question_answer1) The sound wave produced in a gas is always
A) longitudinal done clear
B) transverse done clear
C) stationary done clear
D) electromagnetic done clear
View Answer play_arrowquestion_answer2) Source of sound and the observer are mutually at rest. If the speed of sound is changed, then the frequency of sound heard by the observer will appear to be
A) increased done clear
B) decreased done clear
C) unchanged done clear
D) decreasing exponentially done clear
View Answer play_arrowquestion_answer3) With what velocity should an observer approach stationary sound source, so that the apparent frequency of sound appear to be double of the initial frequency? (given velocity of sound = v)
A) \[{{v}_{o}}=\frac{v}{2}\] done clear
B) \[{{v}_{o}}=3v\] done clear
C) \[{{v}_{o}}=2v\] done clear
D) \[{{v}_{o}}=v\] done clear
View Answer play_arrowquestion_answer4) A charge q is lying at mid-point of the line joining the two similar charges Q. The system will be in equilibrium, if the value of q is
A) \[\frac{Q}{2}\] done clear
B) \[-\frac{Q}{2}\] done clear
C) \[\frac{Q}{4}\] done clear
D) \[-\frac{Q}{4}\] done clear
View Answer play_arrowquestion_answer5) Charges \[2q,\] \[-q\] and \[-q\] lie at the vertices of a triangle. The value of E and Vat the centroid of equilateral triangle will be
A) \[E\ne 0\]and \[V\ne 0\] done clear
B) \[E=0\]and \[V=0\] done clear
C) \[E\ne 0\]and \[V=0\] done clear
D) \[E=0\] and \[V\ne 0\] done clear
View Answer play_arrowquestion_answer6) Infinite charges of magnitude q each are lying at \[x=1,2,4,8,...\]metre on X-axis. The value of intensity of electric field at point \[x=0\]due to these charges will be
A) \[12\times {{10}^{9}}q\,N/C\] done clear
B) zero done clear
C) \[6\times {{10}^{9}}q\,N/C\] done clear
D) \[4\times {{10}^{9}}q\,N/C\] done clear
View Answer play_arrowquestion_answer7) The capacity of parallel plate capacitor in air and on immersing it into oil is \[50\mu F\] and \[110\mu F\]respectively. The dielectric constant of oil is
A) \[0.45\] done clear
B) \[0.55\] done clear
C) \[1.10\] done clear
D) \[2.20\] done clear
View Answer play_arrowquestion_answer8) The energy stored in a condenser is in the form of
A) kinetic energy done clear
B) potential energy done clear
C) elastic energy done clear
D) magnetic energy done clear
View Answer play_arrowquestion_answer9) On increasing the plate separation of a charged condenser, the energy
A) increases done clear
B) decreases done clear
C) remains unchanged done clear
D) becomes zero done clear
View Answer play_arrowquestion_answer10) The ratio of electric fields on the axis and at equator of an electric dipole will be
A) \[1:1\] done clear
B) \[2:1\] done clear
C) \[4:1\] done clear
D) \[1:4\] done clear
View Answer play_arrowquestion_answer11) Some electric bulbs are connected in series across a \[220\text{ }V\]supply in a room. If one bulb is fused, then remaining bulbs are connected again in series across the same supply. The illumination in the room will be
A) increase done clear
B) decrease done clear
C) remain the same done clear
D) not continuous done clear
View Answer play_arrowquestion_answer12) If one junction of thermocouple is kept at \[{{0}^{o}}C\]and its emf is given by \[e=at+b{{t}^{2}},\]then the neutral temperature will be
A) \[\frac{a}{b}\] done clear
B) \[-\frac{a}{b}\] done clear
C) \[\frac{a}{2b}\] done clear
D) \[-\frac{a}{2b}\] done clear
View Answer play_arrowquestion_answer13) A cube is constructed from 12 identical wires. Current enters one comer of the cube and it leaves the opposite comer. If the resistance of each wire is r, then equivalent resistance will be
A) \[\frac{6\,r}{5}\] done clear
B) \[\frac{5\,r}{6}\] done clear
C) \[\frac{5\,r}{12}\] done clear
D) \[\frac{12\,r}{5}\] done clear
View Answer play_arrowquestion_answer14) A source of emf \[E=15V\] and having negligible internal resistance, is connected to a variable resistance, so that the current in the circuit increases with time as \[I=1.2t+3\]. Then, the total charge that will flow in first \[5\text{ }s\]will be
A) \[10\text{ }C\] done clear
B) \[20\text{ }C\] done clear
C) \[30\text{ }C\] done clear
D) \[40\text{ }C\] done clear
View Answer play_arrowquestion_answer15) The magnetic induction at the centre of a current carrying circular of radius r, is
A) directly proportional to r done clear
B) inversely proportional to r done clear
C) directly proportional to \[{{r}^{2}}\] done clear
D) inversely proportional to \[{{r}^{2}}\] done clear
View Answer play_arrowquestion_answer16) A current carrying conductor produces
A) only electric field done clear
B) only magnetic field done clear
C) both electric and magnetic fields done clear
D) neither electric nor magnetic field done clear
View Answer play_arrowquestion_answer17) A proton of energy \[8\text{ }eV\]is moving in a circular path in a uniform magnetic field. The energy of an alpha particle moving in the same magnetic field and along the same path will be
A) \[4\text{ }eV\] done clear
B) \[2\text{ }eV\] done clear
C) \[8\,\,eV\] done clear
D) \[6\,\,eV\] done clear
View Answer play_arrowquestion_answer18) A \[1\text{ }m\]long wire is lying at right angles to the magnetic field. A force of 1 kg wt. is acting on it in a magnetic field of \[0.98\text{ }T\]. The current flowing in it will be
A) \[100\text{ }A\] done clear
B) \[10\text{ }A\] done clear
C) \[1\text{ }A\] done clear
D) zero done clear
View Answer play_arrowquestion_answer19) The resultant magnetic moment of neon atom will be
A) infinity done clear
B) \[{{\mu }_{B}}\] done clear
C) zero done clear
D) \[\frac{{{\mu }_{B}}}{2}\] done clear
View Answer play_arrowquestion_answer20) The temperature at which ferromagnetic material becomes paramagnetic is called a
A) neutral temperature done clear
B) Curie temperature done clear
C) inversion temperature done clear
D) critical temperature done clear
View Answer play_arrowquestion_answer21) The ultimate individual unit of magnetism in any magnet is called
A) north pole done clear
B) south pole done clear
C) dipole done clear
D) quadrupole done clear
View Answer play_arrowquestion_answer22) The power loss in AC circuit will be minimum when
A) resistance is high, inductance is high done clear
B) resistance is high, inductance is low done clear
C) resistance is low, inductance is low done clear
D) None of the above done clear
View Answer play_arrowquestion_answer23) At high frequency, the capacitor offer
A) more reactance done clear
B) less reactance done clear
C) zero reactance done clear
D) infintie reactance done clear
View Answer play_arrowquestion_answer24) The quantity that. remain unchanged in transformer is
A) voltage done clear
B) current done clear
C) frequency done clear
D) None of these done clear
View Answer play_arrowquestion_answer25) A piece of plane glass is placed on a word with letters of different colours. The letters which appear minimum raised are
A) red done clear
B) green done clear
C) yellow done clear
D) violet done clear
View Answer play_arrowquestion_answer26) When light waves suffer reflection at the interface between air and glass, the change of phase of the reflected wave is equal to
A) zero done clear
B) \[\frac{\pi }{2}\] done clear
C) \[\pi \] done clear
D) \[2\pi \] done clear
View Answer play_arrowquestion_answer27) If the wavelength of light is \[4000\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,,\] then the number of waves in 1 mm length will be
A) \[25\] done clear
B) \[0.25\] done clear
C) \[0.25\times {{10}^{4}}\] done clear
D) \[25\times {{10}^{4}}\] done clear
View Answer play_arrowquestion_answer28) The wave theory of light was given by
A) Maxwell done clear
B) Planck done clear
C) Huygen done clear
D) Young done clear
View Answer play_arrowquestion_answer29) In Young's double slit experiment the amplitudes of two sources are \[3a\]and a respectively. The ratio of intensities of bright and dark fringes will be
A) \[3:1\] done clear
B) \[4:1\] done clear
C) \[2:1\] done clear
D) \[9:1\] done clear
View Answer play_arrowquestion_answer30) The diffraction effect can be observed in
A) only sound waves done clear
B) only light waves done clear
C) only ultrasonic waves done clear
D) sound as well as light waves done clear
View Answer play_arrowquestion_answer31) At what distance from a convex lens of focal length 30 cm, an object should be placed, so that the size of the image be \[\frac{1}{2}th\] of the object?
A) \[30\,cm\] done clear
B) \[60\,cm\] done clear
C) \[15\,cm\] done clear
D) \[90\,cm\] done clear
View Answer play_arrowquestion_answer32) Two coherent sources of intensity ratio \[1:4\] produce an interference pattern. The fringe visibility will be
A) \[1\] done clear
B) \[0.8\] done clear
C) \[0.4\] done clear
D) \[0.6\] done clear
View Answer play_arrowquestion_answer33) The specific charge of an electron is
A) \[1.6\times {{10}^{-19}}C\] done clear
B) \[4.8\times {{10}^{-19}}stat-C\] done clear
C) \[1.76\times {{10}^{-11}}C/kg\] done clear
D) \[1.76\times {{10}^{11}}C/kg\] done clear
View Answer play_arrowquestion_answer34) The colour of the second line of Balmer series is:
A) blue done clear
B) yellow done clear
C) red done clear
D) violet done clear
View Answer play_arrowquestion_answer35) If elements with principal quantum number \[n>4\] were not allowed in nature, the number of possible elements would be
A) \[60\] done clear
B) \[32\] done clear
C) \[4\] done clear
D) \[64\] done clear
View Answer play_arrowquestion_answer36) The energy of incident photons corresponding to maximum wavelength of visible light is
A) \[3.2\text{ }eV\] done clear
B) \[7\,eV\] done clear
C) \[1.55\text{ }eV\] done clear
D) \[1\,eV\] done clear
View Answer play_arrowquestion_answer37) If the work function of potassium is \[2\text{ }eV,\]then its photoelectric threshold wavelength is
A) \[310\text{ }nm\] done clear
B) \[620\text{ }nm\] done clear
C) \[6200\text{ }nm\] done clear
D) \[3100\text{ }nm\] done clear
View Answer play_arrowquestion_answer38) Threshold wavelength for a metal\[5200\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,\]. The photoeletrons will be ejected, if it is irradiated by light from
A) \[50\text{ }W\]infrared lamp done clear
B) \[\text{1 }W\] infrared lamp done clear
C) \[\text{50 }W\] ultraviolet lamp done clear
D) \[\text{0}\text{.5 }W\] infrared lamp done clear
View Answer play_arrowquestion_answer39) An electron and a proton are accelerated through the same potential difference. The ratio of their de-Broglie wavelength will be
A) \[{{\left( \frac{{{m}_{p}}}{{{m}_{e}}} \right)}^{1/2}}\] done clear
B) \[\frac{{{m}_{e}}}{{{m}_{p}}}\] done clear
C) \[\frac{{{m}_{p}}}{{{m}_{e}}}\] done clear
D) \[\frac{a}{\sqrt{2}}\] done clear
View Answer play_arrowquestion_answer40) A particle with rest mass zero is moving with speed c. The de-Broglie wavelength associated with it
A) zero done clear
B) infinity done clear
C) \[\frac{hv}{c}\] done clear
D) \[\frac{{{m}_{0}}c}{h}\] done clear
View Answer play_arrowquestion_answer41) The nearest distance between two atoms in case of a bcc lattice is equal to
A) \[\frac{a\sqrt{2}}{3}\] done clear
B) \[\frac{a\sqrt{3}}{2}\] done clear
C) \[a\sqrt{3}\] done clear
D) \[\frac{a}{\sqrt{2}}\] done clear
View Answer play_arrowquestion_answer42) Which of the following is an amorphous substance?
A) Gold done clear
B) Silver done clear
C) Copper done clear
D) Glass done clear
View Answer play_arrowquestion_answer43) The maximum efficiency of full wave rectifier is
A) \[100%\] done clear
B) \[25.20%\] done clear
C) \[40.6%\] done clear
D) \[81.2%\] done clear
View Answer play_arrowquestion_answer44) In a npn-transistor, the collector current is\[10\text{ }mA\]. If \[90%\] of the electrons emitted reach the collector, then the emitter current will be
A) \[9\,\,mA\] done clear
B) \[11\,\,mA\] done clear
C) \[1\,\,mA\] done clear
D) \[0.1\,\,mA\] done clear
View Answer play_arrowquestion_answer45) The given truth table is of
A | B | X |
0 | 0 | 0 |
0 | 1 | 1 |
1 | 0 | 1 |
1 | 1 | 1 |
A) OR gate done clear
B) AND gate done clear
C) NOT gate done clear
D) XOR gate done clear
View Answer play_arrowquestion_answer46) If force (F), length (L) and time (T) are assumed to be the fundamental units, then the dimensional formula of the mass will be
A) \[[F{{L}^{-1}}{{T}^{2}}]\] done clear
B) \[[F{{L}^{-1}}{{T}^{-2}}]\] done clear
C) \[[F{{L}^{-1}}{{T}^{-1}}]\] done clear
D) \[[F{{L}^{2}}{{T}^{2}}]\] done clear
View Answer play_arrowquestion_answer47) The horizontal range of a projectile is \[4\sqrt{3}\] times its maximum height. Its angle of projection will be
A) \[{{45}^{o}}\] done clear
B) \[{{60}^{o}}\] done clear
C) \[{{90}^{o}}\] done clear
D) \[{{30}^{o}}\] done clear
View Answer play_arrowquestion_answer48) Two balls of same size but the density of one is greater than that of the other are dropped from the same height, then which ball will reach the earth first (air resistance is negligible)?
A) Heavy ball done clear
B) Light ball done clear
C) Both simultaneously done clear
D) Will depend upon the density of the balls done clear
View Answer play_arrowquestion_answer49) A person moves \[30\text{ }m\]north and then \[20\text{ }m\] towards east and finally 30^2 min south-west direction. The displacement of the person from the origin will be
A) \[10\text{ }m\]along north done clear
B) \[10\text{ }m\]along south done clear
C) \[10\text{ }m\] along west done clear
D) zero done clear
View Answer play_arrowquestion_answer50) If the velocity of a particle is given by \[v={{(180-16x)}^{1/2}}\,m/s\]. then its acceleration will be
A) zero done clear
B) \[8\text{ }m/{{s}^{2}}\] done clear
C) \[-8\text{ }m/{{s}^{2}}\] done clear
D) \[4\text{ }m/{{s}^{2}}\] done clear
View Answer play_arrowquestion_answer51) Neglecting the air resistance, the time of flight of a projectile is determined by
A) \[{{U}_{vertical}}\] done clear
B) \[{{U}_{horizontal}}\] done clear
C) \[U={{U}_{vertical}}+U_{horizontal}^{2}\] done clear
D) \[U={{(U_{vertical}^{2}+U_{horizontal}^{2})}^{1/2}}\] done clear
View Answer play_arrowquestion_answer52) A train is moving towards east and a car is along north, both with same speed. The observed direction of car to the passenger in the train is
A) east-north direction done clear
B) west-north direction done clear
C) south-east direction done clear
D) None of the above done clear
View Answer play_arrowquestion_answer53) A body moving with velocity v has momentum and kinetic energy numerically equal. What is the value of v?
A) \[2\text{ }m/s\] done clear
B) \[\sqrt{2}\text{ }m/s\] done clear
C) \[1\text{ }m/s\] done clear
D) \[0.2\text{ }m/s\] done clear
View Answer play_arrowquestion_answer54) If the kinetic energy of a body becomes four times, then its momentum will be
A) \[{{P}_{new}}=3{{p}_{initial~}}\] done clear
B) \[{{P}_{new}}=4{{p}_{initial~}}\] done clear
C) \[{{P}_{new}}=2{{p}_{initial~}}\] done clear
D) \[{{P}_{new}}={{p}_{initial~}}\] done clear
View Answer play_arrowquestion_answer55) A block of mass \[2\text{ }kg\]is lying on an inclined plane, inclined to the horizontal at\[{{30}^{o}}\]. If the coefficient of friction between the block and the plane is \[0.7,\] then magnitude of frictional force acting on the block will be
A) \[11.9\text{ }N\] done clear
B) \[1.19N\] done clear
C) \[0.19\text{ }N\] done clear
D) \[11.0\text{ }N\] done clear
View Answer play_arrowquestion_answer56) A ring of mass m and radius r is melted and then moulded into a sphere. The moment of inertia of the sphere will be
A) more than that of the ring done clear
B) less than that of the ring done clear
C) equal to that of the ring done clear
D) None of the above done clear
View Answer play_arrowquestion_answer57) A solid sphere and a hollow sphere of the same material and of a same size can be distinguished without weighing
A) by determining their moments of inertia about their coaxial axes done clear
B) by rolling them simultaneously on an inclined plane done clear
C) by rotating them about a common axis of rotation done clear
D) by applying equal torque on them done clear
View Answer play_arrowquestion_answer58) Point masses \[1,\text{ }2,-3\]and \[4\text{ }kg\]are lying at the point \[(0,0,0)\]\[(2,0,0)\]\[(0,3,0)\] and \[(-2,-2,0)\] respectively. The moment of inertia of this system about x-axis will be
A) \[43\,kg-{{m}^{2}}\] done clear
B) \[34\,kg-{{m}^{2}}\] done clear
C) \[27\,kg-{{m}^{2}}\] done clear
D) \[72\,kg-{{m}^{2}}\] done clear
View Answer play_arrowquestion_answer59) The radius of gyration of a body about an axis at a distance \[6\text{ }cm\] from its centre of mass is\[10\text{ }cm\]. Then its radius of gyration about a parallel axis through its centre of mass will be
A) \[80\,\,cm\] done clear
B) \[8\,\,cm\] done clear
C) \[0.8\,\,cm\] done clear
D) \[80\,\,m\] done clear
View Answer play_arrowquestion_answer60) Two planets of radii in the ratio \[2:3\]are made from the material of density in the ratio\[3:2\]. Then, the ratio of acceleration due to gravity \[\frac{{{g}_{1}}}{{{g}_{2}}}\] at the surface of the two planets will be
A) \[1\] done clear
B) \[2.25\] done clear
C) \[4/9\] done clear
D) \[0.12\] done clear
View Answer play_arrowquestion_answer61) If the radius of the earth contracts to half of its present day value without change in mass, then the length of the day will be
A) \[24\text{ }h\] done clear
B) \[48\text{ }h\] done clear
C) \[\text{6 }h\] done clear
D) \[\text{12 }h\] done clear
View Answer play_arrowquestion_answer62) A person will get more quantity of matter in kg-wt at
A) poles done clear
B) at latitude of \[{{60}^{o}}\] done clear
C) equator done clear
D) satellite done clear
View Answer play_arrowquestion_answer63) The unit of the coefficient of viscosity in SI system is
A) \[m/kg-s\] done clear
B) \[~m-s/k{{g}^{2}}\] done clear
C) \[kg/m-{{s}^{2}}\] done clear
D) \[kg/m-s\] done clear
View Answer play_arrowquestion_answer64) If the excess pressure inside a soap bubble is balanced by oil column of height \[2\text{ }mm,\]then the surface tension of soap solution will be ( \[r=1\text{ }cm\]and density \[d=0.8\text{ }g/\text{ }cc\])
A) \[3.9\text{ }N/m\] done clear
B) \[3.9\times {{10}^{-1}}N/m\] done clear
C) \[3.9\times {{10}^{-2}}N/m\] done clear
D) \[3.9\,dyne/m\] done clear
View Answer play_arrowquestion_answer65) A vessel, whose bottom has round holes with diameter of \[1\text{ }mm\]is filled with water. Assuming that surface tension acts only at holes. Then, the maximum height to which the water can be filled in vessel without leakage is (surface tension of water is \[75\times {{10}^{-3}}\text{ }N/m\]and \[g=10\text{ }m/{{s}^{2}}\])
A) \[3\,cm\] done clear
B) \[0.3\,cm\] done clear
C) \[3\text{ }mm\] done clear
D) \[~3\text{ }m\] done clear
View Answer play_arrowquestion_answer66) For which of the two pairs, the angle of contact is same?
A) Water and glass, glass and mercury done clear
B) Pure water and glass, glass and alcohol done clear
C) Silver and water, mercury and glass done clear
D) Silver and chromium, water and chromium done clear
View Answer play_arrowquestion_answer67) At what temperature the mis velocity of helium molecules will be equal to that of hydrogen moekules at NTP?
A) \[844\text{ }K\] done clear
B) \[64\text{ }K\] done clear
C) \[{{273}^{o}}C\] done clear
D) \[273\text{ }K\] done clear
View Answer play_arrowquestion_answer68) Which of the following is unique function of initial and final states?
A) \[dQ\] done clear
B) \[dW\] done clear
C) \[dU\] done clear
D) \[\Delta Q\,\,and\,\,\Delta W\] done clear
View Answer play_arrowquestion_answer69) If the initial temperatures of metallic sphere and disc of same radius and nature are equal, then the ratio of their rate of cooling will be
A) \[1:4\] done clear
B) \[4:1\] done clear
C) \[1:2\] done clear
D) \[2:1\] done clear
View Answer play_arrowquestion_answer70) What will be the ratio of temperatures of sun and moon, if the wavelengths of their maximum emission radiations rates are \[140\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,\]and \[4200\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,\]respectively?
A) \[1:30\] done clear
B) \[30:1\] done clear
C) \[42:14\] done clear
D) \[14:42\] done clear
View Answer play_arrowquestion_answer71) A bar magnet is oscillating in the earth's magnetic field with time period T. If its mass is increased four times, then its time period will be
A) \[4T\] done clear
B) \[2T\] done clear
C) \[T\] done clear
D) \[r\] done clear
View Answer play_arrowquestion_answer72) The time period of a simple pendulum, when it is made to oscillate on the surface of moon
A) increases done clear
B) decreases done clear
C) remains unchanged done clear
D) becomes infinite done clear
View Answer play_arrowquestion_answer73) A condenser of capacity \[20\mu F\] is first charged and then discharged through a \[10\text{ }mH\] inductance. Neglecting the resistance of the coil, the frequency of the resulting vibrations will be
A) \[356\,cycle/h\] done clear
B) \[356\,cycle/s\] done clear
C) \[356\times {{10}^{3}}\,cycle/s\] done clear
D) \[3.56\,cycle/s\] done clear
View Answer play_arrowquestion_answer74) Infinite springs with force constants k, 2k, 4k and 8 k... respectively are connected in series. The effective force constant of the spring will be
A) \[2k\] done clear
B) \[k\] done clear
C) \[\frac{k}{2}\] done clear
D) \[2048\] done clear
View Answer play_arrowquestion_answer75) The intensity of sound gets reduced by 10% on passing through a slab. The reduction in intensity on passage through three consecutive slabs is
A) \[30%\] done clear
B) \[27.1%\] done clear
C) \[20%\] done clear
D) \[36%\] done clear
View Answer play_arrowquestion_answer76) The hydrogen electrode is dipped in a solution of \[pH=3\]at \[25{{\,}^{o}}C.\] The potential of the cell would be (the value of.2.303 RT/F is 0.059 V)
A) \[~0.177\,V\] done clear
B) \[~0.087\,V\] done clear
C) \[~-0.177\,V\] done clear
D) \[0.059\,V\] done clear
View Answer play_arrowquestion_answer77) Specific conductivity of a solution
A) increases with dilution done clear
B) decreases with dilution done clear
C) remains unchanged with dilution done clear
D) depends on mass of electrolyte done clear
View Answer play_arrowquestion_answer78) \[\text{1 mol}\]of \[{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}\]is mixed with 2 moles of \[\text{NaOH}\text{.}\]The heat evolved will be
A) \[57.3\,kJ\] done clear
B) \[2\times 57.3\,kJ\] done clear
C) \[57.3/2\,kJ\] done clear
D) cannot be predicted done clear
View Answer play_arrowquestion_answer79) In a reversible process, \[\Delta {{S}_{system}}+\Delta {{S}_{\text{surrounding}}}\] is
A) \[~>0\] done clear
B) \[<0\] done clear
C) \[~>0\] done clear
D) \[=0\] done clear
View Answer play_arrowquestion_answer80) For the reaction, \[{{N}_{2}}+3{{H}_{2}}2NH;\Delta H=?\]
A) \[\Delta E=+\,2RT\] done clear
B) \[\Delta E-\,2RT\] done clear
C) \[\Delta E+\,RT\] done clear
D) \[\Delta E-\,RT\] done clear
View Answer play_arrowquestion_answer81) One mole of a perfect gas expands isothermally to ten times of its original volume. The change in entropy is
A) 0.1 R done clear
B) 2.303 R done clear
C) 10.0 R done clear
D) 100.0 R done clear
View Answer play_arrowquestion_answer82) Which of the following solutions will have the highest boiling point?
A) \[\text{0}\text{.1 M FeC}{{\text{l}}_{\text{3}}}\] done clear
B) \[\text{0}\text{.1 M BaC}{{\text{l}}_{2}}\] done clear
C) \[\text{0}\text{.1 M NaCl}\] done clear
D) \[\text{0}\text{.1}\,\text{M}\,\text{urea}\] done clear
View Answer play_arrowquestion_answer83) Maximum freezing point falls in
A) camphor done clear
B) naphthalene done clear
C) benzene done clear
D) water done clear
View Answer play_arrowquestion_answer84) Azeotropic mixture of \[\text{HCl}\]and water has
A) \[\text{48 }\!\!%\!\!\text{ HCl}\] done clear
B) \[\text{ }\!\!~\!\!\text{ 22}\text{.2 }\!\!%\!\!\text{ HCl}\] done clear
C) \[\text{36 }\!\!%\!\!\text{ HCl}\] done clear
D) \[\text{ }\!\!~\!\!\text{ 20}\text{.2 }\!\!%\!\!\text{ HCl}\] done clear
View Answer play_arrowquestion_answer85) Vapour pressure of dilute aqueous solution of glucose is 750 mm of mercury at 373 K. The mole fraction of solute is
A) \[\frac{1}{76}\] done clear
B) \[\frac{1}{7.6}\] done clear
C) \[\frac{1}{38}\] done clear
D) \[\frac{1}{10}\] done clear
View Answer play_arrowquestion_answer86) Volume of \[\text{0}\text{.1}\,\text{M}\,{{\text{K}}_{\text{2}}}\text{C}{{\text{r}}_{\text{2}}}{{\text{O}}_{\text{7}}}\] required to oxidize 35 mL of \[\text{0}\text{.5 M FeS}{{\text{O}}_{\text{4}}}\]solution is
A) 29.2 mL done clear
B) 17.5 mL done clear
C) 175 mL done clear
D) 145 Ml done clear
View Answer play_arrowquestion_answer87) \[100\,cc\]of \[\text{0}\text{.6}\,\text{N}\,{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}\]and \[\text{200 cc}\]of \[\text{0}\text{.3}\,\text{N}\,\text{HCl}\]were mixed together. The normality of the solution will be
A) 0.2 N done clear
B) 0.4 N done clear
C) 0.8 N done clear
D) 0.6 N done clear
View Answer play_arrowquestion_answer88) The rate of diffusion of a gas is proportional to
A) \[\frac{p}{\sqrt{d}}\] done clear
B) \[\sqrt{\frac{p}{d}}\] done clear
C) \[\frac{p}{d}\] done clear
D) \[\frac{\sqrt{p}}{d}\] done clear
View Answer play_arrowquestion_answer89) Molar volume of \[\text{C}{{\text{O}}_{\text{2}}}\]is maximum at
A) NTP done clear
B) \[\text{0}{{\,}^{o}}\text{C}\]and 2.0 atm done clear
C) \[127{{\,}^{o}}C\] and\[\text{ }\!\!~\!\!\text{ 1 atm}\] done clear
D) \[~273{{\,}^{o}}C\] and \[2.0\,\text{atm}\] done clear
View Answer play_arrowquestion_answer90) Number of atoms of oxygen present in 10.6 g of \[\text{N}{{\text{a}}_{\text{2}}}\text{C}{{\text{O}}_{\text{3}}}\]will be
A) \[6.02\times {{10}^{23}}\] done clear
B) \[12.04\times {{10}^{22}}\] done clear
C) \[1.806\times {{10}^{23}}\] done clear
D) \[31.80\times {{10}^{2}}\] done clear
View Answer play_arrowquestion_answer91) The equilibrium \[{{P}_{4}}(s)+6C{{l}_{2}}(g)\rightleftharpoons 4PC{{l}_{3}}(g)\]is attained by mixing equal moles of\[{{\text{P}}_{\text{4}}}\]and\[\text{C}{{\text{l}}_{\text{2}}}\]in an evacuated vessel. Then, at equilibrium
A) \[[C{{l}_{2}}]>[PC{{l}_{3}}]\] done clear
B) \[[C{{l}_{2}}]>[{{P}_{4}}]\] done clear
C) \[[{{P}_{4}}]>[C{{l}_{2}}]\] done clear
D) \[[PC{{l}_{3}}]>[{{P}_{4}}]\] done clear
View Answer play_arrowquestion_answer92) The activation energy for most of the reactions is approximately \[50\,\text{kJ}\,\text{mo}{{\text{l}}^{-1}}.\] The value of temperature coefficient for such reactions is
A) \[~>2\] done clear
B) \[~>3\] done clear
C) \[~<\,\,1\] done clear
D) \[~>4\] done clear
View Answer play_arrowquestion_answer93) If the mass defect of \[_{\text{4}}^{\text{9}}\text{X}\]is\[\text{0}\text{.090 u,}\] then binding energy per nucleon is \[\text{(1}\,\text{u}\,\text{=}\,\text{931}\text{.5}\,\text{MeV)}\]
A) \[\text{9}\text{.315 MeV}\] done clear
B) \[\text{ }\!\!~\!\!\text{ 931}\text{.5 MeV}\] done clear
C) \[\text{ }\!\!~\!\!\text{ 83}\text{.0 MeV}\] done clear
D) \[\text{ }\!\!~\!\!\text{ 8}\text{.38 MeV}\] done clear
View Answer play_arrowquestion_answer94) \[\text{50 mL}\]of\[\text{0}\text{.1}\,\text{M}\,\text{HCl}\] and 50 mL of 0.2 M \[\text{NaOH}\] are mixed. The pH of the resulting solution is
A) 1.30 done clear
B) 4.2 done clear
C) 12.70 done clear
D) 11.70 done clear
View Answer play_arrowquestion_answer95) A substance \[{{A}_{x}}{{B}_{y}}\]crystallises in a face centred cubic lattice in which A atom occupies each comer of cube and atom B occupies the centres of each face of the cube. Identify the correct composition of the substance \[{{A}_{x}}{{B}_{y}}.\]
A) \[A{{B}_{3}}\] done clear
B) \[{{A}_{4}}{{B}_{3}}\] done clear
C) \[{{A}_{3}}B\] done clear
D) composition cannot be specified done clear
View Answer play_arrowquestion_answer96) In coagulating the colloidal solution of \[\text{A}{{\text{s}}_{\text{2}}}{{\text{S}}_{\text{3}}}\]which has the maximum coagulating value?
A) \[\text{NaCl}\] done clear
B) \[KCl\] done clear
C) \[BaC{{l}_{2}}\] done clear
D) \[AlC{{l}_{3}}\] done clear
View Answer play_arrowquestion_answer97) Which of the following is the strongest oxidising agent?
A) \[HOCl\] done clear
B) \[HCl{{O}_{2}}\] done clear
C) \[HCl{{O}_{3}}\] done clear
D) \[HCl{{O}_{4}}\] done clear
View Answer play_arrowquestion_answer98) In the equation \[4M+8C{{N}^{-}}+2{{H}_{2}}O+{{O}_{2}}\xrightarrow{{}}4{{[M{{(CN)}_{2}}]}^{-}}\] \[+\,4\,O{{H}^{-}}\] Identify the metal M.
A) copper done clear
B) iron done clear
C) silver done clear
D) zinc done clear
View Answer play_arrowquestion_answer99) The formula of azurite is
A) \[CuC{{O}_{3}}.Cu{{(OH)}_{2}}\] done clear
B) \[2CuC{{O}_{3}}.Cu{{(OH)}_{2}}\] done clear
C) \[CuC{{O}_{3}}.2Cu{{(OH)}_{2}}\] done clear
D) \[CuS{{O}_{4}}.Cu{{(OH)}_{2}}\] done clear
View Answer play_arrowquestion_answer100) The decreasing order of bond angle is
A) \[N{{O}_{2}}>NO_{2}^{+}>NO_{2}^{-}\] done clear
B) \[NO_{2}^{-}>N{{O}_{2}}>NO_{2}^{+}\] done clear
C) \[NO_{2}^{+}>N{{O}_{2}}>NKO_{2}^{-}\] done clear
D) \[NO_{2}^{+}>NO_{2}^{-}>N{{O}_{2}}\] done clear
View Answer play_arrowquestion_answer101) The fresh precipitate can be transformed in colloidal state by
A) peptization done clear
B) coagulation done clear
C) diffusion done clear
D) none of these done clear
View Answer play_arrowquestion_answer102) Milk is
A) fat disperse4 in water done clear
B) fat dispersed in milk done clear
C) fat dispersed in fat done clear
D) water dispersed in milk done clear
View Answer play_arrowquestion_answer103) Purest form of iron is
A) cast iron done clear
B) pig iron done clear
C) wrought iron done clear
D) steel done clear
View Answer play_arrowquestion_answer104) Most unstable hydride is
A) \[~N{{H}_{3}}\] done clear
B) \[~P{{H}_{3}}\] done clear
C) \[~As{{H}_{3}}\] done clear
D) \[~Bi{{H}_{3}}\] done clear
View Answer play_arrowquestion_answer105) Out of the following metals that cannot be obtained by electrolysis of the aqueous solution of its salts is
A) Ag done clear
B) Cr done clear
C) Cu done clear
D) Mg done clear
View Answer play_arrowquestion_answer106) \[\text{KI}\]and \[\text{CuS}{{\text{O}}_{\text{4}}}\]solution when mixed gives
A) \[Cu{{l}_{2}}+{{K}_{2}}S{{O}_{4}}\] done clear
B) \[C{{u}_{2}}{{I}_{2}}+{{K}_{2}}S{{O}_{4}}\] done clear
C) \[{{K}_{2}}S{{O}_{4}}+C{{u}_{2}}{{I}_{2}}+{{I}_{2}}\] done clear
D) \[{{K}_{2}}S{{O}_{4}}+Cu{{I}_{2}}+{{I}_{2}}\] done clear
View Answer play_arrowquestion_answer107) The strongest reducing agent among the following is
A) \[{{F}^{-}}\] done clear
B) \[C{{l}^{-}}\] done clear
C) \[B{{r}^{-}}\] done clear
D) \[{{I}^{-}}\] done clear
View Answer play_arrowquestion_answer108) \[\text{Xe}{{\text{F}}_{\text{6}}}\]on complete hydrolysis gives
A) \[\text{Xe}\] done clear
B) \[\text{ }\!\!~\!\!\text{ Xe}{{\text{O}}_{\text{2}}}\] done clear
C) \[Xe{{O}_{3}}\] done clear
D) \[\text{ }\!\!~\!\!\text{ Xe}{{\text{O}}_{\text{4}}}\] done clear
View Answer play_arrowquestion_answer109) The correct name of the compound\[[Cu{{(N{{H}_{3}})}_{4}}]{{(N{{O}_{3}})}_{2}},\]according to IUPAC system is
A) cuprammonium nitrate done clear
B) tetrammine copper(II) dinitrate done clear
C) tetrammine copper(II) nitrate done clear
D) tetrammine copper(II) dinitrite done clear
View Answer play_arrowquestion_answer110) Which of the following complex species does not involve inner orbital hybridisation?
A) \[{{[Co{{F}_{6}}]}^{3-}}\] done clear
B) \[{{[Co{{(N{{H}_{3}})}_{6}}]}^{3+}}\] done clear
C) \[{{[Fe{{(CN)}_{6}}]}^{3-}}\] done clear
D) \[{{[Cr{{(N{{H}_{3}})}_{6}}]}^{3+}}\] done clear
View Answer play_arrowquestion_answer111) \[{{\,}_{\text{27}}}\text{C}{{\text{o}}^{\text{60}}}\]is radioactive because
A) its atomic number is high done clear
B) it has high \[\frac{p}{n}\]ratio done clear
C) it has high\[\frac{n}{p}\]ratio done clear
D) none of the above done clear
View Answer play_arrowquestion_answer112) The correct order of solubility of the sulphates of alkaline earth metals in water is
A) \[~Be>Ca>Mg>Ba>Sr\] done clear
B) \[~Mg>Be>Ba>Ca>Sr\] done clear
C) \[Be>Mg>Ca>Sr>Ba\] done clear
D) \[Mg>Ca>Ba>Be>Sr\] done clear
View Answer play_arrowquestion_answer113) Correct order of radii is
A) \[N<Be<B\] done clear
B) \[{{F}^{-}}<{{O}^{2-}}<{{N}^{3-}}\] done clear
C) \[Na<Li<K\] done clear
D) \[F{{e}^{3+}}<F{{e}^{2+}}<F{{e}^{4+}}\] done clear
View Answer play_arrowquestion_answer114) A sudden large jump between the values of first and second ionisation energies of elements would be associated with which of the following electronic configurations?
A) \[1{{s}^{2}},2{{s}^{2}}2{{p}^{6}},3{{s}^{1}}\] done clear
B) \[1{{s}^{2}},2{{s}^{2}}2{{p}^{6}},3{{s}^{2}}3{{p}^{1}}\] done clear
C) \[1{{s}^{2}},2{{s}^{2}}2{{p}^{6}},3{{s}^{1}}3{{p}^{2}}\] done clear
D) \[1{{s}^{2}},2{{s}^{2}}2{{p}^{6}},3{{s}^{2}}\] done clear
View Answer play_arrowquestion_answer115) Which one shows most pronounced inert pair effect?
A) \[\text{Si}\] done clear
B) \[Sn\] done clear
C) \[Pb\] done clear
D) C done clear
View Answer play_arrowquestion_answer116) Which of the following will form a colourless complex?
A) \[N{{i}^{2+}}\] done clear
B) \[C{{u}^{+}}\] done clear
C) \[T{{i}^{2+}}\] done clear
D) \[F{{e}^{3+}}\] done clear
View Answer play_arrowquestion_answer117) Silver containing lead as impurity is purified by
A) poling done clear
B) cupellation done clear
C) lavigation done clear
D) distillation done clear
View Answer play_arrowquestion_answer118) The metal extracted by cyanide process is
A) silver done clear
B) copper done clear
C) iron done clear
D) sodium done clear
View Answer play_arrowquestion_answer119) On the extraction of iron, the slag produced is
A) \[CO\] done clear
B) \[FeSi{{O}_{3}}\] done clear
C) \[MgSi{{O}_{3}}\] done clear
D) \[Casi{{O}_{3}}\] done clear
View Answer play_arrowquestion_answer120) Complex forming tendency is more for
A) \[N{{a}^{+}}\] done clear
B) \[{{K}^{+}}\] done clear
C) \[L{{i}^{+}}\] done clear
D) \[R{{b}^{+}}\] done clear
View Answer play_arrowquestion_answer121) In the reaction, The major product A is
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer122) The IUPAC name of the following compound is
A) propionic anhydride done clear
B) dipropanoic anhydride done clear
C) ethoxy propanoic acid done clear
D) propanoic anhydride done clear
View Answer play_arrowquestion_answer123) Which of the following compounds is not aromatic?
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer124) Which of the following is the most stable cation?
A) \[{{F}_{3}}C-CH_{2}^{\oplus }\] done clear
B) \[{{(C{{H}_{3}})}_{2}}C{{H}^{\oplus }}\] done clear
C) \[CH_{3}^{\oplus }\] done clear
D) \[CF_{3}^{\oplus }\] done clear
View Answer play_arrowquestion_answer125) The product A is
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer126) Tautomerism is not exhibited by
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer127) In the compound Configuration at \[{{C}_{2}}\]and \[{{C}_{3}}\]atoms are
A) \[S,S\] done clear
B) \[R,S\] done clear
C) \[S,R\] done clear
D) \[R,R\] done clear
View Answer play_arrowquestion_answer128) The product A is
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer129) Hinsberg reagent is
A) \[{{C}_{6}}{{H}_{S}}S{{O}_{3}}H\] done clear
B) \[{{C}_{6}}{{H}_{5}}NO\] done clear
C) \[{{C}_{6}}{{H}_{5}}S{{O}_{2}}Cl\] done clear
D) \[{{C}_{6}}{{H}_{5}}{{N}_{2}}Cl\] done clear
View Answer play_arrowquestion_answer130) Acetaldehyde cannot show
A) lodoform test done clear
B) Lucas test done clear
C) Benedict's test done clear
D) Toilers test done clear
View Answer play_arrowquestion_answer131) Ethylbenzene with bromine in presence of \[\text{FeB}{{\text{r}}_{\text{3}}}\text{,}\]predominantly gives
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer132) Which of the following will be most readily dehydrated under acidic conditions?
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer133) Which of the following cannot reduce Fehling solution?
A) \[\text{HCOOH}\] done clear
B) \[\text{ }\!\!~\!\!\text{ }{{\text{H}}_{\text{3}}}\text{CCOOH}\] done clear
C) \[\text{HCHO}\] done clear
D) \[~{{H}_{3}}CCHO\] done clear
View Answer play_arrowquestion_answer134) Absolute alcohol is prepared by
A) vacuum distillation done clear
B) azeotropic distillation done clear
C) steam distillation done clear
D) none of the above done clear
View Answer play_arrowquestion_answer135) Which of the following compounds is resistant to nucleophilic attack by hydroxyl ion?
A) Methylacetate done clear
B) Acetonitrile done clear
C) Acetamide done clear
D) Diethyl ether done clear
View Answer play_arrowquestion_answer136) Hydrogenation of benzoyl chloride in presence of Pd on\[\text{BaS}{{\text{O}}_{\text{4}}}\]gives
A) benzyl alcohol done clear
B) benzaldehyde done clear
C) benzoicacid done clear
D) phenol done clear
View Answer play_arrowquestion_answer137) \[Ph-C\equiv C-C{{H}_{3}}\xrightarrow{H{{g}^{2+}}/{{H}^{+}}}A\]The product A is
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer138) Ethyl amine reacts with nitrous acid to form
A) \[{{C}_{2}}{{H}_{5}}OH\] done clear
B) \[{{C}_{2}}{{H}_{5}}OH,{{N}_{2}},{{H}_{2}}O\] done clear
C) \[{{C}_{2}}{{H}_{5}}N_{2}^{+}C{{l}^{-}}\] done clear
D) \[{{C}_{2}}{{H}_{5}}NHOH,N{{H}_{3}}\] done clear
View Answer play_arrowquestion_answer139) Rice is deficient in
A) lysine done clear
B) alanine done clear
C) glycine done clear
D) leucine done clear
View Answer play_arrowquestion_answer140) Mutarotation does not occur in
A) sucrose done clear
B) D-glucose done clear
C) L-glucose done clear
D) none of these done clear
View Answer play_arrowquestion_answer141) Aldehyde which is formed during photo synthesis of plants is
A) methanol done clear
B) acetaldehyde done clear
C) propanal done clear
D) phenylmethanal done clear
View Answer play_arrowquestion_answer142) Coupling of diazonium salts of following takes place in the order
A) \[IV<II<III<I\] done clear
B) \[IV>III<II<I\] done clear
C) \[II<IV<I<III\] done clear
D) \[I<II<III<IV\] done clear
View Answer play_arrowquestion_answer143) Which is decreasing order of strength of bases? \[\bar{O}H,\bar{N}{{H}_{2}},HC\equiv {{C}^{-}}\]and \[C{{H}_{3}}CH_{2}^{-}\]
A) \[{{H}_{3}}CCH_{2}^{-}>NH_{2}^{-}>HC\equiv {{C}^{-}}>O{{H}^{-}}\] done clear
B) \[HC\equiv {{C}^{-}}>C{{H}_{3}}CH_{2}^{-}>NH_{2}^{-}>O{{H}^{-}}\] done clear
C) \[O{{H}^{-}}>NH_{2}^{-}>C{{H}^{-}}>{{H}_{3}}CCH_{2}^{-}\] done clear
D) \[NH_{2}^{-}>HC\equiv {{C}^{-}}>O{{H}^{-}}>{{H}_{3}}CCH_{2}^{-}\] done clear
View Answer play_arrowquestion_answer144) The reagent that reacts with nitromethane to form methyl hydroxylamine is
A) \[Zn/HCl\] done clear
B) \[Zn/N{{H}_{4}}Cl\] done clear
C) \[Zn/NaOH\] done clear
D) \[Sn/HCl\] done clear
View Answer play_arrowquestion_answer145) Which is most basic?
A) \[{{C}_{6}}{{H}_{5}}N{{H}_{2}}\] done clear
B) \[({{C}_{6}}{{H}_{5}}N{{H}_{2}})\] done clear
C) \[C{{H}_{3}}N{{H}_{2}}\] done clear
D) \[{{(C{{H}_{3}})}_{2}}NH\] done clear
View Answer play_arrowquestion_answer146) For d-electron, the orbital angular momentum is
A) \[\frac{\sqrt{6}h}{2\pi }\] done clear
B) \[\frac{\sqrt{2}h}{2\pi }\] done clear
C) \[\frac{h}{2\pi }\] done clear
D) \[\frac{2h}{\pi }\] done clear
View Answer play_arrowquestion_answer147) Two nodal planes are present in
A) \[{{\pi }^{*}}2{{p}_{x}}\] done clear
B) \[\sigma 2{{p}_{z}}\] done clear
C) \[\pi 2{{p}_{x}}\] done clear
D) \[\pi 2{{p}_{y}}\] done clear
View Answer play_arrowquestion_answer148) One gram mole of a gas at NTP occupies 22.4 L. This fact was derived from
A) law of gaseous volumes done clear
B) Avogadro's hypothesis done clear
C) Berzelius hypothesis done clear
D) Dalton's atomic theory done clear
View Answer play_arrowquestion_answer149) At\[\text{90}{{\,}^{\text{o}}}\text{C,}\] pure water has\[[{{H}_{3}}{{O}^{+}}]={{10}^{-6}}\,mol/L.\] The value of \[{{K}_{w}}\]at \[\text{90}{{\,}^{\text{o}}}\text{C}\]is
A) \[{{10}^{-6}}\] done clear
B) \[{{10}^{-8}}\] done clear
C) \[{{10}^{-12}}\] done clear
D) \[{{10}^{-14}}\] done clear
View Answer play_arrowquestion_answer150) The pH of a buffer solution of \[\text{0}\text{.1}\,\text{M}\,\text{N}{{\text{H}}_{\text{4}}}\text{OH}\]\[\text{ }\!\![\!\!\text{ p}{{\text{K}}_{b}}\text{=5}\text{.0 }\!\!]\!\!\text{ }\]and \[\text{0}\text{.01}\,\text{M}\,\text{N}{{\text{H}}_{\text{4}}}\text{Cl}\]is
A) 1 done clear
B) 4 done clear
C) 10 done clear
D) 13 done clear
View Answer play_arrowquestion_answer151) If a point \[(a{{t}^{2}},\,\,2at)\] be the extremity of a focal Chord of parabola \[{{y}^{2}}=4ax,\] then the length of the focal chord is
A) \[a{{\left( t+\frac{1}{t} \right)}^{2}}\] done clear
B) \[a{{\left( t+\frac{2}{t} \right)}^{3}}\] done clear
C) \[a{{\left( t+\frac{1}{t} \right)}^{3}}\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer152) In a test, an examines either guesses or copies or knows the answer to a multiple choice questions with four choices. The probability that he makes a guess; is \[\frac{1}{3}\] and the probability that he copies the answer is \[\frac{1}{6}\].The probability that his answer is correct given that he copied it is\[\frac{1}{8}\]. The probability that his answer is correct, given that he guessed it is\[\frac{1}{4}\]. The probability that they knew the answer to the questions given that he correctly answered is
A) \[\frac{24}{31}\] done clear
B) \[\frac{31}{24}\] done clear
C) \[\frac{24}{29}\] done clear
D) \[\frac{29}{24}\] done clear
View Answer play_arrowquestion_answer153) Three of the six vertices of a regular hexagon are chosen at random. The probability that the triangle with three vertices is equilateral is equal to
A) \[\frac{1}{2}\] done clear
B) \[\frac{1}{5}\] done clear
C) \[\frac{1}{10}\] done clear
D) \[\frac{1}{20}\] done clear
View Answer play_arrowquestion_answer154) The value of \[\underset{n\to \infty }{\mathop{\lim }}\,\,\cos \left( \frac{x}{2} \right)\cos \left( \frac{x}{4} \right)\,\cos \left( \frac{x}{8} \right).....\,\cos \left( \frac{x}{{{2}^{n}}} \right)\]Is
A) \[\frac{x}{\sin \,x}\] done clear
B) \[\frac{x}{\cos \,x}\] done clear
C) \[\frac{(\sin x)}{x}\] done clear
D) \[\frac{(cosx)}{x}\] done clear
View Answer play_arrowquestion_answer155) The order and degree of the differential equation \[y=\frac{dy}{dx}x+\sqrt{{{a}^{2}}{{\left( \frac{dy}{dx} \right)}^{2}}+{{b}^{2}}}\] is
A) \[3,1\] done clear
B) \[1,2\] done clear
C) \[2,1\] done clear
D) \[1,3\] done clear
View Answer play_arrowquestion_answer156) \[y=a{{e}^{mx}}+b{{e}^{-mx}}\] satisfies which of the following differential equations
A) \[\frac{dy}{dx}-my=0\] done clear
B) \[\frac{dy}{dx}+my=0\] done clear
C) \[\frac{{{d}^{2}}y}{d{{x}^{2}}}-{{m}^{2}}y=0\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer157) If \[f(x)={{\left( \frac{x}{1-|x|} \right)}^{1/2002}},\] then \[{{D}_{f}}\] is
A) \[R-[-1,\,1]\] done clear
B) \[\{-\infty ,1\}\] done clear
C) \[\{-\infty ,-1\}\cup (0,1)\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer158) If \[\vec{a},\vec{b},\vec{c}\] are the unit vectors such that \[\vec{a}\] is perpendicular to the plane \[\vec{b},\vec{c}\] and the angle between \[\vec{b},\vec{c}\] is \[\frac{\pi }{3},\] then \[|\vec{a}+\vec{b}+\vec{c}|\]is equal to
A) \[0\] done clear
B) \[\pm 1\] done clear
C) \[\pm \,2\] done clear
D) \[\pm \,3\] done clear
View Answer play_arrowquestion_answer159) \[\int_{\alpha }^{\beta }{\sqrt{\frac{x-\alpha }{\beta -x}}}\,dx\] is equal to
A) \[\frac{\pi }{2}(\alpha -\beta )\] done clear
B) \[\frac{\pi }{2}(\beta -\alpha )\] done clear
C) \[\pi (\alpha -\beta )\] done clear
D) \[\pi (\beta -\alpha )\] done clear
View Answer play_arrowquestion_answer160) If \[{{a}_{1}},{{a}_{2}}{{a}_{3}},{{a}_{4}},{{a}_{5}},{{a}_{6}}\] are in, AP with common difference \[d\ne 0,\] .then the system of equations \[{{a}_{1}}x+{{a}_{2}}y={{a}_{3}},{{a}_{4}}x+{{a}_{5}}y={{a}_{6}}\]has
A) infinite number of solutions done clear
B) unique solution done clear
C) no solution done clear
D) cannot say anything done clear
View Answer play_arrowquestion_answer161) If the value of \[{{\int_{0}^{\pi }{\left( \frac{x}{1+\sin \,x} \right)}}^{2}}dx=1,\] then the value of the integral \[\int_{0}^{\pi }{\left[ \frac{2{{x}^{2}}\,{{\cos }^{2}}\,x/2}{{{(1+\sin \,x)}^{2}}} \right]}dx\] is equal to
A) \[1+\pi (2-\pi )\] done clear
B) \[1-\pi (\pi -2)\] done clear
C) \[1+\pi (2+\pi )\] done clear
D) \[1-\pi (2+\pi )\] done clear
View Answer play_arrowquestion_answer162) \[\int_{-1}^{1}{(x-[x])\,dx}\] is equal to
A) \[0\] done clear
B) \[1\] done clear
C) \[2\] done clear
D) \[3\] done clear
View Answer play_arrowquestion_answer163) If the normal at ?t? on the parabola \[{{y}^{2}}=4ax\] meets the parabola again at t', then
A) \[t'=-t-\frac{2}{t}\] done clear
B) \[t'=-t+\frac{2}{t}\] done clear
C) \[t'=-t'-\frac{2}{t'}\] done clear
D) \[t'+t'+2tt'\] done clear
View Answer play_arrowquestion_answer164) The complex numbers having positive argument and satisfying \[|2-3i|\,\,<\] is
A) \[\frac{12}{5}+\frac{16}{5}\,i\] done clear
B) \[\frac{4}{5}+\frac{6}{5}\,i\] done clear
C) \[\frac{6}{5}-\frac{5}{2}\,i\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer165) The value of \[\int_{0}^{\pi /2}{\log \,\,\tan \,x\,\,dx}\] is
A) \[\frac{\pi }{8}\] done clear
B) \[\infty \] done clear
C) \[1\] done clear
D) \[0\] done clear
View Answer play_arrowquestion_answer166) Given that. \[\tan \,\,A\] and \[\tan \,\,B\] are the roots of \[{{x}^{2}}-px+q=0,\] then the value of \[{{\sin }^{2}}(A+B)\]is
A) \[\frac{{{p}^{2}}}{\{{{p}^{2}}+{{(1-q)}^{2}}\}}\] done clear
B) \[\frac{{{q}^{2}}}{({{p}^{2}}+{{q}^{2}})}\] done clear
C) \[\frac{{{q}^{2}}}{\{{{p}^{2}}-(1-{{q}^{2}})\}}\] done clear
D) \[\frac{{{p}^{2}}}{({{p}^{2}}+{{q}^{2}})}\] done clear
View Answer play_arrowquestion_answer167) The least positive non-integral solution of \[\sin \,\,\pi ({{x}^{2}}+x)-\sin \,\pi {{x}^{2}}=0\]is
A) rational done clear
B) irrational of the from \[\sqrt{P}\] done clear
C) irrational of the from \[\frac{\sqrt{P}-1}{4}\]when p is an odd integer done clear
D) irrational of the from \[\frac{\sqrt{P}+1}{4}\] where p is an even integer done clear
View Answer play_arrowquestion_answer168) The general solution of \[\frac{dy}{dx}=\frac{2x-y}{x+2y}\] is
A) \[{{x}^{2}}-xy+{{y}^{2}}=c\] done clear
B) \[{{x}^{2}}-xy-{{y}^{2}}=c\] done clear
C) \[{{x}^{2}}+xy-{{y}^{2}}=c\] done clear
D) \[{{x}^{2}}+x{{y}^{2}}=c\] done clear
View Answer play_arrowquestion_answer169) A function \[y=f(x)\] has second order derivative \[f''(x)=6(x-1)\]. If its graph passes through the point \[(2,1)\] and at that point the tangent to the graph is \[y=3x-5,\] then the function is
A) \[{{(x-1)}^{2}}\] done clear
B) \[{{(x-1)}^{3}}\] done clear
C) \[{{(x+1)}^{3}}\] done clear
D) \[{{(x+1)}^{2}}\] done clear
View Answer play_arrowquestion_answer170) If \[f(x)\] is a function satisfying \[f\left( \frac{1}{x} \right)+{{x}^{2}}f(x)=0\]for all non-zero x, then \[\int_{\sin \,\theta }^{\text{cosec }\theta }{f(x)\,\,dx}\]is equal to
A) \[0\] done clear
B) \[1\] done clear
C) \[2\] done clear
D) \[3\] done clear
View Answer play_arrowquestion_answer171) The area bounded by the curves \[{{x}^{2}}+{{y}^{2}}=25,\] \[4y=|4-{{x}^{2}}|\] and \[x=0\] above the x- axis is
A) \[24\,\,{{\sin }^{-1}}\left( \frac{4}{5} \right)\] done clear
B) \[25\,\,{{\sin }^{-1}}\left( \frac{4}{5} \right)\] done clear
C) \[2+\frac{25}{2}{{\sin }^{-1}}\left( \frac{4}{5} \right)\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer172) The curve in which the sub tangent is always bisected at the origin is
A) A parabola done clear
B) A circle done clear
C) A hyperbola done clear
D) None of these done clear
View Answer play_arrowquestion_answer173) The value of \[\int_{0}^{\pi /2}{{{\sin }^{8}}\,x\,\,dx}\] is
A) \[\frac{105\,\pi }{32(4!)}\] done clear
B) \[\frac{105\,\pi }{14\,(4!)}\] done clear
C) \[\frac{105\,}{16\pi \,(4!)}\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer174) A particle is moving in a straight line such that the distance described ?s' and the time taken ?t? are given by \[t=a{{s}^{2}}+bs+c,\,\,\,a>0.\]If v is the velocity of the particle at any time t, then acceleration is
A) \[-2av\] done clear
B) \[-2av\] done clear
C) \[-2av\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer175) If the vectors \[\vec{a}=(c\,\,{{\log }_{2}}\,x)\,\hat{i}-6\hat{j}+3\hat{k}\] and \[\vec{b}=({{\log }_{2}}x)\hat{i}+2\hat{j}+(2c\,{{\log }_{2}}\,x)\hat{k}\] make an obtuse angle for any \[x\,\in \,(0,\infty ),\] then the interval of which 'c? belongs
A) \[\left( \frac{4}{3},0 \right)\] done clear
B) \[\left( -\frac{4}{3},0 \right)\] done clear
C) \[\left( \frac{3}{4},0 \right)\] done clear
D) \[\left( -\frac{3}{4},0 \right)\] done clear
View Answer play_arrowquestion_answer176) Two forces of magnitude 5 and 3 units acting in the directions \[6\hat{i}+2\hat{j}+3\hat{k}\]and \[3\hat{i}-2\hat{j}+6\hat{k}\] respectively act on a particle which is displaced from the point \[(2,2,\,-1)\] to \[(4,3,1)\]. The work done by the forces is
A) \[\frac{149}{7}\] done clear
B) \[\frac{148}{6}\] done clear
C) \[\frac{148}{7}\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer177) The image of the point \[P(1,3,4)\] in the plane \[2x-y+z+3=0\] is
A) \[(3,\,5,\,-2)\] done clear
B) \[(-3,\,5,2)\] done clear
C) \[(3,-\,5,2)\] done clear
D) \[(3,\,5,2)\] done clear
View Answer play_arrowquestion_answer178) If E and F are two events with \[P(E)\le P(F)>0,\]then
A) occurrence of \[E\Rightarrow \]occurrence of F done clear
B) Occurrence of \[F\Rightarrow \]occurrence of? done clear
C) Non-occurrence of \[E\Rightarrow \]non-occurrence of F done clear
D) None of the above implications hold done clear
View Answer play_arrowquestion_answer179) If the normal to the parabola \[{{x}^{2}}=-4ay\] at the points \[({{x}_{1}},\,{{y}_{1}}),\,({{x}_{2}},{{y}_{2}})\] and \[({{x}_{3}},{{y}_{3}})\] are concurrent, then
A) \[{{y}_{1}}+{{y}_{2}}+{{y}_{3}}=0\] done clear
B) \[{{x}_{1}}{{x}_{2}}+{{x}_{2}}{{x}_{2}}+{{x}_{3}}{{x}_{1}}=0\] done clear
C) \[{{x}_{1}}+{{x}_{2}}+{{x}_{3}}=0\] done clear
D) \[{{x}_{1}}{{y}_{1}}+{{x}_{2}}{{y}_{2}}+{{x}_{3}}{{y}_{3}}=0\] done clear
View Answer play_arrowquestion_answer180) If the sum of n terms of the series \[1+\frac{4}{5}+\frac{7}{{{5}^{2}}}+\frac{10}{{{5}^{3}}}+.....\] is \[l+\frac{15}{16}\left( 1-\frac{1}{{{5}^{n-1}}} \right)-\frac{(3n-2)}{4({{5}^{n-1}})},\] then is
A) \[\frac{4}{5}\] done clear
B) \[\frac{5}{4}\] done clear
C) \[\frac{6}{5}\] done clear
D) \[\frac{5}{6}\] done clear
View Answer play_arrowquestion_answer181) It the sides of a triangle are in GP and the largest angle is twice the smallest angle, then the common ratio which is greater than one lies in the interval
A) \[(1,\,\sqrt{3})\] done clear
B) \[(1,\,\sqrt{2})\] done clear
C) \[\left( 1,\frac{\sqrt{5}+1}{2} \right)\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer182) If \[f(x)\] is a differentiable function, then \[\underset{x\to a}{\mathop{\lim }}\,\frac{af\,(x)-x\,f(a)}{x-a}\] is equal to
A) \[af'\,(a)-f(a)\] done clear
B) \[af\,\,(a)+f'(a)\] done clear
C) \[af'\,(a)+f(a)\] done clear
D) \[af\,(a)-f'(a)\] done clear
View Answer play_arrowquestion_answer183) The locus represented by the equation \[|z-1|=|z-i|\] is
A) a circle of radius 1 done clear
B) an ellipse with foci at 1 and \[-i\] done clear
C) a line through the origin done clear
D) a circle on the line joining 1 and \[-i\] as diameter done clear
View Answer play_arrowquestion_answer184) The rank of the matrix \[\left| \begin{matrix} 4 & 2 & (1-x) \\ 5 & k & 1 \\ 6 & 3 & (1+x) \\ \end{matrix} \right|\] is 2, then
A) \[k=\frac{5}{2},\,x=\frac{1}{5}\] done clear
B) \[k=\frac{5}{2},\,x\ne \frac{1}{5}\] done clear
C) \[k=\frac{1}{5},\,x=\frac{5}{2}\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer185) The largest interval lying in \[\left( -\frac{\pi }{2},\frac{\pi }{2} \right)\] n in which the function \[f(x)={{3}^{-{{x}^{2}}}}+{{\cos }^{-1}}\left( \frac{x}{2}-1 \right)+\log \,\,\cos \,x\]is defined as
A) \[[0,\pi ]\] done clear
B) \[\left[ -\frac{\pi }{2},\frac{\pi }{2} \right]\] done clear
C) \[\left[ 0,\frac{\pi }{2} \right)\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer186) If a and B are two fixed points, then the locus of a point which moves in such a way that the angle APB is a right angle is
A) a circle done clear
B) an ellipse done clear
C) a parabola done clear
D) None of these done clear
View Answer play_arrowquestion_answer187) Equation of the circle which of the mirror image of the circle \[{{x}^{2}}+{{y}^{2}}-2x=0\]in the line \[x+y=2\]is
A) \[{{x}^{2}}+{{y}^{2}}-2x+4y+3=0\] done clear
B) \[2({{x}^{2}}+{{y}^{2}})+x+y+1=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}-4x-2y+4=0\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer188) Let \[y=p+q\]where p varies directly as x and q varies inversely as\[{{x}^{2}}\]. If \[y=19\]when \[x=2\] or 3, then y in terms of x is
A) \[36x+\frac{5}{{{x}^{2}}}\] done clear
B) \[\frac{5}{x}\,36{{x}^{2}}\] done clear
C) \[5x+\frac{36}{{{x}^{2}}}\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer189) Seven digits from the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 are written in a random order. The probability that these seven digit number is divisible by 9, is
A) \[\frac{2}{9}\] done clear
B) \[\frac{1}{5}\] done clear
C) \[\frac{1}{3}\] done clear
D) \[\frac{1}{9}\] done clear
View Answer play_arrowquestion_answer190) The orthocenter of a triangle formed by the lines \[x+y=1,\,\,2x+3y=6\]and \[4x-y+4=0\] lies in the
A) Ist quadrant done clear
B) IInd quadrant done clear
C) IIIrd quadrant done clear
D) IVth quadrant done clear
View Answer play_arrowquestion_answer191) If a circle and a parabola intersect at four points, then the y am of the ordinates is equal to
A) AM of radius is of the circle and latusrectum of the par abola done clear
B) GM of the radius and latusrectum done clear
C) HM of the radius and latusrectum done clear
D) Zero done clear
View Answer play_arrowquestion_answer192) In \[\Delta \,ABC\] if \[a=3,\,\,b=4,\,c=5,\] then the value of sin 2B s
A) \[\frac{4}{5}\] done clear
B) \[\frac{3}{20}\] done clear
C) \[\frac{24}{25}\] done clear
D) \[\frac{1}{50}\] done clear
View Answer play_arrowquestion_answer193) The equation of the circle of radius 5 in the first quadrant which touches x-axis and the line \[4y=3x\]is
A) \[{{x}^{2}}+{{y}^{2}}-24x-y-25=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}-30x-10y+225=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}-16x-18y+64=0\] done clear
D) \[{{x}^{2}}+{{y}^{2}}-20x-12y+144=0\] done clear
View Answer play_arrowquestion_answer194) The line \[lx+my+n=0\] is a normal to the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\]
A) \[\frac{{{a}^{2}}}{{{l}^{2}}}+\frac{{{b}^{2}}}{{{m}^{2}}}=\frac{{{({{a}^{2}}-{{b}^{2}})}^{2}}}{{{n}^{2}}}\] done clear
B) \[\frac{{{a}^{2}}}{{{m}^{2}}}+\frac{{{b}^{2}}}{{{l}^{2}}}=\frac{{{({{a}^{2}}-{{b}^{2}})}^{2}}}{{{n}^{2}}}\] done clear
C) \[{{a}^{2}}{{l}^{2}}+{{b}^{2}}{{m}^{2}}={{({{a}^{2}}-{{b}^{2}})}^{2}}{{n}^{2}}\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer195) The equation \[\left| \sqrt{{{x}^{2}}+{{(y-1)}^{2}}}-\sqrt{{{x}^{2}}+{{(y+1)}^{2}}} \right|=k\]will represent a hyperbola for
A) \[k\in (0,2)\] done clear
B) \[k\in (0,1)\] done clear
C) \[k\in (1,\infty )\] done clear
D) \[k\in R'\] done clear
View Answer play_arrowquestion_answer196) Two forces \[{{\vec{F}}_{1}}=3\hat{i}-2\hat{j}+\hat{k}\] and \[{{\vec{F}}_{2}}=\hat{i}-3\hat{j}+5\hat{k}\] acting on a particle at A, move to .6. The work done if the position vector of \[\vec{A}\] and \[\vec{B}\]are \[-2\hat{i}+5\hat{k}\]and \[-3\hat{i}-7\hat{j}+2\hat{k}\]is
A) \[25\] done clear
B) \[13\] done clear
C) \[26\] done clear
D) \[28\] done clear
View Answer play_arrowquestion_answer197) If the three angles' of a quadrilateral are \[{{60}^{o}},\] \[{{80}^{o}}\] and \[\frac{5\pi }{6},\]then the fourth angle is
A) \[{{70}^{o}}\] done clear
B) \[{{79}^{o}}\] done clear
C) \[{{80}^{o}}\] done clear
D) \[{{81}^{o}}\] done clear
View Answer play_arrowquestion_answer198) Which one is not periodic
A) \[|\sin \,3x|+{{\sin }^{2}}\,x\] done clear
B) \[\cos \,\,\sqrt{x}\,+{{\cos }^{2}}\,x\] done clear
C) \[\cos \,4x+{{\tan }^{2}}x\] done clear
D) \[{{\cos }^{2}}x+\sin \,x\] done clear
View Answer play_arrowquestion_answer199) Let R be the relation on the set R of all real numbers defined by aRb if \[|a-b|\le 1,\]then R is
A) Reflexive and symmetric done clear
B) Symmetric only done clear
C) Transitive only done clear
D) Anti symmetric only done clear
View Answer play_arrowquestion_answer200) The expression \[(1+\tan \,x+{{\tan }^{2}}x)\,\,(1-\cot \,x+{{\cot }^{2}}x)\] has the positive values for x, given by
A) \[0\le x\le \frac{\pi }{2}\] done clear
B) \[0\le x\le \pi \] done clear
C) For all \[x\in R\] done clear
D) \[x\ge 0\] done clear
View Answer play_arrowquestion_answer201) The equation of a circle with origin as a centre and passing through an equilateral triangle whose median is of length 3a, is
A) \[{{x}^{2}}+{{y}^{2}}=9{{a}^{2}}\] done clear
B) \[{{x}^{2}}+{{y}^{2}}=16{{a}^{2}}\] done clear
C) \[{{x}^{2}}+{{y}^{2}}=4{{a}^{2}}\] done clear
D) \[{{x}^{2}}+{{y}^{2}}={{d}^{2}}\] done clear
View Answer play_arrowquestion_answer202) The point on the curve \[3{{x}^{2}}-4{{y}^{2}}=72\]which is nearest to the line \[3x+2y-1=0,\] is
A) \[(6,3)\] done clear
B) \[(6,-3)\] done clear
C) \[(6,-6)\] done clear
D) \[(6,5)\] done clear
View Answer play_arrowquestion_answer203) A circle is inscribed in a equilateral triangle of side a. The area of the circle is
A) \[3\pi {{a}^{2}}\] sq unit done clear
B) \[2{{a}^{2}}\] sq unit done clear
C) \[{{a}^{2}}\]sq unit done clear
D) None of these done clear
View Answer play_arrowquestion_answer204) If a, b, c are distinct positive real numbers and \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}=1,\]then \[3{{({{a}^{2}}{{b}^{2}}{{c}^{2}})}^{1/3}}\] is
A) Less than 1 done clear
B) Equal to 1 done clear
C) Greater than 1 done clear
D) any real number done clear
View Answer play_arrowquestion_answer205) If \[\alpha ,\beta ,\gamma ,\delta \] are the smallest positive angles in ascending order of magnitude which have their sines equal to the positive quantity k, then the value of \[4\,\sin \frac{\alpha }{2}+3\sin \frac{\beta }{2}+2\sin \frac{\gamma }{2}+\sin \frac{\delta }{2}\]is equal to
A) \[2\sqrt{1-k}\] done clear
B) \[2\sqrt{1-k}\] done clear
C) \[\frac{\sqrt{1+k}}{2}\] done clear
D) \[\sqrt{1+k}\] done clear
View Answer play_arrowquestion_answer206) If \[x+9\] is a root of \[\left| \begin{matrix} x & 3 & 7 \\ 2 & x & 2 \\ 7 & 6 & x \\ \end{matrix} \right|=0,\]then other roots are
A) \[-9,\,2,\,7\] done clear
B) \[9,\,2,\,7\] done clear
C) \[9,\,2,-\,7\] done clear
D) \[9,-\,2,\,7\] done clear
View Answer play_arrowquestion_answer207) The value of \[\underset{x\to \pi /2}{\mathop{\lim }}\,\frac{\cot \,x-\cos x}{{{(\pi -2x)}^{3}}}\]
A) \[1\] done clear
B) \[\frac{1}{16}\] done clear
C) \[16\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer208) If the tangent \[P(1,1)\] on \[{{y}^{2}}=x{{(2-x)}^{2}}\] meets the curve again at Q, then Q is
A) \[(2,2)\] done clear
B) \[(-1,-2)\] done clear
C) \[\left( \frac{9}{4},\frac{3}{8} \right)\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer209) For the equation \[\frac{1}{x+a}-\frac{1}{x+b}=\frac{1}{x+c},\]if the product of the ratio is zero, then the sum of (he roots is
A) \[0\] done clear
B) \[\frac{2ab}{b+c}\] done clear
C) \[\frac{2ac}{b+c}\] done clear
D) \[-\frac{2ac}{b+c}\] done clear
View Answer play_arrowquestion_answer210) If \[n=2002,\] evaluate \[\frac{1}{{{\log }_{2}}n!}+\frac{1}{{{\log }_{3}}n!}+\frac{1}{{{\log }_{4}}n!}+.....+\frac{1}{{{\log }_{2002}}n!}\]
A) \[1\] done clear
B) \[2\] done clear
C) \[3\] done clear
D) \[4\] done clear
View Answer play_arrowquestion_answer211) A and B are the independent events. The probability that both occur simultaneously is \[\frac{1}{6}\]and the probability that neither occur is \[\frac{1}{3}\]The probability of occurrence of the events A and B
A) \[\frac{1}{2},\frac{3}{2}\] done clear
B) \[\frac{1}{2},\frac{1}{3}\] done clear
C) not possible done clear
D) None of these done clear
View Answer play_arrowquestion_answer212) A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be hearts. The probability of the missing card to be a heart is
A) \[\frac{50}{11}\] done clear
B) \[\frac{51}{11}\] done clear
C) \[\frac{11}{50}\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer213) \[\int_{0}^{\pi /2}{\frac{{{\sin }^{2}}x}{{{\sin }^{2}}x+{{\cos }^{2}}x}}\] is equal to
A) \[\frac{\pi }{4}\] done clear
B) \[2\pi \] done clear
C) \[{{\pi }^{2}}\] done clear
D) \[\frac{1}{2}{{\pi }^{2}}\] done clear
View Answer play_arrowquestion_answer214) The centre and the radius of the circle \[z\bar{z}+(2+3i)\,\,\bar{z}-2(2-3i)z+12=0\] is
A) \[-(2+3i),\,(1)\] done clear
B) \[(3+2i),(1)\] done clear
C) \[(3+6i),(3)\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer215) The weight (in Kilogram) of 15 students are as follows 31, 35, 27, 29, 32, 43, 37, 41, 34, 28, 36,44, 45, 42, 30. If the weight 44 kg is replaced by 46 kg and \[27\text{ }kg\]is by \[25\text{ }kg,\] then new median is
A) \[32\] done clear
B) \[33\] done clear
C) \[34\] done clear
D) \[35\] done clear
View Answer play_arrowquestion_answer216) If \[1,\,{{\log }_{9}}({{3}^{1-x}}+2),{{\log }_{3}}({{4.3}^{x}}-1)\] are in AP, then x equals
A) \[{{\log }_{3}}4\] done clear
B) \[1-{{\log }_{3}}4\] done clear
C) \[1-{{\log }_{4}}3\] done clear
D) \[{{\log }_{4}}3\] done clear
View Answer play_arrowquestion_answer217) If the roots of the equation \[3{{x}^{2}}-6x+5=0\] are \[\alpha \] and \[\beta ,\] then the equation whose roots are \[\alpha +\beta \]and\[\frac{2}{\alpha +\beta }\]will be
A) \[{{x}^{2}}+3x-1=0\] done clear
B) \[{{x}^{2}}+3x-2=0\] done clear
C) \[{{x}^{2}}+3x+2=0\] done clear
D) \[{{x}^{2}}-3x+2=0\] done clear
View Answer play_arrowquestion_answer218) The equation of the locus of a point equidistant from the points \[({{a}_{1}},\,{{b}_{1}})\] and \[({{a}_{2}},\,{{b}_{2}})\] is \[({{a}_{1}}-{{a}_{2}})x+({{b}_{1}}-{{b}_{2}})y+c=0,\] then the value of c is
A) \[\sqrt{(a_{1}^{2}+b_{1}^{2}+c_{1}^{2})}\] done clear
B) \[a_{1}^{2}-b_{1}^{2}-c_{1}^{2}\] done clear
C) \[\frac{1}{2}(a_{2}^{2}+b_{2}^{2}-a_{1}^{2}-b_{1}^{2})\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer219) The general solution of the equation \[{{2}^{\cos \,2x}}+1={{3.2}^{-\sin \,x}}\]is
A) \[n\,\pi \] done clear
B) \[n\,\pi -\pi \] done clear
C) \[n\,\pi +\pi \] done clear
D) None of these done clear
View Answer play_arrowquestion_answer220) Let \[0<x<\pi \] and \[y(x)\] be given by \[(1+\sin \,x){{y}^{3}}-(\cos \,x){{y}^{2}}+2(1+\sin \,x)y-2cos\,x=0\] The derivative of y with respect to \[\frac{x}{2}\]at \[x=\frac{\pi }{2}\] is
A) \[-\frac{1}{2}\] done clear
B) \[\frac{1}{2}\] done clear
C) \[-2\] done clear
D) \[2\] done clear
View Answer play_arrowquestion_answer221) The value of \[\int_{0}^{\pi }{\left( \sum\limits_{r=0}^{3}{{{a}_{r}}\,\,{{\cos }^{3-r\,}}x\,{{\sin }^{r}}x} \right)}dx\]depends upon
A) \[{{a}_{1}}\] and \[{{a}_{2}}\] done clear
B) \[{{a}_{0}}\] and \[{{a}_{3}}\] done clear
C) \[{{a}_{2}}\] and \[{{a}_{3}}\] done clear
D) \[{{a}_{1}}\] and \[{{a}_{3}}\] done clear
View Answer play_arrowquestion_answer222) If the .function \[f:[1,\,\infty )\to [1,\infty )\] is denned by \[f(x)={{2}^{x(x-1)}},\]then \[{{f}^{-1}}(x)\] is
A) \[{{\left( \frac{1}{2} \right)}^{x(x-1)}}\] done clear
B) \[\frac{1}{2}(1+\sqrt{1+4{{\log }_{2}}y})\] done clear
C) \[\frac{1}{2}(1-\sqrt{1+4{{\log }_{2}}y})\] done clear
D) \[\infty \] done clear
View Answer play_arrowquestion_answer223) If the roots of the given equation \[(\cos \,\,p-1){{x}^{2}}+(\cos \,p)x+\sin \,p=0\] are real, then
A) \[p\in (-\pi ,0)\] done clear
B) \[p\in \left( -\frac{\pi }{2},\frac{\pi }{2} \right)\] done clear
C) \[p\in (0,\pi )\] done clear
D) \[p\in (0,2\pi )\] done clear
View Answer play_arrowquestion_answer224) The angle of depression of a boat m in a river is \[{{30}^{o}}\] from the top of a tower, \[87\text{ }m\]high and the speed of the boat is\[5.8\text{ }km/h\]. The time taken by the boat to reach at the base of the tower is
A) \[9\,\,\min \] done clear
B) \[\frac{9\sqrt{3}}{10}\,\,\min \] done clear
C) \[25\,\,\min \] done clear
D) \[15\,\,\min \] done clear
View Answer play_arrowquestion_answer225) If \[\alpha =\frac{3}{5},\,\,(0<\alpha ,\pi )\]and \[\cos \beta =\frac{5}{13},\] then \[(\alpha -\beta )\] lies in the quadrants
A) I, II, IV done clear
B) I, III, IV done clear
C) I, II, III done clear
D) I,IV done clear
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