question_answer1) A Mixture of 2 moles of helium gas\[\left( atomic\text{ }mass=4u \right)\], and 1 mole of argon gas \[\left( atomic\text{ }mass=40u \right)\] is kept at 300 K in a container. The ratio of their rms speeds \[\left[ \frac{{{V}_{rms}}\,(helium)}{{{V}_{rms}}\,(argon\,)} \right]\] , is close to:
A) 0.32 done clear
B) 3.16 done clear
C) 2.24 done clear
D) 0.45 done clear
View Answer play_arrowquestion_answer2) Two coherent sources produce waves of different intensities which interfere. After interference, the ratio of the maximum intensity to the minimum intensity is 16. The intensity of the waves are in the ratio:
A) 25 : 9 done clear
B) 4 : 1 done clear
C) 5 : 3 done clear
D) 16 : 9 done clear
View Answer play_arrowquestion_answer3) A sample of radioactive material A, that has an activity of \[10\text{ }mCi(1\text{ }Ci=3.7\times {{10}^{10}}\,decays/s)\], has twice the number of nuclei as another sample of different radioactive material B which has an activity of \[20\text{ }mCi\]. The correct choices for half-lives of A and B would then be respectively:
A) 10 days and 40 days done clear
B) 20 days and 10 days done clear
C) 5 days and 10 days done clear
D) 20 days and 5 days done clear
View Answer play_arrowquestion_answer4) Temperature difference of \[120{}^\circ \,C\] is maintained between two ends of a uniform rod AB of length 2L. Another bent rod PQ, of same cross-section as AB and length \[\frac{3L}{2}\], is connected across AB (See figure). In steady state, temperature difference between P and Q will be close to:
A) \[45{}^\circ \,C\] done clear
B) \[75{}^\circ C\] done clear
C) \[35{}^\circ C\] done clear
D) \[60{}^\circ C\] done clear
View Answer play_arrowquestion_answer5) A convex lens is put 10 cm from a light source and it makes a sharp image on a screen, kept 10 cm from the lens. Now a glass block (refractive index 1.5) of 1.5 cm thickness is placed in contact with the light source. To get the sharp image again, the screen is shifted by a distance d. Then d is:
A) 0.55 cm towards the lens done clear
B) 0 done clear
C) 0.55 cm away from the lens done clear
D) 1.1 cm away from the lens done clear
View Answer play_arrowquestion_answer6) For a uniformly charged ring of radius R, the electric field on its axis has the largest magnitude at a distance h from its centre. Then value of h is:
A) \[R\sqrt{2}\] done clear
B) R done clear
C) \[\frac{R}{\sqrt{5}}\] done clear
D) \[\frac{R}{\sqrt{2}}\] done clear
View Answer play_arrowquestion_answer7) Drift speed of electrons, when \[1.5\text{ }A\] of current flows in a copper wire of cross section \[5\text{ }m{{m}^{2}}\], is v. If electron density in copper is \[9\times {{10}^{28}}/{{m}^{3}}\] the value of v in mm/s is close to (Take charge of electron to be \[=\text{ }1.6\times {{10}^{-19}}C)\]
A) 0.02 done clear
B) 0.2 done clear
C) 3 done clear
D) 2 done clear
View Answer play_arrowquestion_answer8) A plane electromagnetic wave of frequency 50 MHz travels in free space along the positive x-direction. At a particular point in space and time, \[\overrightarrow{E}=6.3\text{ }\overrightarrow{j}\text{ }V/m\]. The corresponding magnetic field B, at that point will be
A) \[18.9\times {{10}^{-8}}\text{ }\widehat{k}T\] done clear
B) \[2.1\times {{10}^{-8}}\text{ }\widehat{k}T\] done clear
C) \[18.9\times {{10}^{8}}\text{ }\widehat{k}T\] done clear
D) \[6.3\times {{10}^{-8}}\text{ }\widehat{k}T\] done clear
View Answer play_arrowquestion_answer9) A gas can be taken from A to B via two different processes ACB and ADB. When path ACB is used 60 J of heat flows into the system and 30 J of work is done by the system. If path ADB is used work done by the system is 10 J. The heat Flow into the system in path ADB is:
A) 40 J done clear
B) 20 J done clear
C) 100 J done clear
D) 80 J done clear
View Answer play_arrowquestion_answer10) A parallel plate capacitor is made of two square plates of side ?a?, separated by a distance\[d\left( d<<a \right)\]. The lower triangular; portion is filled with a dielectric of dielectric constant K, as shown in the figure. Capacitance of this capacitor is:
A) \[\frac{K{{\in }_{0}}{{a}^{2}}}{2d\,(K+1)}\] done clear
B) \[\frac{K{{\in }_{0}}{{a}^{2}}}{d\,(K-1)}\,\,In\,\,K\] done clear
C) \[\frac{K{{\in }_{0}}{{a}^{2}}}{d}\,\,In\,\,K\] done clear
D) \[\frac{1}{2}\,\,\,\frac{K{{\in }_{0}}{{a}^{2}}}{d}\] done clear
View Answer play_arrowquestion_answer11) Surface of certain metal is first illuminated with light of wavelength \[{{\lambda }_{1}}=350\,nm\] nm and then, by light of wavelength \[{{\lambda }_{2}}=540nm\]. It is found that the maximum speed of the photo electrons in the two cases differ by a factor of 2. The work function of the metal (in eV) is close to : (Energy of photon \[=\frac{1240}{\lambda \,(in\,\,nm)}\,e\,V)\]
A) 5.6 done clear
B) 2.5 done clear
C) 1.8 done clear
D) 1.4 done clear
View Answer play_arrowquestion_answer12) An infinitely long current carrying wire and a small current carrying loop are in the plane of the paper as shown. The radius of the loop is a and distance of its centre from the wire is \[d\left( d>>a \right)\]. If the loop applies a force F on the wire then:
A) \[F\propto \left( \frac{{{a}^{2}}}{{{d}^{3}}} \right)\] done clear
B) \[F\propto \left( \frac{a}{d} \right)\] done clear
C) \[F\,\,=\,\,0\] done clear
D) \[F\propto {{\left( \frac{a}{d} \right)}^{2}}\] done clear
View Answer play_arrowquestion_answer13) A heavy ball the mass M is suspended from the ceiling of a car by a right string of mass m \[\left( m<<M \right)\]. When the car is at rest, the speed of transverse waves in the string is\[60\text{ }m{{s}^{-1}}\]. When the car has acceleration a, the wave-speed increases to\[60.5\text{ }m{{s}^{-1}}\]. The value of a, in terms of gravitational acceleration g, is closest to:
A) \[\frac{g}{20}\] done clear
B) \[\frac{g}{5}\] done clear
C) \[\frac{g}{10}\] done clear
D) \[\frac{g}{30}\] done clear
View Answer play_arrowquestion_answer14) When the switch S, in circuit shown, is closed, then the value of current i will be:
A) 4 A done clear
B) 5 A done clear
C) 3 A done clear
D) 2 A done clear
View Answer play_arrowquestion_answer15) A current loop, having two circular arcs joined by two radial lines y shown in the figure. It carries a current of 10 A. The magnetic field at point 0 will be close to:
A) \[~1.5\,\,\times \,\,\text{1}{{0}^{-5}}\,T\] done clear
B) \[1.0\times {{10}^{-\,5}}\,T\] done clear
C) \[1.5\,\,\times \,\,{{10}^{-7}}\,T~\] done clear
D) \[1.0\times \text{1}{{0}^{-7}}\,T\] done clear
View Answer play_arrowquestion_answer16) Mobility of electrons in a semiconductor is defined as the ratio of their drift velocity to the applied electric field. If, for an n-type semiconductor, the density of electrons is \[{{10}^{19}}{{m}^{-3}}\] and their mobility is \[1.6\text{ }{{m}^{2}}/\left( V.s \right)\] then the resistivity of the semiconductor (since it is an n-type semiconductor contribution of holes is ignored) is close to:
A) \[0.4\text{ }\Omega \,m\] done clear
B) \[2\text{ }\Omega \,m\] done clear
C) \[4\,\,\Omega \,m\] done clear
D) \[0.2\,\,\Omega \,m\] done clear
View Answer play_arrowquestion_answer17) Consider a tank made of glass (refractive index 1.5) with s. thick bottom. It is filled with a liquid of refractive index \[\mu \]. A student finds that, irrespective of what the incident angle I (see figure) is for a beam of light entering the liquid, the light reflected from the liquid glass interface is never completely polarized. For this to happen, the minimum value of \[\mu \] is:
A) \[\sqrt{\frac{5}{3}}\] done clear
B) \[\frac{4}{3}\] done clear
C) \[\frac{5}{\sqrt{3}}\] done clear
D) \[\frac{3}{\sqrt{5}}\] done clear
View Answer play_arrowquestion_answer18) If the angular momentum of a planet of mass m, moving around the Sun in a circular orbit is L, about the center of the Sun, its areal velocity is:
A) \[\frac{L}{m}\] done clear
B) \[\frac{L}{2m}\] done clear
C) \[\frac{4L}{m}\] done clear
D) \[\frac{2L}{m}\] done clear
View Answer play_arrowquestion_answer19) A block of mass 10 kg is kept on a rough inclined plane as shown in the figure. A force of 3 N is applied on the block. The coefficient of static friction between the plane and the block is 0.6. What should be the minimum value of force P, such that the block does not move downward?
A) 32 N done clear
B) 25 N done clear
C) 23 N done clear
D) 18 N done clear
View Answer play_arrowquestion_answer20) A rod, of length L at room temperature and uniform area of cross section A, is made of a metal having coefficient of linear expansion \[a/{}^\circ C\]. It is observed that an external compressive force F, is applied on each of its ends, prevents any change in the length of the rod, when its temperature rises by \[\Delta \] TK. Young?s modulus, Y, for this metal is:
A) \[\frac{F}{A\alpha \Delta T}\] done clear
B) \[\frac{F}{2A\alpha \Delta T}\] done clear
C) \[\frac{2\,F}{A\alpha \Delta T}\] done clear
D) \[\frac{\,F}{A\alpha (\Delta T-273)}\] done clear
View Answer play_arrowquestion_answer21) A particle is moving with a velocity \[\overrightarrow{v}=K\left( y\,\,\overrightarrow{i}+x\,\,\overrightarrow{j} \right)\], where K is a constant. The general equation for its path is:
A) \[y={{x}^{2}}+constant\] done clear
B) \[{{y}^{2}}=\text{ }{{x}^{2}}+constant\] done clear
C) \[{{y}^{2}}=\,\,x+constant\] done clear
D) \[xy\text{ }=\text{ }constant\] done clear
View Answer play_arrowquestion_answer22) A conducting circular loop made of a thin wire, has area \[3.5\,\,\times \,\,{{10}^{-3}}\,{{m}^{2}}\] and resistance 100. It is placed perpendicular to a time dependent magnetic field\[B\left( t \right)=\left( 0.4T \right)sin\left( 50\pi t \right)\]. The field is uniform in space. Then the net charge flowing through the loop during \[t\,\,=\,\,0\] s and \[t\,\,=\,\,0\] ms is close to:
A) 6 mC done clear
B) 14 mC done clear
C) 7 mC done clear
D) 21 mC done clear
E) None of These done clear
View Answer play_arrowquestion_answer23) An L-shaped object, made of thin rods of uniform mass density, is suspended with a string as shown in figure. If \[\,AB=BC\], and the angle made by AB with downward vertical is \[\theta \], then:
A) \[\tan \,\theta \,\,=\,\,\frac{1}{3}\] done clear
B) \[\tan \,\theta \,\,=\,\,\frac{1}{2}\] done clear
C) \[\tan \,\theta \,\,=\,\,\frac{2}{\sqrt{3}}\] done clear
D) \[\tan \,\theta \,\,=\,\,\frac{1}{2\sqrt{3}}\] done clear
View Answer play_arrowquestion_answer24) A copper wire is stretcher! to make it \[0.5\,%\] longer. The percentage change m in its electrical resistance if its volume remain unchanged is:
A) \[0.5\text{ }%\] done clear
B) \[2.5\text{ }%\] done clear
C) \[2.0\text{ }%\] done clear
D) \[1.0\text{ }%\] done clear
View Answer play_arrowquestion_answer25) Three charges +Q, q, +Q are placed respectively, at distance, 0, \[d/2\] and d from the origin, on the x-axis. If the net force experienced \[by+Q\], placed at \[x=0\], is zero then value of q is:
A) +Q/2 done clear
B) -Q/4 done clear
C) +Q/4 done clear
D) -Q/2 done clear
View Answer play_arrowquestion_answer26) A bar magnet is demagnetized by inserting it inside a solenoid of length 0.2 m, 100 turns, and carrying a current of 5.2 A. The coercivity of the bar magnet is:
A) 2600 A/m done clear
B) 1200 A/m done clear
C) 520 A/m done clear
D) 285 A/m done clear
View Answer play_arrowquestion_answer27) A resistance is shown in the figure. Its value and tolerance are given respectively by:
A) \[270\text{ }\Omega ,\text{ }10\text{ }%\] done clear
B) \[270\text{ }\Omega ,\text{ }5\text{ }%\] done clear
C) \[27\text{ }k\Omega ,\text{ }10\,%\] done clear
D) \[27\text{ }k\Omega ,\text{ }20\,%\] done clear
View Answer play_arrowquestion_answer28) A block of mass m, lying on a smooth horizontal surface, is attached to a spring (of negligible mass) of spring constant k. The other end of the spring is fixed, as shown in the figure. The block is initally at rest in its equilibrium position. If now the block is pulled with a constant force F, the maximum speed of the block is
A) \[\frac{2F}{\sqrt{mk}}\] done clear
B) \[\frac{\pi \,F}{\sqrt{mk}}\] done clear
C) \[\frac{F}{\pi \,\sqrt{mk}}\] done clear
D) \[\frac{F}{\sqrt{mk}}\] done clear
View Answer play_arrowquestion_answer29) Two masses m and \[\frac{m}{2}\] are connected at the two ends of a massless rigid rod of length l. The rod is suspended by a thin wire of torsional constant k at the centre of mass of the rod-mass system (see figure). Because of torsional constant k, the restoring torque is \[\tau \,\,=\,\,k\theta \] for angular displacement \[\theta \]. If the rod is rotated by \[{{\theta }_{0}}\] and released, the tension in it when it passes through its mean position will be:
A) \[\frac{2\,k\,{{\theta }_{0}}^{2}}{l}\] done clear
B) \[\frac{k\,{{\theta }_{0}}^{2}}{l}\] done clear
C) \[\frac{3k\,{{\theta }_{0}}^{2}}{l}\] done clear
D) \[\frac{k\,{{\theta }_{0}}^{2}}{2\,l}\] done clear
View Answer play_arrowquestion_answer30) Three blocks A, B and C are lying on a smooth horizontal surface, as shown in the figure. A and B have equal masses, m while C has mass M. Block A is given an initial speed v towards B due to which it collides with B perfectly inelastically \[\frac{5}{6}th\] of the initial kinetic energy is lost in whole process. What is value of M/m?
A) 2 done clear
B) 3 done clear
C) 5 done clear
D) 4 done clear
View Answer play_arrowquestion_answer31) In general the properties that decrease and increase down a group in the periodic table, respectively, are-
A) electronegativity, and atomic radius. done clear
B) electronegativity and electron gain enthalpy. done clear
C) atomic radius and electronegativity. done clear
D) electron gain enthalpy and electronegativity. done clear
View Answer play_arrowquestion_answer32) The major product of following reaction is: \[R-C\equiv N\,\,\xrightarrow[(2)\,\,{{H}_{2}}O]{(1)\,\,AlH\,{{(i-Bu)}_{2}}}\,\,?\]
A) RCHO done clear
B) RCOOH done clear
C) \[RCON{{H}_{2}}\] done clear
D) \[RC{{H}_{2}}N{{H}_{2}}\] done clear
View Answer play_arrowquestion_answer33) Which amongst the following is the strongest acid?
A) \[CHB{{r}_{3}}~\] done clear
B) \[CHC{{l}_{3}}\] done clear
C) \[CH{{\left( CN \right)}_{3}}\] done clear
D) \[CH{{I}_{3}}\] done clear
View Answer play_arrowquestion_answer34) Arrange the following amines in the decreasing order of basicity:
A) \[I>III>II\] done clear
B) \[III>I>II\] done clear
C) \[I>II>III\] done clear
D) \[III>II>I\] done clear
View Answer play_arrowquestion_answer35) The ore that contains both iron and copper is -
A) dolomite done clear
B) malachite done clear
C) copper pyrites done clear
D) azurite done clear
View Answer play_arrowquestion_answer36) The anodic half-cell of lead-acid battery is recharged using electricity of 0.05 Faraday. The amount of \[PbS{{O}_{4}}\] electrolyzed in g during the process is: (Molar mass of \[PbS{{O}_{4}}-=303\text{ }g\text{ }mo{{l}^{-1}}\])
A) 15.2 done clear
B) 7.6 done clear
C) 11.4 done clear
D) 22.8 done clear
View Answer play_arrowquestion_answer37) Correct statements among a to d regarding silicones are - (a) They are polymers with hydrophobic character. (b) They are biocompatible. (c) In general, they have high thermal stability and low dielectric strength. (d) Usually, they are resistant to oxidation and used as greases.
A) (a), (b) and (d) only done clear
B) (a), (b) and (c) only done clear
C) (a), (b), (c) and (d) done clear
D) (a) and (b) only done clear
View Answer play_arrowquestion_answer38) The following results were obtained during kinetic studies of the reaction: \[2A\,\,+\,\,B\,\,\to \] Products
Experi-ment | in \[\mathbf{mol}\text{ }{{\mathbf{L}}^{-\mathbf{1}}}\] | (in \[\mathbf{mol}\text{ }{{\mathbf{L}}^{-\mathbf{1}}}\] | Initial Rate of reaction (in \[\mathbf{mol}\text{ }{{\mathbf{L}}^{-\mathbf{1}}}\] \[\mathbf{mi}{{\mathbf{n}}^{\mathbf{-1}}}\]) |
I | 0.10 | 0.20 | \[6.93\,\,\times \,\,{{10}^{-3}}\] |
II | 0.10 | 0.25 | \[6.93\,\,\times \,\,{{10}^{-3}}\] |
III | 0.20 | 0.30 | \[1.386\,\,\times \,\,{{10}^{-2}}\] |
A) 5 done clear
B) 1 done clear
C) 100 done clear
D) 10 done clear
View Answer play_arrowquestion_answer39) The major product of the following reaction is:
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer40) The one that is extensively used as a piezoelectric material is -
A) mica done clear
B) quartz done clear
C) amorphous silica done clear
D) tridymite done clear
View Answer play_arrowquestion_answer41) 0.5 moles of gas A and x moles of gas B exert a pressure of 200 Pa in a container of volume \[10\text{ }{{m}^{3}}\] at 1000 K. Given R is the gas constant in \[J{{K}^{-1}}\,\,mo{{l}^{-1}}\], x is -
A) \[\frac{2R}{4-R}\] done clear
B) \[\frac{4+R}{2R}\] done clear
C) \[\frac{4-R}{2R}\] done clear
D) \[\frac{2R}{4+R}\] done clear
View Answer play_arrowquestion_answer42) For emission line of atomic hydrogen from \[{{n}_{1}}=8\] to \[{{n}_{f}}=n\], the plot of wave number \[\left( \overline{v} \right)\] against \[\left( \frac{1}{{{n}^{2}}} \right)\] will be (The Rydberg constant, \[{{R}_{H}}\] is wave number unit)
A) Linear with slope - \[{{R}_{H}}\] done clear
B) Linear with slope -\[{{R}_{H}}\] done clear
C) Non linear done clear
D) Linear with intercept - \[{{R}_{H}}\] done clear
View Answer play_arrowquestion_answer43) Major product of the following reaction is:
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer44) The correct decreasing order for acid strength is:
A) \[N{{O}_{2}}C{{H}_{2}}COOH\text{ }>\text{ }FC{{H}_{2}}COOH\text{ }>CNC{{H}_{2}}COOH\text{ }>\text{ }ClC{{H}_{2}}COOH\] done clear
B) \[CNC{{H}_{2}}COOH>{{O}_{2}}NC{{H}_{2}}COOH\text{ }>FC{{H}_{2}}COOH\text{ }>\text{ }ClC{{H}_{2}}COOH\] done clear
C) \[FC{{H}_{2}}COOH>ClC{{H}_{2}}COOH>N{{O}_{2}}C{{H}_{2}}COOH\text{ }>\text{ }ClC{{H}_{2}}COOH\] done clear
D) \[N{{O}_{2}}C{{H}_{2}}COOH>NCC{{H}_{2}}COOH>FC{{H}_{2}}COOH>ClC{{H}_{2}}COOH\] done clear
View Answer play_arrowquestion_answer45) 20 mL of 0.1 M \[{{H}_{2}}S{{O}_{4}}\] solution is added to 30 mL of 0.2 M \[N{{H}_{4}}OH\] solution. The pH of the resultant mixture is: \[[p{{K}_{b}}\text{ }of\text{ }N{{H}_{4}}OH\,\,=\,\,4.7]\].
A) 5.2 done clear
B) 9.4 done clear
C) 9.0 done clear
D) 5.0 done clear
View Answer play_arrowquestion_answer46) The alkaline earth metal nitrate that does not crystallize with water molecules, is -
A) \[Ba{{\left( N{{O}_{3}} \right)}_{2}}\] done clear
B) \[Mg{{\left( N{{O}_{3}} \right)}_{2}}\] done clear
C) \[Ca{{\left( N{{O}_{3}} \right)}_{2}}\] done clear
D) \[Sr{{\left( N{{O}_{3}} \right)}_{2}}\] done clear
View Answer play_arrowquestion_answer47) Consider the reversible isothermal expansion of an ideal gas in a closed system at two different temperatures T1 and \[{{T}_{2}}\left( {{T}_{1}}<\text{ }{{T}_{2}} \right)\]. The correct graphical depiction of the dependence of work done (W) on the final volume (V) is -
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer48) Adsorption of a gas follows Freundlich adsorption isotherm. IN the given plot, x is the mass of the gas adsorbed on mass m of the adsorbent at pressure P. \[\frac{x}{m}\] is proportional to:
A) P done clear
B) \[{{P}^{1/2}}\] done clear
C) \[{{P}^{2}}\] done clear
D) \[{{P}^{1/4}}\] done clear
View Answer play_arrowquestion_answer49) The increasing order of pKa of the following ammo acids in aqueous solution is: Gly Asp Lys Arg
A) \[Asp<Gly<Lys<Arg\] done clear
B) \[Arg<Lys<Gly<Asp\] done clear
C) \[Gly<Asp<Arg<Lys\] done clear
D) \[Asp<Gly<Arg<Lys\] done clear
View Answer play_arrowquestion_answer50) According to molecular orbital theory, which of the following is true with respect to\[{{L}_{i2}}+and\text{ }{{L}_{i2}}-\]?
A) Both are unstable done clear
B) Both are stable done clear
C) \[{{L}_{i2}}+\] is stable and \[{{L}_{i2}}-\] is unstable done clear
D) \[{{L}_{i{{2}^{+}}}}\]is unstable and \[{{L}_{i2}}-\] is stable done clear
View Answer play_arrowquestion_answer51) A water sample has ppm level \[Fe=0.2\]; \[Mn=5.0\] ; \[Cu=3.0\] ; \[Zn=5.0\] The metal that makes the water sample unsuitable for drinking is:
A) Zn done clear
B) Fe done clear
C) Cu done clear
D) Mn done clear
View Answer play_arrowquestion_answer52) Two complexes \[\left[ Cr{{\left( {{H}_{2}}0 \right)}_{6}} \right]C{{l}_{3}}\] and \[\left[ Cr{{\left( N{{H}_{3}} \right)}_{6}} \right]C{{l}_{3}}\] are violet and yellow coloured, respectively. The incorrect statement regarding, them is-
A) \[{{\Delta }_{0}}\] value for is less than that of (B). done clear
B) both absorb energies corresponding to their complementary colors. done clear
C) \[{{\Delta }_{0}}\] values of and are calculated. From the energies of violet and yellow light, respectively. done clear
D) both are paramagnetic with three unpaired electrons. done clear
View Answer play_arrowquestion_answer53) The major product of the following reaction is:
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer54) Which one of the following statements regarding Henery's law is not correct?
A) Different gases have different \[{{K}_{H}}\] (Henry's law constant) values at the same temperature. done clear
B) The partial pressure of the gas in vapour phase is proportional to the mole fraction of the gas in the solution. done clear
C) The value of \[{{K}_{H}}\] increases with increase of temperature and \[{{K}_{H}}\] is function of the nature of the gas. done clear
D) Higher the value of \[{{K}_{H}}\] at a given pressure, higher is the solubility of the gas in the liquids. done clear
View Answer play_arrowquestion_answer55) The compound A and B in the following reaction are respectively:
A) A = Benzyl alcohol, B = Benzyl cyanide done clear
B) A = Benzyl chloride, B = Benzyl cyanide done clear
C) A = Benzyl alcohol, B = Benzyl isocyanide done clear
D) A = Benzyl chloride, B = Benzyl isocyanide done clear
View Answer play_arrowquestion_answer56) The highest value of the calculated spin only magnetic moment (in BM) among all the transition metal complexes is-
A) 6.93 done clear
B) 5.92 done clear
C) 4.90 done clear
D) 3.87 done clear
View Answer play_arrowquestion_answer57) A solution of sodium sulfate contains \[92\text{ }g\text{ }of\text{ }N{{a}^{+}}\] ions per kilogram of water. The molality of \[N{{a}^{+}}\] ions in that solution in \[mol\text{ }k{{g}^{-1}}\] is:
A) 8 done clear
B) 4 done clear
C) 12 done clear
D) 16 done clear
View Answer play_arrowquestion_answer58) The correct match between Item-I am Item-II is:
Item-I (drug) | Item-II (test) | ||
(A) | Chlorozylenol | (P) | Carbolamine test |
(B) | Norethindrone | (Q) | Sodium hydrogen carbonate test |
(C) | Sulphapyridine | (R) | Ferric chlorine test |
(D) | Penicillin | (S) | Bayer's test |
A) \[A\to R;\,\,\,B\to S;\,\,\,C\to P;\,\,\,D\to Q\] done clear
B) \[A\to Q;\,\,\,B\to P;\,\,\,C\to S;\,\,\,D\to R\] done clear
C) \[A\to Q;\,\,\,B\to S;\,\,\,C\to P;\,\,\,D\to R\] done clear
D) \[A\to R;\,\,\,B\to P;\,\,\,C\to S;\,\,\,D\to Q\] done clear
View Answer play_arrowquestion_answer59) The isotopes of hydrogen are:
A) Protium and deuterium only done clear
B) Protium, deuterium and tritium done clear
C) Deuterium and tritium only done clear
D) Tritium and protium only done clear
View Answer play_arrowquestion_answer60) Aluminium is usually found in +3 oxidation state. In contrast, thallium exists in +1 and + 3 oxidation states. This is due to -
A) diagonal relationship done clear
B) lanthanoid contraction done clear
C) inert pair effect done clear
D) lattice effect done clear
View Answer play_arrowquestion_answer61) \[\underset{y\to 0}{\mathop{\lim }}\,\frac{\sqrt{1+\sqrt{1+{{y}^{4}}}}-\sqrt{2}}{{{y}^{4}}}\]
A) exists and equals \[\frac{1}{2\sqrt{2}}\] done clear
B) exists and equals \[\frac{1}{4\sqrt{2}}\] done clear
C) exists and equals \[\frac{1}{2\sqrt{2}(\sqrt{2}+1)}\] done clear
D) does not exist done clear
View Answer play_arrowquestion_answer62) If a, b and c be three distinct real numbers in G.P. and \[a+b+c=xb\], then x cannot be:
A) -2 done clear
B) 2 done clear
C) -3 done clear
D) 4 done clear
View Answer play_arrowquestion_answer63) The maximum volume (in cu. m) of the right circular cone having slant height 3 m is:
A) \[6\pi \] done clear
B) \[\frac{4}{3}\pi \] done clear
C) \[2\sqrt{3}\,\pi \] done clear
D) \[3\sqrt{3}\,\pi \] done clear
View Answer play_arrowquestion_answer64)
The system of linear equations |
\[x+y+z=2\] |
\[2x+3y+2z=\text{ }5\] |
\[2x+3y+\left( {{a}^{2}}-1 \right)z\text{ }=\text{ }a+1\] |
A) has infinitely many solutions for \[a=4\] done clear
B) has a unique solution for I a I \[=\,\,\sqrt{3}\] done clear
C) is inconsistent when I a I = \[=\,\,\sqrt{3}\] done clear
D) is inconsistent when \[a=4\] done clear
View Answer play_arrowquestion_answer65) Let \[f:\,\,R\to R\] be a function defined as Then, f is
A) continuous if \[a=0\] and \[b=5\] done clear
B) continuous if \[a=-5\] and \[b=10\] done clear
C) continuous if \[a=5\] and \[b=5\] done clear
D) not continuous for any values of a and b done clear
View Answer play_arrowquestion_answer66) Axis of a parabola lies along x-axis. If its vertex and focus are at distance 2 and 4 respectively from the origin, on the positive x-axis then which of the following points does not lie on it?
A) \[\left( 8,\text{ }6 \right)\] done clear
B) \[\left( 4,\,-4 \right)\] done clear
C) \[(6,\,\,4\sqrt{2})\] done clear
D) \[(5,\,\,2\sqrt{6})\] done clear
View Answer play_arrowquestion_answer67) Let \[\alpha \text{ }and\text{ }\beta \] be two roots of the equation \[{{x}^{2}}+2x+2=0\], then \[{{\alpha }^{15}}+{{\beta }^{15}}\] is equal to:
A) -256 done clear
B) 512 done clear
C) -512 done clear
D) 256 done clear
View Answer play_arrowquestion_answer68) If the Boolean express. \[(p\oplus q)\,\,\wedge (\sim p\,\odot q)\] is equivalent to \[p\wedge q\], where \[\oplus ,\,\,\odot \,\,\in \{\wedge ,\,\,\vee \},\]then the ordered pair \[(\oplus ,\,\,\odot )\] is
A) \[(\vee ,\,\,\,\vee )\] done clear
B) \[(\wedge ,\,\,\,\wedge )\] done clear
C) \[(\wedge ,\,\,\,\vee )\] done clear
D) \[(\vee ,\,\,\,\wedge )\] done clear
View Answer play_arrowquestion_answer69) Let \[\overrightarrow{a}=\widehat{i}-\widehat{\text{j}}\,,\,\,\,\overrightarrow{b}=\widehat{i}+\widehat{j}+\widehat{k}\,\,\,and\,\,\overrightarrow{c}\,\] and be a vector such that \[\overrightarrow{a}\,\,\times \,\,\overrightarrow{c}\,\,+\,\,\overrightarrow{b}\,\,=\,\,\overrightarrow{0}\] and \[\overrightarrow{a}\text{ }.\text{ }\overrightarrow{c}\text{ }=4\], then \[{{\overrightarrow{\left| \,c\, \right|}}^{2}}\] is equal to:
A) \[\frac{19}{2}\] done clear
B) 8 done clear
C) \[\frac{17}{2}\] done clear
D) 9 done clear
View Answer play_arrowquestion_answer70) 5 students of a class have an average height 150 cm and variance \[18\text{ }c{{m}^{2}}\]. A new student, whose height is 156 cm, joined them. The variance (in \[c{{m}^{2}}\]) of the height of these six students is:
A) 20 done clear
B) 18 done clear
C) 16 done clear
D) 22 done clear
View Answer play_arrowquestion_answer71) For \[x\in R\text{ }-\left\{ 0,\text{ }1 \right\},\text{ }let\text{ }{{f}_{1}}\left( x \right)\,\,=\,\,\frac{1}{x}\,\,,\text{ }{{f}_{2}}\left( x \right)=1-x\] and \[{{f}_{3}}\left( x \right)=\frac{1}{1-x}\] be three given functions. If a function, J(x) satisfies \[\left( fz\circ \text{ }J\circ \,\,{{f}_{1}} \right)\left( x \right)=\text{ }{{f}_{3}}\text{ }\left( x \right)\] then J(x) is equal to:
A) \[\frac{1}{x}{{f}_{3}}\,(x)\] done clear
B) \[{{f}_{2}}\,(x)\] done clear
C) \[{{f}_{3}}\,(x)\] done clear
D) \[{{f}_{1}}\,(x)\] done clear
View Answer play_arrowquestion_answer72) Let A= \[\left\{ \theta \in \left( -\frac{\pi }{2},\,\pi \right):\,\frac{3+2i\,\,\sin \theta }{1-2i\,\,\sin \,\theta }\,is\,\,purely\,\,imaginary \right\}.\] Then the sum of the elements in A is:
A) \[\frac{5\pi }{6}\] done clear
B) \[\frac{3\pi }{4}\] done clear
C) \[\frac{2\pi }{3}\] done clear
D) \[\pi \] done clear
View Answer play_arrowquestion_answer73) Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, if there are two specific boys A and B, who refuse to be the members of the same team, is:
A) 300 done clear
B) 500 done clear
C) 200 done clear
D) 350 done clear
View Answer play_arrowquestion_answer74) For any \[\theta \,\,\,\,\in \,\,\,\,\left( \frac{\pi }{4},\,\,\frac{\pi }{2} \right)\], the expression \[3{{\left( sin\,\theta -cos\,\theta \right)}^{4}}+6{{\left( sin\,\theta +cos\,\theta \right)}^{2}}+4\,si{{n}^{6}}\theta \]equals:
A) \[13-4\,co{{s}^{4}}\theta +2\,si{{n}^{2}}\theta \,co{{s}^{2}}\theta \] done clear
B) \[13-4\,co{{s}^{2}}\theta +6\,si{{n}^{2}}\theta \,co{{s}^{2}}\theta \] done clear
C) \[13-4\text{ }cos{{\,}^{2}}\,\theta +6\,\,co{{s}^{4}}\,\theta \] done clear
D) \[13-4\text{ }cos{{\,}^{6}}\,\theta \] done clear
View Answer play_arrowquestion_answer75) Equation of a common tangent to the circle \[{{x}^{2}}+{{y}^{2}}-6x=0\] and the parabola, \[{{y}^{2}}=4x\], is:
A) \[\sqrt{3}y=x+3\] done clear
B) \[\sqrt{3}y=3x+3\] done clear
C) \[2\sqrt{3}y=\,\,-x-12\] done clear
D) \[2\sqrt{3}\,y=12x+1\] done clear
View Answer play_arrowquestion_answer76) Let \[{{a}_{1}},\text{ }{{a}_{2}},\text{ }.......,\text{ }{{a}_{30}}\] be an A.P., \[S=\sum\limits_{i\,=\,1}^{30}{{{a}_{i}}}\,\,and\,\,T\,\,=\,\,\sum\limits_{i\,=\,1}^{15}{{{a}_{(2i-1)}}}\]If \[{{a}_{5}}=27\] and \[S-2T=75\], then \[{{a}_{10}}\] is equal to:
A) 47 done clear
B) 42 done clear
C) 52 done clear
D) 57 done clear
View Answer play_arrowquestion_answer77) For \[{{x}^{2}}\ne n\pi \,+\,1,\,\,n\in N\] (the set of natural numbers), the integral \[\int{x\,\,\frac{2\,\sin \,({{x}^{2}}-1)\,\,-\,\sin 2\,({{x}^{2}}-1)}{2\,\sin \,({{x}^{2}}-1)+sin\,2({{x}^{2}}-1)}}\,dx\] is equal to: (where c is a constant of integration)
A) \[{{\log }_{e}}\,\left| \sec \,\left( \frac{{{x}^{2}}-1}{2} \right) \right|\,\,+c\] done clear
B) \[{{\log }_{e}}\,\left| \frac{1}{2}{{\sec }^{2}}\,({{x}^{2}}-1) \right|\,\,+c\] done clear
C) \[\frac{1}{2}\,{{\log }_{e}}\,\left| {{\sec }^{2}}\,\left( \frac{{{x}^{2}}-1}{2} \right) \right|\,\,+c\] done clear
D) \[\frac{1}{2}\,{{\log }_{e}}\,\left| \sec ({{x}^{2}}-1) \right|\,\,+\,\,c\] done clear
View Answer play_arrowquestion_answer78) Three circles of radii a, b, c (a < b < c) touch each other externally. If they have x-axis as a common tangent, then:
A) \[\frac{1}{\sqrt{b}}\,\,=\,\,\frac{1}{\sqrt{a}}+\frac{1}{\sqrt{c}}\,\] done clear
B) a, b, c are in A. P. done clear
C) \[\sqrt{a},\,\,\sqrt{b},\,\,\sqrt{c}\,\,are\,\,in\,\,A.P.\] done clear
D) \[\frac{1}{\sqrt{a}}=\frac{1}{\sqrt{b}}+\frac{1}{\sqrt{c}}\] done clear
View Answer play_arrowquestion_answer79) If \[A\,\,=\,\,\left[ \begin{align} & \cos \,\theta \,\,\,\,\,\,-\sin \theta \\ & \sin \,\theta \,\,\,\,\,\,\,\,\,\,\,\cos \,\theta \\ \end{align} \right]\] then matrix \[{{A}^{-50}}\] when \[\theta =\frac{\pi }{12}\], is equal to:
A) \[\left| \begin{align} & \frac{1}{2}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{\sqrt{3}}{2} \\ & -\frac{\sqrt{3}}{2}\,\,\,\,\,\,\,\,\frac{1}{2} \\ \end{align} \right|\] done clear
B) \[\left| \begin{align} & \frac{1}{2}\,\,\,\,\,\,\,\,\,\,\,\,\,-\,\frac{\sqrt{3}}{2} \\ & \frac{\sqrt{3}}{2}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{1}{2} \\ \end{align} \right|\] done clear
C) \[\left| \begin{align} & \frac{\sqrt{3}}{2}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{1}{2}\,\,\, \\ & -\frac{1}{2}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{\sqrt{3}}{2} \\ \end{align} \right|\] done clear
D) \[\left| \begin{align} & \frac{\sqrt{3}}{2}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,-\frac{1}{2}\,\,\, \\ & \frac{1}{2}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{\sqrt{3}}{2} \\ \end{align} \right|\] done clear
View Answer play_arrowquestion_answer80) If \[\cos {{\,}^{-1}}\,\left( \frac{2}{3x} \right)\,\,+\,\,\cos {{\,}^{-1}}\,\left( \frac{3}{4x} \right)\,=\,\frac{\pi }{2}\,\,\left( x>\frac{3}{4} \right)\,\] then x is equal to
A) \[\frac{\sqrt{145}}{10}\] done clear
B) \[\frac{\sqrt{145}}{11}\] done clear
C) \[\frac{\sqrt{145}}{12}\] done clear
D) \[\frac{\sqrt{146}}{12}\] done clear
View Answer play_arrowquestion_answer81) If the fractional part of the number \[\frac{{{2}^{\,403}}}{15}\] is \[\frac{k}{15}\], then k is equal to:
A) 8 done clear
B) 14 done clear
C) 6 done clear
D) 4 done clear
View Answer play_arrowquestion_answer82) Consider the set of all lines \[px+qy+r=0\] such that \[3p+2q+4r=0\]. Which one of the following statements is true?
A) The lines are not concurrent done clear
B) The lines are concurrent at the point\[\left( \frac{3}{4},\,\,\frac{1}{2} \right)\] done clear
C) The lines are all parallel done clear
D) Each line passes through the origin done clear
View Answer play_arrowquestion_answer83) Two cards are drawn successively with replacement from a well-shuffled deck of 52 cards. Let X denote the random variable of number of aces obtained in the two drawn cards. Then \[P\left( X=1 \right)+P\left( X=2 \right)\] equals:
A) 25/169 done clear
B) 24/169 done clear
C) 49/169 done clear
D) 52/169 done clear
View Answer play_arrowquestion_answer84) The equation of the line passing through \[\left( -4,\text{ }3,\text{ }1 \right)\], parallel to the plane \[x+2y-z-5=0\] and intersecting the line\[\frac{x+1}{-3}\,\,\,=\,\,\,\frac{y-3}{2}\,\,=\,\,\frac{z-2}{-1}\]
A) \[\frac{x+4}{3}\,\,\,=\,\,\,\frac{y-3}{-1}\,\,=\,\,\frac{z-1}{1}\] done clear
B) \[\frac{x+4}{1}\,\,\,=\,\,\,\frac{y-3}{1}\,\,=\,\,\frac{z-1}{3}\] done clear
C) \[\frac{x+4}{-1}\,\,\,=\,\,\,\frac{y-3}{1}\,\,=\,\,\frac{z-1}{1}\] done clear
D) \[\frac{x-4}{2}\,\,\,=\,\,\,\frac{y-3}{1}\,\,=\,\,\frac{z+1}{4}\] done clear
View Answer play_arrowquestion_answer85) The plane through the intersection of the planes \[x+y+z=1\text{ }and\text{ }2x+3y-z+4=0\] and parallel to y-axis also passes through the point:
A) (- 3, 1, 1) done clear
B) (-3, 0, -1) done clear
C) (3, 3, -1) done clear
D) (3, 2, 1) done clear
View Answer play_arrowquestion_answer86) If \[\theta \] denotes the acute angle between the curves, \[y=10-{{x}^{2}}\] and \[y=2+{{x}^{2}}\] at a point of their intersection, then \[\left| \tan \,\,\theta \right|\] is equal to:
A) \[\frac{4}{9}\] done clear
B) \[\frac{7}{17}\] done clear
C) \[\frac{8}{17}\] done clear
D) \[\frac{8}{15}\] done clear
View Answer play_arrowquestion_answer87) The value of \[\int\limits_{0}^{\pi }{{{\left| \cos \,\,x \right|}^{3}}\,\,dx}\] is:
A) \[-\frac{4}{3}\] done clear
B) 0 done clear
C) \[\frac{4}{3}\] done clear
D) \[\frac{2}{3}\] done clear
View Answer play_arrowquestion_answer88) The area (in sq. units) bounded by the parabola \[y={{x}^{2}}-1\], the tangent at the point (2, 3) to it and the y-axis is:
A) \[\frac{56}{3}\] done clear
B) \[\frac{32}{3}\] done clear
C) \[\frac{8}{3}\] done clear
D) \[\frac{14}{3}\] done clear
View Answer play_arrowquestion_answer89) If \[y=y\left( x \right)\] is the solution of the differential equation, \[x\frac{dy}{dx}\,\,+\,\,2y\,\,=\,\,{{x}^{2}}\] satisfying \[y\left( 1 \right)=1\], then \[y\left( \frac{1}{2} \right)\] is equal to:
A) \[\frac{7}{64}\] done clear
B) \[\frac{49}{16}\] done clear
C) \[\frac{1}{4}\] done clear
D) \[\frac{13}{16}\] done clear
View Answer play_arrowquestion_answer90) Let \[0<\theta <\frac{\pi }{2}\]. If the eccentricity of the hyperbola \[\frac{{{x}^{2}}}{{{\cos }^{2}}\theta }-\frac{{{y}^{2}}}{{{\sin }^{2}}\,\theta }\,\,=\,\,1\] is greater than 2, then the length of its latus rectum lies in the interval:
A) \[\left( 3,\text{ }\infty \right)\] done clear
B) (1, 3/2] done clear
C) (3/2, 2] done clear
D) (2, 3] done clear
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