question_answer1) A boat carrying a number of large stones is floating in a water tank. What would happen to the water level, if a few stones are unloaded into water?
A) Rises
B) Falls
C) Remains unchanged
D) Rises till half the number of stones are unloaded and then begins to fall
View Answer play_arrowquestion_answer2) A container with square base of side a is filled up to a height H with a liquid. A hole is made at a depth h from the free surface of water. With what acceleration the container must be accelerated, so that the water does not come out?
A) \[g\]
B) \[\frac{g}{2}\]
C) \[\frac{2gH}{2}\]
D) \[\frac{2gh}{2}\]
View Answer play_arrowquestion_answer3) If two soap bubbles of equal radii r coalesce, then the radius of curvature of interface between two bubbles will be
A) r
B) zero
C) infinity
D) \[\frac{1}{2r}\]
View Answer play_arrowquestion_answer4) What is the mass of \[2\text{ }L\]of nitrogen at \[~22.4\text{ }arm\]pressure and \[273\text{ }K\]?
A) \[28\text{ }g\]
B) \[14\times 22.4\text{ }g\]
C) \[56\text{ }g\]
D) None of these
View Answer play_arrowquestion_answer5) \[2\text{ }g\]of water condenses when passed through \[40\text{ }g\]of water initially at\[{{25}^{o}}C\]. The- condensation of steam raises the temperature of water to \[{{54.3}^{o}}C\]. What is the latent heat of steam?
A) \[540\,\,cal/g\]
B) \[536\,\,cal/g\]
C) \[270\,\,cal/g\]
D) \[480\,\,cal/g\]
View Answer play_arrowquestion_answer6) Petrol engine does the work during
A) suction stroke
B) exhaust stroke
C) adiabatic expansion
D) combustion
View Answer play_arrowquestion_answer7) The spectral energy distribution of a star is maximum at twice temperature as that of sun. The total energy radiated by star is
A) twice as that of the sun
B) same as that of the sun
C) sixteen times as that of the sun
D) one-sixteenth of sun
View Answer play_arrowquestion_answer8) Two simple pendulums of lengths \[1.44\text{ }m\]and \[1\text{ }m\] start swinging together. After how many vibrations will they again start swinging together?
A) 5 oscillations of smaller pendulum
B) 6 oscillations of smaller pendulum
C) 4 oscillations of bigger pendulum
D) 6 oscillations of bigger pendulum
View Answer play_arrowquestion_answer9) A wave has velocity u in medium P and velocity \[2u\] in medium Q. If the wave is incident in medium P at an angle \[{{30}^{o}},\]then the angle of refraction will be
A) \[{{30}^{o}}\]
B) \[{{45}^{o}}\]
C) \[{{60}^{o}}\]
D) \[{{90}^{o}}\]
View Answer play_arrowquestion_answer10) In \[1\text{ }m\]long open pipe what is the harmonic of resonance obtained with a tuning fork of frequency \[480\text{ }Hz\]?
A) First
B) Second
C) Third
D) Fourth
View Answer play_arrowquestion_answer11) Three sources of equal intensities with frequencies 400,401 and 402 vib/s are sounded together. The number of beat/s is
A) zero
B) \[1\]
C) \[2\]
D) \[4\]
View Answer play_arrowquestion_answer12) Two pendulums begin to swing simultaneously. If the ratio of the frequency of oscillations of the two is \[7:8,\] then the ratio of lengths of the two pendulums will be
A) \[7:8\]
B) \[8:7\]
C) \[49:64\]
D) \[64:49\]
View Answer play_arrowquestion_answer13) In a resonance pipe the first and second resonances are obtained at depths \[22.7\text{ }cm\]and \[70.2\text{ }cm\]respectively. What will be the end correction?
A) \[1.05\,\,cm\]
B) \[115.5\,\,cm\]
C) \[92.5\,\,cm\]
D) \[113.5\,\,cm\]
View Answer play_arrowquestion_answer14) The intensity level of sound A is 30 dB greater than of B. How many times more intense is the sound A than B?
A) \[10\]
B) \[100\]
C) \[1000\]
D) \[2\]
View Answer play_arrowquestion_answer15) An open tube is in resonance with string. If tube is dipped in water, so that \[75%\]of length of tube is inside water, then the ratio of the frequency \[({{v}_{o}})\] of tube to string is
A) \[{{v}_{o}}\]
B) \[2{{v}_{o}}\]
C) \[\frac{2}{3}{{v}_{o}}\]
D) \[\frac{3}{2}{{v}_{o}}\]
View Answer play_arrowquestion_answer16) Two masses \[{{m}_{1}}\] and \[{{m}_{2}}\] are suspended together by a massless spring of constant k. When the masses are in equilibrium \[{{m}_{1}},\] is removed without disturbing the system. The amplitude of oscillations is
A) \[\frac{{{m}_{1}}g}{k}\]
B) \[\frac{{{m}_{2}}g}{k}\]
C) \[\frac{({{m}_{1}}+{{m}_{2}})g}{k}\]
D) \[\frac{({{m}_{1}}-{{m}_{2}})g}{k}\]
View Answer play_arrowquestion_answer17) If a conducting medium is placed between two charges, then the electric force between will become
A) zero
B) infinity
C) \[1N\]
D) 1 dyne
View Answer play_arrowquestion_answer18) If an electron moves from rest from a point at which potential is \[50\text{ }V\]to another point at which potential is \[70\text{ }V,\] then its kinetic energy in the final state will be
A) \[3.2\times {{10}^{-20}}J~\]
B) \[3.2\times {{10}^{-18}}J\]
C) \[3.2\times {{10}^{-19}}J\]
D) zero
View Answer play_arrowquestion_answer19) In the following diagram the work done in moving a point charge from point P to point A, B and C is respectively as \[{{W}_{A}},\] \[{{W}_{B}}\] and \[{{W}_{C}},\] then
A) \[{{W}_{A}}={{W}_{B}}={{W}_{C}}\]
B) \[{{W}_{A}}={{W}_{B}}={{W}_{C}}=0\]
C) \[{{W}_{A}}>{{W}_{B}}>{{W}_{C}}\]
D) \[{{W}_{A}}<{{W}_{B}}<{{W}_{C}}\]
View Answer play_arrowquestion_answer20) The electric field due to an electric dipole at a distance r from its centre in axial position is E. If the dipole is rotated through an angle of \[{{90}^{o}}\]about its perpendicular axis, the electric field at the same point will be
A) \[E\]
B) \[\frac{E}{4}\]
C) \[\frac{E}{2}\]
D) \[2E\]
View Answer play_arrowquestion_answer21) If eight similar charge drops combine to form a bigger drop, then the ratio of capacitance of bigger drop to that of smaller drop will be
A) \[2:1\]
B) \[8:1\]
C) \[4:1\]
D) \[16:1\]
View Answer play_arrowquestion_answer22) The value of current I in figure is
A) \[4\,A\]
B) \[6\,A\]
C) \[3\,A\]
D) \[5\,A\]
View Answer play_arrowquestion_answer23) The plates of a charged condenser are connected to a voltmeter. If the plates are moved apart, the reading of voltmeter will
A) increase
B) decrease
C) remain unchanged
D) information is insufficient
View Answer play_arrowquestion_answer24) The n rows each containing m cells in series are joined in parallel. Maximum current is taken from this combination across an external resistance of 30 resistance. If the total number of cells used are 24 and internal resistance of each cell is \[0.5\text{ }Q\]then
A) \[m=8,\text{ }n=3\]
B) \[m=6,\text{ }n=4\]
C) \[m=12,\text{ }n=2\]
D) \[m=2,\text{ }n=12\]
View Answer play_arrowquestion_answer25) A railway compartment is lit up by thirteen lamps each taking \[2.1\text{ }A\]at\[15\text{ }V\]. The heat generated per second in each lamp will be m
A) \[4.35\text{ }cal\]
B) \[5.73\text{ }cal\]
C) \[7.5\text{ }cal\]
D) \[2.5\text{ }cal\]
View Answer play_arrowquestion_answer26) The chemical equivalent of copper and zinc are 32 and 108 respectively. When copper and silver voltameter are connected in series and electric current is passed through for sometimes, \[1.6\text{ }g\]of copper is deposited. Then, the mass of silver deposited will be
A) \[3.5\text{ }g\]
B) \[2.8g\]
C) \[5.4\text{ }g\]
D) None of these
View Answer play_arrowquestion_answer27) If the emf of a thermocouple, one junction of which is kept \[0{}^\circ C\]is given by \[e=at+\frac{1}{2}b{{t}^{2}}\] then the neutral temperature will be
A) \[\frac{a}{b}\]
B) \[-\frac{a}{b}\]
C) \[\frac{a}{2b}\]
D) \[-\frac{1}{ab}\]
View Answer play_arrowquestion_answer28) The direction of magnetic lines of force produced by passing a direct current in a conductor is given by
A) Lenz'slaw
B) Fleming's left hand rule
C) Right hand palm rule
D) Maxwell's law
View Answer play_arrowquestion_answer29) A proton, a deuteron and an alpha particle are accelerated through same potential difference and then they enter a normal uniform magnetic field. The ratio of their kinetic energies will be
A) \[2:1:3\]
B) \[1:1:2\]
C) \[1:1:1\]
D) \[1:2:4\]
View Answer play_arrowquestion_answer30) For the magnetic field to be maximum due to a small element of current carrying conductor at a point, the angle between the element and the line joining the element to the given point must be
A) \[{{0}^{o}}\]
B) \[{{90}^{o}}\]
C) \[{{180}^{o}}\]
D) \[{{45}^{o}}\]
View Answer play_arrowquestion_answer31) A circular coil of 20 turns and radius 10 cm is placed in uniform magnetic field of \[0.10\text{ }T\]normal to the plane of the coil. If the current in coil is 5 A, then the torque acting on the coil will be
A) \[31.4\text{ }Nm\]
B) \[3.14\text{ }Nm\]
C) \[0.314\text{ }Nm\]
D) zero
View Answer play_arrowquestion_answer32) The earth's magnetic field inside an iron box as compared to that outside the box is
A) less
B) more
C) zero
D) same
View Answer play_arrowquestion_answer33) The intensity of magnetic field due to an isolated pole of strength m at a point distant r from it will be
A) \[\frac{m}{{{r}^{2}}}\]
B) \[m{{r}^{2}}\]
C) \[\frac{{{r}^{2}}}{m}\]
D) \[\frac{m}{r}\]
View Answer play_arrowquestion_answer34) The dimensions of self-inductance L are
A) \[[M{{L}^{2}}{{T}^{-2}}{{A}^{-2}}]\]
B) \[[M{{L}^{2}}{{T}^{-1}}{{A}^{-2}}]\]
C) \[[M{{L}^{2}}{{T}^{-1}}{{A}^{-1}}]\]
D) \[[M{{L}^{-2}}{{T}^{-2}}{{A}^{-2}}]\]
View Answer play_arrowquestion_answer35) Quantity that remains unchanged in a transformer is
A) voltage
B) current
C) frequency
D) None of these
View Answer play_arrowquestion_answer36) If the capacity of a condenser is 1 F, then its resistance in a DC circuit will be
A) zero
B) infinity
C) \[1\Omega \]
D) \[\frac{1}{2}\,\,\Omega \]
View Answer play_arrowquestion_answer37) The time taken by an alternating current of \[50\text{ }Hz\] in reaching from zero to its maximum value will be
A) \[0.5s\]
B) \[0.005s\]
C) \[0.05\text{ }s\]
D) \[5s\]
View Answer play_arrowquestion_answer38) If the area to be covered for TV telecast is doubled, then height of transmitting antenna (TV tower) will have to be
A) doubled
B) halved
C) quadrupled
D) kept unchanged
View Answer play_arrowquestion_answer39) An electromagnetic radiation has an energy \[14.4\text{ }eV\]. To which region of electromagnetic spectrum does it belong?
A) Ultraviolet region
B) Visible region
C) X-ray region
D) y-ray region
View Answer play_arrowquestion_answer40) When a ray of light is incident normally on a surface, then
A) total internal reflection takes place
B) it passes undeviated
C) it undergoes dispersion
D) it gets absorbed by the surface
View Answer play_arrowquestion_answer41) A ray of light passes through a glass plate of thickness t and refractive index u. If the speed of light in vacuum is c, then the time taken by light in passing through the plate will be
A) \[\mu t\]
B) \[\frac{\mu t}{c}\]
C) \[\frac{tc}{\mu }\]
D) \[\frac{t}{\mu c}\]
View Answer play_arrowquestion_answer42) In Young's double slit experiment with monochromatic light, the central fringe will be
A) coloured
B) white
C) bright
D) black
View Answer play_arrowquestion_answer43) In the phenomenon of interference, energy is
A) destroyed at bright'fringes
B) created at dark fringes
C) conserved but it is redistributed
D) same at all points
View Answer play_arrowquestion_answer44) A very thin film that reflects white light appears
A) coloured
B) white
C) black
D) red
View Answer play_arrowquestion_answer45) The size of an obstacle in order to observe diffraction of light must be
A) of any order
B) of the order of wavelength
C) much larger than wavelength
D) much smaller than wavelength
View Answer play_arrowquestion_answer46) If the binding energies of a deuteron and an alpha-particle are \[1.125\text{ }MeV\]and \[7.2\text{ }MeV,\] respectively, then the more stable of the two is
A) deuteron
B) alpha-particle
C) both [a] and [b]
D) sometimes deuteron and sometimes alpha particle
View Answer play_arrowquestion_answer47) The particle A is converted into C via following reaction, \[A\xrightarrow{{}}B{{+}_{2}}H{{e}^{4}}\] \[B\xrightarrow{{}}C+2{{e}^{-}}\] Then
A) A and C are isobars
B) A and C are isotopes
C) A and B are isobars
D) A and B are isotopes
View Answer play_arrowquestion_answer48) On bombardment of \[{{U}^{235}}\] by slow neutrons, 200 MeV energy is released. If the power output of atomic reactor is \[1.6\text{ }MW,\] then the rate of fission will be
A) \[5\times {{10}^{16}}/s\]
B) \[10\times {{10}^{16}}/s\]
C) \[15\times {{10}^{16}}/s\]
D) \[20\times {{10}^{16}}/s\]
View Answer play_arrowquestion_answer49) The fussion process is possible at high temperatures, because at higher temperatures
A) the nucleus disintegrates
B) the molecules disintegrates
C) atoms become ionized
D) the nucleus get sufficient energy to overcome the strong forces of repulsion
View Answer play_arrowquestion_answer50) For maintaining sustained chain reaction, the following is required
A) protons
B) electrons
C) neutrons
D) positrons
View Answer play_arrowquestion_answer51) Sun maintains its shining because of the
A) fission of helium
B) chemical reaction
C) fusion of hydrogen nuclei
D) burning of carbon
View Answer play_arrowquestion_answer52) Atomic reactor is based on
A) controlled chain reaction
B) uncontrolled chain reaction
C) nuclear fission
D) nuclear fussion
View Answer play_arrowquestion_answer53) If the frequency of light incident on metal surface is doubled, then kinetic energy of emitted electron will become
A) doubled
B) less than double
C) more than double
D) nothing can be said
View Answer play_arrowquestion_answer54) The energy gap of silicon is \[1.14\text{ }eV\]. At what wavelength the silicon will stop to absorb the photon?
A) \[10877\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,\]
B) \[\text{9888 }\overset{\text{o}}{\mathop{\text{A}}}\,\]
C) \[1087.7\,\,\overset{\text{o}}{\mathop{\text{A}}}\,\]
D) \[1000\,\,\overset{\text{o}}{\mathop{\text{A}}}\,\]
View Answer play_arrowquestion_answer55) n-p-n transistor are preferred to p-n-p transistor because they have
A) low cost
B) low dissipation energy
C) capability of handling large power
D) electrons having high mobility than holes
View Answer play_arrowquestion_answer56) In a transistor in common-emitter configuration, the ratio of power gain to voltage gain is
A) \[\alpha \]
B) \[\frac{\beta }{\alpha }\]
C) \[\beta \times \beta \]
D) \[\beta \]
View Answer play_arrowquestion_answer57) The ionic bond is absent in
A) \[NaCl\]
B) \[CsCl\]
C) \[LiF\]
D) \[{{H}_{2}}O\]
View Answer play_arrowquestion_answer58) As the temperature rises the resistance offered by metal
A) increases
B) decreases
C) remains same
D) None of these
View Answer play_arrowquestion_answer59) Density of liquid in CGS system is \[0.625\text{ }g/c{{m}^{3}}\] What is its magnitude in SI system?
A) \[0.625\]
B) \[0.0625\]
C) \[0.00625\]
D) \[625\]
View Answer play_arrowquestion_answer60) If the length of rod A is \[3.25\pm 0.01\,cm\]and that of B is \[4.19\pm 0.01\text{ }cm,\] then the rod B is longer than rod A by
A) \[0.94\pm 0.00\text{ }cm\]
B) \[0.94\pm 0.01\text{ }cm\]
C) \[0.94\pm 0.02\text{ }cm\]
D) \[0.94\pm 0.005\text{ }cm\]
View Answer play_arrowquestion_answer61) A man is \[45\text{ }m\]behind the bus, when the bus start accelerating from rest with-acceleration \[2.5m/{{s}^{2}}\]. With what minimum velocity should the man start running to catch the bus?
A) \[12\text{ }m/s\]
B) \[14\text{ }m/s\]
C) \[15\text{ }m/s\]
D) \[16\text{ }m/s\]
View Answer play_arrowquestion_answer62) A particle moves along x-axis as \[x=4\,(t-2)+a{{(t-2)}^{2}}\] Which of the flowing is true?
A) The initial velocity of particle is 4
B) The acceleration of particle is \[2a\]
C) The particle is at origin at \[t=0\]
D) None of the above
View Answer play_arrowquestion_answer63) The momentum of the particle at any instant is given by \[3\,\cos 4t\,\hat{i}+3\,\sin \,4t\,\hat{j}\]. What is the angle between momentum and force-acting on it?
A) \[{{60}^{o}}\]
B) \[{{30}^{o}}\]
C) \[{{45}^{o}}\]
D) \[{{90}^{o}}\]
View Answer play_arrowquestion_answer64) A boat moves with a speed of \[5\text{ }km/h\]relative to water in a river flowing with a speed of \[3\text{ }km/h\]and having a width of\[1\text{ }km\]. The time taken around a round trip is
A) \[5\text{ }min\]
B) \[60\text{ }min\]
C) \[20\text{ }min\]
D) \[30\text{ }min\]
View Answer play_arrowquestion_answer65) A man is standing at the centre of frictionless pond of ice. How can he get himself to the shore?
A) By throwing his shirt in vertically upward direction
B) By spitting horizontally
C) He will wait for the ice to melt in pond
D) Unable to get at the shore
View Answer play_arrowquestion_answer66) If the heart pushes \[1\text{ }cc\]of blood in 1 s under pressure \[20000\text{ }N{{m}^{2}},\]the power of heart is
A) \[0.02\text{ }W\]
B) \[400\text{ }W\]
C) \[5\times {{10}^{-10}}W\]
D) \[0.2\text{ }W\]
View Answer play_arrowquestion_answer67) A body of mass \[4\text{ }kg\]moving with velocity \[12\text{ }m/s\]collides with another body of mass \[\text{6 }kg\] at rest. If two, bodies stick together after collision, then the loss of kinetic energy of system is
A) zero
B) \[288\text{ }J\]
C) \[172.8\text{ }J\]
D) \[144\text{ }J\]
View Answer play_arrowquestion_answer68) A man does a given amount of work in \[10\text{ }s\]. Another man does the' same amount of work in \[20\text{ }s\]. The ratio of the output power of first man to the second man is
A) \[1\]
B) \[1/2\]
C) \[2/1\]
D) None of these
View Answer play_arrowquestion_answer69) Turning effect is produced by
A) tangential component of force
B) radial component of force
C) transverse component of force
D) None of the above
View Answer play_arrowquestion_answer70) For spheres each of mass M and radius R are placed with their centres on the four comers A, B, C and D of a square of side b. The spheres A and B are hollow and C and D are solids. The moment of inertia of the system about side AD of square is
A) \[\frac{8}{3}M{{R}^{2}}+2M{{b}^{2}}\]
B) \[\frac{8}{5}M{{R}^{2}}+2M{{b}^{2}}\]
C) \[\frac{32}{15}M{{R}^{2}}+2M{{b}^{2}}\]
D) \[32M{{R}^{2}}+4M{{b}^{2}}\]
View Answer play_arrowquestion_answer71) A particle describes a horizontal circle in a conical funnel whose inner surface is smooth with speed of \[0.5\text{ }m/s\]. What is the height of the plane of circle from vertex of the funnel?
A) \[0.25\text{ }cm\]
B) \[2\text{ }cm\]
C) \[4\text{ }cm\]
D) \[2.5\text{ }cm\]
View Answer play_arrowquestion_answer72) Two masses \[{{m}_{1}}\] and \[{{m}_{2}}({{m}_{1}}>{{m}_{2}})\]are connected by massless flexible and inextensible string passed over massless and frictionless pulley. The acceleration of centre of mass is
A) \[{{\left( \frac{{{m}_{1}}-{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}} \right)}^{2}}g\]
B) \[\frac{{{m}_{1}}-{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}}g\]
C) \[\frac{{{m}_{1}}+{{m}_{2}}}{{{m}_{1}}-{{m}_{2}}}g\]
D) zero
View Answer play_arrowquestion_answer73) A satellite moves in a circle around the earth. The radius of this circle is equal to one-half of the radius of the moon's orbit. The satellite completes one revolution is
A) \[\frac{1}{2}\] lunar month
B) \[\frac{2}{3}\] lunar month
C) \[{{2}^{-3/2}}\] lunar month
D) \[{{2}^{3/2}}\] lunar month
View Answer play_arrowquestion_answer74) Earth binds the atmosphere because of
A) gravity
B) oxygen between earth and atmosphere
C) both and
D) None of the above
View Answer play_arrowquestion_answer75) A geostationary satellite is revolving around the earth. To make it escape from gravitational field of earth, its velocity must be increased
A) \[100%\]
B) \[41.4%\]
C) \[50%\]
D) \[59.6%\]
View Answer play_arrowquestion_answer76) Who used the quantum theory for the first time to explain the structure of atom?
A) de-Broglie
B) Bohr
C) Heisenberg
D) Einstein
View Answer play_arrowquestion_answer77) The boiling point of water decreases at high altitudes because
A) the atmospheric pressure is low
B) the temperature is low
C) the atmospheric pressure is high
D) the temperature is high
View Answer play_arrowquestion_answer78) In a solid lattice, the cation has left a lattice site and is located at interstitial position, the lattice defect is
A) interstitial defect
B) vacancy defect
C) Frenkel defect
D) Schottky defect
View Answer play_arrowquestion_answer79) The entropy of crystalline substances at absolute zero going by the third law of thermodynamics should be taken as
A) 100
B) 50
C) zero
D) different for different substances
View Answer play_arrowquestion_answer80) \[\Delta G\]for a spontaneous reaction is
A) zero
B) negative
C) positive
D) could be positive or negative
View Answer play_arrowquestion_answer81) The IUPAC name for \[C{{H}_{3}}CO-C{{H}_{3}}\]is
A) dimethyl ketone
B) acetone
C) propanal
D) propanone
View Answer play_arrowquestion_answer82) Which of the following is not an endothermic reaction?
A) Dehydrogenation
B) Ethane to ethene
C) Combustion of propane
D) Change of chlorine molecule into chlorine atoms
View Answer play_arrowquestion_answer83) A process in which the system does not exchange heat with the surroundings is known as
A) isothermal
B) isobaric
C) isochoric
D) adiabatic
View Answer play_arrowquestion_answer84) Which of the following is not a non-eletrolyte?
A) Acetic acid
B) Glucose
C) Ethanol
D) Urea
View Answer play_arrowquestion_answer85) The unit \[\text{oh}{{\text{m}}^{-1}}\]is used for
A) molar conductivity
B) equivalent conductivity
C) specific conductivity
D) conductance
View Answer play_arrowquestion_answer86) The tendency of an electrode to lose electrons is known as
A) eletrode potential
B) reduction potential
C) oxidation potential
D) emf
View Answer play_arrowquestion_answer87) For the feasibility of a redox reaction in a cell, the emf should be
A) positive
B) fixed
C) zero
D) negative
View Answer play_arrowquestion_answer88) If the rate reaction\[A\to B\]doubles on increasing the concentration of A by 4 times, the order of the reaction is
A) 2
B) 1
C) \[\frac{1}{2}\]
D) 4
View Answer play_arrowquestion_answer89) Fog is a colloidal solution of
A) solid in gas
B) liquid in gas
C) gas in liquid
D) gas in solid
View Answer play_arrowquestion_answer90) Muddy water can be purified through coagulation by using
A) common salt
B) alums
C) sand
D) lime
View Answer play_arrowquestion_answer91) Formation of ammonia from \[{{\text{H}}_{\text{2}}}\]and \[{{\text{N}}_{2}}\]by Haber's process using Fe is an example of
A) heterogeneous catalysis
B) homogeneous catalysis
C) enzyme catalysis
D) non-catalytic process
View Answer play_arrowquestion_answer92) The reason for almost doubling the rate of reaction on increasing the temperature of the reaction system by \[10{{\,}^{o}}C\]is
A) the value of threshold energy increases
B) collision frequency increases
C) the fraction of the molecule having energy equal to threshold energy increases
D) activation energy decreases
View Answer play_arrowquestion_answer93) The pH of an aqueous solution having hydroxide ion concentration as \[1\times {{10}^{-5}}\] is
A) 5
B) 9
C) 4.5
D) 11
View Answer play_arrowquestion_answer94) Which of the following is not a Lewis acid?
A) \[B{{F}_{3}}\]
B) \[AlC{{l}_{3}}\]
C) \[S{{O}_{2}}\]
D) \[{{H}_{2}}O\]
View Answer play_arrowquestion_answer95) The precipitation takes place only when the product of concentrations of ions
A) exceeds the solubility product
B) is less than the solubility product
C) is negligible
D) is equal to the solubility products
View Answer play_arrowquestion_answer96) Which of the following has lowest electron affinity?
A) \[Cl\]
B) \[I\]
C) \[F\]
D) \[Br\]
View Answer play_arrowquestion_answer97) In the calcium fluoride structure the coordination number of the cation and anions are respectively
A) 6, 6
B) 8, 4
C) 4, 4
D) 4, 8
View Answer play_arrowquestion_answer98) The total number of orbitals possible for principal quantum number \[n\] is
A) \[n\]
B) \[{{n}^{2}}\]
C) \[2n\]
D) \[2{{n}^{2}}\]
View Answer play_arrowquestion_answer99) The pair having similar geometry is
A) \[PC{{l}_{3}},N{{H}_{4}}\]
B) \[BeC{{l}_{2}},\,{{H}_{2}}O\]
C) \[C{{H}_{4}},CC{{l}_{4}}\]
D) \[I{{F}_{5}},P{{F}_{5}}\]
View Answer play_arrowquestion_answer100) The \[d-\]orbital invovled in \[s{{p}^{3}}d-\]hybridisation is
A) \[{{d}_{{{x}^{2}}-{{y}^{2}}}}\]
B) \[{{d}_{xy}}\]
C) \[{{d}_{{{z}^{2}}}}\]
D) \[{{d}_{zx}}\]
View Answer play_arrowquestion_answer101) If 8.0 g of a radioactive substance has a half-life of 10 h, the half-life of 2.0 g of the same substance is
A) 2.6 h
B) 5h
C) 10 h
D) 40 h
View Answer play_arrowquestion_answer102) Loss of a beta paticle is equivalent to
A) increase of one neutron only
B) decrease of one neutron only
C) both [a] and [b]
D) none of the above
View Answer play_arrowquestion_answer103) Which of the following is incorrect?
A) Relative lowering of vapour pressure is independent of the nature of the solute and the solvent
B) The ralative lowering of vapour pressure its a colligative property
C) Vapour pressure of a solution is lower than the vapour pressure of the solvent
D) The relative lowering of vapour pressure is directly proportional to the original pressure
View Answer play_arrowquestion_answer104) The presence of the chlorine atom on benzene ring makes the second substituent enter at a position
A) ortho
B) meta
C) para
D) ortho/para
View Answer play_arrowquestion_answer105) Hydrogen is not obtained when zinc reacts with
A) cold water
B) hot \[\text{NaOH}\]solution
C) dil \[{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}\]
D) dil \[\text{HCl}\]
View Answer play_arrowquestion_answer106) The oxidation number of xenon in \[\text{XeO}{{\text{F}}_{2}}\]is
A) zero
B) 2
C) 4
D) 3
View Answer play_arrowquestion_answer107) Which of the following is most volatile?
A) \[\text{HF}\]
B) \[\text{HCl}\]
C) \[\text{HBr}\]
D) \[\text{ }\!\!~\!\!\text{ HI}\]
View Answer play_arrowquestion_answer108) The form of iron having the highest carbon content is
A) cast iron
B) wrought ton
C) stainless steel
D) mild steel
View Answer play_arrowquestion_answer109) Which belongs to the actinides series?
A) \[Ce\]
B) \[~Cf\]
C) \[Ca~\]
D) \[~Cs\]
View Answer play_arrowquestion_answer110) Which of the following is planar?
A) \[Xe{{F}_{2}}\]
B) \[Xe{{O}_{3}}F\]
C) \[Xe{{O}_{2}}{{F}_{2}}\]
D) \[Xe{{F}_{4}}\]
View Answer play_arrowquestion_answer111) \[\text{Cr}{{\text{O}}_{\text{3}}}\]dissovles in aqueous \[\text{NaOH}\]to give
A) \[CrO_{4}^{2-}\]
B) \[Cr(OH)_{3}^{-}\]
C) \[C{{r}_{2}}O_{7}^{2-}\]
D) \[Cr{{(OH)}_{2}}\]
View Answer play_arrowquestion_answer112) Which of the following is a tribasic acid?
A) \[~{{H}_{3}}P{{O}_{4}}\]
B) \[~HP{{O}_{3}}\]
C) \[{{H}_{4}}{{P}_{2}}{{O}_{7}}\]
D) \[~{{H}_{4}}{{P}_{2}}{{O}_{6}}\]
View Answer play_arrowquestion_answer113) Ethylene diamine is an example of
A) monodentate ligand
B) bidentate ligand
C) tridentate ligand
D) polydentate ligand
View Answer play_arrowquestion_answer114) The molecule having a pyramidal shape out of the following is
A) \[C{{O}_{2}}\]
B) \[~B{{F}_{3}}\]
C) \[S{{F}_{4}}\]
D) \[~N{{H}_{3}}\]
View Answer play_arrowquestion_answer115) Which of the following doesn't give a ppt. with silver nitrate solution?
A) Ethyl bromide
B) Sodium bromide
C) Calcium chloride
D) Sodium chloride
View Answer play_arrowquestion_answer116) Which is the most stable carbocation?
A) \[iso-\]propyl cation
B) Triphenylmethyl cation
C) Ethyl cation
D) \[n-\]propyl cation
View Answer play_arrowquestion_answer117) Which is most acidic of the following?
A) Methane
B) Acetylene
C) 1-butene
D) Neo-pentane
View Answer play_arrowquestion_answer118) Which is the most reactive of the following?
A) Ethyl acetate
B) Acetic anhydride
C) Acetamide
D) Acetyl chloride
View Answer play_arrowquestion_answer119) Which of the following will be chiral?
A) \[C{{H}_{3}}CHC{{l}_{2}}\]
B) \[C{{H}_{3}}CHBrCl\]
C) \[C{{D}_{2}}C{{l}_{2}}\]
D) \[C{{H}_{2}}ClBr\]
View Answer play_arrowquestion_answer120) Electronic configuration of deuterium atom is
A) \[1{{s}^{1}}\]
B) \[2{{s}^{2}}\]
C) \[2{{s}^{1}}\]
D) \[1{{s}^{2}}\]
View Answer play_arrowquestion_answer121) Which of the following is a phenol?
A) Pentanoic acid
B) Phthalic acid
C) Picric acid
D) Phosphoric acid
View Answer play_arrowquestion_answer122) Which of the following is not an organometallic compound?
A) \[{{C}_{2}}{{H}_{5}}ONa\]
B) \[C{{H}_{3}}MgI\]
C) Tetraethyl
D) \[K{{C}_{4}}{{H}_{9}}\]
View Answer play_arrowquestion_answer123) The correct order of electron affinity is
A) \[B<C<O>N\]
B) \[B>C>N>O\]
C) \[\text{O}>C>B>N\]
D) \[\text{O}<C<B<N\]
View Answer play_arrowquestion_answer124) Ziegler Natta catalyst is an organometallic compound containing
A) iron
B) titanium
C) rhodium
D) zirconium
View Answer play_arrowquestion_answer125) Which of the following cannot undergo nucleophilic substitution under ordinary conditions?
A) Chlorobenzene
B) Tert-butylchloride
C) Isopropyl chloride
D) None of the above
View Answer play_arrowquestion_answer126) The compound which contains all the four\[{{1}^{o}},{{2}^{o}},{{3}^{o}}\]and \[{{4}^{o}}\] carbon atoms is
A) \[2,3-\]dimethyl pentane
B) \[3-\]chloro\[-2,3-\]dimethylpentane
C) \[2,3,4-\]trimethylpentane
D) \[3,3-\]dimethylpentane
View Answer play_arrowquestion_answer127) Brass, bronze and german silver have one common metal. This is
A) Zn
B) Fe
C) Al
D) Cu
View Answer play_arrowquestion_answer128) Which of the following is the green coloured powder produced when ammoniunium dichromate is used in fire works?
A) \[Zn\]
B) \[Fe\]
C) \[Al\]
D) \[Cu\]
View Answer play_arrowquestion_answer129) The \[\pi -\]bonded organometallic compound which has ethene as one of its component is
A) Zeise's salt
B) ferrocene
C) dibenzene chromium
D) tetraethyl tin
View Answer play_arrowquestion_answer130) Malachite is an ore of
A) \[Fe\]
B) \[Ag\]
C) \[Cr\]
D) \[Cu\]
View Answer play_arrowquestion_answer131) The most acidic of the following is
A) \[ClC{{H}_{2}}COOH\]
B) \[{{C}_{6}}{{H}_{5}}COOH\]
C) \[C{{D}_{3}}COOH\]
D) \[C{{H}_{3}}C{{H}_{2}}COOH\]
View Answer play_arrowquestion_answer132) Which of the following is an electrophile?
A) \[{{H}_{2}}O\]
B) \[S{{O}_{3}}\]
C) \[~N{{H}_{3}}\]
D) \[~ROR\]
View Answer play_arrowquestion_answer133) An aromatic compound among other things should have a\[\pi -\]electron cloud containing \[(4n+2)\,\pi \]electrons where \[n\]can't be
A) 1/2
B) 3
C) 2
D) 1
View Answer play_arrowquestion_answer134) Glycerol is an alcohol which can be classified as
A) trihydric
B) monohydric
C) dihydric
D) hexahydric
View Answer play_arrowquestion_answer135) The oxidation number of cobalt in \[K[Co{{(CO)}_{4}}]\]is
A) \[+\,1\]
B) \[+\,3\]
C) \[~-1\]
D) \[-3\]
View Answer play_arrowquestion_answer136) Bromination of alkanes involves
A) carbanions
B) carbocations
C) carbenes
D) free radicals
View Answer play_arrowquestion_answer137) Methylphenyl ether can be obtained by reacting
A) phenolate ions and methyl iodide
B) methoxide ipns and bromobenzene
C) methanol and phenol
D) bromo benzene and methyl bromide
View Answer play_arrowquestion_answer138) Which is not correct?
A) Phenol is more acidic than acetic acid
B) Ethanol is less acidic than phenol
C) Ethanol has higher boiling point than ethane
D) Ethane is a non-linear molecule
View Answer play_arrowquestion_answer139) Ascorbic acid is also known as
A) vitamin A
B) vitamin B
C) vitamin C
D) vitamin D
View Answer play_arrowquestion_answer140) Reaction of phenol with chloroform/sodium hydroxide to give \[o-\]hydroxy benzaldehyde involves the formation of
A) dichloro carbine
B) trichloro carbene
C) chlorine atoms
D) chlorine molecules
View Answer play_arrowquestion_answer141) One of the following that cannot undergo dehydrohalogenation is
A) \[iso-\]propyl bromide
B) ethariol
C) ethyl bromide
D) none of the above
View Answer play_arrowquestion_answer142) Which requires catalyst?
A) \[S+{{O}_{2}}\to S{{O}_{2}}\]
B) \[2S{{O}_{2}}+\,{{O}_{2}}\to 2S{{O}_{3}}\]
C) \[C+{{O}_{2}}\to C{{O}_{2}}\]
D) All of these
View Answer play_arrowquestion_answer143) Acetic acid will be obtained on oxidation of
A) ethanol
B) propanal
C) methanal
D) glyoxal
View Answer play_arrowquestion_answer144) A carboxylic acid is converted into its anhydride using
A) thionyl chloride
B) sulphur chloride
C) sulphuric acid
D) phosphorus pentoxide
View Answer play_arrowquestion_answer145) Which is false?
A) Glucose is a disaccharide
B) Starch is a polysaccharide
C) Glucose and fructose are not anomers
D) Invert sugar consists of glucose and fructose
View Answer play_arrowquestion_answer146) What kind of isomerism is possible for 1-chloro-2-nitroethene?
A) Functional group isomerism
B) Position isomerism
C) E/Z isomerism
D) Optical isomerism
View Answer play_arrowquestion_answer147) KCN reacts readily to give a cyanide with
A) ethyl alcohol
B) ethyl bromide
C) bromobenzene
D) chlorobenzene
View Answer play_arrowquestion_answer148) Peptides are formed from
A) aliphatic amines
B) carbohydrates
C) a-amino acids
D) aromatic amines
View Answer play_arrowquestion_answer149) Calcium carbide on reaction with water yields
A) methane
B) ethane
C) ethene
D) ethyne
View Answer play_arrowquestion_answer150) The correct set of the four quantum numbers of a \[4d\] electron is
A) \[4,2,1-\frac{1}{2}\]
B) \[4,2,1,0\]
C) \[4,3,2,+\frac{1}{2}\]
D) \[4,3,-2,+\frac{1}{2}\]
View Answer play_arrowquestion_answer151) In a class of 30 pupils. 12 take needls work, 16 take physics and 18 take history. If all the 30 students take at least one subject and no one takes all three, then the number of pupils taking 2 subjects is
A) \[16\]
B) \[6\]
C) \[8\]
D) \[20\]
View Answer play_arrowquestion_answer152) If \[f(2x+3)=\sin x+{{2}^{x}},\] then \[f(4m-2n+3)\] is equal to
A) \[\sin \,(m-2n)+{{2}^{2m-n}}\]
B) \[\sin \,(2m-n)+{{2}^{(m-n)2}}\]
C) \[\sin \,(m-2n)+{{2}^{(m+n)2}}\]
D) \[\sin (2m-n)+{{2}^{2m-n}}\]
View Answer play_arrowquestion_answer153) If \[{{z}_{1}}=1+2i\] and \[{{z}_{2}}=3+5i,\] then \[\operatorname{Re}[{{\bar{z}}_{2}}{{z}_{1}}/{{z}_{2}}]\]is equal to
A) \[-31/17\]
B) \[17/22\]
C) \[-17/31\]
D) \[22/17\]
View Answer play_arrowquestion_answer154) If \[|z+8|+|z-8|=16,\] where z is a complex number, then the point z will lie on
A) circle
B) an ellipse
C) a straight line
D) None of these
View Answer play_arrowquestion_answer155) If twice the 11 th term of an AP is equal to 7times its 21st term, then its 25th term is equal to
A) \[24\]
B) \[120\]
C) \[0\]
D) None of these
View Answer play_arrowquestion_answer156) If one of the roots of equation \[{{x}^{2}}+ax+3=0\] is 3 and one of the roots of the equation \[{{x}^{2}}+ax+b=0\]is three times the other root, then the value of b is equal to
A) \[3\]
B) \[4\]
C) \[2\]
D) \[1\]
View Answer play_arrowquestion_answer157) If S is the sum of an infinite GP, the first term a, then the common ratio r is given by
A) \[\frac{a-S}{S}\]
B) \[\frac{S-a}{S}\]
C) \[\frac{a}{1-S}\]
D) \[\frac{S-a}{a}\]
View Answer play_arrowquestion_answer158) The coefficient of \[{{x}^{4}}\]in the expansion of \[{{\left( \frac{x}{2}-\frac{3}{{{x}^{2}}} \right)}^{10}}\]is.
A) \[405/226\]
B) \[504/289\]
C) \[450/263\]
D) None of the above
View Answer play_arrowquestion_answer159) The figure formed by joining the points \[(4,0)\] s\[(3,5)\]and \[(-1,-1)\] in pairs is
A) a right angled triangle
B) an acute angled triangle
C) an obtuse angled triangle
D) None of the above
View Answer play_arrowquestion_answer160) The ortho centre of the triangle with vertices \[(-2,-6),\,\,\,(-2,4)\] and \[(1,3)\] is
A) \[(3,\,1)\]
B) \[(1,\,1/3)\]
C) \[(1,3)\]
D) None of these
View Answer play_arrowquestion_answer161) The in centre of a triangle with vertices \[(7,1),\] \[(-1,5)\] and \[(3+2\sqrt{3},3+4\sqrt{3})\]is
A) \[\left( 3+\frac{2}{\sqrt{3}},\,3+\frac{4}{\sqrt{3}} \right)\]
B) \[\left( 1+\frac{2}{3\sqrt{3}},1+\frac{4}{3\sqrt{3}} \right)\]
C) \[(7,1)\]
D) None of the above
View Answer play_arrowquestion_answer162) Let a be the distance between line \[-x+y=2\] and \[x-y=2\]and \[\beta \] be the distance between the lines \[4x-3y=5\] and \[6y-8x=1,\] then
A) \[20\sqrt{2}\beta =11\alpha \]
B) \[20\sqrt{2}\alpha =11\beta \]
C) \[11\sqrt{2}\beta =20\alpha \]
D) None of these
View Answer play_arrowquestion_answer163) The equations of the tangents to circle \[5{{x}^{2}}+5{{y}^{2}}=1,\] parallel to line \[3x+4y=1\] are
A) \[3x+4y=\pm 2\sqrt{5}\]
B) \[6x+8y=\pm \sqrt{5}\]
C) \[3x+4y=\pm \sqrt{5}\]
D) None of the above
View Answer play_arrowquestion_answer164) From the point \[(-1,-6)\] two tangents are drawn to the parabola\[{{y}^{2}}=4x\]. Then, the angle between the two tangents is
A) \[{{30}^{o}}\]
B) \[{{45}^{o}}\]
C) \[{{60}^{o}}\]
D) \[{{90}^{o}}\]
View Answer play_arrowquestion_answer165) If the foci of an ellipse are \[(\pm \sqrt{5},0)\] and its eccentricity is \[\sqrt{5}/3,\] then the equation of the ellipse is
A) \[9{{x}^{2}}+4{{y}^{2}}=36\]
B) \[4{{x}^{2}}+9{{y}^{2}}=36\]
C) \[36{{x}^{2}}+9{{y}^{2}}=4\]
D) \[9{{x}^{2}}+36{{y}^{2}}=4\]
View Answer play_arrowquestion_answer166) If \[y=(1+\tan \,A)\,(1-\tan B),\]where \[A-B=\frac{\pi }{4},\]then \[{{(y+1)}^{y+1}}\] is equal to
A) \[9\]
B) \[4\]
C) \[27\]
D) \[81\]
View Answer play_arrowquestion_answer167) If \[x\,\,\sin \theta -y\,\cos \,\theta =0\]and \[x\,{{\sin }^{3}}\theta +y\,{{\cos }^{3}}\theta =\sin \theta \,\,\cos \theta ,\] then \[{{x}^{2}}+{{y}^{2}}\] is equal to
A) \[0\]
B) \[2\]
C) \[4\]
D) \[1\]
View Answer play_arrowquestion_answer168) If \[\tan x=\frac{b}{a},\] then the value of \[a\,\cos \,2x+b\,\sin \,2x\]is
A) \[a\]
B) \[b\]
C) \[a+b\]
D) \[{{a}^{2}}+{{b}^{2}}\]
View Answer play_arrowquestion_answer169) If the expansion in powers of x of the function \[\frac{1}{(1-ax)\,(1-bx)}\]is \[{{a}_{0}}-{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+{{a}_{3}}{{x}^{3}}+.....,\] then \[{{a}_{n}}\] is
A) \[\frac{{{b}^{n+1}}-{{a}^{n+1}}}{b-a}\]
B) \[\frac{{{a}^{n}}-{{b}^{n}}}{b-a}\]
C) \[\frac{{{a}^{n+1}}-{{b}^{n+1}}}{b-a}\]
D) \[\frac{{{b}^{n}}-{{a}^{n}}}{b-a}\]
View Answer play_arrowquestion_answer170) If n is any integer, then the general solution of the equation \[\cos \theta -\sin \theta =\frac{1}{\sqrt{2}}\] is
A) \[\theta =2n\pi -\frac{\pi }{12}\] or\[\theta =2n\pi +\frac{7\pi }{12}\]
B) \[\theta =n\pi +\frac{\pi }{12}\]
C) \[\theta =2n\pi +\frac{\pi }{12}\] or \[\theta =2n\pi -\frac{7\pi }{12}\]
D) \[\theta =2n\pi +\frac{\pi }{12}\] or \[\theta =2n\pi -\frac{7\pi }{12}\]
View Answer play_arrowquestion_answer171) . The value of \[{{\cos }^{-1}}\,(\cos \,12)-{{\sin }^{-1}}\,(\sin 14)\] is
A) \[-2\]
B) \[8\pi -26\]
C) \[4\pi +2\]
D) None of these
View Answer play_arrowquestion_answer172) If a, b and c are the sides of a triangle such that \[{{a}^{4}}+{{b}^{4}}+{{c}^{4}}=2{{c}^{2}}({{a}^{2}}+{{b}^{2}}),\] then the angles opposite to the side C is
A) \[{{45}^{o}}\] or \[{{90}^{o}}\]
B) \[{{30}^{o}}\] or \[{{135}^{o}}\]
C) \[{{45}^{o}}\] or \[{{135}^{o}}\]
D) \[{{60}^{o}}\] or \[{{120}^{o}}\]
View Answer play_arrowquestion_answer173) The value of the determinant \[\left| \begin{matrix} 0 & {{b}^{3}}-{{a}^{3}} & {{c}^{3}}-{{a}^{3}} \\ {{a}^{3}}-{{b}^{3}} & 0 & {{c}^{3}}-{{b}^{3}} \\ {{a}^{3}}-{{c}^{3}} & {{b}^{3}}-{{c}^{3}} & 0 \\ \end{matrix} \right|\]is equal to
A) \[{{a}^{3}}-{{b}^{3}}-{{c}^{3}}\]
B) \[{{a}^{3}}-{{b}^{3}}-{{c}^{3}}\]
C) \[0\]
D) \[-{{a}^{3}}+{{b}^{3}}+{{c}^{3}}\]
View Answer play_arrowquestion_answer174) The integer represented by the determinant \[\left| \begin{matrix} 215 & 342 & 511 \\ 6 & 7 & 8 \\ 36 & 49 & 54 \\ \end{matrix} \right|\] is exactly divisible by
A) \[146\]
B) \[21\]
C) \[20\]
D) \[335\]
View Answer play_arrowquestion_answer175) A root of the equation \[\left| \begin{matrix} 3-x & -6 & 3 \\ -6 & 3-x & 3 \\ 3 & 3 & -6-x \\ \end{matrix} \right|=0\] is given by
A) \[x=0\]
B) \[x=6\]
C) \[x=3\]
D) None of these
View Answer play_arrowquestion_answer176) The determinant \[\left| \begin{matrix} 4+{{x}^{2}} & -6 & -2 \\ -6 & 9+{{x}^{2}} & 3 \\ -2 & 3 & 1+{{x}^{2}} \\ \end{matrix} \right|\] is not divisible by
A) \[x\]
B) \[{{x}^{3}}\]
C) \[14+{{x}^{2}}\]
D) \[{{x}^{5}}\]
View Answer play_arrowquestion_answer177) If X is a square matrix of order \[3\times 3,\lambda \] is a scalar, then adj \[(\lambda x)\]is equal to
A) \[\lambda \,\,adj\,\,(X)\]
B) \[{{\lambda }^{3}}\,\,adj\,\,(X)\]
C) \[{{\lambda }^{2}}\,\,adj\,\,(X)\]
D) \[{{\lambda }^{4}}\,\,adj\,\,(X)\]
View Answer play_arrowquestion_answer178) If \[f(\theta )=\left[ \begin{matrix} \cos \,\theta & -\sin \theta & 0 \\ \sin \,\theta & \cos \,\theta & 0 \\ 0 & 0 & 1 \\ \end{matrix} \right],\]then \[{{\{f(\theta )\}}^{-1}}\]is equal to
A) \[f(-\theta )\]
B) \[f(-\theta )\]
C) \[f(2\theta )\]
D) None of these
View Answer play_arrowquestion_answer179) The minors of \[-4\] and \[9\] and the cofactors of \[-4\]and 9 in matrix \[\left[ \begin{matrix} -1 & -2 & 3 \\ -4 & -5 & -6 \\ -7 & 8 & 9 \\ \end{matrix} \right]\] are respectively
A) \[42,3,-42,3\]
B) \[-42,-3,42\]
C) \[42,3,42,3,-3\]
D) \[42,3,-42,3\]
View Answer play_arrowquestion_answer180) If \[X=\left[ \begin{matrix} -x & -y \\ z & t \\ \end{matrix} \right],\] then transpose of adj (X) is
A) \[\left[ \begin{matrix} t & z \\ -y & -x \\ \end{matrix} \right]\]
B) \[\left[ \begin{matrix} t & y \\ -z & -x \\ \end{matrix} \right]\]
C) \[\left[ \begin{matrix} t & -z \\ y & -x \\ \end{matrix} \right]\]
D) None of these
View Answer play_arrowquestion_answer181) Let PQRS be a parallelogram whose diagonals PR and QS intersect at O?. If O is origin, then \[\overrightarrow{OP}+\overrightarrow{OQ}+\overrightarrow{OR}+\overrightarrow{OS}\]is equal to
A) \[\overrightarrow{OO'}\]
B) \[2\overrightarrow{O}O'\]
C) \[3\overrightarrow{O}Q'\]
D) \[4\overrightarrow{O}O'\]
View Answer play_arrowquestion_answer182) If the vectors \[2\hat{i}+\hat{j}-\hat{k},-\hat{i}+2\hat{j}+\lambda \hat{k}\] and \[-5\,\hat{i}+2\hat{j}-\hat{k}\]are coplanar, then the value of \[\lambda \] is equal to
A) \[-13\]
B) \[13/9\]
C) \[-13/9\]
D) \[-9/13\]
View Answer play_arrowquestion_answer183) If the scalar projection of the vectors \[x\,\hat{i}+\hat{j}+\hat{k}\] on the vector \[2\hat{i}-\hat{j}+5\hat{k}\] is \[\frac{1}{\sqrt{30}},\] then the value of x is
A) \[-3/2\]
B) \[6\]
C) \[-6\]
D) \[3\]
View Answer play_arrowquestion_answer184) If \[\vec{x}+\vec{y}+\vec{z}=\vec{0},\,|\vec{x}|=|\vec{y}|=|\vec{z}|=2\] and \[\theta \] is angle between \[\vec{y}\] and \[\vec{z},\] then the value of \[\text{cose}{{\text{c}}^{2}}\theta +{{\cot }^{2}}\theta \] is equal to
A) \[4/3\]
B) \[5/3\]
C) \[1/3\]
D) \[1\]
View Answer play_arrowquestion_answer185) If the position vectors of two points P and Q are respectively \[9\,\hat{i}-\hat{j}+5\hat{k}\]and \[\hat{i}+3\hat{j}+5\hat{k}\] and the line segment PQ intersects the YOZ plane at a point R, then \[PR:RQ\]is equal to
A) \[9:1\]
B) \[1:9\]
C) \[-1:9\]
D) \[-9:1\]
View Answer play_arrowquestion_answer186) If \[\vec{u},\vec{v}\] and \[\vec{w}\] are three mutually perpendicular unit vectors, then \[|\vec{u}+\vec{v}+\vec{w}|\]is equal to
A) \[\sqrt{3}\]
B) \[1\]
C) \[3\]
D) None of the above
View Answer play_arrowquestion_answer187) The angle between the vectors \[\vec{a}+\vec{b}\] and \[\vec{a}-\vec{b}\]when \[\vec{a}=(1,1,4)\] and \[\vec{b}=(1,-1,4)\] is
A) \[{{90}^{o}}\]
B) \[{{45}^{o}}\]
C) \[{{30}^{o}}\]
D) \[{{15}^{o}}\]
View Answer play_arrowquestion_answer188) The line of intersection of the planes \[\vec{r}.(\hat{i}-3\hat{j}+\hat{k})=1\] and \[\vec{r}.(2\hat{i}+5\hat{j}-3\hat{k})=2\] is parallel to the vector
A) \[-4\hat{i}+5\hat{j}+11\hat{k}\]
B) \[4\hat{i}+5\hat{j}+11\hat{k}\]
C) \[-4\hat{i}-5\hat{j}+11\hat{k}\]
D) \[-4\hat{i}+5\hat{j}-11\hat{k}\]
View Answer play_arrowquestion_answer189) A plane meet the coordinate axes at P, Q and R such that the position vector of the centroid of \[\Delta PQR\] is \[2\hat{i}-5\hat{j}+8\hat{k}\]. Then, the equation of the plane is
A) \[\vec{r}.(20\,\hat{i}-8\hat{j}+5\hat{k})=120\]
B) \[\vec{r}.(20\,\hat{i}-8\hat{j}+5\hat{k})=1\]
C) \[\vec{r}.(20\,\hat{i}-8\hat{j}+5\hat{k})=2\]
D) \[\vec{r}.(20\,\hat{i}-8\hat{j}+5\hat{k})=20\]
View Answer play_arrowquestion_answer190) The distance of the point \[(2,3,4)\] from the line \[1-x=\frac{y}{2}=\frac{1}{3}(1+z)\] is
A) \[\frac{1}{7}\sqrt{35}\]
B) \[\frac{4}{7}\sqrt{35}\]
C) \[\frac{2}{7}\sqrt{35}\]
D) \[\frac{3}{7}\sqrt{35}\]
View Answer play_arrowquestion_answer191) The equation of the plane passing through the points \[(0,1,2)\] and \[(-1,\,0,3)\] and perpendicular to the plane \[2x+3y+z=5\] is
A) \[3x-4y+18z+32=0\]
B) \[3x+4y-18x+32=0\]
C) \[4x+3y-17z+31=0\]
D) \[4x-3y+z+1=0\]
View Answer play_arrowquestion_answer192) A line joining the points \[(1,2,0)\] and \[(4,13,5)\] is perpendicular to a plane. Then, the coefficients of x, y and z in the equation of the plane are; respectively
A) \[5,15,5\]
B) \[3,11,5\]
C) \[3,-11,5\]
D) \[-5,-15,5\]
View Answer play_arrowquestion_answer193) The image of the point \[P(1,3,4)\] in the plane \[2x-y+z+3=0\] is
A) \[(3,\,5,-2)\]
B) \[(-3,\,5,2)\]
C) \[(3,-5,2)\]
D) \[(-1,\,4,2)\]
View Answer play_arrowquestion_answer194) The distance between the line \[\vec{r}=2\hat{i}-2\hat{j}+3\hat{k}+\lambda (\hat{i}-\hat{j}+4\hat{k})\] and the plane \[\vec{r}.(\hat{i}+5\hat{j}+\hat{k})=5\] is
A) \[\frac{10}{3}\]
B) \[\frac{3}{10}\]
C) \[\frac{10}{3\sqrt{3}}\]
D) \[\frac{10}{9}\]
View Answer play_arrowquestion_answer195) The distance between the planes \[2x+y+2z=8\]and \[4x+2y+4z+5=0\]
A) \[3/2\]
B) \[7/2\]
C) \[2/5\]
D) \[0\]
View Answer play_arrowquestion_answer196) If \[\alpha ,\beta \] and \[\gamma \] are the roots of equation \[{{x}^{3}}-3{{x}^{2}}+x+5=0,\] then \[y=\Sigma {{\alpha }^{2}}+\alpha \beta \gamma \]satisfies the equation.
A) \[{{y}^{3}}+y+2=0\]
B) \[{{y}^{3}}-{{y}^{2}}-y-2=0\]
C) \[{{y}^{3}}+3{{y}^{2}}-y-3=0\]
D) \[{{y}^{2}}+4{{y}^{2}}+5y+20=0\]
View Answer play_arrowquestion_answer197) If l(x) is the least integer not less than x and g(,x) is the greatest integer not greater than x, then \[\underset{x\to e+\pi }{\mathop{\lim }}\,\{l(x)+g(x)\}\] is equal to
A) \[9\]
B) \[13\]
C) \[1\]
D) None of these
View Answer play_arrowquestion_answer198) The value of \[\underset{x\to 0}{\mathop{\lim }}\,\frac{{{27}^{x}}-{{9}^{x}}-{{3}^{x}}+1}{\sqrt{5}-\sqrt{4}+\cos x}\] is
A) \[\sqrt{5}\,{{(\log 3)}^{2}}\]
B) \[8\sqrt{5}\,{{(\log 3)}^{2}}\]
C) \[16\sqrt{5}\,(\log 3)\]
D) \[10\sqrt{5}\,{{(\log 3)}^{2}}\]
View Answer play_arrowquestion_answer199) The value of \[\underset{n\to \infty }{\mathop{\lim }}\,\frac{{{x}^{n}}}{{{x}^{n}}+1},\]where \[x<-1\] is
A) \[1/2\]
B) \[-1/2\]
C) \[1\]
D) None of these
View Answer play_arrowquestion_answer200) The value of \[\underset{x\to \pi /2}{\mathop{\lim }}\,\,\frac{{{2}^{\cot \,x}}-{{2}^{\cos \,x}}}{\cot \,x-\,\cos \,x}\]is
A) \[\log \,2\]
B) \[1\]
C) \[2\]
D) None of these
View Answer play_arrowquestion_answer201) The point of discontinuity of tan x is
A) \[x=n\pi \]
B) \[x=n\pi /6\]
C) \[x=(2n+1)\pi /2\]
D) \[x=n\pi /3\]
View Answer play_arrowquestion_answer202) Let \[f(x)=\left\{ \begin{matrix} (1/2)\,\{g(x)+(x)\}\,\,sin\,(x),\,x\ge 1 \\ \sin \,x/x,\,x<1 \\ \end{matrix} \right.\] where \[g(x)=\left\{ \begin{matrix} 1, & if & x>0 \\ -1, & if & x<0 \\ 0, & if & x=0 \\ \end{matrix} \right.\] Then, \[\underset{x\to 1}{\mathop{\lim }}\,\,\,f(x)\] is equal to
A) \[0\]
B) \[2\]
C) \[sin\text{ }1\]
D) None of these
View Answer play_arrowquestion_answer203) The function \[f(x)=\frac{2{{x}^{2}}+7}{{{x}^{3}}+3{{x}^{2}}-x-3}\]is discontinuous for
A) \[x=1\]only
B) \[x=1\] and \[x=-1\]only
C) \[x=1,\,x=-1,\,x=-3\]only
D) \[x=1,\,x=-1,\,x=-3\] and other values of x
View Answer play_arrowquestion_answer204) If \[f(x)=\left\{ \begin{matrix} x, & for & <x<1 \\ 2-x, & for & 1\le x<2 \\ x-(1/2){{x}^{2}}, & for & x=2 \\ \end{matrix} \right.\] Then, \[f'(1)\]is equal to
A) \[-1\]
B) \[1\]
C) \[0\]
D) None of these
View Answer play_arrowquestion_answer205) If \[y={{\cos }^{-1}}\cos (|x|-f(x)),\] where \[f(x)=\left\{ \begin{matrix} 1, & if & x>0 \\ -1, & if & x<0 \\ 0, & if & x=0 \\ \end{matrix} \right.\] Then, \[{{(dy/dx)}_{x=\frac{5\pi }{4}}}\]is equal to
A) \[-1\]
B) \[1\]
C) \[0\]
D) can't be determined
View Answer play_arrowquestion_answer206) If \[{{x}^{m}}{{y}^{n}}={{(x+y)}^{m+n}},\] then \[{{(dy/dx)}_{x=1,\,y=2}}\] is equal to
A) \[1/2\]
B) \[2\]
C) \[2m/n\]
D) \[~m/2n\]
View Answer play_arrowquestion_answer207) The function \[f(x)=2{{x}^{3}}-3{{x}^{2}}+90x+174\] is increasing in the interval
A) \[1/2<x<1\]
B) \[1/2<x<2\]
C) \[3<x<59/4\]
D) \[-\infty <x<\infty \]
View Answer play_arrowquestion_answer208) The equation of the tangent to the curve \[x=2\,{{\cos }^{3}}\theta \] and \[y=3\,{{\sin }^{3}}\theta \] at the point \[\theta =\pi /4\] is
A) \[2x+3y=3\sqrt{2}\]
B) \[2x-3y=3\sqrt{2}\]
C) \[3x+2y=3\sqrt{2}\]
D) \[3x-2y=3\sqrt{2}\]
View Answer play_arrowquestion_answer209) The minimum value of \[4{{e}^{2x}}+9{{e}^{-2x}}\] is
A) \[11\]
B) \[12\]
C) \[10\]
D) \[14\]
View Answer play_arrowquestion_answer210) The point of parabola \[2y={{x}^{2}},\] which is nearest to the point \[(0,\,\,3)\] is
A) \[(\pm 4,\,8)\]
B) \[(\pm 1,1/2)\]
C) \[(\pm 2,2)\]
D) None of these
View Answer play_arrowquestion_answer211) In the mean value theorem \[f(b)-f(a)=(b-a)\,f'(c),\] if \[a=4,\text{ }b=9\]and \[f(x)=\sqrt{x},\] then the value of c is
A) \[8.00\]
B) \[5.25\]
C) \[4.00\]
D) \[6.25\]
View Answer play_arrowquestion_answer212) If x is any arbitrary constant, then \[\int{{{2}^{{{2}^{{{2}^{x}}}}}}}.\,{{2}^{{{2}^{x}}}}.\,{{2}^{x}}\,\,dx\]is equal to
A) \[\frac{\int{{{2}^{{{2}^{x}}}}}\,dx}{{{(In\,\,2)}^{3}}}+c\]
B) \[\frac{\int{{{2}^{{{2}^{{{2}^{x}}}}}}}\,dx}{{{(In\,\,2)}^{3}}}+c\]
C) \[\int{{{2}^{{{2}^{{{2}^{x}}}}}}}\,\,{{(In\,\,2)}^{3}}+c\]
D) None of the above
View Answer play_arrowquestion_answer213) The derivative of function \[f(x)\] is \[{{\tan }^{4}}x\]. If \[f(x)=0,\] then \[\underset{x\to 0}{\mathop{\lim }}\,\frac{f(x)}{x}\]is equal to
A) \[1\]
B) \[0\]
C) \[-1\]
D) none of these
View Answer play_arrowquestion_answer214) The value of \[\int_{1}^{{{e}^{2}}}{\frac{dx}{x{{(1+\log \,x)}^{2}}}}\] is
A) \[2/3\]
B) \[1/3\]
C) \[3/2\]
D) In 2
View Answer play_arrowquestion_answer215) If \[2f(x)-3f(1/x)=x,\] then \[\int_{1}^{2}{f(x)\,\,dx}\] is equal to
A) \[(3/5)\] In 2
B) \[(-3/5)\] (\[1+\]In 2)
C) \[(-3/5)\] In 2
D) None of these
View Answer play_arrowquestion_answer216) If A is the area of the region bounded by the curve \[y=\sqrt{3x+4},\] x-axis and the lines \[x=-1\]and \[x=4\]and B is that area bounded by curve \[{{y}^{2}}=3x+4,\]x axis and the lines \[x=-1\]and \[x=4,\] then \[A:B\]is equal to
A) \[1:1\]
B) \[2:1\]
C) \[1:2\]
D) None of these
View Answer play_arrowquestion_answer217) If c is an arbitrary constant, then the general solution of the differential equation \[ydx-xdy=xy\,\,dx\]is given by
A) \[y=cx{{e}^{-x}}\]
B) \[y=cy{{e}^{-x}}\]
C) \[y+{{e}^{-x}}=cx\]
D) \[y{{e}^{x}}=cx\]
View Answer play_arrowquestion_answer218) The solution of \[dy=\cos \,x(2-y\,\text{cosec x)}\,\text{dx}\]where \[y=\sqrt{2},\] when \[x=\pi /4\] is
A) \[y\sin \,x+\frac{1}{2}\,\text{cosec x}\]
B) \[y=\tan \,(x/2)+\cot (x/2)\]
C) \[y=(1/\sqrt{2})\,\sec \,(x/2)+\sqrt{2}\,\cos \,\,(x/2)\]
D) None of the above
View Answer play_arrowquestion_answer219) The probability that at least one of the event A and B occurs is \[0.6\]. If A and B occur simultaneously with probability \[0.2,\] then \[P(\bar{A})+P(\bar{B})\]is equal to
A) \[0.4\]
B) \[0.8\]
C) \[1.2\]
D) \[1.4\]
View Answer play_arrowquestion_answer220) A die is thrown. If it shows a six, we draw a ball from a bag consisting, if 2 black balls and 6 white balls. If it does not show a six, then we toss a coin. Then, the sample spate of this experiment consists of
A) 13 points
B) 18 points
C) 10 points
D) None of the above
View Answer play_arrowquestion_answer221) The probability of getting a total of at least 6 in the simultaneously throw of three dice is
A) \[6/108\]
B) \[5/27\]
C) \[1/24\]
D) \[103/108\]
View Answer play_arrowquestion_answer222) A sample of a 4 items is drawn at a random without replacement from a lot of 10 items containing 3 defectives. If X denotes the number of defective items in the sample, then \[P(0<X<3)\] is equal to
A) \[3/10\]
B) \[4/5\]
C) \[1/2\]
D) \[1/6\]
View Answer play_arrowquestion_answer223) Two cards are drawn successfully with replacement from a well shuffled deck of 52 cards, then the mean of the number of aces is
A) \[1/13\]
B) \[3/13\]
C) \[2/13\]
D) None of the above
View Answer play_arrowquestion_answer224) An um contains 4 white and 3 red balls. Three balls are drawn with replacement from this um. Then, the standard deviation of the number of red balls drawn is
A) \[6/7\]
B) \[36/49\]
C) \[5/7\]
D) \[25/49\]
View Answer play_arrowquestion_answer225) A and B are two independent events such that \[P(A)=1/2\] and \[P(A)=1/2\] then P (neither A nor B) is equal to
A) \[2/3\]
B) \[1/6\]
C) \[5/6\]
D) \[1/3\]
View Answer play_arrow
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