question_answer1) A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement \[x\] is proportional to
A) \[{{x}^{2}}\]
B) \[{{e}^{x}}\]
C) \[x\]
D) \[{{\log }_{e}}x\]
View Answer play_arrowquestion_answer2) A ball is thrown from a point with a speed \[{{v}_{0}}\] at an angle of projection\[\theta \]. From the same point and at the same instant, a person starts running with a constant speed \[\frac{{{v}_{0}}}{2}\] to catch the ball. Will the person be able to catch the ball? If yes, what should be the angle of projection?
A) Yes,\[{{60}^{o}}\]
B) Yes,\[{{30}^{o}}\]
C) No
D) Yes,\[{{45}^{o}}\]
View Answer play_arrowquestion_answer3) Spherical balls of radius \[R\] are falling in a viscous, fluid of viscosity \[\eta \] with a velocity\[v\]. The retarding viscous force acting on the spherical ball is
A) directly proportional to \[R\] but inversely proportional to\[v\]
B) directly proportional to both radius \[R\] and velocity\[v\]
C) inversely proportional to both radius \[R\] and velocity\[v\]
D) inversely proportional to \[R\] but directly proportional to velocity\[v\]
View Answer play_arrowquestion_answer4) Nickel shows ferromagnetic property at room temperature. If the temperature is increased beyond Curie temperature, then it will show
A) paramagnetism
B) anti-ferromagnetism
C) no magnetic property
D) diamagnetism
View Answer play_arrowquestion_answer5) In radioactive decay process the negatively charged emitted \[\beta -\]particles
A) the electrons present inside the nucleus
B) the electrons produced as a result of the decay of neutrons inside the nucleus
C) the electrons produced as a result of collisions between atoms
D) the electrons orbiting around the nucleus
View Answer play_arrowquestion_answer6) What is the value of inductance \[L\] for which the current is a maximum in a series \[LCR\] circuit with\[C=10\mu F\]and\[\omega =1000{{s}^{-1}}\]?
A) \[100\,\,mH\]
B) \[1\,\,mH\]
C) Cannot be calculated unless R is known
D) \[10\,\,mH\]
View Answer play_arrowquestion_answer7) Three point charges \[+q,\,\,-2q\]and\[+q\] are placed at points \[(x=0,\,\,y=a,\,\,z=0),\]\[(x=0,\,\,y=0,\,\,z=0)\]and\[(x=a,\,\,y=0,\,\,z=0)\], respectively. The magnitude and direction of the electric dipole moment vector of this charge assembly are
A) \[\sqrt{2}qa\]along\[+y\]direction
B) \[\sqrt{2}qa\]along the line joining points \[(x=0,\,\,y=0,\,\,z=0)\] and \[(x=a,\,\,y=a,\,\,z=0)\]
C) \[qa\]along the line joining points \[(x=0,\,\,y=9,\,\,z=0)\] and \[(x=a,\,\,y=a,\,\,z=0)\]
D) \[\sqrt{2}qa\]along \[+x\]direction
View Answer play_arrowquestion_answer8) The following figure shows a logic gate circuit with two inputs \[A\] and \[B\] and the output\[C\]. The voltage waveforms of \[A,\,\,\,B\] and \[C\] are as shown below The logic circuit gate is
A) \[AND\] gate
B) \[NAND\] gate
C) \[NOR\] gate
D) \[OR\] gate
View Answer play_arrowquestion_answer9) Assuming the sun to have a spherical outer surface of radius\[r\], radiating like a black body at temperature\[{{t}^{o}}C\], the power received by a unit surface, (normal to the incident rays) at a distance \[R\] from the centre of the sun is
A) \[\frac{4\pi {{r}^{2}}\sigma {{t}^{4}}}{{{R}^{2}}}\]
B) \[\frac{{{r}^{2}}\sigma {{(t+273)}^{4}}}{4\pi {{R}^{2}}}\]
C) \[\frac{16{{\pi }^{2}}{{r}^{2}}\sigma {{t}^{4}}}{{{R}^{2}}}\]
D) \[\frac{{{r}^{2}}\sigma {{(t+273)}^{4}}}{{{R}^{2}}}\] where \[\sigma \] is the Stefan's constant.
View Answer play_arrowquestion_answer10) The temperature of the two outer surfaces of a composite slab, consisting, of two materials having coefficients of thermal conductivity \[K\] and \[2K\] \[\text{and}\] thickness \[x\] and\[4x\], respectively are \[{{T}_{2}}\] and \[{{T}_{1}}\]\[({{T}_{2}}>{{T}_{1}})\]. The rate of heat transfer through the slab, in a steady state is\[\left( \frac{A({{T}_{2}}-{{T}_{1}})K}{x} \right)f\], with\[f\]equals to
A) \[1\]
B) \[1/2\]
C) \[2/3\]
D) \[1/3\]
View Answer play_arrowquestion_answer11) The maximum number of possible interference maxima for slit-separation equal to twice the wavelength in Young's double-slit experiment, is
A) infinite
B) five
C) three
D) zero
View Answer play_arrowquestion_answer12) Two spherical conductors \[B\] and \[C\] having equal radii and carrying equal charges in them repel each other with a force \[F\] when kept apart at some distance. A third spherical conductor having same radius as that of \[B\] but uncharged, is brought in contact with\[B\], then brought in contact with \[C\] and finally removed away from both. The new force of repulsion between \[B\] and \[C\] is
A) \[\frac{F}{4}\]
B) \[\frac{3F}{4}\]
C) \[\frac{F}{8}\]
D) \[\frac{3F}{8}\]
View Answer play_arrowquestion_answer13) In gamma ray emission from a nucleus
A) both the neutron number and the proton number change
B) there is no change in the proton number and the neutron number
C) only the neutron number changes
D) only the proton number changes
View Answer play_arrowquestion_answer14) A particle starting from the origin \[(0,\,\,0)\] moves in a straight line in the \[(x,\,\,y)\] plane. Its coordinates at a later time are\[(\sqrt{3},\,\,3)\]. The path of the particle makes with the \[x-\]axis an angle of
A) \[{{30}^{o}}\]
B) \[{{45}^{o}}\]
C) \[{{60}^{o}}\]
D) \[{{0}^{o}}\]
View Answer play_arrowquestion_answer15) The resistance of an ammeter is \[13\Omega \] and its scale is graduated for a current upto\[100\,\,A\]. After an additional shunt has been connected to this ammeter it becomes possible to measure currents upto \[750\,\,A\] by this meter. The value of shunt resistance is
A) \[20\,\,\Omega \]
B) \[2\,\,\Omega \]
C) \[0.2\,\,\Omega \]
D) \[2\,\,k\Omega \]
View Answer play_arrowquestion_answer16) The primary and secondary coils of a transformer have \[50\] and \[1500\] turns respectively. If the magnetic flux \[\phi \] linked with the primary coil is given by \[\phi ={{\phi }_{0}}+4t\], where \[\phi \] is in weber, \[t\] is time in second and \[{{\phi }_{0}}\] is a constant, the output voltage across the secondary coil is
A) \[90\,\,V\]
B) \[120\,\,V\]
C) \[220\,\,V\]
D) \[30\,\,V\]
View Answer play_arrowquestion_answer17) A uniform rod \[AB\] of length \[l\] and mass \[m\] is free to rotate about point\[A\]. The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about \[A\] is \[\frac{m{{l}^{2}}}{3}\] the initial angular acceleration of the rod will be
A) \[\frac{2g}{3l}\]
B) \[mg\frac{l}{2}\]
C) \[\frac{3}{2}gl\]
D) \[\frac{3g}{2l}\]
View Answer play_arrowquestion_answer18) In the energy band diagram of a material shown below, the open circles and filled circles denote holes and electrons respectively. The material is a/an
A) \[p-\]type semiconductor
B) insulator
C) metal
D) \[n-\]type semiconductor
View Answer play_arrowquestion_answer19) A particle executes simple harmonic oscillation with an amplitude\[a\]. The period of oscillation is\[T\]. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is
A) \[\frac{T}{4}\]
B) \[\frac{T}{8}\]
C) \[\frac{T}{12}\]
D) \[\frac{T}{2}\]
View Answer play_arrowquestion_answer20) A block \[B\] is pushed' momentarily along a horizontal surface with an initial velocity\[v\]. If \[\mu \] is the coefficient of sliding friction between \[B\] and the surface, block \[B\] will come to rest after a time
A) \[\frac{v}{g\mu }\]
B) \[\frac{g\mu }{v}\]
C) \[\frac{g}{v}\]
D) \[\frac{v}{g}\]
View Answer play_arrowquestion_answer21) A transformer is used to light \[\text{a}\] \[100\,\,W\] and \[110\,\,V\] lamp from a \[220\,\,V\] mains. If the main current is \[0.5\,\,A\], the efficiency of the transformer is approximately
A) \[30%\]
B) \[50%\]
C) \[90%\]
D) \[10%\]
View Answer play_arrowquestion_answer22) A steady current of \[1.5\,\,A\] flows through a copper voltameter for \[10\,\,\min \]. If the electrochemical equivalent of copper is\[30\times {{10}^{-5}}g\,\,{{C}^{-1}}\], the mass of copper deposited on the electrode will be
A) \[0.40\,\,g\]
B) \[0.50\,\,g\]
C) \[0.67\,\,g\]
D) \[0.27\,\,g\]
View Answer play_arrowquestion_answer23) Three resistances \[P,\,\,\,Q,\,\,\,R\] each of \[2\,\,\Omega \] and an unknown resistance \[S\] form the four arms of a Wheatstone's bridge circuit. When a resistance of \[6\,\,\Omega \] is connected in parallel to \[S\] the bridge gets balanced. What is the value of\[S?\]
A) \[2\,\,\Omega \]
B) \[3\,\,\Omega \]
C) \[6\,\,\Omega \]
D) \[1\,\,\Omega \]
View Answer play_arrowquestion_answer24) A mass of \[2.0\,\,kg\] is put on a flat pan attached to a vertical spring fixed on the ground as shown in the figure. The mass of the spring and the pan is negligible. When pressed slightly and released the mass-executes a simple harmonic motion. The spring constant is \[200\,\,N/m\]. What should be the minimum amplitude of the motion, so that the mass gets detached from the pan? (Take\[g=10m/{{s}^{2}})\]
A) \[8.0\,\,cm\]
B) \[10.0\,\,cm\]
C) Any value less than\[12.0\,\,cm\]
D) \[4.0\,\,cm\]
View Answer play_arrowquestion_answer25) Two satellites of earth, \[{{S}_{1}}\] and \[{{S}_{2}}\], are moving in the same orbit. The mass of \[{{S}_{2}}\] is four times the mass of \[{{S}_{2}}\]. Which one of the following statements is true?
A) The time period of \[{{S}_{1}}\] is four times that of\[{{S}_{2}}\].
B) The potential energies of earth and satellite in the two cases are equal.
C) \[{{S}_{1}}\] and \[{{S}_{2}}\] are moving with the same speed.
D) The kinetic energies of the two satellites are equal.
View Answer play_arrowquestion_answer26) Charges \[+q\] and \[-q\] are placed at points \[A\] and \[B\] respectively which are a distance 2E apart, \[C\] is the midpoint between \[A\] and \[B\]. The work done in moving a charge \[+Q\] along the semicircle \[CRD\] is
A) \[\frac{qQ}{4\pi {{\varepsilon }_{0}}L}\]
B) \[\frac{qQ}{2\pi {{\varepsilon }_{0}}L}\]
C) \[\frac{qQ}{6\pi {{\varepsilon }_{0}}L}\]
D) \[-\frac{qQ}{6\pi {{\varepsilon }_{0}}L}\]
View Answer play_arrowquestion_answer27) A beam of electrons passes un deflected through mutually perpendicular electric and magnetic fields. If the electric field is switched off, and the same magnetic field is maintained, the electrons move
A) in an elliptical orbit
B) in a circular orbit
C) along a parabolic path
D) along a straight line
View Answer play_arrowquestion_answer28) Monochromatic light of frequency \[6.0\times {{10}^{14}}Hz\] is produced by a laser. The power emitted is\[2\times {{10}^{-3}}W\]. The number of photons emitted, on the average, by the source per second is
A) \[5\times {{10}^{15}}\]
B) \[5\times {{10}^{16}}\]
C) \[5\times {{10}^{17}}\]
D) \[5\times {{10}^{14}}\]
View Answer play_arrowquestion_answer29) The diagram shows the energy levels for an electron in a certain atom. Which transition shown represents the emission of a photon with the most energy?
A) \[III\]
B) \[IV\]
C) \[I\]
D) \[II\]
View Answer play_arrowquestion_answer30) In the circuit, the galvanometer \[G\] shows zero deflection. If the batteries \[A\] and \[B\] have negligible internal resistance, the value of the resistor \[R\] will be
A) \[200\,\,\Omega \]
B) \[100\,\,\Omega \]
C) \[500\,\,\Omega \]
D) \[1000\,\,\Omega \]
View Answer play_arrowquestion_answer31) When an un polarized light of intensity \[{{I}_{0}}\] is incident on a polarizing sheet, the intensity of the light which does not get transmitted is
A) \[\frac{1}{2}{{I}_{0}}\]
B) \[\frac{1}{4}{{I}_{0}}\]
C) \[zero\]
D) \[{{I}_{0}}\]
View Answer play_arrowquestion_answer32) An observer moves towards a stationary source of sound, with a velocity one-fifth of the velocity of sound. What is the percentage increase in the apparent frequency?
A) \[zero\]
B) \[0.5%\]
C) \[5%\]
D) \[20%\]
View Answer play_arrowquestion_answer33) A particle of mass 100 g is thrown vertically upwards with a speed of 5 m/s. The work done by the force, of gravity during the time the particle goes up is
A) \[-0.5\,\,J\]
B) \[-1.25\,\,J\]
C) \[1.25\,\,J\]
D) \[0.5\,\,J\]
View Answer play_arrowquestion_answer34) A mass of \[M\,\,kg\] is suspended by a weightless string. The horizontal force that is required to displace it until the string makes an angle of \[{{45}^{o}}\] with the initial vertical direction is
A) \[Mg(\sqrt{2}+1)\]
B) \[Mg\sqrt{2}\]
C) \[\frac{Mg}{\sqrt{2}}\]
D) \[Mg(\sqrt{2}-1)\]
View Answer play_arrowquestion_answer35) An electric charge \[{{10}^{-3}}\mu C\] is placed at the origin \[(0,\,\,0)\] of \[X-Y\] coordinate system. Two points \[A\] and \[B\] are situated at \[(\sqrt{2},\,\,\sqrt{2})\] and \[(2,\,\,0)\] respectively. The potential difference between the points \[A\] and \[B\] will be
A) \[9\,\,V\]
B) \[zero\]
C) \[2\,\,V\]
D) \[4.5\,\,V\]
View Answer play_arrowquestion_answer36) A circular disc of radius \[R\] is removed from a bigger circular disc of radius \[2R\], such that the circumference of the discs coincide. The centre of mass of the new disc is \[\alpha R\] from the centre of the bigger disc. The value of \[\alpha \] is
A) \[1/3\]
B) \[1/2\]
C) \[1/6\]
D) \[1/4\]
View Answer play_arrowquestion_answer37) A common-emitter amplifier has a voltage gain of\[50\], an input impedance of \[100\,\,\Omega \] and an output impedance of \[200\,\,\Omega \]. The power gain of the amplifier is
A) \[500\]
B) \[1000\]
C) \[1250\]
D) \[100\]
View Answer play_arrowquestion_answer38) A vertical spring with force constant \[k\] is fixed on a table. A ball of mass \[m\] at a height \[h\] above the free upper end of the spring falls vertically on the spring, so that the spring is compressed by a distance\[d\]. The net work done in the process is
A) \[mg(h+d)+\frac{1}{2}k{{d}^{2}}\]
B) \[mg(h+d)-\frac{1}{2}k{{d}^{2}}\]
C) \[mg(h-d)-\frac{1}{2}k{{d}^{2}}\]
D) \[mg(h-d)+\frac{1}{2}k{{d}^{2}}\]
View Answer play_arrowquestion_answer39) Dimensions of resistance in an electrical circuit, in terms of dimension of mass\[M\], of length\[L\], of time \[T\] and of current\[I\], would be
A) \[[M{{L}^{2}}{{T}^{-3}}{{I}^{-1}}]\]
B) \[[M{{L}^{2}}{{T}^{-2}}]\]
C) \[[M{{L}^{2}}{{T}^{-1}}{{I}^{-1}}]\]
D) \[[M{{L}^{2}}{{T}^{-3}}{{I}^{-2}}]\]
View Answer play_arrowquestion_answer40) The work of \[146\,\,kJ\] is performed in order to compress one kilo mole of a gas adiabatically and in this process the temperature of the gas increases by\[{{7}^{o}}C\]. The gas is \[(R=8.3\,\,J\,\,mo{{l}^{-1}}{{K}^{-1}})\]
A) diatomic
B) triatomic
C) a mixture of monoatomic and diatomic
D) monoatomic
View Answer play_arrowquestion_answer41) Diwali rocket is ejecting \[50g\] of \[gases/\sec \] at a velocity of\[400\,\,m/s\]. The accelerating force on the rocket will be
A) \[22\,\,dyne\]
B) \[20\,\,N\]
C) \[20\,\,dyne\]
D) \[100\,\,N\]
View Answer play_arrowquestion_answer42) A frame made of metallic wire enclosing a surface area \[A\] is covered with a soap film. If the area of the frame of metallic wire is reduced by\[50%\], the energy of the Soap film will be changed by
A) \[100%\]
B) \[75%\]
C) \[50%\]
D) \[25%\]
View Answer play_arrowquestion_answer43) A symmetric double convex lens is cut in two equal parts by a plane perpendicular to the principal axis. If the power of the original lens is\[4D\], the power of a cut lens will be
A) \[2D\]
B) \[3D\]
C) \[4D\]
D) \[5D\]
View Answer play_arrowquestion_answer44) Two non-ideal batteries are connected in parallel. Consider the following statements. (i) The equivalent emf is smaller than either of the two emfs. (ii) The equivalent internal resistance is smaller than either of the two internal resistances.
A) Both (i) and (ii) are correct
B) (i) is correct but (ii) is wrong
C) (ii) is correct but (i) is wrong
D) Both (i) and (ii) are wrong
View Answer play_arrowquestion_answer45) The period of oscillation of a simple pendulum is given by\[T=2\pi \sqrt{\frac{l}{g}}\], where \[l\] is about \[100\,\,cm\] and is known to have \[1\,\,mm\] accuracy. The period is about \[2s\]. The time of \[100\] oscillations is measured by a stop watch of least count\[0.1s\]. The percentage error in \[g\] is
A) \[0.1%\]
B) \[1%\]
C) \[0.2%\]
D) \[0.8%\]
View Answer play_arrowquestion_answer46) The mass of the earth is \[6.00\times {{10}^{24}}kg\] and that of the moon is\[7.40\times {{10}^{22}}kg\]. The constant of gravitation\[G=6.67\times {{10}^{-11}}N\text{-}{{m}^{2}}/k{{g}^{2}}\]. The potential energy of the system is\[-7.79\times {{10}^{28}}J\]. The mean distance between the earth and moon is
A) \[3.80\times {{10}^{8}}m\]
B) \[3.37\times {{10}^{6}}m\]
C) \[7.60\times {{10}^{4}}m\]
D) \[1.90\times {{10}^{2}}m\]
View Answer play_arrowquestion_answer47) If a rubber ball is taken at the depth of \[200\,\,m\] in a pool, its volume-decreases by \[0.1%\]. If the density of water is \[1\times {{10}^{3}}kg/{{m}^{3}}\] and \[g=10\,\,m/{{s}^{2}}\], then the volume of elasticity in \[N/{{m}^{2}}\] will be
A) \[{{10}^{8}}\]
B) \[2\times {{10}^{8}}\]
C) \[{{10}^{9}}\]
D) \[2\times {{10}^{9}}\]
View Answer play_arrowquestion_answer48) At \[100\,\,K\]and \[0.1\] atmospheric pressure, the volume of helium gas is\[10\,\,L\]. If volume and pressure are doubled its temperature will change to
A) \[400\,\,K\]
B) \[127\,\,K\]
C) \[200\,\,K\]
D) \[25\,\,K\]
View Answer play_arrowquestion_answer49) An organ pipe \[{{P}_{1}}\] closed at one end vibrating in its first overtone and another pipe \[{{P}_{2}}\] open at both ends vibrating in its third overtone are in resonance with a given tuning fork. The ratio of lengths of \[{{P}_{1}}\] and \[{{P}_{2}}\] is
A) \[1:2\]
B) \[1:3\]
C) \[3:8\]
D) \[3:4\]
View Answer play_arrowquestion_answer50) Fraunhofer spectrum is a
A) line absorption spectrum
B) band absorption spectrum
C) line emission spectrum
D) band emission spectrum
View Answer play_arrowquestion_answer51) How many unit cells are present in a cube shaped ideal crystal of \[NaCl\] \[\text{of}\] mass\[1.00\,\,g\]? [Atomic masses\[Na=23,\,\,Cl=35.5]\]
A) \[2.57\times {{10}^{21}}\]
B) \[5.14\times {{10}^{21}}\]
C) \[1.28\times {{10}^{21}}\]
D) \[1.71\times {{10}^{21}}\]
View Answer play_arrowquestion_answer52) In acidic medium dichromate ion oxidises ferrous ion to ferric ion. If gram molecular weight of potassium dichromate is \[294\,\,g\], its gram equivalent weight is
A) \[294\,\,g\]
B) \[127\,\,g\]
C) \[49\,\,g\]
D) \[24.5\,\,g\]
View Answer play_arrowquestion_answer53) When \[C{{H}_{2}}=CH-COOH\] is reduced with \[LiAl{{H}_{4}}\], the compound obtained will be
A) \[C{{H}_{3}}-C{{H}_{2}}-COOH\]
B) \[C{{H}_{2}}=CH-C{{H}_{2}}OH\]
C) \[C{{H}_{3}}-C{{H}_{2}}-C{{H}_{2}}OH\]
D) \[C{{H}_{3}}-C{{H}_{2}}-CHO\]
View Answer play_arrowquestion_answer54) Which one of the following compounds has the smallest bond angle in its molecule?
A) \[S{{O}_{2}}\]
B) \[O{{H}_{2}}\]
C) \[S{{H}_{2}}\]
D) \[N{{H}_{3}}\]
View Answer play_arrowquestion_answer55) For the redox reaction \[Zn(s)+C{{u}^{2+}}(0.1\,\,M)\xrightarrow{{}}Z{{n}^{2+}}(1\,\,M)+Cu(s)\] taking 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) \[2.14\,\,V\]
B) \[1.80\,\,V\]
C) \[1.07\,\,V\]
D) \[0.82\,\,V\]
View Answer play_arrowquestion_answer56) The rate law for a reaction between the substances \[A\] and \[B\] is given by rate\[=k{{[A]}^{n}}{{[B]}^{n}}\]. On doubling the concentration of \[A\] and halving the concentration of \[B\], the ratio of the new rate to the earlier rate of the reaction will be as
A) \[\frac{1}{{{2}^{m+n}}}\]
B) \[(m+n)\]
C) \[(n-m)\]
D) \[{{2}^{(n-m)}}\]
View Answer play_arrowquestion_answer57) If at \[298\,\,K\] the bond energies of \[C-H,\,\,C-C,\,\,C=C\] and \[H-H\] bonds are respectively \[414,\,\,347,\,\,615\] and\[435\,\,kJ\,\,mo{{l}^{-1}}\], the value of enthalpy change for the reaction \[{{H}_{2}}C=C{{H}_{2}}(g)+{{H}_{2}}(g)\xrightarrow{{}}{{H}_{3}}C-C{{H}_{3}}(g)\]at \[298\,\,K\] will be
A) \[+250\,\,kJ\]
B) \[-250\,\,kJ\]
C) \[+125\,\,kJ\]
D) \[-125\,\,kJ\]
View Answer play_arrowquestion_answer58) Which one of the following characteristics is not correct for physical adsorption?
A) Adsorption on solids is reversible
B) Adsorption increases with increase in temperature
C) Adsorption is spontaneous
D) Both enthalpy and entropy of adsorption are negative
View Answer play_arrowquestion_answer59) The correct order of increasing basic nature for the bases\[N{{H}_{3}},\,\,C{{H}_{3}}N{{H}_{2}}\]and\[{{(C{{H}_{3}})}_{2}}NH\]is
A) \[C{{H}_{3}}N{{H}_{2}}<N{{H}_{3}}<{{(C{{H}_{3}})}_{2}}NH\]
B) \[{{(C{{H}_{3}})}_{2}}NH<N{{H}_{3}}<C{{H}_{3}}N{{H}_{2}}\]
C) \[N{{H}_{3}}<C{{H}_{3}}N{{H}_{2}}<{{(C{{H}_{3}})}_{2}}NH\]
D) \[C{{H}_{3}}N{{H}_{2}}<{{(C{{H}_{3}})}_{2}}NH<N{{H}_{3}}\]
View Answer play_arrowquestion_answer60) Nylon threads are made up of
A) polyvinyl polymer
B) polyester polymer
C) polyamide polymer
D) polyethylene polymer
View Answer play_arrowquestion_answer61) Due to presence of an unpaired electron, free radicals are
A) cations
B) anions
C) chemically inactive
D) chemically reactive
View Answer play_arrowquestion_answer62) The highest electrical conductivity among the following aqueous solutions, is of
A) \[0.1\,\,M\] difluoroacetic acid
B) \[0.1\,\,M\] fluoroacetic acid
C) \[0.1\,\,M\] chloroacetic acid
D) \[0.1\,\,M\] acetic acid
View Answer play_arrowquestion_answer63) Aluminium oxide may be electrolysed at \[{{1000}^{o}}C\] to furnish aluminium metal (atomic mass\[=27\,\,u;\,\,1F=96500\,\,C)\]. The cathode reaction is\[A{{l}^{3+}}+3{{e}^{-}}\xrightarrow{{}}A{{l}^{0}}\] To prepare \[5.12\,\,kg\] of aluminium metal by this method would require
A) \[5.49\times {{10}^{1}}C\]of electricity
B) \[5.49\times {{10}^{4}}C\]of electricity
C) \[1.83\times {{10}^{7}}C\]of electricity
D) \[5.49\times {{10}^{7}}C\]of electricity
View Answer play_arrowquestion_answer64) The molecular shapes of \[S{{F}_{4}},\,\,Si{{F}_{4}}\] and \[ICI_{4}^{-}\] are
A) different with \[1,\,\,\,0\] and \[2\] lone pairs of electrons on the central atoms, respectively
B) different with \[0,\,\,\,1\] and \[2\] lone pairs of electrons on the central atoms, respectively
C) the same with \[1,\,\,\,1\] and \[1\] lone pair of electrons on the central atoms, respectively
D) the-same with 2, 0 and 1 lone pairs of electrons on the central atoms, respectively
View Answer play_arrowquestion_answer65) Calomel \[(H{{g}_{2}}C{{l}_{2}})\] on reaction with ammonium hydroxide gives
A) \[HgO\]
B) \[H{{g}_{2}}O\]
C) \[N{{H}_{2}}-Hg-Hg-Cl\]
D) \[HgN{{H}_{2}}Cl\]
View Answer play_arrowquestion_answer66) Alkyl halides react with dialkyl copper reagents to give
A) alkenyl halides
B) alkanes
C) alkyl copper halides
D) alkenes
View Answer play_arrowquestion_answer67) Acid catalysed hydration of alkenes except ethene leads to the formation of
A) mixture of secondary and tertiary alcohols
B) mixture of primary and secondary alcohols
C) secondary or tertiary alcohol
D) primary alcohol
View Answer play_arrowquestion_answer68) An aqueous solution of \[6.3\,\,g\] of oxalic acid dihydrate is made upto \[250\,\,mL\]. The volume of \[0.1\,\,N\,\,NaOH\] required to completely neutralise \[10\,\,mL\] of this solution is
A) \[40\,\,mL\]
B) \[20\,\,mL\]
C) \[10\,\,mL\]
D) \[4\,\,mL\]
View Answer play_arrowquestion_answer69) The wavelength of the radiation emitted, when in a hydrogen atom electron falls from infinity to stationary state one, would be (Rydberg constant\[=1.097\times {{10}^{7}}{{m}^{-1}})\]
A) \[91\,\,nm\]
B) \[192\,\,nm\]
C) \[406\,\,nm\]
D) \[9.1\times {{10}^{-8}}nm\]
View Answer play_arrowquestion_answer70) Which one of the following aqueous solutions will exhibit highest boiling point?
A) \[0.01\,\,M\,\,N{{a}_{2}}S{{O}_{4}}\]
B) \[0.01\,\,M\,\,KN{{O}_{3}}\]
C) \[0.015\,\,M\,\,\text{urea}\]
D) \[0.015\,\,M\,\,\text{glucose}\]
View Answer play_arrowquestion_answer71) Which among the following factors is the most important in making fluorine the strongest oxidising agent?
A) Electron affinity
B) lonisation enthalpy
C) Hydration enthalpy
D) Bond dissociation energy
View Answer play_arrowquestion_answer72) What is the equilibrium expression for the reaction,\[{{P}_{4}}(s)+5{{O}_{2}}(g){{P}_{4}}{{O}_{10}}(s)\]?
A) \[{{K}_{c}}=\frac{[{{P}_{4}}{{O}_{10}}]}{[{{P}_{4}}]{{[{{O}_{2}}]}^{5}}}\]
B) \[{{K}_{c}}=\frac{[{{P}_{4}}{{O}_{10}}]}{5[{{P}_{4}}][{{O}_{2}}]}\]
C) \[{{K}_{c}}={{[{{O}_{2}}]}^{5}}\]
D) \[{{K}_{c}}=\frac{1}{{{[{{O}_{2}}]}^{5}}}\]
View Answer play_arrowquestion_answer73) The enthalpies of combustion of carbon and carbon monoxide are \[-393.5\] and \[-283\,\,kJ\,\,mo{{l}^{-1}}\] respectively. The enthalpy of formation of carbon monoxide per mol is
A) \[110.5\,\,kJ\]
B) \[676.5\,\,kJ\]
C) \[-676.5\,\,kJ\]
D) \[-110.5\,\,kJ\]
View Answer play_arrowquestion_answer74) Which one of the following ores is best concentrated by froth-floatation method?
A) Magnetite
B) Cass it erite
C) Galena
D) Malachite
View Answer play_arrowquestion_answer75) Excess of \[KI\] reacts with \[CuS{{O}_{4}}\] solution and then \[N{{a}_{2}}{{S}_{2}}{{O}_{3}}\] solution is added to it. Which of the statements is incorrect for this reaction?
A) \[C{{u}_{2}}{{I}_{2}}\] is formed
B) \[Cu{{I}_{2}}\]is formed
C) \[N{{a}_{2}}{{S}_{2}}{{O}_{3}}\]is oxidised
D) Evolved\[{{I}_{2}}\]is reduced
View Answer play_arrowquestion_answer76) Which one of the following does not have \[s{{p}^{2}}\] hybridised carbon?
A) Acetone
B) Acetic acid
C) Acetonitrile
D) Acetamide
View Answer play_arrowquestion_answer77) Which of the following will have a \[meso-\]isomer also?
A) 2-chlorobutane
B) 2, 3-dichlorobutane
C) 2, 3-dichloropentane
D) 2-hydroxypropanoic acid
View Answer play_arrowquestion_answer78) Consider the acidity of the carboxylic acids (i)\[PhCOOH\] (ii)\[o-N{{O}_{2}}{{C}_{6}}{{H}_{4}}COOH\] (iii)\[p-N{{O}_{2}}{{C}_{6}}{{H}_{4}}COOH\] (iv)\[m-N{{O}_{2}}{{C}_{6}}{{H}_{4}}COOH\] Which of the following orders is correct?
A) (i) > (ii) > (iii) > (iv)
B) (ii) > (iv) > (iii) > (i)
C) (ii) > (iv) > (i) > (iii)
D) (ii) > (iii) > (iv) > (i)
View Answer play_arrowquestion_answer79) The compound formed on heating chlorobenzene with chloral in the presence of concentrated sulphuric acid is
A) gammexane
B) DDT
C) freon
D) hexachloroethane
View Answer play_arrowquestion_answer80) The smog is essentially caused by the pretence of
A) \[{{O}_{2}}\]and\[{{O}_{3}}\]
B) \[{{O}_{2}}\]and\[{{N}_{2}}\]
C) oxides of sulphur and nitrogen
D) \[{{O}_{3}}\]and\[{{N}_{2}}\]
View Answer play_arrowquestion_answer81) The radioisotope, tritium \[(_{1}^{3}H)\] has a half-life of \[12.3\,\,yr\]. If the initial amount of tritium is\[32\,\,mg\], how many milligrams of it would remain after\[49.2\,\,yr?\]
A) \[4\,\,mg\]
B) \[8\,\,mg\]
C) \[1\,\,mg\]
D) \[2\,\,mg\]
View Answer play_arrowquestion_answer82) In this reaction\[C{{H}_{3}}CHO+HCN\xrightarrow{{}}C{{H}_{3}}CH(OH)CN\] \[\xrightarrow{H\cdot OH}C{{H}_{3}}CH(OH)COOH\]an asymmetric centre is generated. The acid obtained would be
A) \[50%\,\,D+50%\,\,L\text{-}\]isomer
B) \[20%\,\,D+80%\,\,L\text{-}\]isomer
C) \[D-\]isomer
D) \[L-\]isomer
View Answer play_arrowquestion_answer83) The method of zone refining of metals is based on the principle of
A) greater noble character of the solid metal than that of the impurity
B) greater solubility of .the impurity in the molten state than in the solid
C) greater mobility of the pure metal than that of impurity
D) higher melting point of the impurity than that of the pure metal
View Answer play_arrowquestion_answer84) The temperature dependence of rate constant \[(k)\] of a chemical reaction is written in terms of Arrhenius equation\[,\]\[k=A{{e}^{-{{E}^{*}}/RT}}\]. Activation energy \[({{E}^{*}})\] of the reaction can be calculated by ploting
A) \[\log k\,\,vs\frac{1}{T}\]
B) \[\log k\,\,vs\frac{1}{\log T}\]
C) \[k\,\,vs\,\,T\]
D) \[k\,\,vs\,\,\frac{1}{\log T}\]
View Answer play_arrowquestion_answer85) In a set of the given reactions, acetic acid yielded a product\[C\]. \[C{{H}_{3}}COOH+PC{{l}_{5}}\xrightarrow{{}}A\]\[A\xrightarrow[anhy\,\,AlC{{l}_{3}}]{{{C}_{6}}{{H}_{6}}}B\xrightarrow[ether]{{{C}_{2}}{{H}_{5}}MgBr}C\]Product \[C\] would be
A) \[C{{H}_{3}}CH(OH){{C}_{6}}{{H}_{5}}\]
B) \[C{{H}_{3}}-\overset{\begin{smallmatrix} {{C}_{2}}{{H}_{5}} \\ | \end{smallmatrix}}{\mathop{C}}\,(OH){{C}_{6}}{{H}_{5}}\]
C) \[C{{H}_{3}}CH(OH){{C}_{2}}{{H}_{5}}\]
D) \[C{{H}_{3}}CO{{C}_{6}}{{H}_{5}}\]
View Answer play_arrowquestion_answer86) Which one of the following compounds, is nota protonic acid?
A) \[SO{{(OH)}_{2}}\]
B) \[S{{O}_{2}}{{(OH)}_{2}}\]
C) \[B{{(OH)}_{3}}\]
D) \[PO{{(OH)}_{3}}\]
View Answer play_arrowquestion_answer87) \[NaCl,\,\,\,NaBr\] and \[NaI\] mixture on heating with conc.\[{{H}_{2}}S{{O}_{4}}\] gives gases, respectively
A) \[HCl,\,\,HBr,\,\,HI\]
B) \[HCl,\,\,B{{r}_{2}},\,\,{{I}_{2}}\]
C) \[C{{l}_{2}},\,\,B{{r}_{2}},\,\,{{I}_{2}}\]
D) \[C{{l}_{2}},\,\,HBr,\,\,HI\]
View Answer play_arrowquestion_answer88) The reaction between aniline and nitrous acid at low temperature yields
A) \[N-\]nitrosamine
B) dizonium salt
C) nitrile
D) amine-nitrite salt
View Answer play_arrowquestion_answer89) The maximum number of molecules is present in
A) \[15\,\,L\]of\[{{H}_{2}}\]gas at\[STP\]
B) \[5\,\,L\]of\[{{N}_{2}}\]gas at\[STP\]
C) \[0.5\,\,g\]of\[{{H}_{2}}\]gas
D) \[10\,\,g\]of\[{{O}_{2}}\]gas
View Answer play_arrowquestion_answer90) Ionic radii are,
A) inversely proportional to effective nuclear charge
B) inversely proportional to square of effective nuclear charge
C) directly proportional to effective nuclear charge
D) directly proportional to square of effective nuclear charge
View Answer play_arrowquestion_answer91) The radioactive isotope \[_{27}^{60}Co\] which is used to the treatment of cancer can be made by \[(n,\,\,p)\] reaction. For this reaction the target nucleus is
A) \[_{28}^{59}Ni\]
B) \[_{27}^{59}Co\]
C) \[_{28}^{60}Ni\]
D) \[_{27}^{60}Co\]
View Answer play_arrowquestion_answer92) The vapour pressure of two liquids \[P\] and \[Q\] are \[80\] and \[60\]\[Torr\], respectively. The total vapour pressure of solution obtained by mixing \[3\] moles of \[P\] and \[2\] moles of \[Q\] would be
A) \[140\,\,Torr\]
B) \[20\,\,Torr\]
C) \[68\,\,Torr\]
D) \[72\,\,Torr\]
View Answer play_arrowquestion_answer93) The energy of second Bohr. orbit of the hydrogen atom is \[-328\,\,kJ\,\,mo{{l}^{-1}}\]; hence the energy of fourth Bohr orbit would be
A) \[-41\,\,kJ\,\,mo{{l}^{-1}}\]
B) \[-1312\,\,kJ\,\,mo{{l}^{-1}}\]
C) \[-164\,\,kJ\,\,mo{{l}^{-1}}\]
D) \[-82\,\,kJ\,\,mo{{l}^{-1}}\]
View Answer play_arrowquestion_answer94) In van der Waals' equation of state of the gas law, the constant \['b'\] is a measure of
A) intermolecular repulsions
B) intermolecular attractions
C) volume occupied by the molecules
D) intermolecular collisions per unit volume
View Answer play_arrowquestion_answer95) Which of the following is responsible for depletion of the ozone layer in the upper strata of the atmosphere?
A) Polyhalogens
B) Ferrocenes
C) Fullerenes
D) Freons
View Answer play_arrowquestion_answer96) What is the correct \[IUPAC\] name of
A) 4-methoxy-2-nitrobenzaldehyde
B) 4-formyl-3-nitro anisole
C) 4-methoxy-6-nitrobenzaldehyde
D) 2-formyl-5-methoxy nitrobenzene
View Answer play_arrowquestion_answer97) Which of the following is anhydride of perchloric acid?
A) \[C{{l}_{2}}{{O}_{7}}\]
B) \[C{{l}_{2}}{{O}_{5}}\]
C) \[C{{l}_{2}}{{O}_{3}}\]
D) \[HClO\]
View Answer play_arrowquestion_answer98) The concentration of \[{{H}_{2}}{{O}_{2}}\] solution of \['10\] volume' is
A) \[30%\]
B) \[3%\]
C) \[1%\]
D) \[10%\]
View Answer play_arrowquestion_answer99) The dipole moment of \[HBr\] is \[1.6\times {{10}^{-3}}C\text{-}m\] and inter-atomic spacing is \[1\,\,A\]. The, \[%\] ionic character of \[HBr\] is
A) \[7\]
B) \[10\]
C) \[15\]
D) \[27\]
View Answer play_arrowquestion_answer100) \[Ca{{C}_{2}}+{{N}_{2}}\xrightarrow{{}}A\], product of\[A\]is
A) \[CaC{{N}_{2}}\]
B) \[CaC{{N}_{2}}\]and\[C\]
C) \[CaC{{N}_{2}}+{{N}_{2}}\]
D) None of these
View Answer play_arrowquestion_answer101) If \[\overset{\to }{\mathop{\mathbf{a}}}\,\] is perpendicular to \[\overset{\to }{\mathop{\mathbf{b}}}\,\] and \[\overset{\to }{\mathop{c}}\,,\,\,\,|\overset{\to }{\mathop{\mathbf{a}}}\,|=2,\]\[|\overset{\to }{\mathop{\mathbf{b}}}\,|=3\] the angle between \[\overset{\to }{\mathop{\mathbf{b}}}\,\] and \[\overset{\to }{\mathop{\mathbf{c}}}\,\] is\[\frac{2\pi }{3}\], then \[[\overrightarrow{\mathbf{a}}\overrightarrow{\mathbf{b}}\overrightarrow{\mathbf{c}}]\] is equal to
A) \[4\sqrt{3}\]
B) \[6\sqrt{3}\]
C) \[12\sqrt{3}\]
D) \[18\sqrt{3}\]
View Answer play_arrowquestion_answer102) The general solution of \[{{y}^{2}}dx+({{x}^{2}}-xy+{{y}^{2}})dy=0\]is
A) \[{{\tan }^{-1}}\left( \frac{x}{y} \right)+\log y+c=0\]
B) \[2{{\tan }^{-1}}\left( \frac{x}{y} \right)+\log x+c=0\]
C) \[\log (y+\sqrt{{{x}^{2}}+{{y}^{2}}})+\log y+c=0\]
D) \[{{\sin }^{-1}}\left( \frac{x}{y} \right)+\log y+c=0\]
View Answer play_arrowquestion_answer103) The vector \[\widehat{\mathbf{i}}+x\widehat{\mathbf{j}}+3\widehat{\mathbf{k}}\] is rotated through an angle \[0\] and doubled in magnitude, then it becomes\[4\widehat{\mathbf{i}}+(4x-2)\widehat{\mathbf{j}}+2\widehat{\mathbf{k}}\]. The value of \[x\] is
A) \[\left\{ -\frac{2}{3},\,\,0 \right\}\]
B) \[\left\{ \frac{1}{3},\,\,2 \right\}\]
C) \[\left\{ \frac{2}{3},\,\,0 \right\}\]
D) \[\{2,\,\,7\}\]
View Answer play_arrowquestion_answer104) Three forces of magnitude \[30,\,\,\,60\] and \[P\] acting at a point are in equilibrium. If the angle between the first two is\[{{60}^{o}}\], then value of \[P\] is
A) \[30\sqrt{7}\]
B) \[30\sqrt{3}\]
C) \[20\sqrt{6}\]
D) \[25\sqrt{2}\]
View Answer play_arrowquestion_answer105) The solution .of the equation\[\frac{{{d}^{2}}y}{d{{x}^{2}}}={{e}^{-2x}}\]is
A) \[y=\frac{1}{4}{{e}^{-2x}}+\frac{cx}{2}+d\]
B) \[y=\frac{1}{4}{{e}^{-2x}}+cx+d\]
C) \[y=\frac{1}{4}{{e}^{-2x}}+c{{x}^{2}}+d\]
D) \[y=\frac{1}{4}{{e}^{-2x}}+c{{x}^{3}}+d\]
View Answer play_arrowquestion_answer106) \[\int{\frac{dx}{{{x}^{2}}+4x+13}}\]is equal to
A) \[\log ({{x}^{2}}+4x+13)+c\]
B) \[\frac{1}{3}{{\tan }^{-1}}\left( \frac{x+2}{3} \right)+c\]
C) \[\log (2x+4)+c\]
D) \[\frac{2x+4}{({{x}^{2}}+4x+13)}+c\]
View Answer play_arrowquestion_answer107) The value of\[\int_{2}^{3}{\frac{x+1}{{{x}^{2}}(x-1)}dx}\]is
A) \[\log \frac{16}{9}+\frac{1}{6}\]
B) \[\log \frac{16}{9}-\frac{1}{6}\]
C) \[2\log 2-\frac{1}{6}\]
D) \[\log \frac{4}{3}-\frac{1}{6}\]
View Answer play_arrowquestion_answer108) \[\int_{0}^{\pi /4}{(\cos x-\sin x)dx}\]\[+\int_{\pi /4}^{5\pi /4}{(\sin x-\cos x)dx}\]\[+\int_{2\pi }^{\pi /4}{(\cos x-\sin x)dx}\] is equal to
A) \[\sqrt{2}-2\]
B) \[2\sqrt{2}-2\]
C) \[3\sqrt{2}-2\]
D) \[4\sqrt{2}-2\]
View Answer play_arrowquestion_answer109) The length of the chord of the parabola \[{{x}^{2}}=4y\] passing through the vertex and having slope \[\cot \alpha \] is
A) \[4\cos \alpha \cos \text{e}{{\text{c}}^{2}}\alpha \]
B) \[4\tan \alpha \sec \alpha \]
C) \[4\sin \alpha {{\sec }^{2}}\alpha \]
D) None of these
View Answer play_arrowquestion_answer110) The equation of tangents to the ellipse\[\frac{{{x}^{2}}}{9}+\frac{{{y}^{2}}}{4}=1\], which are perpendicular to the line \[3x+4y=7\], are
A) \[4x-3y=\pm \sqrt{20}\]
B) \[4x-3y=\pm \sqrt{12}\]
C) \[4x-3y=\pm \sqrt{2}\]
D) \[4x-3y=\pm 1\]
View Answer play_arrowquestion_answer111) From the point \[P(16,\,\,7)\] tangents \[PQ\] and \[PR\] are drawn to the circle\[{{x}^{2}}+{{y}^{2}}-2x-4y-20=0\].If\[c\]be the centre of the circle, then area of quadrilateral \[PQCR\] is
A) \[450\,\,sq\,\,unit\]
B) \[15\,\,sq\,\,unit\]
C) \[50\,\,sq\,\,unit\]
D) \[75\,\,sq\,\,unit\]
View Answer play_arrowquestion_answer112) The distance between the lines \[3x+4y=9\] and\[6x+8y=15\]is
A) \[\frac{3}{2}\]
B) \[\frac{3}{10}\]
C) \[6\]
D) None of these
View Answer play_arrowquestion_answer113) In a \[\Delta ABC\], right angled at \[C\], the value of \[\cot A+\cot B\]is
A) \[\frac{{{c}^{2}}}{ab}\]
B) \[a+b\]
C) \[\frac{{{a}^{2}}}{bc}\]
D) \[\frac{{{b}^{2}}}{ac}\]
View Answer play_arrowquestion_answer114) The records of a hospital show that \[10%\] of the cases of a certain disease are fatal. If \[6\] patients are suffering from the disease, then the probability that only three will die, is
A) \[8748\times {{10}^{-5}}\]
B) \[1458\times {{10}^{-5}}\]
C) \[1458\times {{10}^{-6}}\]
D) \[41\times {{10}^{-6}}\]
View Answer play_arrowquestion_answer115) Out of \[40\] consecutive natural numbers, two are chosen at random. Probability that the sum of the number is odd, is
A) \[\frac{14}{29}\]
B) \[\frac{20}{39}\]
C) \[\frac{1}{2}\]
D) None of these
View Answer play_arrowquestion_answer116) If \[z\] is a complex number such that \[\frac{z-1}{z+1}\] is purely imaginary, then \[|z|\] is equal to
A) \[0\]
B) \[1\]
C) \[\sqrt{2}\]
D) None of these
View Answer play_arrowquestion_answer117) If \[\alpha ,\,\,\,\beta \] are the roots of the equation \[l{{x}^{2}}+mx+n=0\], then the equation whose roots are \[{{\alpha }^{3}}\beta \] and \[\alpha {{\beta }^{3}}\], is
A) \[{{l}^{4}}{{x}^{2}}-nl({{m}^{2}}-2nl)x+{{n}^{4}}=0\]
B) \[{{l}^{4}}{{x}^{2}}-nl({{m}^{2}}-2nl)x+{{n}^{4}}=0\]
C) \[{{l}^{4}}{{x}^{2}}+nl({{m}^{2}}-2nl)x-{{n}^{4}}=0\]
D) \[{{l}^{4}}{{x}^{2}}-nl({{m}^{2}}+2nl)x+{{n}^{4}}=0\]
View Answer play_arrowquestion_answer118) The value of\[{{2}^{1/4}}\cdot {{4}^{1/8}}\cdot {{8}^{1/16}}\cdot {{16}^{1/32}}...\]
A) \[\frac{3}{2}\]
B) \[\frac{5}{2}\]
C) \[2\]
D) \[1\]
View Answer play_arrowquestion_answer119) Out of \[6\] boys and \[4\] girls, a group of \[7\] is to be formed. In how many ways can this be done, if the group is to have a majority of boys?
A) \[120\]
B) \[80\]
C) \[90\]
D) \[100\]
View Answer play_arrowquestion_answer120) The domain of the function\[{{\sin }^{-1}}\left( {{\log }_{2}}\frac{{{x}^{2}}}{2} \right)\]is
A) \[[-1,\,\,2]-\{0\}\]
B) \[[-2,\,\,2]-(-1,\,\,1)\]
C) \[[-2,\,\,2]-\{0\}\]
D) \[[1,\,\,2]\]
View Answer play_arrowquestion_answer121) Function\[f(x)=\left\{ \begin{matrix} x-1, & x<2 \\ 2x-3, & x\ge 2 \\ \end{matrix} \right.\]is a continuous function
A) for\[x=2\] only
B) for all real values of \[x\] such that\[x\ne 2\]
C) for all real values of\[x\]
D) for all integral values of \[x\] only
View Answer play_arrowquestion_answer122) Differential coefficient of\[\sqrt{\sec \sqrt{x}}\]is
A) \[\frac{1}{4\sqrt{x}}\sec \sqrt{x}\sin \sqrt{x}\]
B) \[\frac{1}{4\sqrt{x}}{{(\sec \sqrt{x})}^{3/2}}\cdot \sin \sqrt{x}\]
C) \[\frac{1}{2}\sqrt{x}\sec \sqrt{x}\sin \sqrt{x}\]
D) \[\frac{1}{2}\sqrt{x}{{(\sec \sqrt{x})}^{3/2}}\cdot \sin \sqrt{x}\]
View Answer play_arrowquestion_answer123) The function\[{{x}^{5}}-5{{x}^{4}}+5{{x}^{3}}-1\]is
A) neither maximum nor minimum at\[x=0\]
B) maximum at\[x=0\]
C) maximum at \[x=1\] and minimum at\[x=3\],
D) minimum at\[x=0\]
View Answer play_arrowquestion_answer124) If the planes \[x+2y+kz=0\] and \[2x+y-2z=0\],are at right angles, then the value of \[k\] is
A) \[2\]
B) \[-2\]
C) \[\frac{1}{2}\]
D) \[-\frac{1}{2}\]
View Answer play_arrowquestion_answer125) The ratio in which the line joining \[(2,\,\,4,\,\,5)\], \[(3,\,\,5,\,\,-4)\] is divided by the \[yz-\]plane is
A) \[2:3\]
B) \[3:2\]
C) \[-2:3\]
D) \[4:-3\]
View Answer play_arrowquestion_answer126) The radical centre of the circles \[{{x}^{2}}+{{y}^{2}}-16x+60=0\], \[{{x}^{2}}+{{y}^{2}}-12x+27=0\] and \[{{x}^{2}}+{{y}^{2}}-12y+8=0\]is
A) \[\left( 13,\,\,\frac{33}{4} \right)\]
B) \[\left( \frac{33}{4},\,\,-13 \right)\]
C) \[\left( \frac{33}{4},\,\,13 \right)\]
D) None of these
View Answer play_arrowquestion_answer127) If the lines\[3x+4y+1=0\], \[5x+\lambda y+3=0\] and \[2x+y-1=0\]are concurrent, then \[\lambda \] is equal to
A) \[-8\]
B) \[8\]
C) \[4\]
D) \[-4\]
View Answer play_arrowquestion_answer128) A ball falls from rest from top of a tower. If the ball reaches the foot of the tower in \[3\,\,s\], then height of tower is (take\[g=10\,\,m/{{s}^{2}})\]
A) \[45\,\,m\]
B) \[50\,\,m\]
C) \[40\,\,m\]
D) None of these
View Answer play_arrowquestion_answer129) The value of\[1-\log 2+\frac{{{(\log 2)}^{2}}}{2!}-\frac{{{(\log )}^{3}}}{3!}+...\]is
A) \[\log 3\]
B) \[\log 2\]
C) \[\frac{1}{2}\]
D) None of these
View Answer play_arrowquestion_answer130) The maximum value of\[f(x)=\frac{x}{4+x+{{x}^{2}}}\]on \[[-1,\,\,1]\] is
A) \[-\frac{1}{3}\]
B) \[-\frac{1}{4}\]
C) \[\frac{1}{5}\]
D) \[\frac{1}{6}\]
View Answer play_arrowquestion_answer131) \[\int{\frac{{{e}^{x}}}{(2+{{e}^{x}})+({{e}^{x}}+1)}dx}\]is equal to
A) \[\log \left( \frac{{{e}^{x}}+1}{{{e}^{x}}+2} \right)+c\]
B) \[\log \left( \frac{{{e}^{x}}+2}{{{e}^{x}}+1} \right)+c\]
C) \[\left( \frac{{{e}^{x}}+1}{{{e}^{x}}+2} \right)+c\]
D) \[\left( \frac{{{e}^{x}}+2}{{{e}^{x}}+1} \right)+c\]
View Answer play_arrowquestion_answer132) If the radius of a circle be increasing at a uniform rate of \[2\,\,cm/s\]. The area of increasing of area of circle, at the instant when the radius is \[20\,\,cm\], is
A) \[70\,\pi \,\,c{{m}^{2}}/s\]
B) \[70\,\,c{{m}^{2}}/s\]
C) \[80\,\,\pi \,\,c{{m}^{2}}/s\]
D) \[80\,\,c{{m}^{2}}/s\]
View Answer play_arrowquestion_answer133) The focus of the parabola \[{{y}^{2}}-x-2y+2=0\] is
A) \[\left( \frac{1}{4},\,\,0 \right)\]
B) \[(1,\,\,2)\]
C) \[\left( \frac{5}{4},\,\,1 \right)\]
D) \[\left( \frac{3}{4},\,\,\frac{5}{2} \right)\]
View Answer play_arrowquestion_answer134) The equation of normal at the point (0, 3) of the ellipse \[9{{x}^{2}}+5{{y}^{2}}=45\] is
A) \[x-axis\]
B) \[y-axis\]
C) \[y+3=0\]
D) \[y-3=0\]
View Answer play_arrowquestion_answer135) The equation of the tangent parallel to \[y-x+5=0\]drawn to\[\frac{{{x}^{2}}}{3}-\frac{{{y}^{2}}}{2}=1\]is
A) \[x-y+1=0\]
B) \[x-y+2=0\]
C) \[x+y-1=0\]
D) \[x+y+2=0\]
View Answer play_arrowquestion_answer136) Let the functions \[f,\,\,\,g,\,\,\,h\] are defined from the set of real numbers \[R\] to \[R\] such that \[f(x)={{x}^{2}}-1,\,\,g(x)=\sqrt{({{x}^{2}}+1)}\]and \[h(x)=\left\{ \begin{matrix} 0,if & x\le 0 \\ x,if & x\ge 0 \\ \end{matrix} \right.\], then \[ho(fog)(x)\]is defined by
A) \[x\]
B) \[{{x}^{2}}\]
C) \[0\]
D) None of these
View Answer play_arrowquestion_answer137) The argument of the complex number\[\frac{13-5i}{4-9i}\]is
A) \[\frac{\pi }{3}\]
B) \[\frac{\pi }{4}\]
C) \[\frac{\pi }{5}\]
D) \[\frac{\pi }{6}\]
View Answer play_arrowquestion_answer138) If \[\sin \alpha \] and \[\cos \alpha \] are the roots of the equation\[p{{x}^{2}}+qx+r=0\], then
A) \[{{p}^{2}}+{{q}^{2}}-2pr=0\]
B) \[{{p}^{2}}-{{q}^{2}}+2pr=0\]
C) \[{{p}^{2}}-{{q}^{2}}-2pr=0\]
D) \[{{p}^{2}}+{{q}^{2}}+2qr=0\]
View Answer play_arrowquestion_answer139) In the expansion of\[{{\left( 2{{x}^{2}}-\frac{1}{x} \right)}^{12}}\], the term independent of \[x\] is
A) \[8th\]
B) \[7th\]
C) \[9th\]
D) \[10th\]
View Answer play_arrowquestion_answer140) The general value of 9 in the equation \[\cos \theta =\frac{1}{\sqrt{2}},\,\,\tan \theta =-1\] is
A) \[2n\pi \pm \frac{\pi }{6},\,\,n\in I\]
B) \[2n\pi +\frac{7\pi }{4},\,\,n\in I\]
C) \[n\pi +{{(-1)}^{n}}\frac{\pi }{3},\,\,n\in I\]
D) \[n\pi +{{(-1)}^{n}}\frac{\pi }{4},\,\,n\in I\]
View Answer play_arrowquestion_answer141) In a\[\Delta ABC\], if\[{{r}_{1}}=2{{r}_{2}}=3{{r}_{3}}\], then
A) \[\frac{a}{b}=\frac{4}{5}\]
B) \[\frac{a}{b}=\frac{5}{4}\]
C) \[a+b-2c=0\]
D) \[2a=b+c\]
View Answer play_arrowquestion_answer142) The value of\[\underset{x\to \infty }{\mathop{\lim }}\,\left( \frac{{{x}^{2}}+bx+4}{{{x}^{2}}+ax+5} \right)\]is
A) \[\frac{b}{a}\]
B) \[0\]
C) \[1\]
D) \[\frac{4}{5}\]
View Answer play_arrowquestion_answer143) Let\[f(x)=\left\{ \begin{matrix} \frac{\sin \pi x}{5x}, & x\ne 0 \\ k, & x=0 \\ \end{matrix} \right.\], if \[f(x)\] is continuous at\[x=0\], then \[k\] is equal to
A) \[\frac{\pi }{5}\]
B) \[\frac{5}{\pi }\]
C) \[1\]
D) \[0\]
View Answer play_arrowquestion_answer144) Let \[\overset{\to }{\mathop{\mathbf{a}}}\,,\,\,\,\overset{\to }{\mathop{\mathbf{b}}}\,\] and \[\overset{\to }{\mathop{\mathbf{c}}}\,\] be vectors with magnitudes \[3,\,\,\,4\]and \[5\] respectively and \[\overrightarrow{\mathbf{a}}+\overrightarrow{\mathbf{b}}+\overrightarrow{\mathbf{c}}=0\], then the values of \[\overrightarrow{\mathbf{a}}\cdot \overrightarrow{\mathbf{b}}+\overrightarrow{\mathbf{b}}\cdot \overrightarrow{\mathbf{c}}+\overrightarrow{\mathbf{c}}\cdot \overrightarrow{\mathbf{a}}\] is
A) \[47\]
B) \[25\]
C) \[50\]
D) \[-25\]
View Answer play_arrowquestion_answer145) From a point a metre above a lake the angle of elevation of a cloud \[\alpha \] and the angle of depression of its reflection is \[\beta \]. The height of the cloud is
A) \[\frac{a\sin (\alpha +\beta )}{\sin (\beta -\alpha )}m\]
B) \[\frac{a\sin (\alpha +\beta )}{\sin (\alpha -\beta )}m\]
C) \[\frac{a\sin (\beta -\alpha )}{\sin (\alpha +\beta )}m\]
D) None of these
View Answer play_arrowquestion_answer146) If\[A=diag(2,\,\,-1,\,\,3)\],\[B=diag(-1,\,\,3,\,\,2)\] then \[{{A}^{2}}B\]is equal to
A) \[diag(-4,\,\,3,\,\,18)\]
B) \[diag(5,\,\,4,\,\,11)\]
C) \[diag(3,\,\,1,\,\,8)\]
D) None of these
View Answer play_arrowquestion_answer147) The negation of the proposition \[(p\wedge \tilde{\ }q)\Rightarrow r\]is
A) \[\tilde{\ }p\vee q\Rightarrow \tilde{\ }r\]
B) \[\tilde{\ }r\Rightarrow \tilde{\ }p\vee q\]
C) \[r\Rightarrow p\wedge \tilde{\ }q\]
D) None of these
View Answer play_arrowquestion_answer148) Negation of ?\[2+3=5\]and\[8<10\]? is
A) \[2+3\ne 5\]and\[<10\]
B) \[2+3=5\]and\[8<10\]
C) \[2+3\ne 5\]or\[810\]
D) None of these
View Answer play_arrowquestion_answer149) On the parabola \[y={{x}^{2}}\], the point least distance from the straight line \[y=2x-4\] is
A) \[(1,\,\,1)\]
B) \[(1,\,\,0)\]
C) \[(1,\,\,-1)\]
D) \[(0,\,\,0)\]
View Answer play_arrowquestion_answer150) The number of terms which are free from radical sign in the expansion of \[{{({{y}^{1/5}}+{{x}^{1/10}})}^{55}}\]is
A) \[7\]
B) \[6\]
C) \[5\]
D) None of these
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