question_answer1) A mass of \[0.5\,\,kg\] moving with a speed of \[1.5\,\,m{{s}^{-1}}\] on a horizontal smooth surface, collides with a nearly weightless spring of force constant\[k=50\,\,N{{m}^{-1}}\]. The maximum compression of the spring would be
A) \[0.15\,\,m\] done clear
B) \[0.23\,\,m\] done clear
C) \[1.6\,\,m\] done clear
D) \[0.4\,\,m\] done clear
View Answer play_arrowquestion_answer2) A particle of mass \[{{m}_{1}}\] moves with velocity \[{{\upsilon }_{1}}\] and collides with another particle at rest of equal mass. The velocity of the second particle after the elastic collision is
A) \[3{{v}_{1}}\] done clear
B) \[{{v}_{1}}\] done clear
C) \[-{{v}_{1}}\] done clear
D) \[0\] done clear
View Answer play_arrowquestion_answer3) The ratio of the radii of gyration of a circular disc to that of a circular ring, each of same mass and radius, around their respective axis is
A) \[\sqrt{3}:\sqrt{2}\] done clear
B) \[1:\sqrt{2}\] done clear
C) \[\sqrt{3}:1\] done clear
D) \[\sqrt{5}:\sqrt{3}\] done clear
View Answer play_arrowquestion_answer4) A wheel having moment of inertia\[2kg\,\,{{m}^{-2}}\] about its vertical axis, rotates at the rate of \[60\,\,rpm\] about this axis. The torque which can stop the wheel's rotation in one minute would be
A) \[\frac{2\pi }{13}N-m\] done clear
B) \[\frac{\pi }{14}N-m\] done clear
C) \[\frac{\pi }{15}N-m\] done clear
D) \[\frac{\pi }{20}N-m\] done clear
View Answer play_arrowquestion_answer5) A sphere of diameter \[0.2\,\,m\] and mass \[2\,\,kg\] is rolling on an inclined plane with velocity\[v=0.5m{{s}^{-1}}\]. The kinetic energy of the sphere is
A) \[0.4\,\,J\] done clear
B) \[0.3\,\,J\] done clear
C) \[0.6\,\,J\] done clear
D) \[0.42\,\,J\] done clear
View Answer play_arrowquestion_answer6) If a sphere rolling on an inclined plane with velocity v without slipping, the vertical height of the incline in terms of velocity will be
A) \[\frac{7v}{10g}\] done clear
B) \[\frac{7{{v}^{2}}}{10g}\] done clear
C) \[\frac{2{{v}^{2}}}{5g}\] done clear
D) \[\frac{3v}{5g}\] done clear
View Answer play_arrowquestion_answer7) The height vertically above the earth's surface at which the acceleration due to gravity becomes \[1%\] of its value at the surface is (\[R\] is the radius of the earth)
A) \[8R\] done clear
B) \[9R\] done clear
C) \[10R\] done clear
D) \[20R\] done clear
View Answer play_arrowquestion_answer8) The motion of a particle executing SHM in one dimension is described by\[x=-0.23\sin \left( t+\frac{\pi }{4} \right)\]where, \[x\] is in metre and t in second. The frequency of oscillation in \[Hz\] is
A) \[3\] done clear
B) \[\frac{1}{2\pi }\] done clear
C) \[\frac{\pi }{2}\] done clear
D) \[\frac{1}{\pi }\] done clear
View Answer play_arrowquestion_answer9) The change in the gravitational potential energy when a body of mass \[m\] is raised to a height \[nR\] above the surface of the earth is (here, \[R\] is the radius of the earth)
A) \[\left( \frac{n}{n+1} \right)mgR\] done clear
B) \[\left( \frac{n}{n-1} \right)mgR\] done clear
C) \[nmgR\] done clear
D) \[\frac{mgR}{n}\] done clear
View Answer play_arrowquestion_answer10) A satellite is rotating around a planet in the orbit of radius \[r\] with time period\[T\]. If gravitational force changes according to\[{{r}^{5/2}}\], the \[{{T}^{2}}\] will be
A) \[\propto {{r}^{3}}\] done clear
B) \[\propto {{r}^{7/2}}\] done clear
C) \[{{\propto }^{9/12}}\] done clear
D) \[\propto {{r}^{3/2}}\] done clear
View Answer play_arrowquestion_answer11) A liquid \[X\] of density \[3.36\,\,g/c{{m}^{3}}\] is poured in a U-tube in right arm with height\[10\,\,cm\], which contains\[Hg\]. Another liquid \[Y\] is poured in left arm with height\[8\,\,cm\]. Upper levels of \[X\] and \[Y\] are same. What is the density of\[Y\]?
A) \[0.8\,\,g/cc\] done clear
B) \[1.2\,\,g/cc\] done clear
C) \[1.4\,\,g/cc\] done clear
D) \[1.6\,\,g/cc\] done clear
View Answer play_arrowquestion_answer12) Wafer flows along a horizontal pipe whose cross-section is not, constant. The pressure is \[1\,\,cm\] of\[Hg\], where the velocity is\[35\,\,cm{{s}^{-1}}\]. At a point where the velocity is\[65\,\,cm{{s}^{-1}}\], the pressure will be
A) \[0.89\,\,cm\]of\[Hg\] done clear
B) \[8.9\,\,cm\]of\[Hg\] done clear
C) \[0.5\,\,cm\]of\[Hg\] done clear
D) \[1\,\,cm\]of\[Hg\] done clear
View Answer play_arrowquestion_answer13) A lead bullet of unknown mass is fired-with a speed of \[180\,\,m{{s}^{-1}}\] into a tree in which it stops. Assuming that in this process two-third of heat produced goes into the bullet and one-third into wood. The temperature of the bullet rises by
A) \[{{140}^{o}}C\] done clear
B) \[{{106}^{o}}C\] done clear
C) \[{{90}^{o}}C\] done clear
D) \[{{100}^{o}}C\] done clear
View Answer play_arrowquestion_answer14) The freezer in a refrigerator is located at the top section so that
A) the entire chamber of the refrigerator is cooled quickly due to convection done clear
B) the motor is not heated done clear
C) the heat gained from the environment is high done clear
D) the heat gained from the environment is low done clear
View Answer play_arrowquestion_answer15) Two monoatomic ideal gases \[A\] and \[B\] occupying the same volume \[V\] are at the same temperature \[T\] and pressure\[p\]. If they are mixed, the resultant mixture has volume \[V\] and temperature\[T\]. The pressure of the mixture is
A) \[p\] done clear
B) \[\frac{p}{2}\] done clear
C) \[4p\] done clear
D) \[2p\] done clear
View Answer play_arrowquestion_answer16) The temperature at which the mean \[KE\] of the molecules of gas is one-third of the mean \[KE\] of its molecules at \[{{180}^{o}}C\] is
A) \[-{{122}^{o}}C\] done clear
B) \[-{{90}^{o}}C\] done clear
C) \[{{60}^{o}}C\] done clear
D) \[{{151}^{o}}C\] done clear
View Answer play_arrowquestion_answer17) \[U\] is the \[PE\] of an oscillating particle and \[F\] is the force acting on it at a given instant. Which of the following is true?
A) \[\frac{U}{F}+x=0\] done clear
B) \[\frac{2U}{F}+x=0\] done clear
C) \[\frac{F}{U}+x=0\] done clear
D) \[\frac{F}{2U}+x=0\] done clear
View Answer play_arrowquestion_answer18) The density of newly discovered planet is twice that of the earth. The acceleration due to gravity at the surface of the planet is equal to that at the surface of the earth. If the radius of the earth is\[R\], the radius of the plane would be
A) \[2R\] done clear
B) \[4R\] done clear
C) \[\frac{1}{4}R\] done clear
D) \[\frac{1}{2}R\] done clear
View Answer play_arrowquestion_answer19) The half-life period of a radioactive substance is\[140\,\,days\]. After, how much time, \[15\,\,g\] will decay from a \[16\,\,g\] sample of the substance?
A) \[140\,\,days\] done clear
B) \[280\,\,days\] done clear
C) \[420\,\,days\] done clear
D) \[560\,\,days\] done clear
View Answer play_arrowquestion_answer20) A tuning fork \[A\] produces 4 beats \[{{s}^{-1}}\] with another tuning fork \[B\] of frequency\[320\,\,Hz\]. On filing one of the prongs of\[A\], 4 beats \[{{s}^{-1}}\] are again heard when sounded with the same fork\[B\]. Then, the frequency of 'the fork A before filing is
A) \[328\,\,Hz\] done clear
B) \[316\,\,Hz\] done clear
C) \[324\,\,Hz\] done clear
D) \[320\,\,Hz\] done clear
View Answer play_arrowquestion_answer21) Two cars are moving on two perpendicular roads towards a crossing with uniform speeds of\[72\,\,km/h\]\[\text{and}\]\[36\,\,km/h\]. If first car blows horn of frequency\[280\,\,Hz\], then the frequency of horn heard by the driver of second car when line joining the car makes angle of \[{{45}^{o}}\] with the roads, will.be
A) \[321\,\,Hz\] done clear
B) \[296\,\,Hz\] done clear
C) \[289\,\,Hz\] done clear
D) \[280\,\,Hz\] done clear
View Answer play_arrowquestion_answer22) A particle moves along a straight line\[OX\]. At a time \[t\] (in second) the distance \[x\] of the particle from \[O\] is given by\[x=40+12t-{{t}^{3}}\]. How long would the particle travel before coming to rest?
A) \[24\,\,m\] done clear
B) \[40\,\,m\] done clear
C) \[56\,\,m\] done clear
D) \[16\,\,m\] done clear
View Answer play_arrowquestion_answer23) The capacitance of a spherical conductor with radius \[1\,\,m\] is
A) \[9\times {{10}^{9}}F\] done clear
B) \[1\mu F\] done clear
C) \[1.1\times {{10}^{-10}}F\] done clear
D) \[1\times {{10}^{-6}}F\] done clear
View Answer play_arrowquestion_answer24) The electric field due to an electric dipole at a distance \[r\] from its centre in axial position is\[E\]. If the dipole is rotated through an angle of \[{{90}^{o}}\] about its perpendicular axis, the electric field at the same point will be
A) \[E\] done clear
B) \[\frac{E}{4}\] done clear
C) \[\frac{E}{2}\] done clear
D) \[2E\] done clear
View Answer play_arrowquestion_answer25) Choose the correct statement.
A) When we heat a semiconductor its resistance increases done clear
B) When we heat a semiconductor its resistance decreases done clear
C) When we cool a semiconductor to\[0\,\,K\], then it be cames superconductor done clear
D) Resistance of a semiconductor is independent of temperature done clear
View Answer play_arrowquestion_answer26) A charge \[q\] coulomb makes \[n\] revolutions in one second in a circular orbit of radius r. The magnetic field at the centre of the orbit in\[N{{A}^{-1}}{{m}^{-1}}\]is.
A) \[\frac{2\pi rn}{q}\times {{10}^{-7}}\] done clear
B) \[\left( \frac{2\pi q}{r} \right)\times {{10}^{-7}}\] done clear
C) \[\left( \frac{2\pi q}{nr} \right)\times {{10}^{-7}}\] done clear
D) \[\left( \frac{2\pi nq}{r} \right)\times {{10}^{-7}}\] done clear
View Answer play_arrowquestion_answer27) The path of an electron in a uniform magnetic field may be
A) circular but not helical done clear
B) helical but not circular done clear
C) neither helical nor circular done clear
D) either helical or circular done clear
View Answer play_arrowquestion_answer28) The couple acting on a magnet of length \[10\,\,cm\] and pole strength\[125\,\,A-m\], kept in a field of \[B=2\times {{10}^{-5}}T\], at an angle of \[{{30}^{o}}\] is
A) \[1.5\times {{10}^{-5}}N-m\] done clear
B) \[1.5\times {{10}^{-3}}N-m\] done clear
C) \[1.5\times {{10}^{-2}}N-m\] done clear
D) \[1.5\times {{10}^{-6}}N-m\] done clear
View Answer play_arrowquestion_answer29) \[X\]and\[Y\], two metallic coils are arranged in such a way that, when steady change in current flowing in \[X\] coil is\[4\,\,A\], change in magnetic flux associated with coil \[Y\] is\[0.4\,\,Wb\]. Mutual inductance of the system of these coils is
A) \[0.2\,\,H\] done clear
B) \[5\,\,H\] done clear
C) \[0.8\,\,H\] done clear
D) \[0.1\,\,H\] done clear
View Answer play_arrowquestion_answer30) A sinusoidal voltage of peak value \[300\,\,V\] and an angular frequency \[\omega =400\,\,rad/s\] is applied to series \[L-C-R\] circuit, in which \[R=3\Omega ,\,\,L=20\,\,mH\]and\[C=625\mu F\]. The peak current in the circuit is
A) \[30\sqrt{2}A\] done clear
B) \[60\,\,A\] done clear
C) \[100\,\,A\] done clear
D) \[60\sqrt{2}A\] done clear
View Answer play_arrowquestion_answer31) A fire screen produces sensation of cooling as
A) it allows both infrared and visible light but cuts off ultraviolet done clear
B) it allows infrared and cuts off shorter wavelengths done clear
C) it cuts off both visible light and infrared done clear
D) it allows only visible light and cuts off infrared done clear
View Answer play_arrowquestion_answer32) If the angle of incidence is twice the angle of refraction in a medium of refractive index\[\mu \], then the angle of incidence is
A) \[2{{\cos }^{-1}}\frac{\mu }{2}\] done clear
B) \[2{{\sin }^{-1}}\frac{\mu }{2}\] done clear
C) \[2{{\cos }^{-1}}\mu \] done clear
D) \[2{{\sin }^{-1}}\mu \] done clear
View Answer play_arrowquestion_answer33) The magnification produced by an astronomical telescope for normal adjustment is 10 and the length of the telescope.is\[1.1\,\,m\]. The magnification, when the image is formed atleast distance of distinct vision is
A) \[6\] done clear
B) \[14\] done clear
C) \[16\] done clear
D) \[18\] done clear
View Answer play_arrowquestion_answer34) In Young's double slit experiment with sodium vapour lamp of wavelength \[589\,\,nm\] and the slits \[0.589\,\,mm\] apart, the half angular width of the central maximum is
A) \[{{\sin }^{-1}}(0.01)\] done clear
B) \[{{\sin }^{-1}}(0.0001)\] done clear
C) \[{{\sin }^{-1}}(0.001)\] done clear
D) \[{{\sin }^{-1}}(0.1)\] done clear
View Answer play_arrowquestion_answer35) When the angle of incidence is \[{{60}^{o}}\] on the surface of a glass slab, it is found that the reflected ray is completely polarised. The velocity of light in glass is
A) \[\sqrt{2}\times {{10}^{8}}m{{s}^{-1}}\] done clear
B) \[\sqrt{3}\times {{10}^{8}}m{{s}^{-1}}\] done clear
C) \[2\times {{10}^{8}}m{{s}^{-1}}\] done clear
D) \[3\times {{10}^{8}}m{{s}^{-1}}\] done clear
View Answer play_arrowquestion_answer36) Cathode rays of velocity \[{{10}^{6}}m{{s}^{-1}}\] describe an approximate circular path of radius \[1\,\,m\] in an electric field\[300\,\,Vc{{m}^{-1}}\]. If the velocity of the cathode rays are doubled. The value of electric field so that the rays describe the same circular path, will be
A) \[2400\,\,V\,\,c{{m}^{-1}}\] done clear
B) \[600\,\,V\,\,c{{m}^{-1}}\] done clear
C) \[1200\,\,V\,\,c{{m}^{-1}}\] done clear
D) \[12000\,\,V\,\,c{{m}^{-1}}\] done clear
View Answer play_arrowquestion_answer37) The de-Broglie wavelength of an electron and the wavelength of a photon are the same. The ratio between the energy of that photon and the momentum of that electron is (\[c=\]velocity of light, \[h=\]Planck's constant)
A) \[h\] done clear
B) \[c\] done clear
C) \[\frac{1}{h}\] done clear
D) \[\frac{1}{c}\] done clear
View Answer play_arrowquestion_answer38) When \[1\,\,cm\]thick surface is illuminated with light of wavelength\[\lambda \], the stopping potential is\[V\]. When the same surface is illuminated by light of wavelength\[2\lambda \], the stopping potential is\[\frac{V}{3}\]. Threshold wavelength for metallic surface is
A) \[\frac{4\lambda }{3}\] done clear
B) \[4\lambda \] done clear
C) \[6\lambda \] done clear
D) \[\frac{8\lambda }{3}\] done clear
View Answer play_arrowquestion_answer39) For photoelectric emission, tungsten requires light of\[2300\,\,\overset{\text{o}}{\mathop{\text{A}}}\,\]. If light of \[1800\,\,\overset{\text{o}}{\mathop{\text{A}}}\,\] wavelength is incident, then emission
A) takes place done clear
B) doesn't take place done clear
C) may or may not take place done clear
D) depends on frequency done clear
View Answer play_arrowquestion_answer40) X-rays are used in determining the molecular structure of crystalline, because
A) its energy is high done clear
B) it can penetrate the material done clear
C) its wavelength is comparable to interatomic distance done clear
D) its frequency is low done clear
View Answer play_arrowquestion_answer41) The frequency of vibration of string is given by \[v=\frac{p}{2l}{{\left[ \frac{F}{m} \right]}^{1/2}}\] Here, \[p\] is the number of segments m the string and \[l\] is the length. The dimensional formula for \[m\] will be
A) \[[{{M}^{0}}L{{T}^{-1}}]\] done clear
B) \[[M{{L}^{0}}{{T}^{-1}}]\] done clear
C) \[[M{{L}^{-1}}{{T}^{0}}]\] done clear
D) \[[{{M}^{0}}{{L}^{0}}{{T}^{0}}]\] done clear
View Answer play_arrowquestion_answer42) A stone is thrown vertically upwards. When the stone is at a height equal to half of its maximum height its speed will be\[10\,\,m/s\], then the maximum height attained by the stone (Take\[g=10\,\,m/{{s}^{2}})\]
A) \[3\,\,m\] done clear
B) \[15\,\,m\] done clear
C) \[1\,\,m\] done clear
D) \[10\,\,m\] done clear
View Answer play_arrowquestion_answer43) A string of length /fixed at one end carries mass \[m\] at the other end. The string makes\[\frac{2}{\pi }\,\,rev/s\] around the horizontal axis through the it fixed end as shown in the figure, the tension in the string is
A) \[16\,\,ml\] done clear
B) \[6\,\,ml\] done clear
C) \[5\,\,ml\] done clear
D) \[3\,\,ml\] done clear
View Answer play_arrowquestion_answer44) A gardener pushes a lawn roller through distance\[20\,\,m\]. If he applies a force of \[20\,\,kg-w\] in a direction inclined at \[{{60}^{o}}\] to the ground, the work done by him is
A) \[1960\,\,J\] done clear
B) \[196\,\,J\] done clear
C) \[1.96\,\,J\] done clear
D) \[196\,\,kJ\] done clear
View Answer play_arrowquestion_answer45) The breaking stress of a wire depends upon
A) material of wire done clear
B) length of wire done clear
C) radius of wire done clear
D) shape of cross-section done clear
View Answer play_arrowquestion_answer46) \[Li\] nucleus has three protons and four neutrons. Mass of lithium nucleus is\[7.016005\,\,amu\]. Mass of proton is \[1.007277\,\,amu\] and mass of neutron is\[1.008665\,\,amu\]. Mass defect for lithium nucleus in \[amu\] is
A) \[0.04048\] done clear
B) \[0.04050\] done clear
C) \[0.04052\] done clear
D) \[0.04055\] done clear
View Answer play_arrowquestion_answer47) A voltmeter of range \[2V\] and resistance \[300\Omega \] cannot be converted into ammeter of range
A) \[1\,\,A\] done clear
B) \[1\,\,mA\] done clear
C) \[100\,\,mA\] done clear
D) \[10\,\,mA\] done clear
View Answer play_arrowquestion_answer48) The values of two resistors are \[{{R}_{1}}=(6+0.3)k\Omega \] and\[{{R}_{2}}=(10\pm 0.2)k\Omega \]. The percentage error in the equivalent resistance when, they are connected in parallel is
A) \[5.125%\] done clear
B) \[2%\] done clear
C) \[10.125%\] done clear
D) \[7%\] done clear
View Answer play_arrowquestion_answer49) A body of mass \[2\,\,kg\] is projected from the ground with a velocity \[20\,\,m{{s}^{-1}}\] at an angle \[{{30}^{o}}\] with the vertical. If \[{{t}_{1}}\] is the time in second at which the body is projected and \[{{t}_{2}}\] is the time in second at which it reaches the ground, the change in momentum in \[kgm{{s}^{-1}}\] during the time \[({{t}_{2}}-{{t}_{1}})\] is
A) \[40\sqrt{2}\] done clear
B) \[40\sqrt{3}\] done clear
C) \[25\sqrt{3}\] done clear
D) \[45\] done clear
View Answer play_arrowquestion_answer50) The position vector of a particle is\[r=(a\cos \omega t)\widehat{\mathbf{i}}+(a\sin \omega t)\widehat{\mathbf{j}}\]. The velocity vector of the particle is
A) parallel to position vector done clear
B) perpendicular to position vector done clear
C) directed towards the origin done clear
D) directed away from the origin done clear
View Answer play_arrowquestion_answer51) The major product of the reaction between m-dinitrobenzene and \[N{{H}_{4}}HS\]is
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer52) Correct order of nucleophilicity is
A) \[CH_{3}^{-}<NH_{2}^{-}<O{{H}^{-}}<{{F}^{-}}\] done clear
B) \[{{F}^{-}}<O{{H}^{-}}<CH_{3}^{-}<NH_{2}^{-}\] done clear
C) \[O{{H}^{-}}<NH_{2}^{-}<{{F}^{-}}<CH_{3}^{-}\] done clear
D) \[{{F}^{-}}<O{{H}^{-}}<NH_{2}^{-}<CH_{3}^{-}\] done clear
View Answer play_arrowquestion_answer53) The main product of the reaction would be 2-butene + chloroform\[\xrightarrow{NaOH}\]?
A) butanoic acid done clear
B) 2-methyl butanoic acid done clear
C) 1, 1, 1-trichloro-2-methyl butane done clear
D) 1, 4-butane diol done clear
View Answer play_arrowquestion_answer54) The end product of\[C{{H}_{3}}COOH\xrightarrow{CaC{{O}_{3}}}A\xrightarrow{Heat}B\xrightarrow{N{{H}_{2}}OH}C\]
A) acetaldehyde done clear
B) acetoxime done clear
C) formaldehyde done clear
D) methyl cyanide done clear
View Answer play_arrowquestion_answer55) Calorific value is in the order
A) Fats > Carbohydrates > Proteins done clear
B) Carbohydrates > Fats > Proteins done clear
C) Proteins > Carbohydrates > Fats done clear
D) Fats > Proteins > Carbohydrates done clear
View Answer play_arrowquestion_answer56) The monomeric unit of orlon molecule is
A) \[C{{H}_{2}}=CH-Cl\] done clear
B) \[C{{H}_{3}}COO-CH=C{{H}_{2}}\] done clear
C) \[C{{H}_{2}}=CH-CN\] done clear
D) \[{{C}_{6}}{{H}_{5}}-CH=C{{H}_{2}}\] done clear
View Answer play_arrowquestion_answer57) Which of the following acids possesses oxidising, reducing and complex forming properties?
A) \[HCl\] done clear
B) \[HN{{O}_{2}}\] done clear
C) \[{{H}_{2}}S{{O}_{4}}\] done clear
D) \[HN{{O}_{3}}\] done clear
View Answer play_arrowquestion_answer58) Cassiterite is concentrated by
A) levigation done clear
B) electromagnetic separation done clear
C) floatation done clear
D) liquefaction done clear
View Answer play_arrowquestion_answer59) The stability of the following alkali metal chlorides follows the order
A) \[LiCl>KCl>NaCl>CsCl\] done clear
B) \[CsCl>KCl>NaCl>LiCl\] done clear
C) \[NaCl>KCl>LiCl>CsCl\] done clear
D) \[KCl>CsCl>NaCl>LiCl\] done clear
View Answer play_arrowquestion_answer60) The complex \[{{[Fe{{({{H}_{2}}O)}_{5}}NO]}^{2+}}\] is formed in the brown ring test for nitrates when freshly prepared \[FeS{{O}_{4}}\] solution is added to aqueous solution of \[NO_{3}^{-}\] followed by addition of conc. \[{{H}_{2}}S{{O}_{4}}\]. Select the correct statement about this complex.
A) Colour change is due to charge transfer done clear
B) It has iron in \[+1\] oxidation state and nitrosyl as\[N{{O}^{+}}\] done clear
C) It has, magnetic moment of \[3.87\,\,BM\] confirming three unpaired electrons in\[Fe\] done clear
D) All the above are correct statements done clear
View Answer play_arrowquestion_answer61) Consider the following statements. I. Colour of a transition metal complex is dependent on energy difference between two \[d-\]levels. II. Colour of the complex is dependent on the nature of the ligand and the type of complex formed. III. \[ZnS{{O}_{4}}\] and \[Ti{{O}_{2}}\] are white as in both,\[d-d\] spectra are impossible. Select the correct statements.
A) I, II and III done clear
B) I and II done clear
C) II and III done clear
D) I and III done clear
View Answer play_arrowquestion_answer62) The outermost electronic configuration of the most electronegative element is
A) \[n{{s}^{2}}n{{p}^{3}}\] done clear
B) \[n{{s}^{2}}n{{p}^{4}}\] done clear
C) \[n{{s}^{2}}n{{p}^{5}}\] done clear
D) \[n{{s}^{2}}n{{p}^{6}}\] done clear
View Answer play_arrowquestion_answer63) Standard enthalpy and standard entropy change for the oxidation of \[N{{H}_{3}}\] at \[298\,\,K\] are \[-382.64\,\,kJ\,\,mo{{l}^{-1}}\]and\[-145.6\,\,J\,\,mo{{l}^{-1}}\]respectively. Standard Gibbs energy change for the same reaction at \[298\,\,K\] is
A) \[+339.3\,\,kJ\,\,mo{{l}^{-1}}\] done clear
B) \[-439.3\,\,kJ\,\,mo{{l}^{-1}}\] done clear
C) \[-339.3\,\,kJ\,\,mo{{l}^{-1}}\] done clear
D) \[-393.3\,\,kJ\,\,mo{{l}^{-1}}\] done clear
View Answer play_arrowquestion_answer64) According to the Arrhenius equation, a straight line is to be obtained by plotting the logarithm of the rate constant of a chemical reaction \[(\log k)\] against
A) \[T\] done clear
B) \[\log T\] done clear
C) \[\frac{1}{T}\] done clear
D) \[\log \frac{1}{T}\] done clear
View Answer play_arrowquestion_answer65) Which of the following is not a reducing agent?
A) \[S{{O}_{2}}\] done clear
B) \[{{H}_{2}}{{O}_{2}}\] done clear
C) \[C{{O}_{2}}\] done clear
D) \[N{{O}_{2}}\] done clear
View Answer play_arrowquestion_answer66) For a dilute solution, Raoult's law states that
A) the lowering of vapour pressure is equal to the mole fraction of the solute done clear
B) the relative lowering of vapour pressure is equal to the mole fraction of solute done clear
C) the relative lowering of vapour pressure is equal to the amount of the solution done clear
D) the vapour pressure of the solution, is equal to the mole fraction of the solvent done clear
View Answer play_arrowquestion_answer67) The bond dissociation energies of gaseous \[{{H}_{2}},\,\,C{{l}_{2}}\] and \[HCl\] are \[104,\,\,58\] and \[103\,\,kcal\] respectively. The enthalpy of formation of \[HCl\] gas would be
A) \[-44\,\,kcal\] done clear
B) \[44\,\,kcal\] done clear
C) \[-22\,\,kcal\] done clear
D) \[22\,\,kcal\] done clear
View Answer play_arrowquestion_answer68) Species acting both as Bronsted acid and base is
A) \[HSO_{4}^{-}\] done clear
B) \[N{{a}_{2}}C{{O}_{3}}\] done clear
C) \[N{{H}_{3}}\] done clear
D) \[O{{H}^{-}}\] done clear
View Answer play_arrowquestion_answer69) The solubility of \[Agl\] in \[Nal\] solution is less than that in pure water because
A) \[Agl\] forms complex with\[Nal\] done clear
B) of common ion effect done clear
C) solubility product of \[Agl\] is less done clear
D) the temperature of the solution decreases done clear
View Answer play_arrowquestion_answer70) \[Zn|Z{{n}^{2+}}(a=0.1\,\,M)||F{{e}^{2+}}(a=0.01\,\,M)|Fe.\]The emf of the above cell is\[0.2905\,\,V\]. Equilibrium constant for the cell reaction is
A) \[{{10}^{0.32/0.0591}}\] done clear
B) \[{{10}^{0.32/0.0295}}\] done clear
C) \[{{10}^{0.26/0.0295}}\] done clear
D) \[{{10}^{0.26/0.0295}}\] done clear
View Answer play_arrowquestion_answer71) \[50\,\,mL\] of \[1\,\,M\] oxalic acid (molar mass\[=126\]) is shaken with \[0.5\,\,g\] of wood charcoal. The final concentration of the solution after adsorption is\[0.5\,\,M\]. What is the amount of oxalic acid adsorbed per gram of carbon?
A) \[3.15\] done clear
B) \[1.575\] done clear
C) \[6.30\] done clear
D) \[12.60\] done clear
View Answer play_arrowquestion_answer72) A dust particle has mass equal to\[{{10}^{-11}}g\], diameter \[{{10}^{-4}}cm\] and velocity\[{{10}^{-4}}cm/s\]. The error in measurement of velocity is\[0.1\,\,%\]. What will be the uncertainty in its position?
A) \[0.527\times {{10}^{10}}cm\] done clear
B) \[5.27\times {{10}^{9}}cm\] done clear
C) \[0.527\times {{10}^{-15}}cm\] done clear
D) \[0.527\times {{10}^{-9}}cm\] done clear
View Answer play_arrowquestion_answer73) The value of compression factor, \[Z\] for critical constants is
A) \[\frac{1}{2}\] done clear
B) \[\frac{3}{4}\] done clear
C) \[\frac{2}{3}\] done clear
D) \[\frac{3}{8}\] done clear
View Answer play_arrowquestion_answer74) At what temperature, the \[rms\] velocity of \[S{{O}_{2}}\] be same as that of \[{{O}_{2}}\] at\[303\,\,K\]?
A) \[273\,\,K\] done clear
B) \[606\,\,K\] done clear
C) \[303\,\,K\] done clear
D) \[403\,\,K\] done clear
View Answer play_arrowquestion_answer75) The percentage of water of crystallisation of a sample of blue vitriol is
A) \[34.07%\] done clear
B) \[35.07%\] done clear
C) \[36.07%\] done clear
D) \[37.07%\] done clear
View Answer play_arrowquestion_answer76) Which of the following series of elements have nearly the same atomic radii?
A) \[F,\,\,Cl,\,\,Br,\,\,I\] done clear
B) \[Na,\,\,K,\,\,Rb,\,\,Cs\] done clear
C) \[Li,\,\,Be,\,\,B,\,\,C\] done clear
D) \[Fe,\,\,Co,\,\,Ni,\,\,Cu\] done clear
View Answer play_arrowquestion_answer77) The volume strength of 1 molar solution of\[{{H}_{2}}{{O}_{2}}\]is
A) \[11.2\] done clear
B) \[22.4\] done clear
C) \[5.6\] done clear
D) \[56\] done clear
View Answer play_arrowquestion_answer78) Maximum amount of carbon is present in
A) wrought iron done clear
B) cast iron done clear
C) stainless steel done clear
D) German silver done clear
View Answer play_arrowquestion_answer79) What is the best way to carry out the following transformation? \[1-\text{pentyne}\xrightarrow{{}}\text{pentanal}\]
A) \[HgS{{O}_{4}}/{{H}_{2}}S{{O}_{4}}\] done clear
B) \[{{H}_{2}}/Lindlar's\,\,catalyst;\,\,{{O}_{3}};\,\,Zn-{{H}_{2}}O\] done clear
C) \[Hl{{O}_{4}}/{{H}_{2}}O\] done clear
D) \[B{{H}_{3}};\,\,{{H}_{2}}{{O}_{2}}/NaOH\] done clear
View Answer play_arrowquestion_answer80) Product of this reaction is
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer81) Etherates are
A) ethers done clear
B) solution in ether done clear
C) complexes of ethers with Lewis acid done clear
D) complexes of ethers with Lewis base done clear
View Answer play_arrowquestion_answer82) Tranquillisers are the substances used for the treatment of
A) cancer done clear
B) AIDS done clear
C) mental diseases done clear
D) physical disorders done clear
View Answer play_arrowquestion_answer83) Which of the following carbonyl compounds on condensation gives an aromatic compound?
A) \[C{{H}_{3}}CHO\] done clear
B) \[HCHO\] done clear
C) \[C{{H}_{3}}COC{{H}_{3}}\] done clear
D) \[C{{H}_{3}}C{{H}_{2}}CHO\] done clear
View Answer play_arrowquestion_answer84) Iron crystallises in a bcc system with a lattice parameter of\[2.861\,\,\overset{\text{o}}{\mathop{\text{A}}}\,\]. Calculate the density of iron in the bcc system (atomic weight of\[Fe=56,\,\,{{N}_{A}}=6.02\times {{10}^{23}}mo{{l}^{-1}})\].
A) \[7.94\,\,g\,\,m{{L}^{-1}}\] done clear
B) \[8.96\,\,g\,\,m{{L}^{-1}}\] done clear
C) \[2.78\,\,g\,\,m{{L}^{-1}}\] done clear
D) \[6.72\,\,g\,\,m{{L}^{-1}}\] done clear
View Answer play_arrowquestion_answer85) Which particle among the following will have the smallest de-Broglie wavelength, assuming that they have the same velocity?
A) A positron done clear
B) A photon done clear
C) An \[\alpha -\]particle done clear
D) A neutron done clear
View Answer play_arrowquestion_answer86) The equilibrium constant for the reaction,\[{{H}_{2}}(g)+{{I}_{2}}(g)2HI(g)\]is 64. If the volume of the container is reduced to half of the original volume, the value of the equilibrium constant will be
A) \[16\] done clear
B) \[32\] done clear
C) \[64\] done clear
D) \[128\] done clear
View Answer play_arrowquestion_answer87) For the reaction,\[Zn(s)+C{{u}^{2+}}(0.1M)\xrightarrow{{}}Z{{n}^{2+}}(1M)+Cu(s)t\]akmg place in a cell;\[E_{cell}^{\text{o}}\]is\[1.10\,\,V\].\[{{E}_{cell}}\] for the cell will be\[\left( 2.303\frac{RT}{F}=0.0591 \right)\]
A) \[1.80\,\,V\] done clear
B) \[1.07\,\,V\] done clear
C) \[0.82\,\,V\] done clear
D) \[2.14\,\,V\] done clear
View Answer play_arrowquestion_answer88) Surface of the eye is protected from bacterial infection by enzyme
A) carbonic enhydrase done clear
B) urease done clear
C) lysozyme done clear
D) zymase done clear
View Answer play_arrowquestion_answer89) The number of \[\sigma \]bonds in \[{{P}_{4}}{{O}_{10}}\] is
A) \[6\] done clear
B) \[16\] done clear
C) \[20\] done clear
D) \[7\] done clear
View Answer play_arrowquestion_answer90) Indicate the wrongly named compound.
A) \[C{{H}_{3}}-\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\mathop{C}}\,H-C{{H}_{2}}-C{{H}_{2}}-CHO\] (4-methyl-1-pentanal) done clear
B) \[C{{H}_{3}}-\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\mathop{C}}\,H-C\equiv C-COOH\] (4-methyl-2-pentyn-1-oic acid) done clear
C) \[C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}-\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\mathop{C}}\,H-COOH\] (2-methyl-1-pentanoic acid) done clear
D) \[C{{H}_{3}}C{{H}_{2}}-CH=CH-\overset{\begin{smallmatrix} O \\ || \end{smallmatrix}}{\mathop{C}}\,-C{{H}_{3}}\] (3-hexen-5-one) done clear
View Answer play_arrowquestion_answer91) Identify the vitamin whose deficiency in our blood decreases reproductive power?
A) Vitamin E done clear
B) Vitamin D done clear
C) Vitamin A done clear
D) Vitamin C done clear
View Answer play_arrowquestion_answer92) Give the major product of the following reaction,
A) done clear
B) done clear
C) done clear
D) Cannot say done clear
View Answer play_arrowquestion_answer93) \[Phenol\xrightarrow[(ii)\,\,C{{O}_{2}}/{{140}^{o}}C]{(i)\,\,NaOH}A\xrightarrow{{{H}^{+}}/{{H}_{2}}O}B\xrightarrow{A{{c}_{2}}O}C\]In this reaction, the end product \['C'\] is
A) salicylaldehyde done clear
B) salicylic acid done clear
C) phenyl acetate done clear
D) aspirin done clear
View Answer play_arrowquestion_answer94) What will be the degree of ionisation of \[0.05\,\,M\] acetic acid if its \[p{{K}_{a}}\] value is\[4.74\]?
A) \[0.019%\] done clear
B) \[1.9%\] done clear
C) \[3.0%\] done clear
D) \[4.74%\] done clear
View Answer play_arrowquestion_answer95) Which of the reactions defines\[\Delta H_{f}^{\text{o}}\]?
A) \[{{C}_{diamond}}+{{O}_{2}}(g)\xrightarrow{{}}C{{O}_{2}}(g)\] done clear
B) \[\frac{1}{2}{{H}_{2}}(g)+\frac{1}{2}{{F}_{2}}(g)\xrightarrow{{}}HF(g)\] done clear
C) \[{{N}_{2}}(l)+3{{H}_{2}}(g)\xrightarrow{{}}2N{{H}_{3}}(g)\] done clear
D) \[CO(g)+\frac{1}{2}{{O}_{2}}(g)\xrightarrow{{}}C{{O}_{2}}(g)\] done clear
View Answer play_arrowquestion_answer96) The equivalent weight of \[N{{a}_{2}}{{S}_{2}}{{O}_{3}}\] in the following reaction is \[2N{{a}_{2}}{{S}_{2}}{{O}_{3}}+{{I}_{2}}\xrightarrow{{}}N{{a}_{2}}{{S}_{4}}{{O}_{6}}+2NaI\]
A) \[M\] done clear
B) \[M/8\] done clear
C) \[M/0.5\] done clear
D) \[M/2\] done clear
View Answer play_arrowquestion_answer97) The half-life period for first order reaction having activation energy \[39.3\,\,kcal\,\,mo{{l}^{-1}}\] at \[{{300}^{o}}C\] and frequency constant \[1.11\times {{10}^{11}}{{s}^{-1}}\] will be
A) \[1\,\,h\] done clear
B) \[1.68\,\,h\] done clear
C) \[1.28\,\,h\] done clear
D) \[1.11\,\,h\] done clear
View Answer play_arrowquestion_answer98) Water is brought to boil under a pressure of\[1.0\,\,atm\]. When an electric current of \[0.50\,\,A\] from a \[12\,\,V\] supply is passed for \[300\,\,s\] through a resistance in thermal contact with it, it is found that \[0.798\,\,g\] of water is vaporised. Calculate the molar internal energy change at boiling point\[(373.15\,\,K)\].
A) \[375\,\,kJ\,\,mo{{l}^{-1}}\] done clear
B) \[3.75\,\,kJ\,\,mo{{l}^{-1}}\] done clear
C) \[42.6\,\,kJ\,\,mo{{l}^{-1}}\] done clear
D) \[4.26\,\,kJ\,\,mo{{l}^{-1}}\] done clear
View Answer play_arrowquestion_answer99) The electrons, identified by quantum numbers\[n\] and\[l\], (i)\[n=4,\,\,l=1\](ii)\[n=4,\,\,l=0\] (iii)\[n=3,\,\,l=2\](iv)\[n=3,\,\,l=1\]can be placed in order of increasing energy, from the lowest to highest, as
A) (iv) < (ii) < (iii) < (i) done clear
B) (ii) < (iv) < (i) < (iii) done clear
C) (i) < (iii) < (ii) < (ii) done clear
D) (iii) < (i) < (iv) < (ii) done clear
View Answer play_arrowquestion_answer100) At certain temperature and a total pressure of\[{{10}^{5}}\,\,Pa\], iodine vapours contains \[40%\] by volume of iodine atoms. \[{{K}_{p}}\] for the equilibrium, \[{{I}_{2}}(g)2I(g)\];will be
A) \[0.67\] done clear
B) \[1.5\] done clear
C) \[2.67\times {{10}^{4}}\] done clear
D) \[9.0\times {{10}^{4}}\] done clear
View Answer play_arrowquestion_answer101) The area of the triangle formed by the lines \[{{x}^{2}}-4{{y}^{2}}=0\] and\[x=a\], is
A) \[2{{a}^{2}}\] done clear
B) \[\frac{{{a}^{2}}}{2}\] done clear
C) \[\frac{\sqrt{3}{{a}^{2}}}{2}\] done clear
D) \[\frac{2{{a}^{2}}}{\sqrt{3}}\] done clear
View Answer play_arrowquestion_answer102) There were two women participating in a chess tournament. Every participant played two games with the other participants. The number of games that the men played between themselves proved to exceed by 66 the number of games that the men played with the women. The number of participants is
A) 6 done clear
B) 11 done clear
C) 13 done clear
D) None of these done clear
View Answer play_arrowquestion_answer103) For which interval, the given function \[f(x)=-2{{x}^{3}}-9{{x}^{2}}-12x+1\]is decreasing?
A) \[(-2,\,\,\infty )\] done clear
B) \[(-2,\,\,-1)\] done clear
C) \[(-\infty ,\,\,-1)\] done clear
D) \[(-\infty ,\,\,-2)\]and\[(-1,\,\,\infty )\] done clear
View Answer play_arrowquestion_answer104) The value of\[x=\sqrt{2+\sqrt{2+\sqrt{2+...}}}\]is
A) \[-1\] done clear
B) \[1\] done clear
C) \[2\] done clear
D) \[3\] done clear
View Answer play_arrowquestion_answer105) For what value\[k\], will the equation \[{{x}^{2}}-(3k-1)x+2{{k}^{2}}+2k=11\]have equal roots?
A) \[5\] done clear
B) \[9\] done clear
C) Both [a] and [b] done clear
D) \[0\] done clear
View Answer play_arrowquestion_answer106) A student is to answer \[10\] out of \[13\] questions in an examination such that he must choose atleast \[4\] from the first five questions. The number of choices available to him is
A) \[140\] done clear
B) \[196\] done clear
C) \[280\] done clear
D) \[346\] done clear
View Answer play_arrowquestion_answer107) The equations of the tangent and normal at point \[(3,\,\,-2)\] of ellipse \[4{{x}^{2}}+9{{y}^{2}}=36\] are
A) \[\frac{x}{3}-\frac{y}{2}=1,\,\,\frac{x}{2}+\frac{y}{3}=\frac{5}{6}\] done clear
B) \[\frac{x}{3}+\frac{y}{2}=1,\,\,\frac{x}{2}-\frac{y}{3}=\frac{5}{6}\] done clear
C) \[\frac{x}{2}+\frac{y}{3}=1,\,\,\frac{x}{3}-\frac{y}{2}=\frac{5}{6}\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer108) The angle between the lines whose direction cosines satisfy the equations\[l+m+n=0,\,\,{{l}^{2}}+{{m}^{2}}-{{n}^{2}}=0\], is given by
A) \[\frac{2\pi }{3}\] done clear
B) \[\frac{\pi }{6}\] done clear
C) \[\frac{5\pi }{3}\] done clear
D) \[\frac{\pi }{3}\] done clear
View Answer play_arrowquestion_answer109) The equation of the plane containing the line of intersection of the planes \[2x-y=0\] and \[y-3z=0\] and perpendicular to the plane \[4x+5y-3z-8=0\] is
A) \[28x-17y+9z=0\] done clear
B) \[28x+17y+9z=0\] done clear
C) \[28x-17y-9z=0\] done clear
D) \[7x-3y+z=0\] done clear
View Answer play_arrowquestion_answer110) If \[f(x)\] and \[g(x)\] are two functions with \[g(x)=x-\frac{1}{x}\]and \[fog(x)={{x}^{3}}-\frac{1}{{{x}^{3}}}\], then\[f'(x)\] is equal to
A) \[3{{x}^{2}}+3\] done clear
B) \[{{x}^{2}}-\frac{1}{{{x}^{2}}}\] done clear
C) \[1+\frac{1}{{{x}^{2}}}\] done clear
D) \[3{{x}^{2}}+\frac{3}{{{x}^{4}}}\] done clear
View Answer play_arrowquestion_answer111) The function \[f:R\to R\] defined as\[f(x)=(x-1)(x-2)(x-3)\]is
A) one-one but not onto done clear
B) onto but not one-one done clear
C) both one-one and onto done clear
D) neither one-one nor onto done clear
View Answer play_arrowquestion_answer112) If\[f(x)=\left\{ \begin{matrix} -{{x}^{2}}, & when\,\,x\le 0 \\ 5x-4, & when\,\,0<x\le 1 \\ 4{{x}^{2}}-3x, & when\,\,1<x<2 \\ 3x+4, & when\,\,x\ge 2 \\ \end{matrix} \right.\]then
A) \[f(x)\]is continuous at\[x=0\] done clear
B) \[f(x)\]is continuous at\[x=2\] done clear
C) \[f(x)\]is discontinuous at\[x=1\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer113) \[f(x)=\sqrt{ax}+\frac{{{a}^{2}}}{\sqrt{ax}}\], then\[f'(\alpha )\] is equal to
A) \[-1\] done clear
B) \[1\] done clear
C) \[0\] done clear
D) \[a\] done clear
View Answer play_arrowquestion_answer114) If\[y={{t}^{10}}+1\]and\[x={{t}^{8}}\], then \[\frac{{{d}^{2}}y}{d{{x}^{2}}}\] is equal to
A) \[\frac{5}{2}t\] done clear
B) \[20{{t}^{8}}\] done clear
C) \[\frac{5}{16{{t}^{6}}}\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer115) The value of \[b\] such that scalar product of the vector \[(\widehat{\mathbf{i}}+\widehat{\mathbf{j}}+\widehat{\mathbf{k}})\] with the unit vector parallel to sum of the vectors \[(2\widehat{\mathbf{i}}+4\widehat{\mathbf{j}}-5\widehat{\mathbf{k}})\] and \[(b\widehat{\mathbf{i}}+2\widehat{\mathbf{j}}+3\widehat{\mathbf{k}})\] is\[1\], is
A) \[-2\] done clear
B) \[-1\] done clear
C) \[0\] done clear
D) \[1\] done clear
View Answer play_arrowquestion_answer116) Angle between the vectors \[\sqrt{3}(\mathbf{a}\times \mathbf{b})\] and\[b-(\mathbf{a}\cdot \mathbf{b})\mathbf{a}\]
A) \[\frac{\pi }{2}\] done clear
B) \[\frac{\pi }{4}\] done clear
C) \[0\] done clear
D) \[\frac{\pi }{3}\] done clear
View Answer play_arrowquestion_answer117) The point of contact of the line \[y=x-1\] with\[3x-4{{y}^{2}}=12\]is
A) \[(4,\,\,3)\] done clear
B) \[(3,\,\,4)\] done clear
C) \[(4,\,\,-3)\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer118) \[\int{\frac{\text{cosec}\,x}{{{\cos }^{2}}\left( 1+\log \tan \frac{x}{2} \right)}dx}\]axis equal to
A) \[{{\sin }^{2}}\left[ 1+\log \tan \frac{x}{2} \right]+C\] done clear
B) \[\tan \left[ 1+\log \tan \frac{x}{2} \right]+C\] done clear
C) \[{{\sec }^{2}}\left[ 1+\log \tan \frac{x}{2} \right]+C\] done clear
D) \[-\tan \left[ 1+\log \tan \frac{x}{2} \right]+C\] done clear
View Answer play_arrowquestion_answer119) \[\int_{2}^{\pi }{\sqrt{\frac{1+\cos 2x}{2}}dx}\]is equal to
A) \[0\] done clear
B) \[2\] done clear
C) \[1\] done clear
D) \[-1\] done clear
View Answer play_arrowquestion_answer120) The distance of the point \[(-1,\,\,5,\,\,-10)\] from the point of intersection of the line \[\frac{x-2}{3}=\frac{y+1}{4}=\frac{z-2}{12}\] and the plane\[x-y+z=5\], is
A) \[10\] done clear
B) \[11\] done clear
C) \[12\] done clear
D) \[13\] done clear
View Answer play_arrowquestion_answer121) The angle between two diagonals of a cube will be
A) \[{{\sin }^{-1}}\left( \frac{1}{3} \right)\] done clear
B) \[{{\cos }^{-1}}\left( \frac{1}{3} \right)\] done clear
C) variable done clear
D) None of these done clear
View Answer play_arrowquestion_answer122) Domain of function \[f(x)={{\sin }^{-1}}5x\] is
A) \[\left( -\frac{1}{5},\,\,\frac{1}{5} \right)\] done clear
B) \[\left[ -\frac{1}{5},\,\,\frac{1}{5} \right]\] done clear
C) \[R\] done clear
D) \[\left( 0,\,\,\frac{1}{5} \right)\] done clear
View Answer play_arrowquestion_answer123) Range of the function \[f(x)={{\sin }^{2}}({{x}^{4}})+{{\cos }^{2}}({{x}^{4}})\]is
A) \[(-\infty ,\,\,\infty )\] done clear
B) \[\{1\}\] done clear
C) \[(-1,\,\,1)\] done clear
D) \[(0,\,\,1)\] done clear
View Answer play_arrowquestion_answer124) If\[x+y=10\], then the maximum value of \[xy\] is
A) \[5\] done clear
B) \[20\] done clear
C) \[25\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer125) The value of\[\sin \frac{\pi }{14}\sin \frac{3\pi }{14}\sin \frac{5\pi }{14}\sin \frac{7\pi }{14}\sin \frac{9\pi }{14}\sin \frac{11\pi }{14}\sin \frac{13\pi }{14}\]is equal to
A) \[\frac{1}{8}\] done clear
B) \[\frac{1}{16}\] done clear
C) \[\frac{1}{32}\] done clear
D) \[\frac{1}{64}\] done clear
View Answer play_arrowquestion_answer126) \[\cos 2\theta +2\cos \theta \]is always
A) greater than\[-\frac{3}{2}\] done clear
B) less than or equal to\[\frac{3}{2}\] done clear
C) greater than or equal to \[\frac{-3}{2}\] and less than or equal to\[3\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer127) In the expansion of\[{{(1+3x+2{{x}^{2}})}^{6}}\], the coefficient of \[{{x}^{11}}\] is
A) \[144\] done clear
B) \[288\] done clear
C) \[216\] done clear
D) \[576\] done clear
View Answer play_arrowquestion_answer128) If the second, third and fourth terms in the expansion of \[{{(x+a)}^{n}}\] are \[240,\,\,\,720\] and \[1080\] respectively, then the value of \[n\] is
A) \[15\] done clear
B) \[20\] done clear
C) \[10\] done clear
D) \[5\] done clear
View Answer play_arrowquestion_answer129) The values of \[x\] and \[y\] for which the numbers \[3+i{{x}^{2}}y\]and \[{{x}^{2}}+y+4i\] are conjugate complex, can be
A) \[(-2,\,\,-1)\]or\[(2,\,\,-1)\] done clear
B) \[(-1,\,\,2)\]or\[(-2,\,\,1)\] done clear
C) \[(1,\,\,2)\]or\[(-1,\,\,-2)\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer130) The value of the expression \[1\cdot (2-\omega )(2-{{\omega }^{2}})+2\cdot (3-\omega )(3-{{\omega }^{2}})+...\] \[+(n-1)(n-\omega )(n-{{\omega }^{2}})\], where \[\omega \] is an imaginary cube root of unity, is
A) \[\frac{1}{2}(n-1)n({{n}^{2}}+3n+4)\] done clear
B) \[\frac{1}{4}(n-1)n({{n}^{2}}+3n+4)\] done clear
C) \[\frac{1}{2}(n+1)n({{n}^{2}}+3n+4)\] done clear
D) \[\frac{1}{4}(n+1)n({{n}^{2}}+3n+4)\] done clear
View Answer play_arrowquestion_answer131) If the first term of a \[GP\,\,{{\alpha }_{1}},\,\,{{\alpha }_{2}},\,\,{{\alpha }_{3}},...\]is unity such that \[4{{\alpha }_{2}}+5{{\alpha }_{3}}\] is least, then the common ratio of \[GP\] is
A) \[\frac{-2}{5}\] done clear
B) \[\frac{-3}{5}\] done clear
C) \[\frac{2}{5}\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer132) If the \[AM\] of two numbers is greater than \[GM\] of the numbers by \[2\] and the ratio of the numbers is\[4:1\], then the numbers are
A) \[4,\,\,1\] done clear
B) \[12,\,\,3\] done clear
C) \[16,\,\,4\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer133) If \[3x+2y=I\] and \[2x-y=O\], where \[I\] and \[O\] are unit and null matrices of order \[3\] respectively, then
A) \[x=\frac{1}{7},\,\,y=\frac{2}{7}\] done clear
B) \[x=\frac{2}{7},\,\,y=\frac{1}{7}\] done clear
C) \[x=\left( \frac{1}{7} \right)l,\,\,y=\left( \frac{2}{7} \right)l\] done clear
D) \[x=\left( \frac{2}{7} \right)l,\,\,y=\left( \frac{1}{7} \right)l\] done clear
View Answer play_arrowquestion_answer134) Matrix \[A\] is such that\[{{A}^{2}}=2A-I\], where \[I\] is the identity matrix. Then, for \[n\ge 2,\,\,{{A}^{n}}\] is equal to
A) \[nA-(n-1)l\] done clear
B) \[nA-l\] done clear
C) \[{{2}^{n-1}}A-(n-1)l\] done clear
D) \[{{2}^{n-1}}A-l\] done clear
View Answer play_arrowquestion_answer135) If\[3f(x)-2f\left( \frac{1}{x} \right)=x\], then \[f'(x)\] is equal to
A) \[\frac{2}{7}\] done clear
B) \[\frac{1}{2}\] done clear
C) \[2\] done clear
D) \[\frac{7}{2}\] done clear
View Answer play_arrowquestion_answer136) \[\underset{x\to 0}{\mathop{\lim }}\,\frac{{{2}^{x}}-1}{{{(1+x)}^{1/2}}-1}\]is equal to
A) \[\log 2\] done clear
B) \[\log 4\] done clear
C) \[\log \sqrt{2}\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer137) On the parabola\[y={{x}^{2}}\], the point least distant from the straight line \[y=2x-4\] is
A) \[(1,\,\,1)\] done clear
B) \[(1,\,\,0)\] done clear
C) \[(1,\,\,-1)\] done clear
D) \[(0,\,\,0)\] done clear
View Answer play_arrowquestion_answer138) The general value of \[\theta \] in the equation\[2\sqrt{3}\cos \theta =\tan \theta \]
A) \[2n\pi \pm \frac{\pi }{6}\] done clear
B) \[2n\pi \pm \frac{\pi }{4}\] done clear
C) \[n\pi +{{(-1)}^{n}}\frac{\pi }{3}\] done clear
D) \[n\pi +{{(-1)}^{n}}\frac{\pi }{4}\] done clear
View Answer play_arrowquestion_answer139) If\[\sec x\cos 5x+1=0\], where\[0<x<2\pi \], then the value of \[x\] is
A) \[\frac{\pi }{5},\,\,\frac{\pi }{4}\] done clear
B) \[\frac{\pi }{5}\] done clear
C) \[\frac{\pi }{4}\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer140) The solution of the differential equation\[({{x}^{2}}-y{{x}^{2}})\frac{dy}{dx}+{{y}^{2}}+x{{y}^{2}}=0\]is
A) \[\log \left( \frac{x}{y} \right)=\frac{1}{x}+\frac{1}{y}+C\] done clear
B) \[\log \left( \frac{y}{x} \right)=\frac{1}{x}+\frac{1}{y}+C\] done clear
C) \[\log (xy)=\frac{1}{x}+\frac{1}{y}+C\] done clear
D) \[\log (xy)+\frac{1}{x}+\frac{1}{y}=C\] done clear
View Answer play_arrowquestion_answer141) The general solution of, the differential equation\[(x+y)dx+xdy=0\]is
A) \[{{x}^{2}}+{{y}^{2}}=C\] done clear
B) \[2{{x}^{2}}-{{y}^{2}}=C\] done clear
C) \[{{x}^{2}}+2xy=C\] done clear
D) \[{{y}^{2}}+2xy=C\] done clear
View Answer play_arrowquestion_answer142) The tangent to the curve \[y=a{{x}^{2}}+bx\] at\[(2,\,\,-8)\] is parallel to\[X-axis\]. Then,
A) \[a=2,\,\,b=-2\] done clear
B) \[a=2,\,\,b=-4\] done clear
C) \[a=2,\,\,b=-8\] done clear
D) \[a=4,\,\,b=-4\] done clear
View Answer play_arrowquestion_answer143) The mean of a set of observations is\[x\]. If each observation is divided by \[\alpha ,\,\,\alpha \ne 0\] and then is increased by\[10\], then the mean of the new set is
A) \[\frac{{\bar{x}}}{\alpha }\] done clear
B) \[\frac{\bar{x}+10}{\alpha }\] done clear
C) \[\frac{\bar{x}+10\alpha }{\alpha }\] done clear
D) \[\alpha \bar{x}+10\] done clear
View Answer play_arrowquestion_answer144) \[\tilde{\ }(p\vee q)\vee (\tilde{\ }p\wedge q)\]is logically equivalent to
A) \[\tilde{\ }p\] done clear
B) \[p\] done clear
C) \[q\] done clear
D) \[\tilde{\ }q\] done clear
View Answer play_arrowquestion_answer145) If \[\frac{|z-2|}{|z-3|}=2\] represents a circle, then its radius is equal to
A) \[1\] done clear
B) \[\frac{1}{3}\] done clear
C) \[\frac{3}{4}\] done clear
D) \[\frac{2}{3}\] done clear
View Answer play_arrowquestion_answer146) The angle of elevation of the top of a tower from the top of a house is \[{{60}^{o}}\] and the angle of depression of its base is\[{{30}^{o}}\]. If the horizontal distance between the house and the tower be \[12\,\,m\], then the height of the tower is
A) \[48\sqrt{3}m\] done clear
B) \[16\sqrt{3}m\] done clear
C) \[24\sqrt{3}m\] done clear
D) \[\frac{16}{\sqrt{3}}m\] done clear
View Answer play_arrowquestion_answer147) Period of\[\frac{\sin \theta +\sin 2\theta }{\cos \theta +\cos 2\theta }\]is
A) \[2\pi \] done clear
B) \[\pi \] done clear
C) \[\frac{2\pi }{3}\] done clear
D) \[\frac{\pi }{3}\] done clear
View Answer play_arrowquestion_answer148) If \[x\] is parallel to \[y\] and\[z\], where\[\mathbf{x}=2\widehat{\mathbf{i}}+\widehat{\mathbf{j}}+\alpha \widehat{\mathbf{k}}\],\[\mathbf{y}=\alpha \widehat{\mathbf{i}}+\widehat{\mathbf{k}}\]and\[\mathbf{z}=5\widehat{\mathbf{i}}-\widehat{\mathbf{j}}\], then a is equal to
A) \[\pm \sqrt{5}\] done clear
B) \[\pm \sqrt{6}\] done clear
C) \[\pm \sqrt{7}\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer149) If\[y={{(x+\sqrt{1+{{x}^{2}}})}^{n}}\], then\[(1+{{x}^{2}})\frac{{{d}^{2}}y}{d{{x}^{2}}}+x\frac{dy}{dx}\]is equal to
A) \[{{n}^{2}}y\] done clear
B) \[-{{n}^{2}}y\] done clear
C) \[-y\] done clear
D) \[2{{x}^{2}}y\] done clear
View Answer play_arrowquestion_answer150) The values of a for which\[({{a}^{2}}-1){{x}^{2}}+2(a-1)x+2\] is positive for any\[x\], are
A) \[a\ge 1\] done clear
B) \[a\le 1\] done clear
C) \[a>-3\] done clear
D) \[a<-3\]or\[a>1\] done clear
View Answer play_arrow
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