\alpha ,\]\[\beta \]and \[\gamma \]are the roots of \[{{x}^{3}}+a{{x}^{2}}+b=0,\] then the value of \[\left| \begin{matrix} \alpha & \beta & \gamma \\ \beta & \gamma & \alpha \\ \gamma & \alpha & \beta \\ \end{matrix} \right|\]is
A) \[-{{a}^{3}}\]
B) \[{{a}^{3}}-3b\]
C) \[{{a}^{3}}\]
D) \[{{a}^{2}}-3b\]
View Answer play_arrowquestion_answer105) If the axes are shifted to the point \[(1,\,\,-2)\] without solution, then the equation \[2{{x}^{2}}+{{y}^{2}}-4x+4y=0\] becomes
A) \[2{{X}^{2}}+3{{Y}^{2}}=6\]
B) \[2{{X}^{2}}+{{Y}^{2}}=6\]
C) \[{{X}^{2}}+2{{Y}^{2}}=6\]
D) None of the above
View Answer play_arrowquestion_answer106) If \[f(x)=\left\{ \begin{align} & \,\,\,\,\,\,\,\,\,{{x}^{2}},\,\,\,x\le 0 \\ & 2\,\sin x,\,\,\,x>0 \\ \end{align} \right.\,\,,\] then \[x=0\]is
A) point of minima
B) point of maxima
C) point of discontinuity
D) None of the above
View Answer play_arrowquestion_answer107) In a group \[(G,\,*),\] then equation \[x\,\,*\,\,a=b\] has a
A) unique solution \[b\,\,\,*\,\,{{a}^{-1}}\]
B) unique solution \[{{a}^{-1}}\,\,*\,\,b\]
C) unique solution \[{{a}^{-1}}\,\,*\,\,{{b}^{-1}}\]
D) many solutions
View Answer play_arrowquestion_answer108) A die is rolled twice and the sum of the numbers appearing on them is observed to be 7. What is the conditional probability that the number 2 has appeared at least once?
A) \[\frac{1}{2}\]
B) \[\frac{1}{3}\]
C) \[\frac{2}{3}\]
D) \[\frac{2}{5}\]
View Answer play_arrowquestion_answer109) The locus of the mid-points of the focal chord of the parabola\[{{y}^{2}}=4ax\]is
A) \[{{y}^{2}}=a\,(x-a)\]
B) \[{{y}^{2}}=2a\,(x-a)\]
C) \[{{y}^{2}}=4a\,(x-a)\]
D) None of these
View Answer play_arrowquestion_answer110) Find the value of \[\sin 12{}^\circ \,\sin 48{}^\circ \,\sin 54{}^\circ .\]
A) \[\frac{1}{2}\]
B) \[\frac{1}{4}\]
C) \[\frac{1}{6}\]
D) \[\frac{1}{8}\]
View Answer play_arrowquestion_answer111) In an equilateral triangle, the in radius, circumradius and one of the exradii are in the ratio
A) \[2:3:5\]
B) \[1:2:3\]
C) \[1:3:7\]
D) \[3:7:9\]
View Answer play_arrowquestion_answer112) Let p and q be two statements. Then, \[p\vee q\]is false, if
A) p is false and q is true
B) both p and q are false
C) both p and q are true
D) None of the above
View Answer play_arrowquestion_answer113) In how many ways 6 letters be posted in 5 different letter boxes?
A) \[{{5}^{6}}\]
B) \[{{6}^{5}}\]
C) \[5!\]
D) \[6!\]
View Answer play_arrowquestion_answer114) If A and B be two sets that \[A\times B\] consists of 6 elements. If three elements \[A\times B\]are (1, 4) (2, 6) and (3, 6), find \[B\times A\].
A) {(1, 4), (1, 6), (2, 4), (2, 6), (3, 4), (3, 6)}
B) {(4, 1), (4, 2), (4, 3), (6, 1), (6, 2), (6, 3)}
C) {(4, 4), (6, 6)}
D) {(4, 1), (6, 2), (6, 3)}
View Answer play_arrowquestion_answer115) Let \[f:R\to R\]be defined as \[f(x)={{x}^{2}}+1,\] find \[{{f}^{-1}}(-5).\]
A) \[\{\,\phi \,\}\]
B) \[\phi \]
C) \[\{\,5\,\}\]
D) \[\{\,-5,\,\,5\,\}\]
View Answer play_arrowquestion_answer116) If \[X\] is a poisson variate such that \[P(X=1)=P(X=2),\] then \[P\,(X=4)\]is equal to
A) \[\frac{1}{2{{e}^{2}}}\]
B) \[\frac{1}{3{{e}^{2}}}\]
C) \[\frac{2}{3{{e}^{2}}}\]
D) \[\frac{1}{{{e}^{2}}}\]
View Answer play_arrowquestion_answer117) The area enclosed by \[y=3x-5,\] \[y=0,\] \[x=3\] and \[x=5\]is
A) 12 sq units
B) 13 sq units
C) \[13\frac{1}{2}\] sq units
D) 14 sq units
View Answer play_arrowquestion_answer118) The order and degree of the differential equation \[{{\left( 1+4\frac{dy}{dx} \right)}^{2/3}}=4\frac{{{d}^{2}}y}{d{{x}^{2}}}\] are respectively
A) \[1,\,\frac{2}{3}\]
B) \[3,\,2\]
C) \[2,\,3\]
D) \[2,\,\frac{2}{3}\]
View Answer play_arrowquestion_answer119) The solution of the differential equation \[\frac{dy}{dx}={{(4x+y+1)}^{2}},\] is
A) \[(4x+y+1)=\tan \,(2x+C)\]
B) \[{{(4x+y+1)}^{2}}=2\tan \,(2x+C)\]
C) \[{{(4x+y+1)}^{3}}=3\tan \,(2x+C)\]
D) \[(4x+y+1)=2\tan \,(2x+C)\]
View Answer play_arrowquestion_answer120) The system of equations \[2x+y-5=0,\] \[x-2y+1=0,\] \[2x-14y-a=0,\] is consistent. Then, a is equal to
A) 1
B) 2
C) 5
D) None of these
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