question_answer1) The difference between the apparent frequency of a source of sound as perceived by the observer during its approach and recession is 2% of the frequency of the source. If the speed of sound in air is 300 ms-1, the velocity of the source is:
A) \[1.5\text{ }m{{s}^{-1}}\]
B) \[12\text{ }m{{s}^{-1}}\]
C) \[6\text{ }m{{s}^{-1}}\]
D) \[3\text{ }m{{s}^{-1}}\]
View Answer play_arrowquestion_answer2) Three long straight wires A, B and C are carrying currents as shown in figure. Then the resultant force on B is directed:
A) perpendicular to the plane of paper and outward
B) perpendicular to the plane of paper and inward
C) towards A
D) towards C
View Answer play_arrowquestion_answer3) Curie - Weiss law is obeyed by iron:
A) at Curie temperature only
B) at all temperatures
C) below Curie temperature
D) above Curie temperature
View Answer play_arrowquestion_answer4) A magnet N-S is suspended from a spring and when it oscillates, the magnet moves in and out of the coil C. The coil is connected to a galvanometer G. Then, as the magnet oscillates:
A) G shows no deflection
B) G shows deflection to the left and right but the amplitude steadily decreases
C) G Shows deflection to the left and right with constant amplitude
D) G shows deflection on one side.
View Answer play_arrowquestion_answer5) The dimensional formula for inductance is:
A) \[\left[ M{{L}^{2}}{{T}^{-2}}{{A}^{-2}} \right]\]
B) \[\left[ M{{L}^{2}}T{{A}^{-2}} \right]\]
C) \[\left[ M{{L}^{2}}{{T}^{-1}}{{A}^{-2}} \right]\]
D) \[\left[ M{{L}^{2}}{{T}^{-2}}{{A}^{-1}} \right]\]
View Answer play_arrowquestion_answer6) The maximum current that can be measured by a galvanometer of resistance \[40\,\,\Omega \], is 10 mA. It is converted into a voltmeter that can read upto 50 V. The resistance to be connected in series with the galvanometer (in ohms) is:
A) 2010
B) 4050
C) 5040
D) 4960
View Answer play_arrowquestion_answer7) The spectrum obtained from the chromosphere of the sun at the time of total solar eclipse is:
A) line emission spectrum
B) band emission spectrum
C) continuous emission spectrum
D) line absorption spectrum
View Answer play_arrowquestion_answer8) Heavy water is:
A) compound of deuterium and oxygen
B) water at \[{{4}^{o}}C\]
C) water, in which soap does not lather
D) compound of heavy oxygen and heavy hydrogen
View Answer play_arrowquestion_answer9) The nuclear reactor at Kaiga is a:
A) research reactor
B) fusion reactor
C) breeder reactor
D) power reactor
View Answer play_arrowquestion_answer10) When a body moves in a circular path, no work is done by the force since:
A) force and displacement are perpendicular to each other
B) the force is always away from the centre
C) there is no displacement
D) there is no net force
View Answer play_arrowquestion_answer11) A bullet moving with a speed of \[100\text{ }m{{s}^{-1}}\] can just penetrate two planks of equal thickness. Then, the number of such planks penetrated by the same bullet when the speed is doubled will be:
A) 6
B) 10
C) 4
D) 8
View Answer play_arrowquestion_answer12) Two bodies of masses 1 kg and 2 kg have equal momentum. Then, the ratio of their kinetic energies is:
A) \[2:1\]
B) \[3:1\]
C) \[1:3\]
D) \[1:1\]
View Answer play_arrowquestion_answer13) Absorption coefficient of an open window is:
A) 1
B) 0.25
C) zero
D) 0.5
View Answer play_arrowquestion_answer14) The loudness and pitch of a sound note depend on:
A) intensity and velocity
B) frequency and velocity
C) intensity and frequency
D) frequency and number of harmonics
View Answer play_arrowquestion_answer15) In Meldes experiment in the transverse mode, the frequency of the tuning fork and the frequency of the waves in the string are in the ratio:
A) \[2:1\]
B) \[4:1\]
C) \[1:1\]
D) \[1:2\]
View Answer play_arrowquestion_answer16) An electron is accelerated through a potential difference of 45.5 volt. The velocity acquired by it is (in \[m{{s}^{-1}}\]):
A) \[{{10}^{6}}\]
B) zero
C) \[4\times {{10}^{6}}\]
D) \[4\times {{10}^{4}}\]
View Answer play_arrowquestion_answer17) An unknown resistance R1 is connected in series with a resistance of \[10\,\Omega \]. This combination is connected to one gap a metre bridge while a resistance \[{{R}_{2}}\] is connected in the other gap. The balance point is at 50 cm. Now, when the \[10\,\Omega \] resistance is removed the balance point shifts to 40 cm. The value of \[{{R}_{1}}\] is (in ohms):
A) 20
B) 10
C) 60
D) 40
View Answer play_arrowquestion_answer18) In the circuit shown, the internal resistance 3f the cell is negligible. The steady state current in the \[2\,\Omega \] resistor is:
A) 0.6 A
B) 1.2 A
C) 0.9 A
D) 1.5 A
View Answer play_arrowquestion_answer19) A rectangular coil of 300 turns has an average area of \[25\text{ }cm\times 10\text{ }cm\]. The coil rotates with a speed of 50 cps in uniform magnetic field of strength \[4\times {{10}^{-2}}T\]about an axis perpendicular to the field. The peak value of the induced emf is (in volt)
A) \[300\,\pi \]
B) \[3000\,\pi \]
C) \[3\,\pi \]
D) \[30\,\pi \]
View Answer play_arrowquestion_answer20) In an LCR circuit the potential difference between the terminals of the inductance is 60 V, between the terminals of the capacitor is 30 V and that between the terminals of resistance is 40 V. The supply voltage will be equal to:
A) 130 V
B) 10 V
C) 50 V
D) 70 V
View Answer play_arrowquestion_answer21) A vertical circular coil of radius 0.1 m and having 10 turns carries a steady current. When the plane of the coil is normal to the magnetic meridian, a neutral point is observed at the centre of the coil. If\[{{B}_{H}}=0.314\times {{10}^{-4}}T\], the current in the coil is:
A) 0.5 A
B) 0.25 A
C) 2 A
D) 1 A
View Answer play_arrowquestion_answer22) A thread is tied slightly loose to a wire frame as in figure and the frame is dipped into a soap solution and taken out. The frame is completely covered with the film. When the portion A is punctured with a pin, the thread:
A) becomes concave towards A
B) becomes convex towards A
C) either (a) or (b) depending on the size of A with respect to B
D) remains in the initial position
View Answer play_arrowquestion_answer23) Oxygen is 16 times heavier than hydrogen. Equal volumes of hydrogen and oxygen are mixed. The ratio of speed of sound in the mixture to that in hydrogen is:
A) \[\sqrt{8}\]
B) \[\sqrt{2/17}\]
C) \[\sqrt{1/8}\]
D) \[\sqrt{32/17}\]
View Answer play_arrowquestion_answer24) If two waves of the same frequency and amplitude respectively on superposition produce a resultant disturbance of the same amplitude, the waves differ in phase by:
A) \[\pi \]
B) zero
C) \[\pi /3\]
D) \[2\,\pi /3\]
View Answer play_arrowquestion_answer25) A man, standing between two cliffs, claps his hands and starts hearing a series of echoes at intervals of one second. If the speed of sound in air is \[340\,m{{s}^{-1}}\], the distance between the cliffs is:
A) 680 m
B) 1700 m
C) 340 m
D) 1620 m
View Answer play_arrowquestion_answer26) A beam of light of wavelength 600 nm from a source falls on a single slit 1 mm wide and the resulting diffraction pattern is observed on a screen 2 m away. The distance between the first dark fringes on either side of the central bright fringe is:
A) 2.4 cm
B) 2.4 mm
C) 1.2 mm
D) 1.2 cm
View Answer play_arrowquestion_answer27) Specific rotation of sugar solution is units. \[200\text{ }kg{{m}^{-3}}\] of impure sugar solution is taken in a polarimeter tube of length 0.25 m and an optical rotation of 0.4 rad is observed. The percentage of purity of sugar in the sample is:
A) 11%
B) 20%
C) 80%
D) 89%
View Answer play_arrowquestion_answer28) The emitter - base junction of a transistor is ......... biased while the collector - base junction is ......... biased.
A) forward, forward
B) forward, reverse
C) reverse, forward
D) reverse, reverse
View Answer play_arrowquestion_answer29) In a forward biased p-n junction diode, the potential barrier in the depletion region is of the form:
A)
B)
C)
D)
View Answer play_arrowquestion_answer30) A cylinder of radius r and length \[l\] is placed in an uniform electric field E parallel to the axis of the cylinder. The total flux for the surface of the cylinder is given by:
A) zero
B) \[2\pi {{r}^{2}}E\]
C) \[\pi {{r}^{2}}E\]
D) \[(\pi {{r}^{2}}+\pi {{l}^{2}})\,E\]
View Answer play_arrowquestion_answer31) Two electric bulbs A and B are rated as 60 W and 100 W. They are connected in parallel to the same source. Then:
A) B draws more current than A
B) currents drawn are in the ratio of their resistances
C) both draw the same current
D) A draws more current than B
View Answer play_arrowquestion_answer32) A thin plano-convex lens acts like a concave mirror of focal length 0.2 m when silvered from its plane surface. The refractive index of the material of the lens is 1.5. The radius of curvature of the convex surface of the lens will be:
A) 0.1 m
B) 0.75 m
C) 0.4 m
D) 0.2 m
View Answer play_arrowquestion_answer33) The physical quantity having the same dimensions as Plancks constant h is:
A) linear momentum
B) angular momentum
C) Boltzmann constant
D) force
View Answer play_arrowquestion_answer34) A balloon is rising vertically up with a velocity of \[29\text{ }m{{s}^{-1}}\]. A stone is dropped from it and it reaches the ground in 10 seconds. The height of the balloon when the stone was dropped from it is \[(g=9.8\text{ }m{{s}^{-1}})\]:
A) 400 m
B) 150 m
C) 100 m
D) 200 m
View Answer play_arrowquestion_answer35) A wire has a resistance of \[6\,\Omega \]. It is cut into two parts and both half values are connected in parallel. The new resistance is:
A) \[3\,\Omega \]
B) \[6\,\Omega \]
C) \[12\,\,\Omega \]
D) \[1.5\,\,\Omega \]
View Answer play_arrowquestion_answer36) In a Youngs double slit experiment, the separation between the two slits is 0.9 mm and the fringes are observed one metre away. If it produces the second dark fringe at a distance of 1 mm from the central fringe, the wavelength of the monochromatic source of light used is:
A) 450 nm
B) 400 nm
C) 500 nm
D) 600 nm
View Answer play_arrowquestion_answer37) When light is incident on a diffraction grating, the zero order principal maximum will be:
A) spectrum of the colours
B) white
C) one of the component colours
D) absent
View Answer play_arrowquestion_answer38) H-polaroid is prepared by:
A) orienting herapathite crystal in the same direction in nitrocellulose
B) using thin tourmaline crystals
C) stretching polyvinyl alcohol and then heated with dehydrating agent
D) stretching polyvinyl alcohol and then impregnating with iodine
View Answer play_arrowquestion_answer39) SI unit of permittivity is:
A) \[{{C}^{2}}{{m}^{2}}{{N}^{2}}\]
B) \[{{C}^{2}}{{m}^{-2}}{{N}^{-1}}\]
C) \[{{C}^{2}}{{m}^{2}}{{N}^{-1}}\]
D) \[{{C}^{-1}}{{m}^{2}}{{N}^{-2}}\]
View Answer play_arrowquestion_answer40) A spherical drop of capacitance \[1\,\mu F\] is broken into eight drops of equal radius. Then, the capacitance of each small drop is:
A) \[\frac{1}{2}\mu F\]
B) \[\frac{1}{4}\mu F\]
C) \[\frac{1}{8}\mu F\]
D) \[8\,\mu F\]
View Answer play_arrowquestion_answer41) Two equal forces (P each) act at a point inclined to each other at an angle of \[{{120}^{o}}\]. The magnitude of their resultant is:
A) \[P/2\]
B) \[P/4\]
C) P
D) \[2P\]
View Answer play_arrowquestion_answer42) Threshold wavelength for photoelectric emission from a metal surface is \[5200\text{ }\overset{o}{\mathop{A}}\,\]. Photoelectrons will be emitted when this surface is illuminated with monochromatic radiation from:
A) 1 W IR lamp
B) 50 W UV lamp
C) 50 W IR lamp
D) 10 W IR lamp
View Answer play_arrowquestion_answer43) In Youngs double slit experiment if monochromatic light used is replaced by white light, then:
A) no fringes are observed
B) only central fringe is white, all other fringes are colored
C) all bright fringes become white
D) all bright fringes have colours between violet and red
View Answer play_arrowquestion_answer44) Which state of triply ionised Beryllium \[(B{{e}^{+++}})\] has the same orbital radius as that of the ground state of hydrogen?
A) \[n=3\]
B) \[n=4\]
C) \[n=1\]
D) \[n=2\]
View Answer play_arrowquestion_answer45) If M is the atomic mass and A is the mass number, packing fraction is given by:
A) \[\frac{M}{M-A}\]
B) \[\frac{M-A}{A}\]
C) \[\frac{A}{M-A}\]
D) \[\frac{A-M}{A}\]
View Answer play_arrowquestion_answer46) A count rate meter shows a count of 240 per minute from a given radioactive source. One hour later the meter shows a count rate of 30 per minute. The half-life of the source is:
A) 80 min
B) 120 min
C) 20 min
D) 30 mm
View Answer play_arrowquestion_answer47) Two conductors of the same material have their diameters in the ratio \[1:2\] and their lengths in the ratio \[2:1\]. If the temperature difference between their ends is the same, then the ratio of amounts of heat conducted per second through them will be:
A) \[4:1\]
B) \[1:4\]
C) \[8:1\]
D) \[1:8\]
View Answer play_arrowquestion_answer48) Blowing air with open mouth is an example of:
A) isobaric process
B) isochoric process
C) isothermal process
D) adiabatic process.
View Answer play_arrowquestion_answer49) Sound waves in air are always longitudinal because:
A) of the inherent characteristics of sound waves in air
B) air does not have a modulus of rigidity
C) air is a mixture of several gases
D) density of air is very small
View Answer play_arrowquestion_answer50) An uncharged sphere of metal is placed inside a charged parallel plate capacitor. The lines of force will look like:
A)
B)
C)
D)
View Answer play_arrowquestion_answer51) A current flows in a conductor from east to west. The direction of the magnetic field at a point above the conductor is :
A) towards east
B) towards west
C) towards north
D) towards south
View Answer play_arrowquestion_answer52) A bar magnet is equivalent to :
A) torroid carrying current
B) straight conductor carrying current
C) solenoid carrying current
D) circular coil carrying current.
View Answer play_arrowquestion_answer53) Excitation energy of a hydrogen like ion in its first excitation state is 40.8 eV. Energy needed to remove the electron from the ion in ground state is :
A) 40.8 eV
B) 27.2 eV
C) 54.4 eV
D) 13.6 eV
View Answer play_arrowquestion_answer54) The refractive index of a particular material is 1.67 for blue light, 1.65 for yellow light and 1.63 for red light. The dispersive power of the material is :
A) 0.031
B) 1.60
C) 0.0615
D) 0.024
View Answer play_arrowquestion_answer55) An ideal gas heat engine operates in a Carnots cycle between \[{{227}^{o}}C\] and \[{{127}^{o}}C\]. It absorbs \[6\times {{10}^{4}}J\] at high temperature. The amount of heat converted into work is :
A) \[1.6\times {{10}^{4}}J\]
B) \[1.2\times {{10}^{4}}J\]
C) \[4.8\times {{10}^{4}}J\]
D) \[3.5\times {{10}^{4}}J\]
View Answer play_arrowquestion_answer56) Which one of the following graphs represents the behaviour of an ideal gas?
A)
B)
C)
D)
View Answer play_arrowquestion_answer57) Rainbow is formed due to :
A) total internal reflection
B) scattering
C) refraction
D) dispersion and total internal reflection
View Answer play_arrowquestion_answer58) A beam of parallel rays is brought to focus by a plano-convex lens. A thin concave lens of the same focal length is joined to the first lens. The effect of this is :
A) the focus shifts to infinity
B) the focal point shifts towards the lens by a small distance
C) the focal point shifts away from die lens by a small distance
D) the focus remains undisturbed
View Answer play_arrowquestion_answer59) When a body is earth connected, electrons from the earth flow into the body. This means the body is :
A) charged negatively
B) an insulator
C) uncharged
D) charged positively
View Answer play_arrowquestion_answer60) Effective capacitance between A and B in the figure shown is (all capacitances are in \[\mu F\]) :
A) \[\frac{3}{14}\mu F\]
B) \[\frac{14}{3}\mu F\]
C) \[21\,\mu F\]
D) \[23\,\mu F\]
View Answer play_arrowquestion_answer61) Which one of the following is not an amphoteric substance?
A) \[HN{{O}_{3}}\]
B) \[HCO_{3}^{-}\]
C) \[{{H}_{2}}O\]
D) \[N{{H}_{3}}\]
View Answer play_arrowquestion_answer62) When \[50\text{ }c{{m}^{3}}\] of \[0.2\,N\,{{H}_{2}}S{{O}_{4}}\] is mixed with \[50\,\,c{{m}^{3}}\] of 1 N KOH, the heat liberated is:
A) 11.46 kJ
B) 57.3 kJ
C) 573 kJ
D) 573 J
View Answer play_arrowquestion_answer63) An artificial radioactive isotope gave 7 N after two successive P-particle emissions. The number of neutrons in the parent nucleus must be:
A) 9
B) 14
C) 5
D) 7
View Answer play_arrowquestion_answer64) Stainless steel does not rust because :
A) chromium and nickel combine with iron
B) chromium forms an oxide layer and protects iron from rusting
C) nickel present in it, does not rust
D) iron forms a hard chemical compound with chromium present in it
View Answer play_arrowquestion_answer65) Which of the following combinations can be used to synthesise ethanol?
A) \[C{{H}_{3}}MgI\] and \[C{{H}_{3}}COC{{H}_{3}}\]
B) \[C{{H}_{3}}MgI\] and \[{{C}_{2}}{{H}_{5}}OH\]
C) \[C{{H}_{3}}MgI\] and \[CH{{H}_{3}}COO{{C}_{2}}{{H}_{5}}\]
D) \[C{{H}_{3}}MgI\] and \[HCOO{{C}_{2}}{{H}_{5}}\]
View Answer play_arrowquestion_answer66) A solution contains \[1.2046\times {{10}^{-24}}\] hydrochloric acid molecules in one \[d{{m}^{3}}\] of the solution. The strength of the solution is :
A) 6 N
B) 2 N
C) 4 N
D) 8 N
View Answer play_arrowquestion_answer67) Nuclear theory of the atom was put forward by:
A) Rutherford
B) Aston
C) Neils Bohr
D) J.J. Thomson
View Answer play_arrowquestion_answer68) In acetylene molecule, the two carbon atoms are linked by :
A) one sigma-bond and two pi-bonds
B) two sigma-bonds and one pi-bond
C) three sigma-bonds
D) three pi-bonds
View Answer play_arrowquestion_answer69) The enthalpy of reaction,\[{{H}_{2}}(g)+\frac{1}{2}{{O}_{2}}(g)\to {{H}_{2}}O(g)\] is \[\Delta {{H}_{1}}\] and that of\[{{H}_{{{2}_{(g)}}}}+\frac{1}{2}{{O}_{2}}(g)\to {{H}_{2}}{{O}_{(l)}}\] is \[\Delta {{H}_{2}}\]. Then:
A) \[\Delta {{H}_{1}}<\Delta {{H}_{2}}\]
B) \[\Delta {{H}_{1}}+\Delta {{H}_{2}}=0\]
C) \[\Delta {{H}_{1}}>\Delta {{H}_{2}}\]
D) \[\Delta {{H}_{1}}=\Delta {{H}_{2}}\]
View Answer play_arrowquestion_answer70) A radioactive isotope decays at such a rate that after 192 minutes only 1/16 of the original amount remains :
A) 32 min
B) 48 min
C) 12 min
D) 24 min
View Answer play_arrowquestion_answer71) The pressure and temperature of \[4\text{ }d{{m}^{3}}\] of carbon dioxide gas are doubled. Then the volume of carbon dioxide gas would be :
A) \[2\text{ }d{{m}^{3}}\]
B) \[3\text{ }d{{m}^{3}}\]
C) \[4\text{ }d{{m}^{3}}\]
D) \[8\text{ }d{{m}^{3}}\]
View Answer play_arrowquestion_answer72) 4g of copper was dissolved in concentrated nitric acid. The copper nitrate solution on strong heating gave 5 g of its oxide. The equivalent weight of copper is:
A) 23
B) 32
C) 12
D) 20
View Answer play_arrowquestion_answer73) In the manufacture of ammonia by Habers process,\[{{N}_{2(g)}}+3{{H}_{2}}2N{{H}_{3(g)}}+92.3\,\,kJ\]which of the following conditions is unfavourable?
A) Increasing the temperature
B) Increasing the pressure
C) Reducing the temperature
D) Removing ammonia as it is formed
View Answer play_arrowquestion_answer74) The chemical equilibrium of a reversible reaction is not influenced by :
A) pressure
B) catalyst
C) concentration of the reactants
D) temperature
View Answer play_arrowquestion_answer75) Cumene process is the most important commercial method for the manufacture of phenol. Cumene is :
A) 1-methyl ethyl benzene
B) ethyl benzene
C) vinyl benzene
D) propyl benzene
View Answer play_arrowquestion_answer76) The reagent which does not give acid chloride on treating with a carboxylic acid is :
A) \[PC{{l}_{5}}\]
B) \[C{{l}_{2}}\]
C) \[SOC{{l}_{2}}\]
D) \[PC{{l}_{3}}\]
View Answer play_arrowquestion_answer77) Among the halogens, the one which is oxidised by nitric acid is :
A) fluorine
B) iodine
C) chlorine
D) bromine
View Answer play_arrowquestion_answer78) The metal which does not form ammonium nitrate by reaction with dilute nitric acid is :
A) \[Al\]
B) Fe
C) Pb
D) Mg
View Answer play_arrowquestion_answer79) The elements with atomic numbers 9, 17, 35, 53, 85 are all :
A) noble gases
B) halogens
C) heavy metals
D) light metals
View Answer play_arrowquestion_answer80) In the electrolytic method of obtaining aluminium from purified bauxite, Cryolite is added to the charge in order to :
A) minimise the heat loss due to radiation
B) protect aluminium produced from oxygen
C) dissolve bauxite and render it conductor of electricity
D) lower the melting point of bauxite
View Answer play_arrowquestion_answer81) The number of 2p electrons having spin quantum number \[s=-1/2\] are :
A) 6
B) 0
C) 2
D) 3
View Answer play_arrowquestion_answer82) Pick out the alkane which differs from the other members of the group:
A) 2,2-dimethyl propane
B) pentane
C) 2-methyl butane
D) 2,2-dimethyl butane
View Answer play_arrowquestion_answer83) 56 g of nitrogen and 8g of hydrogen gas are heated in a closed vessel. At equilibrium 34 g of ammonia are present. The equilibrium number of moles of nitrogen, hydrogen and ammonia are respectively:
A) 1, 2, 2
B) 2, 2, 1
C) 1, 1, 2
D) 2, 1, 2
View Answer play_arrowquestion_answer84) A process is taking place at constant temperature and pressure. Then:
A) \[\Delta H=\Delta E\]
B) \[\Delta H=T\Delta S\]
C) \[\Delta H=0\]
D) \[\Delta S=0\]
View Answer play_arrowquestion_answer85) In a galvanic cell, the electrons flow from:
A) anode to cathode through the solution
B) cathode to anode through the solution
C) anode to cathode through the external circuit
D) cathode to anode through the external circuit
View Answer play_arrowquestion_answer86) The reaction, \[2\,S{{O}_{2(g)}}+{{O}_{2(g)}}2S{{O}_{3(g)}}\] is carried out in a \[1\,\,d{{m}^{3}}\] vessel and \[2\,\,d{{m}^{3}}\] vessel separately. The ratio of the reaction velocities will be:
A) 1 : 8
B) 1 : 4
C) 4 : 1
D) 8 : 1
View Answer play_arrowquestion_answer87) In a mixture of acetic acid and sodium acetate the ratio of concentrations of the salt to the acid is increased ten times. Then the pH of the solution :
A) increases by one
B) decreases by one
C) decreases ten fold
D) increases ten fold
View Answer play_arrowquestion_answer88) When a mixture of methane and oxygen is passed through heated molybdenum oxide, the main product formed is :
A) methanoic acid
B) ethanol
C) methanol
D) methanol
View Answer play_arrowquestion_answer89) Benzene can be obtained by heating either benzoic acid with X or phenol with Y.X and Y are respectively:
A) zinc dust and soda lime
B) soda lime and zinc dust
C) zinc dust and sodium hydroxide
D) soda lime and copper
View Answer play_arrowquestion_answer90) An organic compound is boiled with alcoholic potash. The product is cooled and acidified with \[HCl\]. A white solid separates out. The starting compound may be:
A) ethyl benzoate
B) ethyl formate
C) ethyl acetate
D) methyl acetate
View Answer play_arrowquestion_answer91) A nitrogen containing organic compound gave an oily liquid on heating with bromine and potassium hydroxide solution. On shaking the product with acetic anhydride, an antipyretic drug was obtained. The reactions indicate that the starting compound is:
A) aniline
B) benzamide
C) acetamide
D) nitrobenzene
View Answer play_arrowquestion_answer92) The silver salt of a fatty acid on refluxing with an alkyl halide gives an :
A) acid
B) ester
C) ether
D) amine
View Answer play_arrowquestion_answer93) Pick out the one which does not belong to the family:
A) pepsin
B) cellulose
C) ptyalin
D) lipase
View Answer play_arrowquestion_answer94) Which one of the following is wrongly matched?
A) Saponification of\[C{{H}_{3}}COO{{C}_{2}}{{H}_{5}}\] - second order reaction
B) Hydrolysis of\[C{{H}_{3}}COOC{{H}_{3}}\] - pseudo animalcular
C) Decomposition\[{{H}_{2}}{{O}_{2}}\] - first order rof reaction
D) Combination of \[{{H}_{2}}\]and \[B{{r}_{2}}\] to give HBr - first order reaction
View Answer play_arrowquestion_answer95) The diameter of colloidal particles range from:
A) \[{{10}^{-6}}\,m\] to \[{{10}^{-9}}\,m\]
B) \[{{10}^{-9}}\,m\] to \[{{10}^{-12}}\,m\]
C) \[{{10}^{-3}}\,m\] to \[{{10}^{-3}}\,m\]
D) \[{{10}^{-3}}\,m\] to \[{{10}^{-6}}\,m\]
View Answer play_arrowquestion_answer96) On treating a mixture of two alkyl halides with sodium metal in dry ether, 2-methyl propane was obtained. The alkyl halides are :
A) 2-chloropropane and chloromethane
B) 2-chloropropane and chloroethane
C) chloromethane and chloroethane
D) chloromethane and 1-chloropropane
View Answer play_arrowquestion_answer97) Which of the following statements about benzyl chloride is incorrect?
A) It is less reactive than alkyl halides
B) It can be oxidised to benzaldehyde by boiling with copper nitrate solution
C) It is a lachrymatory liquid and answers Beilsteins test
D) It gives a white precipitate with alcoholic silver nitrate
View Answer play_arrowquestion_answer98) The main product obtained when a solution of sodium carbonate reacts with mercuric chloride is :
A) \[Hg{{(OH)}_{2}}\]
B) \[HgC{{O}_{3}}\,.\,HgO\]
C) \[HgC{{O}_{3}}\]
D) \[HgC{{O}_{3}}\,.\,Hg{{(OH)}_{2}}\]
View Answer play_arrowquestion_answer99) In the electrothermal process, the compound displaced by silica from calcium phosphate is:
A) calcium phosphide
B) phosphine
C) phosphorus
D) - phosphorus pentoxide
View Answer play_arrowquestion_answer100) The enthalpy of combustion of methane at \[{{25}^{o}}C\] is 890 kJ. The heat liberated when 3.2 g of methane is burnt is air is :
A) 445 kJ
B) 278 kJ
C) -890 kJ
D) 178 kJ
View Answer play_arrowquestion_answer101) The velocity constant of a reaction at 290 K was found to be \[3.2\times {{10}^{-3}}\,\,{{s}^{-1}}\]. When the temperature is raised to 310 K, it will be about:
A) \[6.4\times {{10}^{-3}}\]
B) \[3.2\times {{10}^{-4}}\]
C) \[9.6\times {{10}^{-3}}\]
D) \[1.28\times {{10}^{-2}}\]
View Answer play_arrowquestion_answer102) Select the \[p{{K}_{a}}\] value of the strongest acid from the following:
A) 1.0
B) 3.0
C) 2.0
D) 4.5
View Answer play_arrowquestion_answer103) Pick out the unsaturated fatty acid from the following:
A) stearic acid
B) lauric acid
C) oleic acid
D) palmitic acid
View Answer play_arrowquestion_answer104) Nylon is not a:
A) condensation polymer
B) polyamide
C) copolymer
D) homopolymer
View Answer play_arrowquestion_answer105) The coal tar fraction which contains phenol is:
A) middle oil
B) green oil
C) heavy oil
D) light oil
View Answer play_arrowquestion_answer106) The compounds A and B are mixed in equimolar proportion to form the products,\[A+BC+D\]. At equilibrium, one third of A and B are consumed. The equilibrium constant for die reaction is:
A) 0.5
B) 4.0
C) 2.5
D) 0.25
View Answer play_arrowquestion_answer107) In froth floatation process for the purification of ores, the particles of ore float because:
A) their surface is not easily wetted by water
B) they are light
C) they are insoluble
D) they bear electrostatic charge
View Answer play_arrowquestion_answer108) Which of the following statements about amorphous solids is incorrect?
A) They melt over a range of temperature
B) They are anisotropic
C) There is no orderly arrangement of particles
D) They are rigid and incompressible
View Answer play_arrowquestion_answer109) Hydrogen diffuses six times faster than gas A. The molar mass of gas A is:
A) 72
B) 6
C) 24
D) 36
View Answer play_arrowquestion_answer110) Dulong and Petits law is valid only for:
A) metals
B) non-metals
C) gaseous elements
D) solid elements
View Answer play_arrowquestion_answer111) Identify the gas which is readily adsorbed by activated charcoal:
A) \[{{N}_{2}}\]
B) \[S{{O}_{2}}\]
C) \[{{H}_{2}}\]
D) \[{{O}_{2}}\]
View Answer play_arrowquestion_answer112) If the distance between \[N{{a}^{+}}\] and \[C{{l}^{-}}\] ions in sodium chloride crystal is X pm, the length of the edge of the unit cell is :
A) 4 X pm
B) X/4 pm
C) X/2 pm
D) 2 X pm
View Answer play_arrowquestion_answer113) Which of the following statements is incorrect?
A) In \[{{K}_{3}}\,[Fe{{(CN)}_{6}}]\], the ligand has satisfied only the secondary valency of ferric ion
B) In \[{{K}_{3}}\,[Fe{{(CN)}_{6}}]\], the ligand has satisfied both primary and secondary valancies of ferric ion
C) In \[{{K}_{4}}\,[Fe{{(CN)}_{6}}]\] the ligand has satisfied both primary and secondary valancies of ferrous ion
D) In \[[Cu{{(N{{H}_{3}})}_{4}}]S{{O}_{4}}\] the ligand has satisfied only the secondary valency of copper
View Answer play_arrowquestion_answer114) 2-acetoxy benzoic acid is used as an:
A) antimalarial
B) antidepressant
C) antiseptic
D) antipyretic
View Answer play_arrowquestion_answer115) A nucleoside on hydrolysis gives :
A) a heterocyclic base and orthophosphoric acid
B) an aldopentose, a heterocyclic base and orthophosphoric acid
C) an aldopentose and a heterocyclic base
D) an aldopentose and orthophosphoric acid
View Answer play_arrowquestion_answer116) In qualitative analysis, in order to detect second group basic radical, \[{{H}_{2}}S\] gas is passed
A) in the presence of dilute \[HCl\] to:
B) increase the dissociation of \[{{H}_{2}}S\] decrease the dissociation of salt solution
C) decrease the dissociation of \[{{H}_{2}}S\]
D) increase the dissociation of salt solution
View Answer play_arrowquestion_answer117) Aluminium displaces hydrogen from dilute \[HCl\] whereas silver does not. The e.m.f. of a cell prepared by combining \[Al/A{{l}^{3+}}\] and \[Ag/A{{g}^{+}}\] is 2.46V. The reduction potential of silver electrode is + 0.80 V. The reduction potential of aluminium electrode is :
A) + 1.66 V
B) -3.26 V
C) 3.26 V
D) -1.66 V
View Answer play_arrowquestion_answer118) The first fraction obtained during the fractionation of petroleum is :
A) hydrocarbon gases
B) -kerosene oil
C) gasoline
D) diesel oil
View Answer play_arrowquestion_answer119) Which of the following compounds gives trichloromethane on distilling with bleaching powder?
A) Methanal
B) Phenol
C) Ethanol
D) Methanol
View Answer play_arrowquestion_answer120) Benzoin is:
A) compound containing an aldehyde and a ketonic group
B) \[\alpha \], P-unsaturated acid
C) \[\alpha \]-hydroxy aldehyde
D) \[\alpha \]-hydroxy ketone
View Answer play_arrowquestion_answer121) \[\sim p\wedge q\] is logically equivalent to :
A) \[p\to q\]
B) \[q\to p\]
C) \[\sim (p\to q)\]
D) \[\sim (q\to p)\]
View Answer play_arrowquestion_answer122) Which of the following is the inverse of the proposition: If a number is a prime then it is odd?
A) If a number is not a prime then it is odd
B) If a number is not a prime then it is not odd
C) If a number is not odd then it is not a prime
D) If a number is odd then it is a prime
View Answer play_arrowquestion_answer123) What must be the matrix X if\[2\,X+\left[ \begin{matrix} 1 & 2 \\ 3 & 4 \\ \end{matrix} \right]=\left[ \begin{matrix} 3 & 8 \\ 7 & 2 \\ \end{matrix} \right]\,\,?\]
A) \[\left[ \begin{matrix} 1 & 3 \\ 2 & -1 \\ \end{matrix} \right]\]
B) \[\left[ \begin{matrix} 1 & -3 \\ 2 & -1 \\ \end{matrix} \right]\]
C) \[\left[ \begin{matrix} 2 & 6 \\ 4 & -2 \\ \end{matrix} \right]\]
D) \[\left[ \begin{matrix} 2 & -6 \\ 4 & -2 \\ \end{matrix} \right]\]
View Answer play_arrowquestion_answer124) The value of be \[\left| \begin{matrix} 1 & 1 & 1 \\ bc & ca & ab \\ b+c & c+a & a+b \\ \end{matrix} \right|\] is :
A) 1
B) 0
C) \[(a-b)(b-c)(c-a)\]
D) \[(a+b)(b+c)(c+a)\]
View Answer play_arrowquestion_answer125) The value of \[\left| \begin{matrix} 441 & 442 & 443 \\ 445 & 446 & 447 \\ 449 & 450 & 451 \\ \end{matrix} \right|\] is :
A) \[441\times 446\times 4510\]
B) 0
C) -1
D) 1
View Answer play_arrowquestion_answer126) \[(\vec{a}.\,\hat{i})\,\hat{i}+(\vec{a}\,.\,\hat{j})\,\hat{j}+\,(\vec{a}\,.\,\hat{k})\,\hat{k}\] is equal to :
A) \[\vec{a}\]
B) \[2\,\vec{a}\]
C) \[3\,\vec{a}\]
D) \[\vec{0}\]
View Answer play_arrowquestion_answer127) Inverse of the matrix \[\left[ \begin{matrix} \cos 2\theta & -\sin 2\theta \\ \sin 2\theta & \cos 2\theta \\ \end{matrix} \right]\] is :
A) \[\left[ \begin{matrix} \cos 2\theta & -\sin 2\theta \\ \sin 2\theta & \cos 2\theta \\ \end{matrix} \right]\]
B) \[\left[ \begin{matrix} \cos 2\theta & \sin 2\theta \\ \sin 2\theta & -\cos 2\theta \\ \end{matrix} \right]\]
C) \[\left[ \begin{matrix} \cos 2\theta & \sin 2\theta \\ \sin 2\theta & \cos 2\theta \\ \end{matrix} \right]\]
D) \[\left[ \begin{matrix} \cos 2\theta & \sin 2\theta \\ -\sin 2\theta & \cos 2\theta \\ \end{matrix} \right]\]
View Answer play_arrowquestion_answer128) If \[|\overrightarrow{a}|=3,\,\,|\overrightarrow{b}|=4\], then a value of \[\lambda \] for which\[\overrightarrow{a}+\lambda ,\overrightarrow{b}\] is perpendicular to \[\overrightarrow{a}-\lambda ,\overrightarrow{b}\] is :
A) \[\frac{9}{16}\]
B) \[\frac{3}{4}\]
C) \[\frac{3}{2}\]
D) \[\frac{3}{2}\]
View Answer play_arrowquestion_answer129) The projection of \[\vec{a}=2\,\hat{i}+3\,\hat{j}-2\hat{k}\] on\[\vec{b}=\,\hat{i}+2\,\hat{j}+3\hat{k}\] is :
A) \[\frac{1}{\sqrt{14}}\]
B) \[\frac{2}{\sqrt{14}}\]
C) \[\sqrt{14}\]
D) \[\frac{-2}{\sqrt{14}}\]
View Answer play_arrowquestion_answer130) In the group ( 1, 2, 3, 4, 5, 6) under multiplication modulo \[7,{{2}^{-1}}\times 4\] is equal to :
A) 1
B) 4
C) 2
D) 3
View Answer play_arrowquestion_answer131) The maximum of the function \[3\cos x-4\sin x\] is :
A) 2
B) 3
C) 4
D) 5
View Answer play_arrowquestion_answer132) If the distance s metres traversed by a particle in t seconds is given by \[s={{t}^{3}}-3{{t}^{2}}\], then the velocity of the particle when the acceleration is zero, in metre/sec, is :
A) 3
B) - 2
C) - 3
D) 2
View Answer play_arrowquestion_answer133) For the curve \[{{y}^{n}}={{a}^{n-1}}\] if the subnormal at any point is a constant then n is equal to :
A) 1
B) 2
C) - 2
D) - 1
View Answer play_arrowquestion_answer134) If \[x=A\cos 4t+B\sin 4t\] then \[\frac{{{d}^{2}}x}{d{{t}^{2}}}\] is equal to :
A) \[-16\text{ }x\]
B) \[16x\]
C) \[x\]
D) \[-x\]
View Answer play_arrowquestion_answer135) If tangent to the curve \[x=a{{t}^{2}},y=2at\] is perpendicular to x-axis, then its point of contact is :
A) \[(a,\,a)\]
B) \[(0,\,a)\]
C) \[(0,0)\]
D) \[(0,0)\]
View Answer play_arrowquestion_answer136) The general solution of the differential equation \[\frac{dy}{dx}+\frac{1+\cos 2y}{1-\cos 2y}=0\] is given by :
A) \[\tan y+\cot x=c\]
B) \[\tan y-\cot x=c\]
C) \[\tan x-\cot y=c\]
D) \[\tan x+\cot x=c\]
View Answer play_arrowquestion_answer137) The degree of the differential equation\[{{\left( 1+{{\left( \frac{dy}{dx} \right)}^{2}} \right)}^{3/4}}={{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{1/3}}\] is:
A) 2
B) 4
C) 9
D) 1
View Answer play_arrowquestion_answer138) The area enclosed between the curves \[y={{x}^{3}}\] and \[y=\sqrt{x}\] is, (in square units) :
A) \[\frac{5}{3}\]
B) \[\frac{5}{4}\]
C) \[\frac{5}{12}\]
D) \[\frac{12}{5}\]
View Answer play_arrowquestion_answer139) \[\int_{0}^{\pi /8}{{{\cos }^{3}}4\,\theta \,d\,\theta }\] is equal to :
A) \[\frac{5}{3}\]
B) \[\frac{5}{4}\]
C) \[\frac{1}{3}\]
D) \[\frac{1}{6}\]
View Answer play_arrowquestion_answer140) \[\int_{0}^{\pi /2}{\frac{\cos x-\sin x}{1+\cos x\sin x}dx}\] is equal to :
A) 0
B) \[\frac{\pi }{2}\]
C) \[\frac{\pi }{4}\]
D) \[\frac{\pi }{6}\]
View Answer play_arrowquestion_answer141) If \[a{{x}^{2}}-{{y}^{2}}+4x-y=0\] represents a pair of lines, then a is equal to :
A) - 16
B) 16
C) 4
D) - 4
View Answer play_arrowquestion_answer142) What is the equation of the locus of a point which moves such that 4 times its distance from the x-axis is the square of its distance from the origin?
A) \[{{x}^{2}}+{{y}^{2}}-4y=0\]
B) \[{{x}^{2}}+{{y}^{2}}-4|y|=0\]
C) \[{{x}^{2}}+{{y}^{2}}-4x=0\]
D) \[{{x}^{2}}+{{y}^{2}}-4|x|=0\]
View Answer play_arrowquestion_answer143) Equation of the straight line making equal intercepts on the axes and passing through the point (2, 4) is :
A) \[4x-y-4=0\]
B) \[2x+y-8=0\]
C) \[x+y-6=0\]
D) \[x+2y-10=0\]
View Answer play_arrowquestion_answer144) If the area of the triangle with vertices \[(x,\text{ }0),\text{ (}1,1\text{)}\] and \[(0,2)\] is 4 square units, then the value of x is :
A) -2
B) -4
C) - 6
D) 8
View Answer play_arrowquestion_answer145) \[\underset{x\to \frac{\pi }{2}}{\mathop{\lim }}\,\frac{\frac{\pi }{2}-\theta }{\cot \theta }\]
A) 0
B) - 1
C) 1
D) \[\infty \]
View Answer play_arrowquestion_answer146) The co-axial system of circles given by\[{{x}^{2}}+{{y}^{2}}+2gx+c=0\] for \[c<0\] represents :
A) intersecting circles
B) non intersecting circles
C) touching circles
D) touching or non-intersecting circles
View Answer play_arrowquestion_answer147) The radius of the circle passing through the point (6, 2) and two of whose diameters are \[x+y=6\] and \[x+2y=4\] is :
A) 4
B) 6
C) 20
D) \[\sqrt{20}\]
View Answer play_arrowquestion_answer148) If (0, 6) and (0, 3) arc respectively the vertex and focus of a parabola, then its equation is :
A) \[{{x}^{2}}+12y=72\]
B) \[{{x}^{2}}-12y=72\]
C) \[{{y}^{2}}-12x=72\]
D) \[{{y}^{2}}+12x=72\]
View Answer play_arrowquestion_answer149) For the ellipse\[24{{x}^{2}}+9{{y}^{2}}-150x-90y+225=0\] the eccentricity e is equal to :
A) \[\frac{2}{5}\]
B) \[\frac{3}{5}\]
C) \[\frac{4}{5}\]
D) \[\frac{1}{5}\]
View Answer play_arrowquestion_answer150) If the foci of the ellipse \[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] and the hyperbola \[\frac{{{x}^{2}}}{144}-\frac{{{y}^{2}}}{81}=\frac{1}{25}\] coincide, then the value of \[{{b}^{2}}\] is :
A) 1
B) 7
C) 5
D) 9
View Answer play_arrowquestion_answer151) The differential coefficient is \[f(\sin x)\] with respect to \[x\] where \[f(x)=\log \,x\] is :
A) \[\tan x\]
B) \[\cot x\]
C) \[f(\cos x)\]
D) \[\frac{1}{x}\]
View Answer play_arrowquestion_answer152) If \[f(x)=\left\{ \frac{1-\cos x}{\begin{align} & x\,\,x=0 \\ & k \\ \end{align}}x\ne 0 \right.\] is continuous at\[x=0\], then the value of k is :
A) 0
B) \[\frac{1}{2}\]
C) \[\frac{1}{4}\]
D) \[-\frac{1}{2}\]
View Answer play_arrowquestion_answer153) If \[\omega =\frac{-1+\sqrt{3}i}{2}\] then \[{{(3+\omega +3{{\omega }^{2}})}^{4}}\] is :
A) 16
B) - 16
C) \[16\,\omega \]
D) \[16\,{{\omega }^{2}}\]
View Answer play_arrowquestion_answer154) If \[y={{\tan }^{-1}}(\sec \,x-\tan x)\], then \[\frac{d\,y}{d\,x}\] is equal to:
A) 2
B) -2
C) \[\frac{1}{2}\]
D) \[\frac{d\,y}{d\,x}\]
View Answer play_arrowquestion_answer155) If \[x+\frac{1}{x}=2\cos \alpha \] then \[{{x}^{n}}+\frac{1}{{{x}^{n}}}\] is equal to :
A) \[{{2}^{n}}\cos \alpha \]
B) \[{{2}^{n}}\cos n\alpha \]
C) \[2i\sin n\alpha \]
D) \[2\cos \,n\alpha \]
View Answer play_arrowquestion_answer156) \[\int_{-1}^{1}{\,|1-x|\,dx}\] is equal to :
A) -2
B) 0
C) 2
D) 4
View Answer play_arrowquestion_answer157) \[\int{\frac{d\,x}{x\,({{x}^{7}}+1)}}\] is equal to :
A) \[\log \left( \frac{{{x}^{7}}}{{{x}^{7}}+1} \right)+c\]
B) \[\frac{1}{7}\log \left( \frac{{{x}^{7}}}{{{x}^{7}}+1} \right)+c\]
C) \[\log \left( \frac{{{x}^{7}}+1}{{{x}^{7}}} \right)+c\]
D) \[\frac{1}{7}\log \left( \frac{{{x}^{7}}+1}{{{x}^{7}}} \right)+c\]
View Answer play_arrowquestion_answer158) \[\int{\sqrt{x}\,{{e}^{\sqrt{x}}}}dx\] is equal to :
A) \[2\sqrt{x}\,-{{e}^{\sqrt{x}}}-4\sqrt{x{{e}^{\sqrt{x}}}}+c\]
B) \[(2x-4\sqrt{x}\,+4){{e}^{\sqrt{x}}}+c\]
C) \[(2x+4\sqrt{x}\,+4){{e}^{\sqrt{x}}}+c\]
D) \[(1-4\sqrt{x}){{e}^{\sqrt{x}}}+c\]
View Answer play_arrowquestion_answer159) \[\int{\frac{d\,x}{{{x}^{2}}+2x+2}}\] is equal to :
A) \[{{\sin }^{-1}}(x+1)+c\]
B) \[\sin \,\,{{h}^{-1}}(x+1)+c\]
C) \[\tan \,\,{{h}^{-1}}(x+1)+c\]
D) \[{{\tan }^{-1}}(x+1)+c\]
View Answer play_arrowquestion_answer160) If a tangent to the curve \[y=6x-{{x}^{2}}\] is parallel to the line \[4x-2y-1=0\], then the point of tangency on the curve is :
A) (2, 8)
B) (8, 2)
C) (6, 1)
D) (4, 2)
View Answer play_arrowquestion_answer161) 0.5737373 ... is equal to :
A) \[\frac{284}{497}\]
B) \[\frac{284}{495}\]
C) \[\frac{568}{999}\]
D) \[\frac{567}{990}\]
View Answer play_arrowquestion_answer162) The number of solutions for the equation\[{{x}^{2}}-5\,|x|+6=0\] is :
A) 4
B) 3
C) 2
D) 1
View Answer play_arrowquestion_answer163) How many numbers of 6 digits can be formed from the digits of the number 112233?
A) 30
B) 60
C) 90
D) 120
View Answer play_arrowquestion_answer164) The last digit in 7300 is :
A) 7
B) 9
C) 1
D) 3
View Answer play_arrowquestion_answer165) If \[\frac{\log x}{a-b}=\frac{\log y}{b-c}=\frac{\log z}{c-a}\], then \[xyz\] is equal to :
A) 0
B) 1
C) -1
D) 2
View Answer play_arrowquestion_answer166) The smallest positive integer n for which\[{{(1+i)}^{2n}}={{(1-i)}^{2n}}\] is :
A) 1
B) 2
C) 3
D) 4
View Answer play_arrowquestion_answer167) If \[{{\cos }^{-1}}p+{{\cos }^{-1}}q+{{\cos }^{-1}}r=\pi \] then\[{{p}^{2}}+{{q}^{2}}+{{r}^{2}}+2pqr\] is equal to :
A) 3
B) 1
C) 2
D) - 1
View Answer play_arrowquestion_answer168) If \[{{\sin }^{-1}}\frac{x}{5}+\cos e{{c}^{-1}}\frac{5}{4}=\frac{\pi }{2}\], then \[x\] is equal to :
A) 1
B) 4
C) 3
D) 5
View Answer play_arrowquestion_answer169) If \[0\le x\le \pi \] and \[{{81}^{{{\sin }^{2}}x}}+{{81}^{{{\cos }^{2}}x}}=30\], then \[x\] is equal to :
A) \[\frac{\pi }{6}\]
B) \[\frac{\pi }{2}\]
C) \[\frac{\pi }{4}\]
D) \[\frac{3\pi }{4}\]
View Answer play_arrowquestion_answer170) The equation of the director circle of the hyperbola \[\frac{{{x}^{2}}}{16}-\frac{{{y}^{2}}}{4}=1\] is given by :
A) \[{{x}^{2}}+{{y}^{2}}=16\]
B) \[{{x}^{2}}+{{y}^{2}}=4\]
C) \[{{x}^{2}}+{{y}^{2}}=20\]
D) \[{{x}^{2}}+{{y}^{2}}=12\]
View Answer play_arrowquestion_answer171) If \[{{Q}_{1}}\] is the set of all relations other than 1 with the binary operation * defined by \[a\,*b=a+b-ab\] for all a, b in \[{{Q}_{1}}\], then the identity in \[{{Q}_{1}}\] with respect to * is :
A) 1
B) 0
C) -1
D) 2
View Answer play_arrowquestion_answer172) The circle \[{{x}^{2}}+{{y}^{2}}-8x+4y+4=0\] touches :
A) x-axis
B) y-axis
C) both axis
D) neither .y-axis nor y-axis
View Answer play_arrowquestion_answer173) Which of the following is true?
A) The set of all fourth roots of unity is a multiplicative group
B) The set of all cube roots of unity is an additive group
C) \[{{(ab)}^{-1}}={{a}^{-1}}{{b}^{-1}}\] for all a, b in any group G
D) If \[{{(ab)}^{2}}={{a}^{2}}{{b}^{2}}\] for all a, b in any group G, then the group G is non abelian
View Answer play_arrowquestion_answer174) The set of all integral multiples of 5 is a subgroup of :
A) The set of all rational numbers under multiplication
B) The set of all integers under multiplication
C) The set of all non zero rational numbers under multiplication
D) The set of all integers under addition
View Answer play_arrowquestion_answer175) The value of \[k\] so that \[{{x}^{2}}+{{y}^{2}}+kx+4y+2=0\] and\[2({{x}^{2}}+{{y}^{2}})-4x-3y+k=0\] cut orthogonally is :
A) \[\frac{10}{3}\]
B) \[-\frac{8}{3}\]
C) \[-\frac{10}{3}\]
D) \[\frac{8}{3}\]
View Answer play_arrowquestion_answer176) \[\underset{x\to \infty }{\mathop{\lim }}\,{{\left( 1-\frac{4}{x-1} \right)}^{3x-1}}\] is equal to :
A) \[{{e}^{12}}\]
B) \[{{e}^{-12}}\]
C) \[{{e}^{4}}\]
D) \[{{e}^{3}}\]
View Answer play_arrowquestion_answer177) If \[A+B+C={{180}^{o}}\] then \[\sum \tan \frac{A}{2}\tan \frac{B}{2}\] is equal to :
A) 0
B) 1
C) 2
D) 3
View Answer play_arrowquestion_answer178) In a triangle ABC if \[b=2,B={{30}^{o}}\] then the area of the circumcircle of triangle ABC in square units is :
A) \[\pi \]
B) \[2\,\pi \]
C) \[4\,\pi \]
D) \[6\,\pi \]
View Answer play_arrowquestion_answer179) If \[\sin x+{{\sin }^{2}}x=1\], then\[{{\cos }^{12}}x+3{{\cos }^{10}}x+3{{\cos }^{8}}x+{{\cos }^{6}}x\] is equal to:
A) 1
B) 2
C) 3
D) 0
View Answer play_arrowquestion_answer180) If R denotes the set of all real number, then the function \[f:R\to R\] defined \[f(x)=|x|\] is :
A) one-one only
B) onto only
C) both one-one and onto
D) neither one-one nor onto
View Answer play_arrow
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