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) \[1.5\text{ }m{{s}^{-1}}\] done clear
B) \[12\text{ }m{{s}^{-1}}\] done clear
C) \[6\text{ }m{{s}^{-1}}\] done clear
D) \[3\text{ }m{{s}^{-1}}\] done clear
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 done clear
B) perpendicular to the plane of paper and inward done clear
C) towards A done clear
D) towards C done clear
View Answer play_arrowquestion_answer3) Curie - Weiss law is obeyed by iron:
A) at Curie temperature only done clear
B) at all temperatures done clear
C) below Curie temperature done clear
D) above Curie temperature done clear
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 done clear
B) G shows deflection to the left and right but the amplitude steadily decreases done clear
C) G Shows deflection to the left and right with constant amplitude done clear
D) G shows deflection on one side. done clear
View Answer play_arrowquestion_answer5) The dimensional formula for inductance is:
A) \[\left[ M{{L}^{2}}{{T}^{-2}}{{A}^{-2}} \right]\] done clear
B) \[\left[ M{{L}^{2}}T{{A}^{-2}} \right]\] done clear
C) \[\left[ M{{L}^{2}}{{T}^{-1}}{{A}^{-2}} \right]\] done clear
D) \[\left[ M{{L}^{2}}{{T}^{-2}}{{A}^{-1}} \right]\] done clear
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 done clear
B) 4050 done clear
C) 5040 done clear
D) 4960 done clear
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 done clear
B) band emission spectrum done clear
C) continuous emission spectrum done clear
D) line absorption spectrum done clear
View Answer play_arrowquestion_answer8) Heavy water is:
A) compound of deuterium and oxygen done clear
B) water at \[{{4}^{o}}C\] done clear
C) water, in which soap does not lather done clear
D) compound of heavy oxygen and heavy hydrogen done clear
View Answer play_arrowquestion_answer9) The nuclear reactor at Kaiga is a:
A) research reactor done clear
B) fusion reactor done clear
C) breeder reactor done clear
D) power reactor done clear
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 done clear
B) the force is always away from the centre done clear
C) there is no displacement done clear
D) there is no net force done clear
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 done clear
B) 10 done clear
C) 4 done clear
D) 8 done clear
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) \[2:1\] done clear
B) \[3:1\] done clear
C) \[1:3\] done clear
D) \[1:1\] done clear
View Answer play_arrowquestion_answer13) Absorption coefficient of an open window is:
A) 1 done clear
B) 0.25 done clear
C) zero done clear
D) 0.5 done clear
View Answer play_arrowquestion_answer14) The loudness and pitch of a sound note depend on:
A) intensity and velocity done clear
B) frequency and velocity done clear
C) intensity and frequency done clear
D) frequency and number of harmonics done clear
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) \[2:1\] done clear
B) \[4:1\] done clear
C) \[1:1\] done clear
D) \[1:2\] done clear
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) \[{{10}^{6}}\] done clear
B) zero done clear
C) \[4\times {{10}^{6}}\] done clear
D) \[4\times {{10}^{4}}\] done clear
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 done clear
B) 10 done clear
C) 60 done clear
D) 40 done clear
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 done clear
B) 1.2 A done clear
C) 0.9 A done clear
D) 1.5 A done clear
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) \[300\,\pi \] done clear
B) \[3000\,\pi \] done clear
C) \[3\,\pi \] done clear
D) \[30\,\pi \] done clear
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 done clear
B) 10 V done clear
C) 50 V done clear
D) 70 V done clear
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 done clear
B) 0.25 A done clear
C) 2 A done clear
D) 1 A done clear
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 done clear
B) becomes convex towards A done clear
C) either (a) or (b) depending on the size of A with respect to B done clear
D) remains in the initial position done clear
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) \[\sqrt{8}\] done clear
B) \[\sqrt{2/17}\] done clear
C) \[\sqrt{1/8}\] done clear
D) \[\sqrt{32/17}\] done clear
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) \[\pi \] done clear
B) zero done clear
C) \[\pi /3\] done clear
D) \[2\,\pi /3\] done clear
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 done clear
B) 1700 m done clear
C) 340 m done clear
D) 1620 m done clear
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 done clear
B) 2.4 mm done clear
C) 1.2 mm done clear
D) 1.2 cm done clear
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% done clear
B) 20% done clear
C) 80% done clear
D) 89% done clear
View Answer play_arrowquestion_answer28) The emitter - base junction of a transistor is ......... biased while the collector - base junction is ......... biased.
A) forward, forward done clear
B) forward, reverse done clear
C) reverse, forward done clear
D) reverse, reverse done clear
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) done clear
B) done clear
C) done clear
D) done clear
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 done clear
B) \[2\pi {{r}^{2}}E\] done clear
C) \[\pi {{r}^{2}}E\] done clear
D) \[(\pi {{r}^{2}}+\pi {{l}^{2}})\,E\] done clear
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 done clear
B) currents drawn are in the ratio of their resistances done clear
C) both draw the same current done clear
D) A draws more current than B done clear
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 done clear
B) 0.75 m done clear
C) 0.4 m done clear
D) 0.2 m done clear
View Answer play_arrowquestion_answer33) The physical quantity having the same dimensions as Plancks constant h is:
A) linear momentum done clear
B) angular momentum done clear
C) Boltzmann constant done clear
D) force done clear
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 done clear
B) 150 m done clear
C) 100 m done clear
D) 200 m done clear
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) \[3\,\Omega \] done clear
B) \[6\,\Omega \] done clear
C) \[12\,\,\Omega \] done clear
D) \[1.5\,\,\Omega \] done clear
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 done clear
B) 400 nm done clear
C) 500 nm done clear
D) 600 nm done clear
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 done clear
B) white done clear
C) one of the component colours done clear
D) absent done clear
View Answer play_arrowquestion_answer38) H-polaroid is prepared by:
A) orienting herapathite crystal in the same direction in nitrocellulose done clear
B) using thin tourmaline crystals done clear
C) stretching polyvinyl alcohol and then heated with dehydrating agent done clear
D) stretching polyvinyl alcohol and then impregnating with iodine done clear
View Answer play_arrowquestion_answer39) SI unit of permittivity is:
A) \[{{C}^{2}}{{m}^{2}}{{N}^{2}}\] done clear
B) \[{{C}^{2}}{{m}^{-2}}{{N}^{-1}}\] done clear
C) \[{{C}^{2}}{{m}^{2}}{{N}^{-1}}\] done clear
D) \[{{C}^{-1}}{{m}^{2}}{{N}^{-2}}\] done clear
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) \[\frac{1}{2}\mu F\] done clear
B) \[\frac{1}{4}\mu F\] done clear
C) \[\frac{1}{8}\mu F\] done clear
D) \[8\,\mu F\] done clear
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) \[P/2\] done clear
B) \[P/4\] done clear
C) P done clear
D) \[2P\] done clear
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 done clear
B) 50 W UV lamp done clear
C) 50 W IR lamp done clear
D) 10 W IR lamp done clear
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 done clear
B) only central fringe is white, all other fringes are colored done clear
C) all bright fringes become white done clear
D) all bright fringes have colours between violet and red done clear
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) \[n=3\] done clear
B) \[n=4\] done clear
C) \[n=1\] done clear
D) \[n=2\] done clear
View Answer play_arrowquestion_answer45) If M is the atomic mass and A is the mass number, packing fraction is given by:
A) \[\frac{M}{M-A}\] done clear
B) \[\frac{M-A}{A}\] done clear
C) \[\frac{A}{M-A}\] done clear
D) \[\frac{A-M}{A}\] done clear
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 done clear
B) 120 min done clear
C) 20 min done clear
D) 30 mm done clear
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) \[4:1\] done clear
B) \[1:4\] done clear
C) \[8:1\] done clear
D) \[1:8\] done clear
View Answer play_arrowquestion_answer48) Blowing air with open mouth is an example of:
A) isobaric process done clear
B) isochoric process done clear
C) isothermal process done clear
D) adiabatic process. done clear
View Answer play_arrowquestion_answer49) Sound waves in air are always longitudinal because:
A) of the inherent characteristics of sound waves in air done clear
B) air does not have a modulus of rigidity done clear
C) air is a mixture of several gases done clear
D) density of air is very small done clear
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) done clear
B) done clear
C) done clear
D) done clear
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 done clear
B) towards west done clear
C) towards north done clear
D) towards south done clear
View Answer play_arrowquestion_answer52) A bar magnet is equivalent to :
A) torroid carrying current done clear
B) straight conductor carrying current done clear
C) solenoid carrying current done clear
D) circular coil carrying current. done clear
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 done clear
B) 27.2 eV done clear
C) 54.4 eV done clear
D) 13.6 eV done clear
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 done clear
B) 1.60 done clear
C) 0.0615 done clear
D) 0.024 done clear
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) \[1.6\times {{10}^{4}}J\] done clear
B) \[1.2\times {{10}^{4}}J\] done clear
C) \[4.8\times {{10}^{4}}J\] done clear
D) \[3.5\times {{10}^{4}}J\] done clear
View Answer play_arrowquestion_answer56) Which one of the following graphs represents the behaviour of an ideal gas?
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer57) Rainbow is formed due to :
A) total internal reflection done clear
B) scattering done clear
C) refraction done clear
D) dispersion and total internal reflection done clear
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 done clear
B) the focal point shifts towards the lens by a small distance done clear
C) the focal point shifts away from die lens by a small distance done clear
D) the focus remains undisturbed done clear
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 done clear
B) an insulator done clear
C) uncharged done clear
D) charged positively done clear
View Answer play_arrowquestion_answer60) Effective capacitance between A and B in the figure shown is (all capacitances are in \[\mu F\]) :
A) \[\frac{3}{14}\mu F\] done clear
B) \[\frac{14}{3}\mu F\] done clear
C) \[21\,\mu F\] done clear
D) \[23\,\mu F\] done clear
View Answer play_arrowquestion_answer61) Which one of the following is not an amphoteric substance?
A) \[HN{{O}_{3}}\] done clear
B) \[HCO_{3}^{-}\] done clear
C) \[{{H}_{2}}O\] done clear
D) \[N{{H}_{3}}\] done clear
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 done clear
B) 57.3 kJ done clear
C) 573 kJ done clear
D) 573 J done clear
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 done clear
B) 14 done clear
C) 5 done clear
D) 7 done clear
View Answer play_arrowquestion_answer64) Stainless steel does not rust because :
A) chromium and nickel combine with iron done clear
B) chromium forms an oxide layer and protects iron from rusting done clear
C) nickel present in it, does not rust done clear
D) iron forms a hard chemical compound with chromium present in it done clear
View Answer play_arrowquestion_answer65) Which of the following combinations can be used to synthesise ethanol?
A) \[C{{H}_{3}}MgI\] and \[C{{H}_{3}}COC{{H}_{3}}\] done clear
B) \[C{{H}_{3}}MgI\] and \[{{C}_{2}}{{H}_{5}}OH\] done clear
C) \[C{{H}_{3}}MgI\] and \[CH{{H}_{3}}COO{{C}_{2}}{{H}_{5}}\] done clear
D) \[C{{H}_{3}}MgI\] and \[HCOO{{C}_{2}}{{H}_{5}}\] done clear
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 done clear
B) 2 N done clear
C) 4 N done clear
D) 8 N done clear
View Answer play_arrowquestion_answer67) Nuclear theory of the atom was put forward by:
A) Rutherford done clear
B) Aston done clear
C) Neils Bohr done clear
D) J.J. Thomson done clear
View Answer play_arrowquestion_answer68) In acetylene molecule, the two carbon atoms are linked by :
A) one sigma-bond and two pi-bonds done clear
B) two sigma-bonds and one pi-bond done clear
C) three sigma-bonds done clear
D) three pi-bonds done clear
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) \[\Delta {{H}_{1}}<\Delta {{H}_{2}}\] done clear
B) \[\Delta {{H}_{1}}+\Delta {{H}_{2}}=0\] done clear
C) \[\Delta {{H}_{1}}>\Delta {{H}_{2}}\] done clear
D) \[\Delta {{H}_{1}}=\Delta {{H}_{2}}\] done clear
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 done clear
B) 48 min done clear
C) 12 min done clear
D) 24 min done clear
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) \[2\text{ }d{{m}^{3}}\] done clear
B) \[3\text{ }d{{m}^{3}}\] done clear
C) \[4\text{ }d{{m}^{3}}\] done clear
D) \[8\text{ }d{{m}^{3}}\] done clear
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 done clear
B) 32 done clear
C) 12 done clear
D) 20 done clear
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 done clear
B) Increasing the pressure done clear
C) Reducing the temperature done clear
D) Removing ammonia as it is formed done clear
View Answer play_arrowquestion_answer74) The chemical equilibrium of a reversible reaction is not influenced by :
A) pressure done clear
B) catalyst done clear
C) concentration of the reactants done clear
D) temperature done clear
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 done clear
B) ethyl benzene done clear
C) vinyl benzene done clear
D) propyl benzene done clear
View Answer play_arrowquestion_answer76) The reagent which does not give acid chloride on treating with a carboxylic acid is :
A) \[PC{{l}_{5}}\] done clear
B) \[C{{l}_{2}}\] done clear
C) \[SOC{{l}_{2}}\] done clear
D) \[PC{{l}_{3}}\] done clear
View Answer play_arrowquestion_answer77) Among the halogens, the one which is oxidised by nitric acid is :
A) fluorine done clear
B) iodine done clear
C) chlorine done clear
D) bromine done clear
View Answer play_arrowquestion_answer78) The metal which does not form ammonium nitrate by reaction with dilute nitric acid is :
A) \[Al\] done clear
B) Fe done clear
C) Pb done clear
D) Mg done clear
View Answer play_arrowquestion_answer79) The elements with atomic numbers 9, 17, 35, 53, 85 are all :
A) noble gases done clear
B) halogens done clear
C) heavy metals done clear
D) light metals done clear
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 done clear
B) protect aluminium produced from oxygen done clear
C) dissolve bauxite and render it conductor of electricity done clear
D) lower the melting point of bauxite done clear
View Answer play_arrowquestion_answer81) The number of 2p electrons having spin quantum number \[s=-1/2\] are :
A) 6 done clear
B) 0 done clear
C) 2 done clear
D) 3 done clear
View Answer play_arrowquestion_answer82) Pick out the alkane which differs from the other members of the group:
A) 2,2-dimethyl propane done clear
B) pentane done clear
C) 2-methyl butane done clear
D) 2,2-dimethyl butane done clear
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 done clear
B) 2, 2, 1 done clear
C) 1, 1, 2 done clear
D) 2, 1, 2 done clear
View Answer play_arrowquestion_answer84) A process is taking place at constant temperature and pressure. Then:
A) \[\Delta H=\Delta E\] done clear
B) \[\Delta H=T\Delta S\] done clear
C) \[\Delta H=0\] done clear
D) \[\Delta S=0\] done clear
View Answer play_arrowquestion_answer85) In a galvanic cell, the electrons flow from:
A) anode to cathode through the solution done clear
B) cathode to anode through the solution done clear
C) anode to cathode through the external circuit done clear
D) cathode to anode through the external circuit done clear
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 done clear
B) 1 : 4 done clear
C) 4 : 1 done clear
D) 8 : 1 done clear
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 done clear
B) decreases by one done clear
C) decreases ten fold done clear
D) increases ten fold done clear
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 done clear
B) ethanol done clear
C) methanol done clear
D) methanol done clear
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 done clear
B) soda lime and zinc dust done clear
C) zinc dust and sodium hydroxide done clear
D) soda lime and copper done clear
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 done clear
B) ethyl formate done clear
C) ethyl acetate done clear
D) methyl acetate done clear
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 done clear
B) benzamide done clear
C) acetamide done clear
D) nitrobenzene done clear
View Answer play_arrowquestion_answer92) The silver salt of a fatty acid on refluxing with an alkyl halide gives an :
A) acid done clear
B) ester done clear
C) ether done clear
D) amine done clear
View Answer play_arrowquestion_answer93) Pick out the one which does not belong to the family:
A) pepsin done clear
B) cellulose done clear
C) ptyalin done clear
D) lipase done clear
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 done clear
B) Hydrolysis of\[C{{H}_{3}}COOC{{H}_{3}}\] - pseudo animalcular done clear
C) Decomposition\[{{H}_{2}}{{O}_{2}}\] - first order rof reaction done clear
D) Combination of \[{{H}_{2}}\]and \[B{{r}_{2}}\] to give HBr - first order reaction done clear
View Answer play_arrowquestion_answer95) The diameter of colloidal particles range from:
A) \[{{10}^{-6}}\,m\] to \[{{10}^{-9}}\,m\] done clear
B) \[{{10}^{-9}}\,m\] to \[{{10}^{-12}}\,m\] done clear
C) \[{{10}^{-3}}\,m\] to \[{{10}^{-3}}\,m\] done clear
D) \[{{10}^{-3}}\,m\] to \[{{10}^{-6}}\,m\] done clear
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 done clear
B) 2-chloropropane and chloroethane done clear
C) chloromethane and chloroethane done clear
D) chloromethane and 1-chloropropane done clear
View Answer play_arrowquestion_answer97) Which of the following statements about benzyl chloride is incorrect?
A) It is less reactive than alkyl halides done clear
B) It can be oxidised to benzaldehyde by boiling with copper nitrate solution done clear
C) It is a lachrymatory liquid and answers Beilsteins test done clear
D) It gives a white precipitate with alcoholic silver nitrate done clear
View Answer play_arrowquestion_answer98) The main product obtained when a solution of sodium carbonate reacts with mercuric chloride is :
A) \[Hg{{(OH)}_{2}}\] done clear
B) \[HgC{{O}_{3}}\,.\,HgO\] done clear
C) \[HgC{{O}_{3}}\] done clear
D) \[HgC{{O}_{3}}\,.\,Hg{{(OH)}_{2}}\] done clear
View Answer play_arrowquestion_answer99) In the electrothermal process, the compound displaced by silica from calcium phosphate is:
A) calcium phosphide done clear
B) phosphine done clear
C) phosphorus done clear
D) - phosphorus pentoxide done clear
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 done clear
B) 278 kJ done clear
C) -890 kJ done clear
D) 178 kJ done clear
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) \[6.4\times {{10}^{-3}}\] done clear
B) \[3.2\times {{10}^{-4}}\] done clear
C) \[9.6\times {{10}^{-3}}\] done clear
D) \[1.28\times {{10}^{-2}}\] done clear
View Answer play_arrowquestion_answer102) Select the \[p{{K}_{a}}\] value of the strongest acid from the following:
A) 1.0 done clear
B) 3.0 done clear
C) 2.0 done clear
D) 4.5 done clear
View Answer play_arrowquestion_answer103) Pick out the unsaturated fatty acid from the following:
A) stearic acid done clear
B) lauric acid done clear
C) oleic acid done clear
D) palmitic acid done clear
View Answer play_arrowquestion_answer104) Nylon is not a:
A) condensation polymer done clear
B) polyamide done clear
C) copolymer done clear
D) homopolymer done clear
View Answer play_arrowquestion_answer105) The coal tar fraction which contains phenol is:
A) middle oil done clear
B) green oil done clear
C) heavy oil done clear
D) light oil done clear
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 done clear
B) 4.0 done clear
C) 2.5 done clear
D) 0.25 done clear
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 done clear
B) they are light done clear
C) they are insoluble done clear
D) they bear electrostatic charge done clear
View Answer play_arrowquestion_answer108) Which of the following statements about amorphous solids is incorrect?
A) They melt over a range of temperature done clear
B) They are anisotropic done clear
C) There is no orderly arrangement of particles done clear
D) They are rigid and incompressible done clear
View Answer play_arrowquestion_answer109) Hydrogen diffuses six times faster than gas A. The molar mass of gas A is:
A) 72 done clear
B) 6 done clear
C) 24 done clear
D) 36 done clear
View Answer play_arrowquestion_answer110) Dulong and Petits law is valid only for:
A) metals done clear
B) non-metals done clear
C) gaseous elements done clear
D) solid elements done clear
View Answer play_arrowquestion_answer111) Identify the gas which is readily adsorbed by activated charcoal:
A) \[{{N}_{2}}\] done clear
B) \[S{{O}_{2}}\] done clear
C) \[{{H}_{2}}\] done clear
D) \[{{O}_{2}}\] done clear
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 done clear
B) X/4 pm done clear
C) X/2 pm done clear
D) 2 X pm done clear
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 done clear
B) In \[{{K}_{3}}\,[Fe{{(CN)}_{6}}]\], the ligand has satisfied both primary and secondary valancies of ferric ion done clear
C) In \[{{K}_{4}}\,[Fe{{(CN)}_{6}}]\] the ligand has satisfied both primary and secondary valancies of ferrous ion done clear
D) In \[[Cu{{(N{{H}_{3}})}_{4}}]S{{O}_{4}}\] the ligand has satisfied only the secondary valency of copper done clear
View Answer play_arrowquestion_answer114) 2-acetoxy benzoic acid is used as an:
A) antimalarial done clear
B) antidepressant done clear
C) antiseptic done clear
D) antipyretic done clear
View Answer play_arrowquestion_answer115) A nucleoside on hydrolysis gives :
A) a heterocyclic base and orthophosphoric acid done clear
B) an aldopentose, a heterocyclic base and orthophosphoric acid done clear
C) an aldopentose and a heterocyclic base done clear
D) an aldopentose and orthophosphoric acid done clear
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: done clear
B) increase the dissociation of \[{{H}_{2}}S\] decrease the dissociation of salt solution done clear
C) decrease the dissociation of \[{{H}_{2}}S\] done clear
D) increase the dissociation of salt solution done clear
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 done clear
B) -3.26 V done clear
C) 3.26 V done clear
D) -1.66 V done clear
View Answer play_arrowquestion_answer118) The first fraction obtained during the fractionation of petroleum is :
A) hydrocarbon gases done clear
B) -kerosene oil done clear
C) gasoline done clear
D) diesel oil done clear
View Answer play_arrowquestion_answer119) Which of the following compounds gives trichloromethane on distilling with bleaching powder?
A) Methanal done clear
B) Phenol done clear
C) Ethanol done clear
D) Methanol done clear
View Answer play_arrowquestion_answer120) Benzoin is:
A) compound containing an aldehyde and a ketonic group done clear
B) \[\alpha \], P-unsaturated acid done clear
C) \[\alpha \]-hydroxy aldehyde done clear
D) \[\alpha \]-hydroxy ketone done clear
View Answer play_arrowquestion_answer121) \[\sim p\wedge q\] is logically equivalent to :
A) \[p\to q\] done clear
B) \[q\to p\] done clear
C) \[\sim (p\to q)\] done clear
D) \[\sim (q\to p)\] done clear
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 done clear
B) If a number is not a prime then it is not odd done clear
C) If a number is not odd then it is not a prime done clear
D) If a number is odd then it is a prime done clear
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) \[\left[ \begin{matrix} 1 & 3 \\ 2 & -1 \\ \end{matrix} \right]\] done clear
B) \[\left[ \begin{matrix} 1 & -3 \\ 2 & -1 \\ \end{matrix} \right]\] done clear
C) \[\left[ \begin{matrix} 2 & 6 \\ 4 & -2 \\ \end{matrix} \right]\] done clear
D) \[\left[ \begin{matrix} 2 & -6 \\ 4 & -2 \\ \end{matrix} \right]\] done clear
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 done clear
B) 0 done clear
C) \[(a-b)(b-c)(c-a)\] done clear
D) \[(a+b)(b+c)(c+a)\] done clear
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) \[441\times 446\times 4510\] done clear
B) 0 done clear
C) -1 done clear
D) 1 done clear
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) \[\vec{a}\] done clear
B) \[2\,\vec{a}\] done clear
C) \[3\,\vec{a}\] done clear
D) \[\vec{0}\] done clear
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) \[\left[ \begin{matrix} \cos 2\theta & -\sin 2\theta \\ \sin 2\theta & \cos 2\theta \\ \end{matrix} \right]\] done clear
B) \[\left[ \begin{matrix} \cos 2\theta & \sin 2\theta \\ \sin 2\theta & -\cos 2\theta \\ \end{matrix} \right]\] done clear
C) \[\left[ \begin{matrix} \cos 2\theta & \sin 2\theta \\ \sin 2\theta & \cos 2\theta \\ \end{matrix} \right]\] done clear
D) \[\left[ \begin{matrix} \cos 2\theta & \sin 2\theta \\ -\sin 2\theta & \cos 2\theta \\ \end{matrix} \right]\] done clear
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) \[\frac{9}{16}\] done clear
B) \[\frac{3}{4}\] done clear
C) \[\frac{3}{2}\] done clear
D) \[\frac{3}{2}\] done clear
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) \[\frac{1}{\sqrt{14}}\] done clear
B) \[\frac{2}{\sqrt{14}}\] done clear
C) \[\sqrt{14}\] done clear
D) \[\frac{-2}{\sqrt{14}}\] done clear
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 done clear
B) 4 done clear
C) 2 done clear
D) 3 done clear
View Answer play_arrowquestion_answer131) The maximum of the function \[3\cos x-4\sin x\] is :
A) 2 done clear
B) 3 done clear
C) 4 done clear
D) 5 done clear
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 done clear
B) - 2 done clear
C) - 3 done clear
D) 2 done clear
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 done clear
B) 2 done clear
C) - 2 done clear
D) - 1 done clear
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) \[-16\text{ }x\] done clear
B) \[16x\] done clear
C) \[x\] done clear
D) \[-x\] done clear
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) \[(a,\,a)\] done clear
B) \[(0,\,a)\] done clear
C) \[(0,0)\] done clear
D) \[(0,0)\] done clear
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) \[\tan y+\cot x=c\] done clear
B) \[\tan y-\cot x=c\] done clear
C) \[\tan x-\cot y=c\] done clear
D) \[\tan x+\cot x=c\] done clear
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 done clear
B) 4 done clear
C) 9 done clear
D) 1 done clear
View Answer play_arrowquestion_answer138) The area enclosed between the curves \[y={{x}^{3}}\] and \[y=\sqrt{x}\] is, (in square units) :
A) \[\frac{5}{3}\] done clear
B) \[\frac{5}{4}\] done clear
C) \[\frac{5}{12}\] done clear
D) \[\frac{12}{5}\] done clear
View Answer play_arrowquestion_answer139) \[\int_{0}^{\pi /8}{{{\cos }^{3}}4\,\theta \,d\,\theta }\] is equal to :
A) \[\frac{5}{3}\] done clear
B) \[\frac{5}{4}\] done clear
C) \[\frac{1}{3}\] done clear
D) \[\frac{1}{6}\] done clear
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 done clear
B) \[\frac{\pi }{2}\] done clear
C) \[\frac{\pi }{4}\] done clear
D) \[\frac{\pi }{6}\] done clear
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 done clear
B) 16 done clear
C) 4 done clear
D) - 4 done clear
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) \[{{x}^{2}}+{{y}^{2}}-4y=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}-4|y|=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}-4x=0\] done clear
D) \[{{x}^{2}}+{{y}^{2}}-4|x|=0\] done clear
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) \[4x-y-4=0\] done clear
B) \[2x+y-8=0\] done clear
C) \[x+y-6=0\] done clear
D) \[x+2y-10=0\] done clear
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 done clear
B) -4 done clear
C) - 6 done clear
D) 8 done clear
View Answer play_arrowquestion_answer145) \[\underset{x\to \frac{\pi }{2}}{\mathop{\lim }}\,\frac{\frac{\pi }{2}-\theta }{\cot \theta }\]
A) 0 done clear
B) - 1 done clear
C) 1 done clear
D) \[\infty \] done clear
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 done clear
B) non intersecting circles done clear
C) touching circles done clear
D) touching or non-intersecting circles done clear
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 done clear
B) 6 done clear
C) 20 done clear
D) \[\sqrt{20}\] done clear
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) \[{{x}^{2}}+12y=72\] done clear
B) \[{{x}^{2}}-12y=72\] done clear
C) \[{{y}^{2}}-12x=72\] done clear
D) \[{{y}^{2}}+12x=72\] done clear
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) \[\frac{2}{5}\] done clear
B) \[\frac{3}{5}\] done clear
C) \[\frac{4}{5}\] done clear
D) \[\frac{1}{5}\] done clear
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 done clear
B) 7 done clear
C) 5 done clear
D) 9 done clear
View Answer play_arrowquestion_answer151) The differential coefficient is \[f(\sin x)\] with respect to \[x\] where \[f(x)=\log \,x\] is :
A) \[\tan x\] done clear
B) \[\cot x\] done clear
C) \[f(\cos x)\] done clear
D) \[\frac{1}{x}\] done clear
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 done clear
B) \[\frac{1}{2}\] done clear
C) \[\frac{1}{4}\] done clear
D) \[-\frac{1}{2}\] done clear
View Answer play_arrowquestion_answer153) If \[\omega =\frac{-1+\sqrt{3}i}{2}\] then \[{{(3+\omega +3{{\omega }^{2}})}^{4}}\] is :
A) 16 done clear
B) - 16 done clear
C) \[16\,\omega \] done clear
D) \[16\,{{\omega }^{2}}\] done clear
View Answer play_arrowquestion_answer154) If \[y={{\tan }^{-1}}(\sec \,x-\tan x)\], then \[\frac{d\,y}{d\,x}\] is equal to:
A) 2 done clear
B) -2 done clear
C) \[\frac{1}{2}\] done clear
D) \[\frac{d\,y}{d\,x}\] done clear
View Answer play_arrowquestion_answer155) If \[x+\frac{1}{x}=2\cos \alpha \] then \[{{x}^{n}}+\frac{1}{{{x}^{n}}}\] is equal to :
A) \[{{2}^{n}}\cos \alpha \] done clear
B) \[{{2}^{n}}\cos n\alpha \] done clear
C) \[2i\sin n\alpha \] done clear
D) \[2\cos \,n\alpha \] done clear
View Answer play_arrowquestion_answer156) \[\int_{-1}^{1}{\,|1-x|\,dx}\] is equal to :
A) -2 done clear
B) 0 done clear
C) 2 done clear
D) 4 done clear
View Answer play_arrowquestion_answer157) \[\int{\frac{d\,x}{x\,({{x}^{7}}+1)}}\] is equal to :
A) \[\log \left( \frac{{{x}^{7}}}{{{x}^{7}}+1} \right)+c\] done clear
B) \[\frac{1}{7}\log \left( \frac{{{x}^{7}}}{{{x}^{7}}+1} \right)+c\] done clear
C) \[\log \left( \frac{{{x}^{7}}+1}{{{x}^{7}}} \right)+c\] done clear
D) \[\frac{1}{7}\log \left( \frac{{{x}^{7}}+1}{{{x}^{7}}} \right)+c\] done clear
View Answer play_arrowquestion_answer158) \[\int{\sqrt{x}\,{{e}^{\sqrt{x}}}}dx\] is equal to :
A) \[2\sqrt{x}\,-{{e}^{\sqrt{x}}}-4\sqrt{x{{e}^{\sqrt{x}}}}+c\] done clear
B) \[(2x-4\sqrt{x}\,+4){{e}^{\sqrt{x}}}+c\] done clear
C) \[(2x+4\sqrt{x}\,+4){{e}^{\sqrt{x}}}+c\] done clear
D) \[(1-4\sqrt{x}){{e}^{\sqrt{x}}}+c\] done clear
View Answer play_arrowquestion_answer159) \[\int{\frac{d\,x}{{{x}^{2}}+2x+2}}\] is equal to :
A) \[{{\sin }^{-1}}(x+1)+c\] done clear
B) \[\sin \,\,{{h}^{-1}}(x+1)+c\] done clear
C) \[\tan \,\,{{h}^{-1}}(x+1)+c\] done clear
D) \[{{\tan }^{-1}}(x+1)+c\] done clear
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) done clear
B) (8, 2) done clear
C) (6, 1) done clear
D) (4, 2) done clear
View Answer play_arrowquestion_answer161) 0.5737373 ... is equal to :
A) \[\frac{284}{497}\] done clear
B) \[\frac{284}{495}\] done clear
C) \[\frac{568}{999}\] done clear
D) \[\frac{567}{990}\] done clear
View Answer play_arrowquestion_answer162) The number of solutions for the equation\[{{x}^{2}}-5\,|x|+6=0\] is :
A) 4 done clear
B) 3 done clear
C) 2 done clear
D) 1 done clear
View Answer play_arrowquestion_answer163) How many numbers of 6 digits can be formed from the digits of the number 112233?
A) 30 done clear
B) 60 done clear
C) 90 done clear
D) 120 done clear
View Answer play_arrowquestion_answer164) The last digit in 7300 is :
A) 7 done clear
B) 9 done clear
C) 1 done clear
D) 3 done clear
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 done clear
B) 1 done clear
C) -1 done clear
D) 2 done clear
View Answer play_arrowquestion_answer166) The smallest positive integer n for which\[{{(1+i)}^{2n}}={{(1-i)}^{2n}}\] is :
A) 1 done clear
B) 2 done clear
C) 3 done clear
D) 4 done clear
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 done clear
B) 1 done clear
C) 2 done clear
D) - 1 done clear
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 done clear
B) 4 done clear
C) 3 done clear
D) 5 done clear
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) \[\frac{\pi }{6}\] done clear
B) \[\frac{\pi }{2}\] done clear
C) \[\frac{\pi }{4}\] done clear
D) \[\frac{3\pi }{4}\] done clear
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) \[{{x}^{2}}+{{y}^{2}}=16\] done clear
B) \[{{x}^{2}}+{{y}^{2}}=4\] done clear
C) \[{{x}^{2}}+{{y}^{2}}=20\] done clear
D) \[{{x}^{2}}+{{y}^{2}}=12\] done clear
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 done clear
B) 0 done clear
C) -1 done clear
D) 2 done clear
View Answer play_arrowquestion_answer172) The circle \[{{x}^{2}}+{{y}^{2}}-8x+4y+4=0\] touches :
A) x-axis done clear
B) y-axis done clear
C) both axis done clear
D) neither .y-axis nor y-axis done clear
View Answer play_arrowquestion_answer173) Which of the following is true?
A) The set of all fourth roots of unity is a multiplicative group done clear
B) The set of all cube roots of unity is an additive group done clear
C) \[{{(ab)}^{-1}}={{a}^{-1}}{{b}^{-1}}\] for all a, b in any group G done clear
D) If \[{{(ab)}^{2}}={{a}^{2}}{{b}^{2}}\] for all a, b in any group G, then the group G is non abelian done clear
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 done clear
B) The set of all integers under multiplication done clear
C) The set of all non zero rational numbers under multiplication done clear
D) The set of all integers under addition done clear
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) \[\frac{10}{3}\] done clear
B) \[-\frac{8}{3}\] done clear
C) \[-\frac{10}{3}\] done clear
D) \[\frac{8}{3}\] done clear
View Answer play_arrowquestion_answer176) \[\underset{x\to \infty }{\mathop{\lim }}\,{{\left( 1-\frac{4}{x-1} \right)}^{3x-1}}\] is equal to :
A) \[{{e}^{12}}\] done clear
B) \[{{e}^{-12}}\] done clear
C) \[{{e}^{4}}\] done clear
D) \[{{e}^{3}}\] done clear
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 done clear
B) 1 done clear
C) 2 done clear
D) 3 done clear
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) \[\pi \] done clear
B) \[2\,\pi \] done clear
C) \[4\,\pi \] done clear
D) \[6\,\pi \] done clear
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 done clear
B) 2 done clear
C) 3 done clear
D) 0 done clear
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 done clear
B) onto only done clear
C) both one-one and onto done clear
D) neither one-one nor onto done clear
View Answer play_arrow
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