question_answer1) In a communication system operating at wavelength 800 nm, only one percent of source frequency is available as signal bandwidth. The number of channels accommodated for transmitting TV signals of band width 6 MHz are (Take velocity of light \[c\text{ }=\text{ }3\text{ }\times \text{ }{{10}^{8}}\,m/s,\text{ }h=6.6\,\,\times \,\,{{10}^{-\,34}}J-s)\]
A) \[3.75\text{ }\times \text{ }{{10}^{6}}\] done clear
B) \[4.87\text{ }\times \text{ }{{10}^{5}}\] done clear
C) \[6.25\text{ }\times \text{ }{{10}^{5}}\] done clear
D) \[3.86\text{ }\times \text{ }{{10}^{6}}\] done clear
View Answer play_arrowquestion_answer2) The magnetic field associated with a light wave is given, at the origin, by \[B\text{ }=\text{ }{{B}_{0}}\] \[[sin(3.14\,\times \,\,{{10}^{7}})ct+sin(6.28\,\,\times \,{{10}^{6}})ct]\] If this light falls on a silver plate having a work function of 4.7 eV, what will be the maximum kinetic energy of the photo electrons? \[\left( c=3\text{ }\times \text{ }{{10}^{8}}\text{ }m{{s}^{-\,1}},\text{ }h\,\,=\,\,6.6\,\,\times \,\,{{10}^{-34}}\,J-s \right)\]
A) \[6.82\text{ }eV\] done clear
B) \[8.52\text{ }eV\] done clear
C) \[12.5\text{ }eV\] done clear
D) \[7.55\text{ }eV\] done clear
View Answer play_arrowquestion_answer3) The top of a water tank is open to air and its water level maintained. It is giving out \[0.74\text{ }{{m}^{3}}\] water per minute through a circular opening of 2 cm radius is its wall. The depth of the centre of the opening from the level of water in the tank is close to:
A) 6.0 m done clear
B) 9.6 m done clear
C) 2.9 m done clear
D) 4.8 m done clear
View Answer play_arrowquestion_answer4) A rod of mass 'M' and length '2L' is suspended at its middle by a wire. It exhibits torsional oscillations; If two masses each of 'm' are attached at distance 'L/2' from its centre on both sides, it reduces the oscillation frequency by \[20%\] The value of ratio m/M is close to:
A) 0.37 done clear
B) 0.57 done clear
C) 0.77 done clear
D) 0.17 done clear
View Answer play_arrowquestion_answer5) A parallel plate capacitor with square plates is filled with four dielectrics of dielectric constants \[{{K}_{1}},\text{ }{{K}_{2}},\text{ }{{K}_{3}},\text{ }{{K}_{4}}\] arranged as shown in the figure. The effective dielectric constant K will be:
A) \[K\,\,=\,\,\frac{({{K}_{1}}+{{K}_{2}})({{K}_{2}}+{{K}_{4}})}{{{K}_{1}}+{{K}_{2}}+{{K}_{3}}+{{K}_{4}}}\] done clear
B) \[K\,\,=\,\,\frac{({{K}_{1}}+{{K}_{2}})({{K}_{2}}+{{K}_{4}})}{2({{K}_{1}}+{{K}_{2}}+{{K}_{3}}+{{K}_{4}})}\] done clear
C) \[K\,\,=\,\,\frac{({{K}_{1}}+{{K}_{2}})({{K}_{3}}+{{K}_{4}})}{({{K}_{1}}+{{K}_{2}}+{{K}_{3}}+{{K}_{4}})}\] done clear
D) \[K\,\,=\,\,\frac{({{K}_{1}}+{{K}_{4}})({{K}_{2}}+{{K}_{3}})}{2({{K}_{1}}+{{K}_{2}}+{{K}_{3}}+{{K}_{4}})}\] done clear
E) None of these done clear
View Answer play_arrowquestion_answer6) A carbon resistance has a following colour code. What is the value of the resistance?
A) \[5.3\,M\,\Omega \,\,\pm \,\,5\,%\] done clear
B) \[530\,k\,\Omega \,\,\pm \,\,5%\] done clear
C) \[6.4\,k\,\Omega \,\,\pm \,10%\] done clear
D) \[6.4\,M\Omega \,\,\pm \,\,5%\] done clear
View Answer play_arrowquestion_answer7) A series AC circuit containing an inductor\[\left( 20\text{ }mH \right)\], a capacitor \[\left( 120\text{ }\mu F \right)\] and a resistor \[\left( 60\text{ }\Omega \right)\] is driven by an AC source of\[24\text{ }V/50\text{ }Hz\]. The energy dissipated in the circuit in 60 s is:
A) \[5.65\text{ }\times \text{ }{{10}^{2}}J\] done clear
B) \[2.26\text{ }\times {{10}^{3}}J\] done clear
C) \[5.17\text{ }\times \text{ }{{10}^{2}}\,J~\] done clear
D) \[3.39\text{ }\times \text{ }{{10}^{3}}\,J\] done clear
View Answer play_arrowquestion_answer8) A force acts on a 2 kg object so that its position is given as a function of time as\[x=3{{t}^{2}}+5\]. What is the work done by this force in first 5 seconds?
A) 950 J done clear
B) 900 J done clear
C) 875 J done clear
D) 850 J done clear
View Answer play_arrowquestion_answer9) One of the two identical conducting wires of length L is bent in the form of a circular loop and the other one into a circular coil. If the same current is passed in both, the ratio of the magnetic field at the central of the loop \[({{B}_{L}}),\,\,\,\,i.e.\,\,\,\frac{{{B}_{L}}}{{{B}_{C}}}\]will be:
A) \[\frac{1}{N}\] done clear
B) N done clear
C) \[{{N}^{2}}\] done clear
D) \[\frac{1}{{{N}^{2}}}\] done clear
View Answer play_arrowquestion_answer10) In a young's double slit experiment, the slits are placed 0.320 mm apart. Light of wavelength \[\lambda \text{ }=\text{ }500\text{ }nm\] is incident on the slits. The total number of bright fringes that are observed in the angular range \[-30{}^\circ \le \,\theta \le 30{}^\circ \] is:
A) 640 done clear
B) 641 done clear
C) 320 done clear
D) 321 done clear
View Answer play_arrowquestion_answer11) Two Carnot engines A and B are operated in series. The first one, A, receives heat at \[{{T}_{1}}\left( =600\text{ }K \right)\] and rejects to a reservoir at temperature Ta. The second engine B receives heat rejected by the first engine and, in turn, rejects to a heat reservoir at\[{{T}_{3}}(=400\text{ }K)\]. Calculate the temperature \[{{T}_{2}}\] if the work outputs of the engines are equal:
A) 500K done clear
B) 300K done clear
C) 600 K done clear
D) 400 K done clear
View Answer play_arrowquestion_answer12) At a given instant, say\[t=0\], two radioactive substances A and B have equal activities. The ratio \[\frac{{{R}_{B}}}{{{R}_{A}}}\] of their activities after time t itself decays with time t as \[{{e}^{-3t}}\]. If the half-life of A is ln2, the half-life of B is-
A) \[\frac{In\,2}{4}\] done clear
B) \[4\ln 2\] done clear
C) 2ln2 done clear
D) \[\frac{In\,2}{2}\] done clear
View Answer play_arrowquestion_answer13) Two plane mirrors are inclined to each other such that a ray of light incident on the first mirror \[\left( {{M}_{1}} \right)\] and parallel to the second mirror \[({{M}_{2}})\] is finally reflected from the second mirror \[({{M}_{2}})\] parallel to the first mirror\[\left( {{M}_{1}} \right)\]. The angle between the two mirrors will be:
A) \[60{}^\circ \] done clear
B) \[75{}^\circ \] done clear
C) \[45{}^\circ \] done clear
D) \[90{}^\circ \] done clear
View Answer play_arrowquestion_answer14) [a] In the given circuit the internal resistance of the 18 V cell is negligible. If \[{{R}_{1}}\,\,=\,\,400\,\Omega \], \[{{R}_{3}}=100\text{ }\Omega \] and \[{{R}_{4}}=500\Omega \]and the reading of an ideal voltmeter across \[{{R}_{4}}\] is 5 V, then the value of \[{{R}_{2}}\] will be:
A) \[550\text{ }\Omega \] done clear
B) \[450\text{ }\Omega \] done clear
C) \[230\,\,\Omega \] done clear
D) \[300\,\,\Omega \] done clear
View Answer play_arrowquestion_answer15) Charge is distributed within a sphere of radius R with a volume charge density\[\rho (r)=\frac{A}{{{r}^{2}}}{{e}^{{}^{-2r}/{}_{a}}}\], where A and a are constants. If Q is the total charge of this charge distribution, the radius R is:
A) \[\frac{a}{2}\,\log \,\left( 1-\frac{Q}{2\,\pi \,a\,A} \right)\] done clear
B) \[\frac{a}{2}\,\log \,\left( 1-\frac{1}{\frac{Q}{2\,\pi \,a\,A}} \right)\] done clear
C) \[a\,\,\log \,\,\left( \frac{1}{1-\frac{Q}{2\,\pi \,a\,A}} \right)\] done clear
D) \[a\,\,\log \,\,\left( 1-\frac{Q}{2\,\pi \,a\,A} \right)\] done clear
View Answer play_arrowquestion_answer16) Expression for time in terms of G (universal gravitational constant), h (Planck constant) and c (speed of light) is proportional to:
A) \[\sqrt{\frac{Gh}{{{c}^{5}}}}\] done clear
B) \[\sqrt{\frac{h{{c}^{5}}}{G}}\] done clear
C) \[\sqrt{\frac{Gh}{{{c}^{3}}}}\] done clear
D) \[\sqrt{\frac{{{c}^{3}}}{Gh}}\] done clear
View Answer play_arrowquestion_answer17) In a car race on straight road, car A takes a time t less than car B at the finish and passes finishing point with a speed 'v' more than that of car B. Both the cars start, from rest and travel with constant acceleration \[{{a}_{1}}\text{ }and\text{ }{{a}_{2}}\] respectively. Then 'v' is equal to:
A) \[\sqrt{{{a}_{1}}\,{{a}_{2}}}\,\,t\] done clear
B) \[\frac{2{{a}_{1}}{{a}_{2}}}{{{a}_{1}}+{{a}_{2}}}\,\,t\] done clear
C) \[\frac{{{a}_{1}}+{{a}_{2}}}{2}\,\,t\] done clear
D) \[\sqrt{2{{a}_{1}}{{a}_{2}}}\,\,t\] done clear
View Answer play_arrowquestion_answer18) A mass of 10 kg is suspended vertically by a rope from the roof. When a horizontal force is applied on the rope at some point, the rope deviated at an angle of \[45{}^\circ \] at the roof point. If the suspended mass is at equilibrium, the magnitude of the force applied is \[\left( g=10\text{ }m{{s}^{-}}^{2} \right)\]
A) 100 N done clear
B) 70 N done clear
C) 140 N done clear
D) 200 N done clear
View Answer play_arrowquestion_answer19) The pitch and the number of divisions, on the circular scale, for a given screw gauge are 0.5 mm and 100 respectively. When the screw gauge is fully tightened without any object, the zero of its circular scale lies 3 divisions below the mean line. The readings of the main scale and the circular scale, for a thin sheet, are 5.5 mm and 48 respectively, the thickness of this sheet is:
A) 5.725 mm done clear
B) 5.950 mm done clear
C) 5.755 mm done clear
D) 5.740 mm done clear
View Answer play_arrowquestion_answer20) A power transmission line feeds input power at 2300 V to a step down transformer with its primary windings having 4000 turns. The output power is delivered at 230 V by the transformer. If the current in the primary of the transformer is 5A and its efficiency is \[90%\], the output current would be:
A) 45 A done clear
B) 35 A done clear
C) 25 A done clear
D) 50 A done clear
View Answer play_arrowquestion_answer21) A 15 g mass of nitrogen gas is enclosed in a vessel at a temperature\[27{}^\circ C\]. Amount of heat transferred to the gas, so that rms velocity of molecules is doubled, is about: [Take\[\,R=8.3\] J/K mole]
A) 10 kJ done clear
B) 0.9 KJ done clear
C) 14 kJ done clear
D) 6 kJ done clear
View Answer play_arrowquestion_answer22) The position co-ordinates of a particle moving in a 3-D coordinate system is given by \[~x=a\text{ }cos\omega t\] \[y=a\text{ }sin\omega t\] and \[z=a\omega t\] The speed of the particle is:
A) \[a\omega \] done clear
B) \[\sqrt{3}\,a\omega \] done clear
C) \[\sqrt{2}\,a\omega \] done clear
D) \[2\,a\omega \] done clear
View Answer play_arrowquestion_answer23) A particle is executing simple harmonic motion (SHM) of amplitude A, along the x-axis, about\[x=0\]. When its potential Energy (PE) equals kinetic energy (KE), the position of the particle will be:
A) \[\frac{A}{2\sqrt{2}}\] done clear
B) \[\frac{A}{\sqrt{2}}\] done clear
C) \[\frac{A}{2}\] done clear
D) A done clear
View Answer play_arrowquestion_answer24) The energy required to take a satellite to a height 'h' above Earth surface (radius of Earth \[=6.4\times {{10}^{3}}km\]) is \[{{E}_{1}}\] and kinetic energy required for the satellite to be in a circular orbit at this height is \[{{E}_{2}}\]. The value of h for which \[{{E}_{1}}\] and \[{{E}_{2}}\] are equal, is:
A) \[3.2\times {{10}^{3}}\text{ }km\] done clear
B) \[1.6\times {{10}^{3}}km\] done clear
C) \[1.28\times {{10}^{4}}km\] done clear
D) \[6.4\times {{10}^{3}}km\] done clear
View Answer play_arrowquestion_answer25) A musician using an open flute of length 50 cm produces second harmonic sound waves. A person runs towards the musician from another end of a hall at n speed of 10 km/h. If the wave speed is 330 m/s, the frequency heard by the running person shall be close to:
A) 753 Hz done clear
B) 666 Hz done clear
C) 500 Hz done clear
D) 333 Hz done clear
View Answer play_arrowquestion_answer26) A particle having the same charge as of electron moves in a circular path of radius 0.5 cm under the influence of a magnetic field of 0.5 T. If an electric field of 100 V/m makes it to move in a straight path, then the mass of the particle is (Given charge of electron \[=1.6\,\times \,{{10}^{-19}}C\])
A) \[1.6\times {{10}^{-19}}kg\] done clear
B) \[1.6\times {{10}^{-27}}\text{ }kg\] done clear
C) \[9.1\times {{10}^{-}}^{31}kg\] done clear
D) \[2.0\times {{10}^{-}}^{24}kg\] done clear
View Answer play_arrowquestion_answer27) A rod of length 50 cm is pivoted at one end. It is raised such that if makes an angle of \[30{}^\circ \]from the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal (in rad \[{{s}^{-1}}\]) will be (\[g=10\text{ }m{{s}^{-2}}\])
A) \[\sqrt{\frac{30}{2}}\] done clear
B) \[\frac{\sqrt{20}}{3}\] done clear
C) \[\frac{\sqrt{30}}{2}\] done clear
D) \[\sqrt{30}\] done clear
View Answer play_arrowquestion_answer28) The energy associated with electric field is (\[{{U}_{E}}\]) and with magnetic field is (\[{{U}_{B}}\]) for an electromagnetic wave in free space. Then:
A) \[{{U}_{E}}<{{U}_{B}}\] done clear
B) \[{{U}_{E}}=\,\frac{{{U}_{B}}}{2}\] done clear
C) \[{{U}_{E}}={{U}_{B}}\] done clear
D) \[{{U}_{E}}>{{U}_{B}}\] done clear
View Answer play_arrowquestion_answer29) Two point charges \[{{q}_{1}}\,(\sqrt{10}\,\mu C)\]and \[{{q}_{2}}(-25\,\,\mu C)\] are placed on the x-axis at \[x=1\,m\] and \[x=4\,m\]respectively. The electric field (in V/m) at a point \[y=3\]m on y-axis is, [take\[\frac{1}{4\pi {{\in }_{0}}}\,\,=\,\,9\,\times {{10}^{9}}\,N{{m}^{2}}{{C}^{-}}^{2}\]]
A) \[(-81\widehat{i}\,\,+\,\,81\widehat{j})\,\,\times \,{{10}^{2}}\] done clear
B) \[(81\widehat{i}-81\widehat{j})\times {{10}^{2}}\] done clear
C) \[(63\widehat{i}\,\,-\,\,27\widehat{j})\,\,\times \,{{10}^{2}}\] done clear
D) \[(-63\widehat{i}+27\widehat{j})\times {{10}^{2}}\] done clear
View Answer play_arrowquestion_answer30) Ge and Si diodes start conducting at 0.3 V and 0.7 V respectively. In the following figure if Ge diode connection are reversed, the value of \[{{V}_{0}}\] changes by: (assume that the Ge diode has large breakdown voltage)
A) 0.4 V done clear
B) 0.6 V done clear
C) 0.8 V done clear
D) 0.2 V done clear
View Answer play_arrowquestion_answer31) Which of the following combination of statements is true regarding the interpretation of the atomic orbitals?
[A] An electron in an orbital of high angular momentum stays away from the nucleus than an electron in the orbital of lower angular momentum. |
[B] For a given value of the principal quantum number, the size of the orbit is inversely proportional to the azimuthal quantum number. |
[C] According to wave mechanics, the ground state angular momentum is equal to\[\frac{h}{2\pi }\]. |
[D] The plot of \[\psi \,Vs\,\,r\]for various azimuthal quantum numbers, shows peak shifting towards higher r value. |
A) [B], [C] done clear
B) [A], [D] done clear
C) [A], [B] done clear
D) [A], [C] done clear
View Answer play_arrowquestion_answer32) A solution containing 62 g ethylene glycol in 250 g water is cooled to\[-10{}^\circ C\]. If \[{{K}_{f}}\] for water is \[1.86\text{ }K\text{ }kg\text{ }mo{{l}^{-1}}\], the amount of water (in g) separated as ice is:
A) 32 done clear
B) 16 done clear
C) 64 done clear
D) 48 done clear
View Answer play_arrowquestion_answer33) For coagulation of arsenious sulphide sol which one of the following salt solution will be most effective?
A) \[AlC{{l}_{3}}\] done clear
B) \[NaCl\] done clear
C) \[N{{a}_{3}}P{{O}_{4}}~~~~~~~~\] done clear
D) \[BaC{{l}_{2}}\] done clear
View Answer play_arrowquestion_answer34) In which of the following processes, the bond order has increased and paramagnetic character has changed to diamagnetic?
A) \[NO\,\,\to \,\,N{{O}^{+}}\] done clear
B) \[{{O}_{2}}\to {{O}_{{{2}^{+}}}}\] done clear
C) \[{{N}_{2}}\,\,\to \,\,{{N}_{{{2}^{+}}}}\] done clear
D) \[{{O}_{2}}\,\,\to \,\,{{O}_{{{2}^{2-}}}}\] done clear
View Answer play_arrowquestion_answer35) The complex that has highest crystal field splitting energy \[(\Delta )\], is:
A) \[{{K}_{3}}\left[ Co{{\left( CN \right)}_{6}} \right]\] done clear
B) \[{{K}_{2}}\left[ CoC{{l}_{4}} \right]\] done clear
C) \[\left[ Co{{\left( N{{H}_{3}} \right)}_{5}}Cl \right]\text{ }C{{l}_{2}}\] done clear
D) \[\left[ Co{{\left( N{{H}_{3}} \right)}_{5}}\left( {{H}_{2}}O \right)C{{l}_{3}} \right]\] done clear
View Answer play_arrowquestion_answer36) For the following reaction, the mass of water produced from 4.45 g of \[{{C}_{57}}{{H}_{110}}{{O}_{6}}\] is: \[2{{C}_{57}}{{H}_{110}}{{O}_{6}}(s)+163{{O}_{2}}(g)\to 114C{{O}_{2}}(g)+110{{H}_{2}}O(\ell )\]
A) 445 g done clear
B) 490 g done clear
C) 495g done clear
D) 890 g done clear
View Answer play_arrowquestion_answer37) If the standard electrode potential for a cell is 2 V at 300 K, the equilibrium constant (K) for the reaction \[Zn(s)+C{{u}^{2+}}(aq)\,\,\,\rightleftharpoons \,\,Z{{n}^{2+}}(aq)+Cu\,(s)\] At 300 K is approximately \[\left( R=8J{{K}^{-}}^{1}mo{{l}^{-1}},\text{ }F\,\,=\,\,96000\text{ }C\text{ }mo{{l}^{-1}} \right)\]
A) \[{{e}^{160}}\] done clear
B) \[{{e}^{-160}}\] done clear
C) \[{{e}^{-80}}\] done clear
D) \[{{e}^{320}}\] done clear
View Answer play_arrowquestion_answer38) The entropy change associated with the conversion of 1 kg of ice at 273 K to water vapours at 383 K is: (Specific heat of water liquid and water vapour are \[4.2\text{ }kJ\text{ }{{K}^{-1}}\,k{{g}^{-}}^{1}\] and \[2.0\text{ }kJ\text{ }{{K}^{-1}}\,k{{g}^{-}}^{1}\]heat of liquid fusion and vapourisation of water are \[334\text{ }kJ\text{ }k{{g}^{-1}}\] and \[2491\text{ }kJ\text{ }k{{g}^{-1}}\], respectively), \[(log\text{ }273\,\,\,=\,\,2.436\], \[log\text{ }373=2.572,\text{ }log\text{ }383\,\,\text{=}\,\,2.583)\]
A) \[2.64\text{ }kJ\text{ }k{{g}^{-1}}\text{ }{{K}^{-1}}\] done clear
B) \[9.26\text{ }kJ\text{ }k{{g}^{-1}}\text{ }{{K}^{-1}}\] done clear
C) \[7.90\text{ }kJ\text{ }k{{g}^{-1}}\text{ }{{K}^{-1}}~\] done clear
D) \[8.49\text{ }kJ\text{ }k{{g}^{-1}}\text{ }{{K}^{-1}}\] done clear
View Answer play_arrowquestion_answer39) For the reaction, \[2A\,\,+\,\,B\,\,\to \] products, when the concentrations of A and B both were doubled, the rate of the reaction increased from \[0.3\text{ }mol\text{ }{{L}^{-1}}{{s}^{-}}^{1}\] to\[2.4\text{ }mol\text{ }{{L}^{-1}}{{s}^{-}}^{1}\]. When the concentration of A alone is doubled, the rate increased from \[0.3\text{ }mol\text{ }{{L}^{-}}^{1}\,{{s}^{-}}^{1}\] to\[0.6\text{ }mol\,\,L{{\,}^{-}}^{1}s{{\,}^{-1}}\]. Which one of the following statements is correct?
A) Order of the reaction with respect to A is 2. done clear
B) Total order of the reaction is 4. done clear
C) Order of the reaction with respect to B is 1. done clear
D) Order of the reaction with respect to B is 2. done clear
View Answer play_arrowquestion_answer40) 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_answer41) The increasing basicity order of the following compounds is:
[a] |
[b] |
[c] |
[d] |
A) [a] <[b] < [c] < [d] done clear
B) [d] < [c] < [b] < [a] done clear
C) [d] < [c] < [a] < [b] done clear
D) [a] < [b] < [d] < [c] done clear
View Answer play_arrowquestion_answer42) Homoleptic octahedral complexes of a metal ion \[{{M}^{3+}}\] with three monodentate ligands \[{{L}_{1}},\text{ }{{L}_{2}}and\text{ }{{L}_{3}}\] absorb wavelengths in the region of green, blue and red respectively. The increasing order of the ligand strength is-
A) \[{{L}_{3}}<{{L}_{2}}<{{L}_{1}}\] done clear
B) \[{{L}_{3}}<{{L}_{1}}<{{L}_{2}}\] done clear
C) \[{{L}_{1}}<{{L}_{2}}<{{L}_{3}}\] done clear
D) \[{{L}_{2}}<{{L}_{1}}<{{L}_{3}}\] done clear
View Answer play_arrowquestion_answer43) When the first electron gain enthalpy \[\left( {{\Delta }_{eg}}H \right)\] of oxygen is \[-141\text{ }kJ/mol\], Its second electron gain enthalpy is:
A) a positive value done clear
B) a more negative value than the first done clear
C) almost the same as that of the first done clear
D) negative, but less negative than the first done clear
View Answer play_arrowquestion_answer44) Consider the following reversible chemical reactions:
\[{{A}_{2}}(g)\,\,+\,\,{{B}_{2}}\,(g)\,\,\,\,\,2AB\,(g)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,.......\,(1)\] |
\[6AB\,(g)\,\,\,\,\,3{{A}_{2}}\,(g)\,\,+3{{B}_{2}}\,(g)\,\,\,\,\,\,\,\,\,\,\,\,\,.......\,\,(2)\] |
A) \[{{K}_{2}}={{K}_{1}}^{-3}\] done clear
B) \[{{K}_{1}}{{K}_{2}}\,\,=\,\,\frac{1}{3}\] done clear
C) \[{{K}_{1}}{{K}_{2}}\,\,=\,\,3\] done clear
D) \[{{K}_{2}}={{K}_{1}}^{3}\] done clear
View Answer play_arrowquestion_answer45) Good reducing nature of \[{{H}_{3}}P{{O}_{2}}\] attributed to the presence of:
A) One \[P-H\] bond done clear
B) Two \[P-OH\] bonds done clear
C) One \[P-OH\] bond done clear
D) Two \[P-H\]bonds done clear
View Answer play_arrowquestion_answer46) The tests performed on compound X and their inferences are:
Test | Inference | |
[A] | 2, 4-DNP test | Coloured Precipitate |
[B] | Iodoform test | Yellow Precipitate |
[C] | Azo-dye test | No dye precipitate |
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer47) The pH rain water, is approximately:
A) 5.6 done clear
B) 6.5 done clear
C) 7.5 done clear
D) 7.0 done clear
View Answer play_arrowquestion_answer48) Which of the following compounds is not aromatic?
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer49) The correct statement regarding the given Ellingham diagram is:
A) Coke cannot be used for the extraction of Cu from \[C{{u}_{2}}O\] done clear
B) At\[500{}^\circ C\], coke can be used for the extraction of Zn from \[ZnO\] done clear
C) At\[1400{}^\circ C\], Al can be used for the extraction of Zn from \[ZnO\] done clear
D) At \[800{}^\circ C\] Cu can be used for the extraction of Zn from \[ZnO\] done clear
View Answer play_arrowquestion_answer50) The temporary hardness of water is due to:
A) \[N{{a}_{2}}S{{O}_{4}}\] done clear
B) \[CaC{{l}_{2}}\] done clear
C) \[NaCI\] done clear
D) \[Ca{{\left( HC{{O}_{3}} \right)}_{2}}_{~}~~~~~~~~~\] done clear
View Answer play_arrowquestion_answer51) The major product of the following reaction is:
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer52) The products formed in the reaction of cumene with \[{{O}_{2}}\] followed by treatment with dil. HCl are:
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer53) At\[100{}^\circ C\], copper (Cu) has FCC unit cell structure with cell edge length of x \[\overset{o}{\mathop{A}}\,\]. What is the approximate density of Cu (in\[g\text{ }c{{m}^{-}}^{3}\]) at this temperature? [Atomic Mass of \[Cu\,\,=\,\,63.55\,u\]]
A) \[\frac{422}{{{x}^{3}}}\] done clear
B) \[\frac{205}{{{x}^{3}}}\] done clear
C) \[\frac{211}{{{x}^{3}}}\] done clear
D) \[\frac{105}{{{x}^{3}}}\] done clear
View Answer play_arrowquestion_answer54) The transition element that has lowest enthalpy of atomization, is:
A) Zn done clear
B) Fe done clear
C) Cu done clear
D) V done clear
View Answer play_arrowquestion_answer55) Which of the following conditions in drinking water causes methemoglobinemia?
A) > 50 ppm of nitrate done clear
B) > 50 ppm of chloride done clear
C) > 50 ppm of lead done clear
D) > 100 ppm of sulphate done clear
View Answer play_arrowquestion_answer56) The major product formed in the following reaction is:
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer57) The correct match between Item-I and Item-II is:
Item-I | Item-II | ||
[A] | Benzaldehyde | (P) | Mobile phase |
[B] | Alumina | (Q) | Adorbent |
[C] | Acetonitrile | (R) | Adsorbate |
A) [A] \[\to \] (Q); [B] \[\to \] (P); [C] \[\to \] (R) done clear
B) [A] \[\to \] (Q); [B] \[\to \] (R); [C] \[\to \] (P) done clear
C) [A] \[\to \] (P); [B] \[\to \] (R); [C] \[\to \] (Q) done clear
D) [A] \[\to \] (R); [B] \[\to \] (Q); [C] \[\to \] (P) done clear
View Answer play_arrowquestion_answer58) The metal that forms nitride by reacting directly with N2 of air, is:
A) Li done clear
B) Cs done clear
C) K done clear
D) Rb done clear
View Answer play_arrowquestion_answer59) The major product of the following reaction is:
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer60) The correct sequence of amino acids present in the tripetide given below is:
A) Val - Ser - Thr done clear
B) Thr - Ser - Vnl done clear
C) Thr - Ser - Leu done clear
D) Leu - Ser - Thr done clear
View Answer play_arrowquestion_answer61) Let \[{{z}_{0}}\] be a root of the quadratic equation, \[{{x}^{2}}+x+1=0\]. If \[z=3+6i\,{{z}_{0}}^{81}-\,3i\,{{z}_{0}}^{93}\], then arg z is equal to:
A) \[\frac{\pi }{6}\,\] done clear
B) \[\frac{\pi }{3}\,\] done clear
C) 0 done clear
D) \[\frac{\pi }{4}\,\] done clear
View Answer play_arrowquestion_answer62) Let f: \[\left[ 0,\text{ }1 \right]\,\,\to \,\,R\] be such that\[f\left( xy \right)=f\left( x \right).f\left( y \right)\], for all \[x,\,\,y\,\,\in \,\,\,[0,\,\,\,1]\] and\[f(0)\,\,\ne \,\,0\]. If \[y\,\,=\,\,y(x)\]satisfies the differential equation, \[\frac{dy}{dx}\,\,=\,\,f(x)\,\]with \[y\left( 0 \right)\,\,=\,\,1\], then \[y\left( \frac{1}{4} \right)+y\left( \frac{3}{4} \right)\]is equal to:
A) 2 done clear
B) 3 done clear
C) 5 done clear
D) 4 done clear
View Answer play_arrowquestion_answer63) The coefficient of \[{{t}^{4}}\] in the expansion of \[{{\left( \frac{1-{{t}^{6}}}{1-t} \right)}^{3}}\]
A) 15 done clear
B) 10 done clear
C) 14 done clear
D) 12 done clear
View Answer play_arrowquestion_answer64) Let \[\overrightarrow{a}=\widehat{i}+\widehat{j}\,\,+\sqrt{2}\widehat{k},\,\,\,\overrightarrow{b}={{b}_{1}}\widehat{i}\,\,+\,{{b}_{2}}\widehat{j}\,\,+\,\,\sqrt{2}\widehat{k}\]and \[\overrightarrow{c}=5\widehat{i}\,\,+\,\,\widehat{j}\,\,+\,\,\sqrt{2}\widehat{k}\] be three vectors such that the projection vector of \[\overrightarrow{b}\] on \[\overrightarrow{a}\] is \[\overrightarrow{a}\]. If \[\overrightarrow{a}\,\,+\,\,\overrightarrow{b}\] is perpendicular to \[\overrightarrow{c}\], then \[\left| \overrightarrow{b} \right|\] is equal to:
A) 4 done clear
B) \[\sqrt{22}\] done clear
C) 6 done clear
D) \[\sqrt{32}\] done clear
View Answer play_arrowquestion_answer65) If \[f\left( x \right)\,\,=\,\int{\frac{5{{x}^{8}}+7{{x}^{6}}}{{{({{x}^{2}}+1+2{{x}^{7}})}^{2}}}}\,\,dx\,,\,\,\,(x\,\,\ge \,\,0)\,\], and \[f\left( 0 \right)\,\,\,=\,\,0\], then the value of f(1) is:
A) \[-\frac{1}{2}\] done clear
B) \[-\frac{1}{4}\] done clear
C) \[\frac{1}{4}\] done clear
D) \[\frac{1}{2}\] done clear
View Answer play_arrowquestion_answer66) If \[x\,\,=\,\,3\text{ }tan\text{ }t\] and \[y\,\,=\,\,3\text{ }sec\text{ }t\], then the value of \[\frac{{{d}^{2}}y}{d{{x}^{2}}}\] at \[t=\frac{\pi }{4}\]is:
A) \[\frac{3}{2\sqrt{2}}\] done clear
B) \[\frac{1}{6}\] done clear
C) \[\frac{1}{6\sqrt{2}}\] done clear
D) \[\frac{1}{3\sqrt{2}}\] done clear
View Answer play_arrowquestion_answer67) The sum of the following series \[1+6+\frac{9({{1}^{2}}+{{2}^{2}}+{{3}^{2}})}{7}\,\,+\,\,\frac{12({{1}^{2}}+{{2}^{2}}+{{3}^{2}}+{{4}^{2}})}{9}+\] \[\frac{15({{1}^{2}}+{{2}^{2}}+......\,\,+{{5}^{2}})}{11}\,+\,.....\]up to 15 terms, is:
A) 7830 done clear
B) 7520 done clear
C) 7820 done clear
D) 7510 done clear
View Answer play_arrowquestion_answer68) Let a, b and c be the\[{{7}^{th}}\], \[{{11}^{th}}\] and \[{{13}^{th}}\] terms respectively of a non-constant A.P. If these are also the three consecutive terms of a G.P., then \[\frac{a}{c}\] is equal to:
A) \[\frac{7}{13}\] done clear
B) 2 done clear
C) 4 done clear
D) \[\frac{1}{2}\] done clear
View Answer play_arrowquestion_answer69) A hyperbola has its centre at the origin, passes through the point \[\left( 4,\text{ }2 \right)\] and has transverse axis of length 4 along the x-axis. Then the eccentricity of the hyperbola is:
A) \[\frac{3}{2}\] done clear
B) \[\frac{2}{\sqrt{3}}\] done clear
C) 2 done clear
D) \[\sqrt{3}\] done clear
View Answer play_arrowquestion_answer70) Let the equations of two sides of a triangle be \[3x-2y+6=0\] and\[4x+5y-20=0\]. If the orthocentre of this triangle is at \[\left( 1,\text{ }1 \right)\], then the equation of its third side is:
A) \[26x\,-\,122y\,-\,1675\,=\,0\] done clear
B) \[26x\,+61y\,+\,1675\,=\,0\] done clear
C) \[122y\,-\,\,26x\,-\,1675\,=\,0\] done clear
D) \[122y\,+\,\,26x\,+\,1675\,=\,0\] done clear
View Answer play_arrowquestion_answer71) A data consists of n observations: \[{{x}_{1}},\,\,{{x}_{2}},\,\,\,....,\,\,{{x}_{n}},\]. If \[\sum\limits_{i\,=\,1}^{n}{{{({{x}_{i}}+1)}^{2}}\,\,=\,\,9n}\] and \[\sum\limits_{i\,=\,1}^{n}{{{({{x}_{i}}-1)}^{2}}=5n}\]then the standard deviation of this data is:
A) 2 done clear
B) 4 done clear
C) 3 done clear
D) 1 done clear
View Answer play_arrowquestion_answer72) If \[0\,\,\le \,\,x\,<\,\,\frac{\pi }{2}\] , then the number of values of x for which \[\sin \,\,x-sin\text{ 2}x+sin\text{ }3x=0\] is
A) 2 done clear
B) 4 done clear
C) 3 done clear
D) 1 done clear
View Answer play_arrowquestion_answer73) If the tines \[x=ay+b,\]\[z=cy+d\]and \[x=a'z\,\,+b'\], \[y\,\,=\,\,c'z\,\,+d'\] are perpendicular then:
A) \[cc'+a+a'=0\] done clear
B) \[aa'+c+c'=0\] done clear
C) \[bb'+cc'+1=0\] done clear
D) \[ab'+bc'+1=0\] done clear
View Answer play_arrowquestion_answer74) The equation of the plane containing the straight line \[\frac{x}{2}\,\,=\,\,\frac{y}{3}\,\,=\,\,\frac{z}{4}\]and perpendicular to the plane containing the straight lines \[\frac{x}{3}=\frac{y}{4}=\frac{z}{2}\,\,and\,\,\frac{x}{4}=\frac{y}{2}=\frac{z}{3}\]
A) \[3x+2y-3z\,\,=\,\,0\] done clear
B) \[x+2y-2z\,\,=\,\,0\] done clear
C) \[x-2y+z=0\] done clear
D) \[~5x+2y-4z=0\] done clear
View Answer play_arrowquestion_answer75) Let f be a differentiable function from, R to R such that\[\left| f(x)-f(y) \right|\,\,\le \,\,2\,\,{{\left| x-y \right|}^{3/2}}\], for all\[x,\,\,y\,\,\in \,\,\,R.\,\]. If \[f\left( 0 \right)=1\] then \[\int\limits_{0}^{1}{{{f}^{2}}\left( x \right)dx}\] is equal to:
A) 2 done clear
B) \[\frac{1}{2}\] done clear
C) 0 done clear
D) 1 done clear
View Answer play_arrowquestion_answer76) Let S be the set of all triangles in the xy-plane, each having one vertex at the origin and the other two vertices lie on coordinate axes with integral coordinates. If each triangle in S has area 50 sq. units, then the number of elements in the set S is:
A) 32 done clear
B) 36 done clear
C) 9 done clear
D) 18 done clear
View Answer play_arrowquestion_answer77) The area of the region \[A=\{(x,\,\,y):0\,\,\le \,\,y\,\,\le \,\,x|x|+1\,\,and\,\,-\,1\le x\le 1\}\]in sq. units, is :
A) \[\frac{4}{3}\] done clear
B) \[\frac{1}{3}\] done clear
C) \[\frac{2}{3}\] done clear
D) 2 done clear
View Answer play_arrowquestion_answer78) If the circles \[{{x}^{2}}+{{y}^{2}}-16x-20y+164={{r}^{2}}\]and \[{{\left( x-4 \right)}^{2}}+{{\left( y-7 \right)}^{2}}=36\] intersect at two distinct points, then
A) \[r\,\,>\,\,11\] done clear
B) \[r\,\,=\,\,11\] done clear
C) \[1\,\,<\,\,r\,\,<\,\,11\] done clear
D) \[0\,\,<\,\,r\,\,<\,\,1\] done clear
View Answer play_arrowquestion_answer79) An urn contains 5 red and 2 green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red, is:
A) \[\frac{27}{49}\] done clear
B) \[\frac{26}{49}\] done clear
C) \[\frac{32}{49}\] done clear
D) \[\frac{21}{49}\] done clear
View Answer play_arrowquestion_answer80) If then A is:
A) invertible only if \[t=n\] done clear
B) invertible for all \[t\,\,\in \,\,R\] done clear
C) invertible only if \[t=\frac{\pi }{2}\] done clear
D) not invertible for any \[t\text{ }\in \text{ }R\] done clear
View Answer play_arrowquestion_answer81) The number of natural numbers less than 7,000 which can be formed by using the digits 0, 1, 3, 7, 9 (repetition of digits allowed) is equal to:
A) 372 done clear
B) 375 done clear
C) 250 done clear
D) 374 done clear
View Answer play_arrowquestion_answer82) If \[\int\limits_{0}^{\pi /3}{\frac{\tan \,\theta }{\sqrt{2\,k\,\,\sec \,\theta }}}\,d\,\theta \,\,=\,\,1-\frac{1}{\sqrt{2}}\,,\text{ }\left( k\,\,>\,\,0 \right)\], then the value of k is:
A) 2 done clear
B) 1 done clear
C) 4 done clear
D) \[\frac{1}{2}\] done clear
View Answer play_arrowquestion_answer83) The number of all possible positive integral values of a for which the roots of the quadratic equation, \[6{{x}^{2}}-11x+\alpha =0\] are rational numbers is:
A) 4 done clear
B) 2 done clear
C) 5 done clear
D) 3 done clear
View Answer play_arrowquestion_answer84) The logical statement \[[\tilde{\ }\left( \tilde{\ }p\vee q \right)\vee (p\wedge r)]\,\,\wedge \,(\sim q\wedge r)\,\] is equivalent to:
A) \[(\sim p\wedge \sim q)\wedge r\] done clear
B) \[(p\wedge \sim q)\vee r\] done clear
C) \[\left( p\wedge r \right)\,\,\wedge \tilde{\ }\,q\] done clear
D) \[\tilde{\ }p\wedge r\] done clear
View Answer play_arrowquestion_answer85) If the system of linear equations
\[x-4y+7z=g\] |
\[3y-5z=h\] |
\[-2x+5y-9z=k\] |
A) \[g+2h+k=0\] done clear
B) \[g+h+2k=0\] done clear
C) \[g+h+k=0\] done clear
D) \[2g+h+k=0\] done clear
View Answer play_arrowquestion_answer86) If both the roots of the quadratic equation \[{{x}^{2}}-mx+4=0\] are real and distinct and they lie in the interval \[\left[ 1,\text{ }5 \right]\], then m lies in the interval:
A) (4, 5) done clear
B) (\[-5,\,\,-4\]) done clear
C) (3, 4) done clear
D) (5, 6) done clear
View Answer play_arrowquestion_answer87) If \[x=si{{n}^{-1}}\left( sin\text{ }10 \right)\] and \[y=co{{s}^{-1}}\,\,cos10)\], then \[y-x\] is equal to:
A) 0 done clear
B) \[7\,\pi \] done clear
C) \[\pi \] done clear
D) 10 done clear
View Answer play_arrowquestion_answer88) Let \[A=\{x\text{ }\in \text{ }R:x\] is not a positive integer}. Define a function \[f:A\to R\] as \[f(x)\,\,=\,\,\frac{2x}{x-1}\], then f is:
A) not injective done clear
B) surjective but not injective done clear
C) injective but not surjective done clear
D) neither injective nor surjective done clear
View Answer play_arrowquestion_answer89) For each\[x\text{ }\in \text{ }R\], let [x] be the greatest integer less than or equal to x. Then\[\underset{x\to {{0}^{-}}}{\mathop{\lim }}\,\,\frac{x([x]+\left| x \right|)\,sin\,[x]}{\left| x \right|}\]
A) 1 done clear
B) 0 done clear
C) \[sin\text{ }1\] done clear
D) \[-sin\text{ }1\] done clear
View Answer play_arrowquestion_answer90) Let A(\[4,\text{ }-4\]) and B(9, 6) be points on the parabola, \[{{y}^{2}}=4x\]. Let C be chosen on the arc AOB of the parabola, where 0 is the origin, such that the area of \[\Delta \,ACB\] is maximum. Then, the area (in sq. units) of \[\Delta \,ACB\], is:
A) 32 done clear
B) \[31\frac{3}{4}\] done clear
C) \[30\frac{1}{2}\] done clear
D) \[31\frac{1}{4}\] done clear
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