Solved papers for CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2000

done CET - Karnataka Engineering Solved Paper-2000

  • question_answer1) The equation of progressive wave is: \[y=0.2\sin 2\pi \left[ \frac{t}{0.01}-\frac{x}{0.3} \right]\]where\[x\]and\[y\]are in metre and t is in second. The velocity of propagation of the wave is:

    A) 30 m/s

    B) 40 m/s

    C) 300 m/s

    D) 400 m/s

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  • question_answer2) A chimpanzee swinging on a swing in a sitting position, stands up suddenly, the time period will:

    A) become infinite

    B) remain same

    C) increase

    D) decrease

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  • question_answer3) If the ratio of radii of two spheres of same material is 1 : 4 then the ratio of their heat capacities is:

    A) \[\frac{1}{64}\]

    B) \[\frac{1}{32}\]

    C) \[\frac{1}{16}\]

    D) \[\frac{1}{4}\]

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  • question_answer4) Transverse waves can propagate in:

    A) liquids

    B) solids

    C) gases

    D) none of these

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  • question_answer5) A box is lying on an inclined plane what is the coefficient of static friction if the box starts sliding when an angle of inclination is\[{{60}^{o}}\]:

    A) \[1.173\]

    B) \[~1.732\]

    C) \[2.732\]

    D) \[~1.677\]

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  • question_answer6) For which of the following combination of working temperatures, the efficiency of Carnot's engines is highest?

    A)  100 K, 80 K                         

    B)  80 K, 60 K

    C)  60 K, 40 K                             

    D)  40 K, 20 K

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  • question_answer7) Myopia is corrected by:

    A) cylindrical lens

    B) bifocal lens

    C) concave lens

    D) convex lens

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  • question_answer8) On increasing the temperature of a substance gradually, which of the following colours will be noticed by you:

    A) white

    B) yellow

    C) green

    D) red

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  • question_answer9) The relation between \[{{n}_{1}}\]and \[{{n}_{2}},\]if behaviour of light rays is as shown in figure is:

    A) \[{{n}_{1}}>{{n}_{2}}\]

    B) \[{{n}_{2}}>{{n}_{1}}\]

    C) \[{{n}_{1}}>{{n}_{2}}\]

    D) \[{{n}_{1}}={{n}_{2}}\]

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  • question_answer10) An aeroplane is flying with a uniform speed of 100 m/s along a circular path of radius 100 m. The angular speed of the aeroplane will be:

    A) 1 rad/sec

    B) 2 rad/sec

    C) 3 rad/sec

    D) 4 rad/sec

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  • question_answer11) In an A.C. circuit the reactance of a coil is \[\sqrt{3}\] times its resistance, the phase difference between the voltage across the coil to the current through the coil will be:

    A) \[\pi /3\]

    B) \[\pi /2\]

    C) \[\pi /4\]

    D) \[\pi /6\]

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  • question_answer12) \[{{\upsilon }_{1}}\]and\[{{\upsilon }_{2}}\] are the velocities of sound at the same temperature in two monoatomic gases of densities \[{{\rho }_{1}}\]and \[{{\rho }_{2}}\]respectively. If\[{{\rho }_{1}}.{{\rho }_{2}}=\frac{1}{4},\]then the ratio of velocities \[{{\upsilon }_{1}}\]and \[{{\upsilon }_{2}}\]will be:

    A) \[1:2\]

    B) \[4:1\]

    C) \[2:1\]

    D) \[1:4\]

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  • question_answer13) The resistance of a conductor is 5 ohm at\[50{{\,}^{o}}C\] and 6 ohm at \[100{{\,}^{o}}C.\] Its resistance at \[0{{\,}^{o}}C\]is:

    A) 1 ohm

    B) 2 ohm

    C) 3 ohm

    D) 4 ohm

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  • question_answer14) \[n\]identical droplets charged to the same potential\[V\]coalesce to form a single bigger drop. The potential of the new drop will be:

    A) \[nV\]

    B) \[\frac{V}{n}\]

    C) \[{{n}^{2/3}}V\]

    D) \[n{{V}^{2}}\]

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  • question_answer15) If in a wire of Young's modulus Y, longitudinal strain X is produced, then the value of potential energy stored in its unit volume will be:

    A) \[0.5\,Y{{X}^{2}}\]

    B) \[0.5\,{{Y}^{2}}X\]

    C) \[2Y{{X}^{2}}\]

    D) \[Y{{X}^{2}}\]

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  • question_answer16) Light is incident on a glass plate at an angle \[{{60}^{o}},\] the reflected and refracted rays arc mutually perpendicular to each other, then the refractive index of plate will be:

    A) 1.732

    B) 1.5

    C) 1.4

    D) 1.5

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  • question_answer17) A sound source is moving towards a stationary listener with 1/10th of the speed of the sound. The ratio of apparent to real speed will be:

    A) \[{{\left( \frac{11}{10} \right)}^{2}}\]

    B) \[{{\left( \frac{9}{10} \right)}^{2}}\]

    C) \[\frac{10}{9}\]

    D) \[\frac{11}{10}\]

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  • question_answer18) The Young's double slit experiment, the separation between the slits is halved and the distance between slits and screen is doubled. The fringes width will:

    A) remain the same

    B) be quadrupled

    C) be doubled

    D) be halved

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  • question_answer19) A source X of unknown frequency produces 8 beats per second, with a source of 250 Hz and 12 beats per second with a source of 270 Hz. Then the frequency of the source X will be:

    A) 284 Hz

    B) 265 Hz

    C) 258 Hz

    D) 252 Hz

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  • question_answer20) The relation between \[\alpha \] and\[\beta \] parameters of a transistor is given by:

    A) \[\alpha =\frac{1-\beta }{\beta }\]

    B) \[\frac{\beta }{1-\beta }\]

    C) \[\alpha =\frac{1+\beta }{\beta }\]

    D) \[\alpha =\frac{\beta }{1+\beta }\]

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  • question_answer21) A diffraction is obtained by using a beam of red light. What will happen if the red light is replaced by the blue light?

    A) bands will narrower and crowd full together

    B) bands become broader and further apart

    C) no change will take place

    D) bands disappear

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  • question_answer22) After an interval of one day, 1/6th of the initial amount of a radioactive material remains in a sample. Its half life will be:

    A) 2 hour

    B) 3 hour

    C) 6 hour

    D) 12 hour

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  • question_answer23) Two coherent light beams of intensity I and \[\text{4I}\] are superimposed. The maximum and minimum possible intensities in the resulting beam are:

    A) \[9I\]and \[3I\]

    B) \[9I\]and\[I\]

    C) \[5I\]and \[3I\]

    D) \[5I\]and \[I\]

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  • question_answer24) If the energy released in the fission of one nucleus is 200 MeV. Then the number of nuclei required per second in a power plant of 16 kW will be:

    A) \[0.5\times {{10}^{14}}\]

    B) \[0.5\times {{10}^{12}}\]

    C) \[5\times {{10}^{12}}\]

    D) \[5\times {{10}^{14}}\]

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  • question_answer25) Diffraction effects are easier to notice in the case of sound waves than in case of light waves, because the sound waves are:

    A) of longer wavelengths

    B) of shorter wavelengths

    C) longitudinal waves

    D) mechanical waves

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  • question_answer26) If R is the Rydberg's constant for hydrogen the wave number of the first line in the Lyman series will be:

    A) \[\frac{R}{4}\]

    B) \[\frac{3R}{4}\]

    C) \[\frac{R}{2}\]

    D) \[2R\]

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  • question_answer27) The resistance of an ideal ammeter will be:

    A) zero

    B) small

    C) very high

    D) infinite

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  • question_answer28) The energy that should be added to an electron, to reduce its de-Broglie wavelengths from \[{{10}^{-10}}\text{m}\] to\[0.5\times {{10}^{-10}}m,\] will be:

    A) four times the initial energy

    B) thrice the initial energy

    C) equal to the initial energy

    D) twice the initial energy

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  • question_answer29) A cube of side b has a charge q at each of its vertices. The electric field at the centre of the cube is:

    A) \[\frac{2q}{{{b}^{2}}}\]

    B) \[\frac{q}{2{{b}^{2}}}\]

    C) zero

    D) \[\frac{q}{{{b}^{2}}}\]

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  • question_answer30) The magnetic flux linked with a coil, in we bers, is given by the equations \[\text{o }\!\!|\!\!\text{ = 3}{{\text{t}}^{2}}+4t+9.\] Then the magnitude of induced emf at \[t=2\]second will be

    A) 2 volt

    B) 4 volt

    C) 8 volt

    D) 16 volt

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  • question_answer31) A hot wire ammeter reads 10 amp. In an A.C. circuit. The peak value of the current will be:

    A) \[\frac{3}{\pi }\text{amp}\]

    B) \[\frac{10}{\sqrt{2}}\text{amp}\]

    C) \[10\sqrt{2}\,\text{amp}\]

    D) \[6\pi \,\text{amp}\]

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  • question_answer32) A and B are two concentric circular conductors of centre O and carrying currents\[{{i}_{1}}\]and\[{{i}_{2}}\]as shown in the diagram. If ratio of their radii is 1 : 2 and ratio of the flux densities at O due to A and is 1 : 3 then the value of \[\frac{{{i}_{1}}}{{{i}_{2}}}\] will be:

    A) \[\frac{1}{2}\]

    B) \[\frac{1}{3}\]

    C) \[\frac{1}{4}\]

    D) \[\frac{1}{6}\]

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  • question_answer33) Two capacitors of capacitance \[{{C}_{1}}\]and \[{{C}_{2}}\]are charged to potentials \[{{V}_{1}}\]and\[{{V}_{2}}\] respectively. When they are connected in parallel the ratio of their respective charges will be:

    A) \[\frac{{{C}_{1}}}{{{C}_{2}}}\]

    B) \[\frac{C_{1}^{2}}{C_{2}^{2}}\]

    C) \[\frac{{{V}_{1}}}{{{V}_{2}}}\]

    D) \[\frac{V_{1}^{2}}{V_{2}^{2}}\]

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  • question_answer34) An example of a diamagnetic substance is:

    A) aluminium

    B) copper

    C) iron

    D) nickel

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  • question_answer35) In a charged capacitor, the energy is stored in:

    A) centre of the plates

    B) edges of the plates

    C) between the plates

    D) none of these

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  • question_answer36) Relative permeability of iron is 5500, then its magnetic susceptibility will be:

    A) \[5500\times {{10}^{7}}\]

    B) \[5500\times {{10}^{-7}}\]

    C) \[5501\]

    D) \[5499\]

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  • question_answer37) In a typical Wheatstone network the resistances in cyclic order are \[A=10\,\Omega ,B=5\Omega ,\,C=4\,\Omega \] and\[D=4\Omega \]for the bridge to be balanced:

    A) \[10\,\Omega \]should be connected in parallel with A

    B) \[10\,\Omega \] should be connected in series with A

    C) \[5\,\Omega \] should be connected in series with B

    D) \[5\,\Omega \] should be connected in parallel with B

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  • question_answer38) An electron of mass m and charge q is travelling with a speed v along a circular path of radius r at right angles to a uniform magnetic field B, if speed of the electron is doubled and magnetic field is halved, then the resulting path would have a radius:

    A) \[4r\]

    B) \[2r\]

    C) \[\frac{r}{2}\]

    D) \[\frac{r}{4}\]

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  • question_answer39) Two resistances \[{{r}_{1}}\]and\[{{r}_{2}}({{r}_{1}}<{{r}_{2}})\]are connected in parallel. The equivalent resistance R is such that:

    A) \[R>({{r}_{1}}+{{r}_{2}})\]

    B) \[{{r}_{2}}<R<({{r}_{1}}+{{r}_{2}})\]

    C) \[{{r}_{1}}<R<{{r}_{2}}\]

    D) \[R<{{r}_{1}}\]

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  • question_answer40) The potential at a point, due to a positive charge of \[\text{100}\,\text{ }\!\!\mu\!\!\text{ C}\]at a distance of 9 m, is:

    A) \[{{10}^{7}}\,\text{volt}\]

    B) \[{{10}^{6}}\,\text{volt}\]

    C) \[{{10}^{5}}\,\text{volt}\]

    D) \[{{10}^{4}}\,\text{volt}\]

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  • question_answer41) Four wires of identical length, diameters and of the same material are stretched on a sonometre wire. If the ratio of their tensions is 1 : 4 : 9 : 16 then the ratio of their fundamental frequencies are:

    A) 16 : 9 : 4 : 1

    B) 4 : 3 : 2 : 1

    C) 1 : 4 : 2 : 16

    D) 1 : 2 : 3 : 4

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  • question_answer42) An echo is heard when the minimum distance of the reflecting surface is:

    A) 47 m

    B) 34 m

    C) 17 m

    D) 9 m

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  • question_answer43) In which process the P-V indicator diagram is a straight line parallel to volume axis?

    A) irreversible

    B) adiabatic

    C) isothermal

    D) isobaric

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  • question_answer44) The kinetic energy of a body becomes four times its initial value. Then the linear momentum will be:

    A) four times the initial value

    B) three times the initial value

    C) twice the initial value

    D) same as the initial value

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  • question_answer45) At which temperature, the Fahrenheit and Centigrade scales are equal:

    A) \[-{{48}^{o}}\]

    B) \[-{{40}^{o}}\]

    C) \[{{37}^{o}}\]

    D) \[{{40}^{o}}\]

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  • question_answer46) A uniform wire of resistance R is uniformly compressed along its length, until the radius becomes\[n\]times the original radius. Now resistance of the wire becomes:

    A) \[nR\]

    B) \[\frac{R}{n}\]

    C) \[\frac{R}{{{n}^{2}}}\]

    D) \[\frac{R}{{{n}^{4}}}\]

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  • question_answer47) The impurity atom that should be added the germanium to make it \[n-\]type will be:

    A) aluminium

    B) arsenic

    C) indium

    D) iodine

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  • question_answer48) The waves that can not be polarized are:

    A) electromagnetic waves

    B) longitudinal waves

    C) transverse waves

    D) light waves

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  • question_answer49) An empty vessel is partially filled with water, then the frequency of vibration of air column in the vessel:

    A) remains same

    B) decreases

    C) increases

    D) first increases then decreases

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  • question_answer50) A man suffering from short sight is unable to see objects distinctly at a distance more than 2m. The power of lens required to correct this defect of the eye should be:

    A) \[~+\,2D\]

    B) \[~+\text{ }0.50\,D\]

    C) \[-2D\]

    D) \[-0.5D\]

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  • question_answer51) A monoatomic gas is suddenly compressed to l/8th of its initial volume adiabatically. The ratio of its final pressure to initial pressure will be \[(\gamma =5/3):\]

    A) 8

    B) 24

    C) 32

    D) 40

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  • question_answer52) 2 kg mass is rotating on a circular path of radius 0.8 m with an angular velocity of 44 rad/sec. If the radius of the path becomes 1 m. Then value of angular velocity is:

    A) \[35.32\,\text{rad/sec}\]

    B) \[28.16\,\text{rad/sec}\]

    C) \[14-08\,\text{rad/sec}\]

    D) \[7\,\text{rad/sec}\]

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  • question_answer53) A whistle of frequency 500 Hz tied to the end of a string of length 1-2 m revolves at 400 rev/min. A listener standing some distance away in the plane of rotation of whistle nears frequencies in the rays (speed of sound =340 m/s) :

    A) 436 to 586

    B) 426 to 574

    C) 436 to 574

    D) 436 to 574

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  • question_answer54) The dispersive powers of crown and flint glasses are 0-02 and 0-04 respectively. In an achromatic combination of lenses the focal length of flint glass lens is 40 cm. The focal length of crown glass lens will be:

    A) - 20 cm

    B) + 20 cm

    C) -10 cm

    D) + 20 cm

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  • question_answer55) Two insulated metallic spheres of capacitances \[\text{3 }\!\!\mu\!\!\text{ F}\]and \[\text{5 }\!\!\mu\!\!\text{ F}\]are charged to 300 volts and 500 volts respectively. The energy loss when they are connected by a wire is:

    A) \[0-035\text{ J}\]

    B) \[1-5\,\text{J}\]

    C) \[3-75\,\text{J}\]

    D) \[\text{ }\!\!~\!\!\text{ 0}\text{.0375 J}\]

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  • question_answer56) The gardner waters the plants by a pipe of diameter 1 mm. The water comes out at the rate of \[\text{10}\,\text{c}{{\text{m}}^{\text{3}}}\text{/sec}\]. The reactionary force exerted on the hand of the gardner is:

    A) zero

    B) \[1.27\times {{10}^{-2}}N\]

    C) \[1.27\times {{10}^{-4}}N\]

    D) \[0.127\,N\]

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  • question_answer57) A thin hollow cylinder open at both ends: (i) sliding without rotating (ii) rolls without slipping, with the same speed the ratio of kinetic energy in the two cases is:

    A) 1:1

    B) 4:1

    C) 1:2

    D) 2:1

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  • question_answer58) A rain drop of radius 0.3 mm has a terminal velocity of 1 m/s in air. The viscosity of air is \[18\times {{10}^{-5}}\]poise. The visious forces on the drop will be:

    A) \[16.95\times {{10}^{-9}}N\]

    B) \[1.695\times {{10}^{-9}}N\]

    C) \[10.17\times {{10}^{-9}}N\]

    D) \[101.73\times {{10}^{-9}}N\]

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  • question_answer59) The force required to separate two glass plates of area \[{{10}^{-2}}{{\text{m}}^{\text{2}}}\]with a film of water 0.05 mm thick between them, is (Surface tension of water is \[70\times {{10}^{-3}}N/m\])

    A) 28 N

    B) 14 N

    C) 50 N

    D) 38 N

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  • question_answer60) The dimension of\[\frac{1}{2}{{\varepsilon }_{0}}{{E}^{2}}\](\[{{\varepsilon }_{0}}\]is the permittivity of free space, and E is electric field), is:

    A) \[[M{{L}^{2}}{{T}^{-1}}]\]

    B) \[[M{{L}^{-1}}{{T}^{-2}}]\]

    C) \[[M{{L}^{2}}{{T}^{-2}}]\]

    D) \[[ML{{T}^{-1}}]\]

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  • question_answer61) Which one of the following defects in the crystals lowers its density?

    A) F centres

    B) Interstitial defect

    C) Frenkel defect

    D) Schottky

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  • question_answer62) \[{{H}_{2}}(g)+C{{l}_{2}}(g)\to 2HCl(g).\] \[\Delta H=-44k.cal\] \[2Na(s)+2HCl(g)\to 2NaCl(s)+{{H}_{2}}(g).\] \[\Delta H=-152\,\text{k}\text{.cal}\] For the reaction, \[Na(s)+\frac{1}{2}C{{l}_{2}}(g)\to NaCl(s),\Delta  H =?\]

    A)  \[-108\,k.cal\]                  

    B)  \[-196\,k.cal\]

    C)  \[-98\,k.cal\]                    

    D)  \[54\,k.cal\]

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  • question_answer63) The fatty acid that shows reducing property is:

    A) acetic acid

    B) ethanoic acid

    C) oxalic acid

    D) formic acid

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  • question_answer64) By adding =\[\text{20}\,\text{ml}\,\text{0}\text{.1}\,\text{N}\,\text{HCl}\]to 20 ml \[\text{0}\text{.001}\,\text{N}\,\text{KOH,}\]the pH of the obtained solution will be:

    A) 2

    B) 1.3

    C) 0

    D) 7

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  • question_answer65) In the synthesis of ammonia \[{{N}_{2}}(g)+3{{H}_{2}}\rightleftharpoons 2N{{H}_{3}}(g)\] When 100 ml. of \[{{\text{N}}_{\text{2}}}\] has reacted, the volume of \[{{H}_{2}}\] which has also reacted and ammonia produced are:

    A) \[\text{300 ml}\text{. }{{\text{H}}_{\text{2 }}}\]and \[\text{200 ml}\text{. N}{{\text{H}}_{\text{3}}}\]

    B) \[\text{ }\!\!~\!\!\text{ 300 ml}\text{. }{{\text{H}}_{\text{2}}}\] and \[\text{300 ml}\text{. N}{{\text{H}}_{\text{3}}}\]

    C) \[\text{100 ml}\text{. }{{\text{H}}_{\text{2}}}\]and \[\text{100 ml}\text{. N}{{\text{H}}_{\text{3}}}\]

    D) \[\text{100 ml}\text{. }{{\text{H}}_{\text{2}}}\]and \[\text{200 ml}\text{. N}{{\text{H}}_{\text{3}}}\]

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  • question_answer66) When 9-65 coulombs of electricity is passed through a solution of silver nitrate     (atomic     mass     of\[Ag=108\,g\,mo{{l}^{-1}}\]), the amount of silver deposited is:

    A) 16 - 2 mg                               

    B) 21 - 2 mg

    C) 10 - 8 mg                              

    D) 6 - 4 mg

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  • question_answer67) The strongest Bronsted base in the following anion is:

    A) \[ClO_{3}^{-}\]

    B) \[ClO_{4}^{-}\]

    C) \[Cl{{O}^{-}}\]

    D) \[ClO_{2}^{-}\]

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  • question_answer68) Bleaching powder loses its power on keeping for a long time because:

    A) it changes into calcium hypochlorate

    B) it changes into calcium chloride and calcium hydroxide

    C) it absorbs moisture

    D) it changes into calcium chloride and calcium chlorate

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  • question_answer69) When potassium ferrocyanide crystals are heated with concentrated sulphuric acid, the gas evolved is:

    A) sulphur dioxide

    B) ammonia

    C) carbon dioxide

    D) carbon monoxide

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  • question_answer70) \[{{H}_{2}}+C{{l}_{2}}\xrightarrow{{}}2HCl,\Delta H=194\,kJ.\]In this reaction heat of formation of HCl in kJ is:

    A) \[+914\,kJ\]

    B) \[+\,97\,kJ\]

    C) \[-\,97\,kJ\]

    D) \[-194\,kJ\]

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  • question_answer71) One mole of an ideal gas is allowed to expand reversibly and adiabatically from a temperature of \[\text{27}{{\,}^{\text{o}}}\text{C}\text{.}\] If the work done during the process is 3 kJ, the final temperature will be equal to\[\text{(C}\upsilon \text{=20}\,\text{J}\,{{\text{K}}^{-1}}\text{)}\]

    A) \[~150\text{ }K\]

    B) \[~100\text{ }K\]

    C) \[26.85{{\,}^{o}}C\]

    D) \[~295K\]

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  • question_answer72) Solution of sodium metal in liquid ammonia is strongly reducing due to the presence in the solution of the following:

    A) sodium hydride

    B) odium amide

    C) sodium atoms

    D) solvated electrons

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  • question_answer73) The IUPAC name of\[C{{H}_{3}}-C{{H}_{2}}-\underset{C{{H}_{3}}}{\overset{H}{\mathop{\underset{|}{\overset{|}{\mathop{C}}}\,}}}\,-\underset{C{{H}_{3}}}{\overset{{{C}_{4}}{{H}_{9}}}{\mathop{\underset{|}{\overset{|}{\mathop{C}}}\,}}}\,-C{{H}_{3}}\]is:

    A) 3, 4, 4-trimethyl-heptane

    B) 3, 4, 4-trimethyl-octane

    C) 2-butyl, 2-methyl, 3 ethyl butane

    D) 2-ethyl, 3, 3-dimethyl-heptane

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  • question_answer74) Which of the following has lowest percentage of carbon?

    A) steel

    B) all have same percentage

    C) cast ion

    D) wrought iron

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  • question_answer75) When ethanal is heated with Fehling's solution it gives a precipitate of:

    A) \[\text{CuO}\]

    B) \[\text{C}{{\text{u}}_{\text{2}}}\text{O}\,\text{+}\,\text{CuO}\]

    C) \[\text{Cu}\]

    D) \[C{{u}_{2}}O\]

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  • question_answer76) The number of unpaired electrons in\[F{{e}^{3+}}(Z=26)\] are:

    A) 5

    B) 6

    C) 3

    D) 4

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  • question_answer77) The\[pKa\]of a certain weak acid is 4-0. What should be the [salt] to [acid] ratio if we have to prepare a buffer with pH=5 using the acid and one of the salts?

    A) 10:1

    B) 1:10

    C) 4:5

    D) 5:4

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  • question_answer78) Which one of the following contains both covalent and ionic bonds?

    A) \[N{{H}_{4}}Cl\]

    B) \[{{H}_{2}}O\]

    C) \[CC{{l}_{4}}\]

    D) \[CaC{{l}_{2}}\]

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  • question_answer79) The nitride ion in lithium nitride is composed of:

    A) 7 protons + 10 electrons

    B) 10 protons + 10 electrons

    C) 7 protons + 7 protons

    D) 10 protons + 7 electrons

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  • question_answer80) In a face centred cubic cell, an atom at the face contributes to the unit cell:

    A) 1/4 part

    B) 1/8 part

    C) 1 part

    D) 1/2 part

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  • question_answer81) Unpleasant smelling carbylamines are formed by heating alkali and chloroform with:

    A) any aliphatic amine

    B) any aromatic amine

    C) any amine

    D) any primary amine

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  • question_answer82) Which of the following alkyl halides is used as a methylating agent?

    A) \[{{C}_{2}}{{H}_{5}}Br\]

    B) \[{{C}_{6}}{{H}_{5}}Cl\]

    C) \[C{{H}_{3}}Cl\]

    D) \[{{C}_{2}}{{H}_{5}}Cl\]

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  • question_answer83) A radioactive isotope having a half life of 3 days was received after 12 days. It was found that there were 3 g of the isotope in the container. The initial weight of the isotope when packed was:

    A) 36 g

    B) 48 g

    C) 12 g

    D) 24 g

    View Answer play_arrow
  • question_answer84) Cuprous ion is colourless while cupric ion is coloured because:

    A) both have half filled p and d-orbitals

    B) cuprous ion has incomplete d-orbital and cupric ion has a complete \[d-\]orbital

    C) both have unpaired electrons in the d-orbitals

    D) cuprous ion has a complete d-orbital and cupric ion has an incomplete \[d-\]orbital

    View Answer play_arrow
  • question_answer85) Which of the following ions can cause coagulation of proteins?

    A) \[A{{g}^{+}}\]

    B) \[N{{a}^{+}}\]

    C) \[M{{g}^{+\,+}}\]

    D) \[C{{a}^{+\,+}}\]

    View Answer play_arrow
  • question_answer86) Number of molecules in one litre of water is close to:

    A) \[\frac{18}{22.4}\times {{10}^{23}}\]

    B) \[55.5\times 6.023\times {{10}^{23}}\]

    C) \[\frac{6.023}{23.4}\times {{10}^{23}}\]

    D) \[18\times 6.023\times {{10}^{23}}\]

    View Answer play_arrow
  • question_answer87) Which of the following alkali metal ions has lowest ionic mobility in aqueous solution?

    A) \[R{{b}^{+}}\]

    B) \[C{{s}^{+}}\]

    C) \[Li\]

    D) \[N{{a}^{+}}\]

    View Answer play_arrow
  • question_answer88) At \[\text{490}{{\,}^{o}}\text{C,}\] the equilibrium constant for the synthesis of \[\text{HI}\] is 50, the value of K for the dissociation of HI will be:

    A) \[\text{20}\text{.0}\]                                    

    B) \[2.0\]

    C) \[0.2\]                                  

    D) \[0.02\]

    View Answer play_arrow
  • question_answer89) For which of the following reactions are the numerical value of \[{{K}_{p}}\]and \[{{K}_{c}}\]the same?

    A) \[{{H}_{2}}(g)+C{{l}_{2}}(g)\rightleftharpoons 2HCl(g)\]

    B) \[{{H}_{2}}(g)+{{I}_{2}}(g)\rightleftharpoons 2HI(g)\]

    C) \[2NOCl(g)\rightleftharpoons 2NO(g)+C{{l}_{2}}(g)\]

    D) \[{{N}_{2}}(g)+3{{H}_{2}}(g)\rightleftharpoons 2N{{H}_{3}}(g)\]

    View Answer play_arrow
  • question_answer90) The number of \[\pi -\]bonds in\[C{{H}_{2}}=CH-CH=CH-C\equiv CH\]is:

    A) 2

    B) 5

    C) 4

    D) 3

    View Answer play_arrow
  • question_answer91) The normality of \[2.3\,\text{M}\,{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}\]solution is:

    A) \[2.3\,N\]

    B) \[4.6\,N\]

    C) \[0.46\,N\]

    D) \[0.23\,N\]

    View Answer play_arrow
  • question_answer92) Hydrolytic reaction of fats with caustic soda is known as:

    A) acetylation

    B) carboxylation

    C) esterification

    D) saponification

    View Answer play_arrow
  • question_answer93) Aluminium chloride is a/an:

    A) Bronsted Lowry acid

    B) Arrhenius acid

    C) Lewis acid

    D) Lewis acid

    View Answer play_arrow
  • question_answer94) A reaction is \[A+B\rightleftharpoons C+D\]initially. We start with equal concentration of A arid B. At equilibrium we find the moles of C is two times that of A. What is the equilibrium constant of the reaction?

    A) 1/4

    B) 1/2

    C) 4

    D) 2

    View Answer play_arrow
  • question_answer95) Which of the following is not used in Friedel-Crafts reaction?

    A) phenyl acetanilide

    B) bromobenzene

    C) benzene

    D) chlorobenzene

    View Answer play_arrow
  • question_answer96) On heating sodium metal in current of dry ammonia, the compound formed is:

    A) sodium amide

    B) sodium azide

    C) sodium nitride

    D) sodium hydride

    View Answer play_arrow
  • question_answer97) Hydrogen bonding is maximum in:

    A) ethyl chloride

    B) triethyl amine

    C) ethanol

    D) diethyl ether

    View Answer play_arrow
  • question_answer98) Phenol is heated with pthalic anhydride in presence of cone. \[{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}\text{.}\]The product gives pink colour with alkali. The product is:

    A) phenolphthalein

    B) bakelite

    C) salicylic acid

    D) fluorescein

    View Answer play_arrow
  • question_answer99) A reaction that is of the first order with respect to reactant A has a rate constant \[6\,{{\min }^{-1}}.\]If we start with \[[A]=\text{0}\text{.5}\,\text{mol}\,{{\text{L}}^{-1}},\] when would [A] reach the value \[0.05\,\text{mol}\,{{\text{L}}^{-1}}?\]

    A) \[\text{0}\text{.384 min}\]

    B) \[\text{0}\text{.15}\,\text{min}\]

    C) 3 min

    D) \[\text{3}\text{.84}\,\text{min}\]

    View Answer play_arrow
  • question_answer100) Helium atom is two times heavier than a hydrogen molecule at 298 K. The average kinetic energy of helium is:

    A) four times that of a hydrogen molecule

    B) half that of a hydrogen molecule

    C) two times that of a hydrogen molecule

    D) same as that of a hydrogen molecule

    View Answer play_arrow
  • question_answer101) Froth floatation process is used for the metallurgy of:

    A) chloride ores

    B) amalgams

    C) oxide ores

    D) sulphide ores

    View Answer play_arrow
  • question_answer102) 10 litre solution of urea contains 240 g urea. The active mass of urea will be:

    A) \[0.04\]

    B) \[0.02\]

    C) \[0.4\]

    D) \[0.2\]

    View Answer play_arrow
  • question_answer103) Which of the following does not reduce Benedict's solution?

    A) sucrose

    B) aldehyde

    C) glucose

    D) fructose

    View Answer play_arrow
  • question_answer104) Matte contains mainly:

    A) \[\text{C}{{\text{u}}_{\text{2}}}\text{S}\]and \[\text{FeS}\]

    B) \[\text{CuS}\]and \[\text{F}{{\text{e}}_{\text{2}}}{{\text{S}}_{\text{3}}}\]

    C) \[\text{Fe}\]

    D) \[\text{C}{{\text{u}}_{\text{2}}}\text{S}\]

    View Answer play_arrow
  • question_answer105) The name of the product obtained by the addition of\[\text{HI}\]to propene in presence of peroxide catalyst is:

    A) isopropyl iodide

    B) 2-iodo propene

    C) 2-iodopropane

    D) 1-iodopropane

    View Answer play_arrow
  • question_answer106) In Nessler's reagent the ion present is:

    A) \[\text{Hg}{{\text{I}}^{2-}}\]

    B) \[\text{HgI}_{4}^{2-}\]

    C) \[H{{g}^{+}}\]

    D) \[\text{H}{{\text{g}}^{\text{+}\,\text{+}}}\]

    View Answer play_arrow
  • question_answer107) The calorific value is maximum in case of:

    A) milk

    B) minerals

    C) carbohydrates

    D) proteins

    View Answer play_arrow
  • question_answer108) Flux is used to:

    A) remove all impurities from ores

    B) reduce metal oxide

    C) remove silica

    D) remove silica and undesirable metal oxides

    View Answer play_arrow
  • question_answer109) Which of the following molecules has the largest root mean square velocity at \[\text{25}{{\,}^{\text{o}}}\text{C?}\]

    A) \[\text{C}{{\text{O}}_{\text{2}}}\]

    B) \[\text{S}{{\text{O}}_{\text{2}}}\]

    C) \[{{H}_{2}}S\]

    D) \[N{{H}_{3}}\]

    View Answer play_arrow
  • question_answer110) Stainless steel contains:

    A) \[Fe+Cr+Cu\]

    B) \[Fe+C+Ni\]

    C) \[Fe+Cr+Ni\]

    D) \[Fe+Ni+Cu\]

    View Answer play_arrow
  • question_answer111) The limiting radius ratio for tetrahedral shape is:

    A) 0.225 to 0.414

    B) 0.414 to 0.732

    C) 0 to 0.155

    D) 0.155 to 0.225

    View Answer play_arrow
  • question_answer112) For the process dry \[\text{ice}\xrightarrow{{}}\text{C}{{\text{O}}_{\text{2}}}\text{(g)}\]

    A) \[\Delta H\]is positive while \[\Delta \rho \]is negative

    B) both\[\Delta H\] and are negative

    C) both \[\Delta H\]and \[\Delta \rho \]are positive

    D) \[\Delta H\]is negative while \[\Delta \rho \]is positive

    View Answer play_arrow
  • question_answer113) \[N{{H}_{3}}\]and \[B{{F}_{3}}\]form an adduct readily because they form:

    A) a co-ordinate bond

    B) a hydrogen bond

    C) an ionic bond

    D) a covalent bond

    View Answer play_arrow
  • question_answer114) The brown ring test for \[\text{N}{{\text{O}}_{\text{2}}}\]and \[\text{NO}_{3}^{-}\]is due to the formation of complex ion with the formula:

    A) \[{{[Fe{{({{H}_{2}}O)}_{6}}]}^{2+}}\]

    B) \[{{[Fe(NO){{(CN)}_{5}}]}^{2+}}\]

    C) \[{{[Fe{{({{H}_{2}}O)}_{5}}NO]}^{2+}}\]

    D) \[{{[Fe({{H}_{2}}O){{(NO)}_{5}}]}^{2+}}\]

    View Answer play_arrow
  • question_answer115) Amino acids usually exist in the from of Zwitter ions. This means that it consists of:

    A) the basic group \[-\text{N}{{\text{H}}_{\text{2}}}\]and the acidic group\[-\text{COOH}\]

    B) the basic group\[-\text{NH}_{\text{3}}^{\text{+}}\]and the acidic group\[-\text{C}{{\text{O}}_{\text{2}}}\]

    C) the basic group \[-\text{CO}_{2}^{-}\]and the acidic group\[-\text{NH}_{\text{3}}^{\text{+}}\]

    D) no acidic or basic group

    View Answer play_arrow
  • question_answer116) A certain compound gives negative test with ninhydrin and positive test with Benedict's solution; it is:

    A) an ammo acid

    B) a monosaccharide

    C) a lipid

    D) a protein

    View Answer play_arrow
  • question_answer117) If formaldehyde and KOH are heated we get:

    A) methane

    B) methyl alcohol

    C) ethyl for mate

    D) acetylene

    View Answer play_arrow
  • question_answer118) Which of the following reagents is used to distinguish ethene from ethyne?

    A) bromine in \[CC{{l}_{4}}\]

    B) ammonical \[C{{u}_{2}}C{{l}_{2}}\]

    C) bromine water

    D) alkaline \[KMn{{O}_{4}}\]

    View Answer play_arrow
  • question_answer119) Brass is an alloy of:

    A) \[Al\]and \[Zn\]

    B) \[Cu\]and\[Al\]

    C) \[Ni\]and \[Zn\]

    D) \[Cu\]and \[Zn\]

    View Answer play_arrow
  • question_answer120) 60. In the above reaction X stands for:

    A) \[SnC{{l}_{2}}\]

    B) \[NH_{3}^{+}C{{l}^{-}}\]

    C) \[N{{H}_{2}}\]

    D) \[Cl\]

    View Answer play_arrow
  • question_answer121) If \[a=\cos \theta +i\sin \theta ,\]then \[\frac{1+a}{1-a}=\]

    A) \[\cot \theta \]

    B) \[\cot \theta /2\]

    C) \[i\cot \theta /2\]

    D) \[i\tan \theta /2\]

    View Answer play_arrow
  • question_answer122) General solution of tan \[5\theta =\cot 2\theta \] is:

    A) \[\theta =\frac{n\pi }{7}+\frac{\pi }{14}\]

    B) \[\theta =\frac{n\pi }{7}+\frac{\pi }{5}\]

    C) \[\theta =\frac{n\pi }{7}+\frac{\pi }{2}\]

    D) \[\theta =\frac{n\pi }{7}+\frac{\pi }{3},n\in Z\]

    View Answer play_arrow
  • question_answer123) If \[\sin y=x\sin (a+y),\]then\[\frac{dy}{dx}=\]

    A) \[\frac{\sin \sqrt{a}}{\sin (a+y)}\]

    B) \[\frac{{{\sin }^{2}}(a+y)}{\sin a}\]

    C) \[\frac{\sin (a+y)}{\sin a}\]

    D) \[\frac{\cos (a+y)}{\cos a}\]

    View Answer play_arrow
  • question_answer124) If \[x=\frac{1-{{t}^{2}}}{1+{{t}^{2}}}\]and \[y=\frac{2t}{1+{{t}^{2}}}\]then \[\frac{dy}{dx}\]

    A) \[-y/x\]

    B) \[y/x\]

    C) \[-x/y\]

    D) \[x/y\]

    View Answer play_arrow
  • question_answer125) If \[{{2}^{x}}+{{2}^{y}}={{2}^{x+y}},\]then the value of \[\frac{dy}{dx}\]at \[x=y=1\]is:

    A) zero

    B) \[-1\]

    C) 1

    D) 2

    View Answer play_arrow
  • question_answer126) The angle of elevation of the top of a tower A from the top B and bottom D at a building of height a are \[{{30}^{o}}\] and\[{{45}^{o}}\]respectively. If the tower and the building stand at the same level, then the height of the tower is:

    A) \[a\sqrt{3}\]

    B) \[\frac{a\sqrt{3}}{\sqrt{3}-1}\]

    C) \[\frac{a(3+\sqrt{3})}{2}\]

    D) none of these

    View Answer play_arrow
  • question_answer127) If \[\log x256=8/5,\]then \[x\]is equal to:

    A) 64

    B) 16

    C) 32

    D) 8

    View Answer play_arrow
  • question_answer128) If \[\log 2,\log ({{2}^{x}}-1)\]and \[\log ({{2}^{x}}+3)\]are in A.P., then \[x\] is equal to:

    A) 5/2

    B) log 25

    C) log 23

    D) logs 2

    View Answer play_arrow
  • question_answer129) The set of all \[2\times 2\] matrices over the real numbers is not a group under matrix multiplication because:

    A) identity element does not exist

    B) closure property is not satisfied

    C) association property is not satisfied

    D) inverse axiom may not be satisfied

    View Answer play_arrow
  • question_answer130) The sum of the products of elements of any row of a determinant A with the same row is always equal to:

    A) 1

    B) zero

    C) \[|A|\]

    D) \[|A|/2\]

    View Answer play_arrow
  • question_answer131) The direction cosines of the vector\[3\vec{i}-4\vec{j}+5\vec{k}\]are:

    A) \[\frac{3}{5},\frac{-4}{5},\frac{1}{5}\]

    B) \[\frac{3}{5\sqrt{2}},\frac{-4}{5\sqrt{2}},\frac{1}{\sqrt{2}}\]

    C) \[\frac{3}{\sqrt{2}},\frac{-4}{\sqrt{2}},\frac{1}{\sqrt{2}}\]

    D) none of these

    View Answer play_arrow
  • question_answer132) If A, B, C are the vertices of a triangle whose position vectors are \[\vec{a},\vec{b},\vec{c}\]a and G the centroid of the \[\Delta A B C,\] then\[G\vec{A}+G\vec{B}+G\vec{C}=\]

    A)  \[\vec{0}\]                                        

    B)  \[\vec{A}+\vec{B}+\vec{C}\]

    C)  \[\frac{\vec{a}+\vec{b}+\vec{c}}{3}\]                   

    D)  \[\frac{\vec{a}-\vec{b}-\vec{c}}{3}\]

    View Answer play_arrow
  • question_answer133) If \[\underset{x\to \infty }{\mathop{\lim }}\,\left[ \frac{{{x}^{3}}+1}{{{x}^{2}}+1}-(ax-b) \right]=2,\]then:

    A) \[a=1\]and \[b=1\]

    B) \[a=1\]and \[b=-1\]

    C) \[a=1\]and \[b=-2\]

    D) \[a=1\]and \[b=2\]

    View Answer play_arrow
  • question_answer134) \[\underset{x\to 1}{\mathop{\lim }}\,\frac{1+\log x-x}{1-2x+{{x}^{2}}}=\]

    A) 1

    B) \[-1\]

    C) zero

    D) \[-1/2\]

    View Answer play_arrow
  • question_answer135) The sum of all positive divisors of 960 is:

    A) 3048

    B) 3087

    C) 3047

    D) 2180

    View Answer play_arrow
  • question_answer136) If \[\vec{a},\vec{b},\vec{c}\]are unit vectors, such that\[\vec{a}+\vec{b}+\vec{c}=0\] then value of \[\vec{a}.\vec{b}+\vec{b}.\vec{c}+\vec{c}.\vec{a}\]is:

    A) \[3/2\]

    B) \[-3/2\]

    C) \[2/3\]

    D) \[-2/3\]

    View Answer play_arrow
  • question_answer137) If the vectors \[\vec{i}+3\vec{j}-2\vec{k},2\vec{i}-\vec{j}+4\vec{k}\]and \[3\vec{i}+2\vec{j}+x\vec{k}\]are coplanar, then the value of \[x\] is:

    A) \[-2\]

    B) 2

    C) 1

    D) 3

    View Answer play_arrow
  • question_answer138) The radius of the circle \[{{x}^{2}}+{{y}^{2}}+4x-6y-12=0\]is:

    A) 9

    B) 5

    C) \[-3\]

    D) \[-6\]

    View Answer play_arrow
  • question_answer139) The equation of a circle parsing through (1, 0) and (0, 1) and having smallest possible radius is:

    A) \[{{x}^{2}}+{{y}^{2}}-x-y=0\]

    B) \[{{x}^{2}}+{{y}^{2}}+x+y=0\]

    C) \[2{{x}^{2}}+{{y}^{2}}-2x-y=0\]

    D) \[{{x}^{2}}+2{{y}^{2}}-x-2y=0\]

    View Answer play_arrow
  • question_answer140) If g is the inverse function of \[f\] and \[f'(x)=\frac{1}{1+{{x}^{n}}},\] then the value of\[g'(x)=\]

    A) \[{{(g(x))}^{n}}\]

    B) \[1+{{(g(x))}^{n}}\]

    C) \[1-{{(g(x))}^{n}}\]

    D) zero

    View Answer play_arrow
  • question_answer141) If\[\cos A=\cos B=\cos C\]and \[A+B+C=\pi ,\]then \[\cot B\cot C\]will be equal to:

    A) 1/2

    B) 5/4

    C) \[SinA\sin B\]

    D) \[\cos A\cos B\]

    View Answer play_arrow
  • question_answer142) If \[{{P}_{n}}={{\cos }^{n}}\theta +{{\sin }^{n}}\theta ,\]then

    A) 1

    B) zero

    C) 2

    D) 3

    View Answer play_arrow
  • question_answer143) The radical axis of the circles belong to the coaxial system of circles, whose limiting points are (1, 3) and (2, 6) is:

    A) \[x-3y-15=0\]

    B) \[x+3y-15=0\]

    C) \[x-3y+15=0\]

    D) \[2x+3y-16=0\]

    View Answer play_arrow
  • question_answer144) If the latus ractum of an ellipse is one half of its minor axis then its eccentricity is equal to:

    A) \[\sqrt{3}/2\]

    B) \[\sqrt{3}/4\]

    C) 1/2

    D) \[1/\sqrt{2}\]

    View Answer play_arrow
  • question_answer145) A force \[\vec{F}=2\vec{i}+\vec{j}-\vec{k}\]acts at a point A whose position vector is \[2\vec{i}-\vec{j}.\] The moment of \[\vec{F}\]about the origin is:

    A) \[\vec{i}+2\vec{j}-4\vec{k}\]

    B) \[\vec{i}-2\vec{j}-4\vec{k}\]

    C) \[\vec{i}+2\vec{j}+4\vec{k}\]

    D) \[\vec{i}-2\vec{j}+4\vec{k}\]

    View Answer play_arrow
  • question_answer146) Identify the false statement:

    A) \[(G,*),ab=ac\Rightarrow b=c\forall a,b,c\in C\]

    B) In an abelian group,\[{{(ab)}^{2}}={{a}^{2}}{{b}^{2}},\forall a,b,\in G\]

    C) Cube roots of unity forms an additive abelian group

    D) In a group of even order, there exist an element other than identity which is its own inverse.

    View Answer play_arrow
  • question_answer147) \[\underset{x\to 0}{\mathop{\lim }}\,\frac{{{a}^{\sin x}}-1}{{{b}^{\sin x}}-1}\]is equal to:

    A) a/b

    B) b/a

    C) \[\frac{\log a}{\log b}\]

    D) \[\frac{\log b}{\log a}\]

    View Answer play_arrow
  • question_answer148) The coefficient of the term independent of \[x\] in the expansion of\[{{\left( \sqrt{x/3}+\frac{3}{2{{x}^{2}}} \right)}^{10}}\]is: \[{{\left( \sqrt{x/3}+\frac{3}{2{{x}^{2}}} \right)}^{10}}\]is:

    A) \[5/4\]

    B) 7/4

    C) \[9/4\]

    D) \[3/4\]

    View Answer play_arrow
  • question_answer149) If \[2\sec 2\alpha =\tan \beta +\cot \beta ,\] then one the value of \[(\alpha +\beta )\] is:

    A) \[\pi /4\]

    B) \[\pi /2\]

    C) \[\pi \]

    D) \[2\pi \]

    View Answer play_arrow
  • question_answer150) If \[{{(x+iy)}^{1/3}}=a+ib,\]then \[\frac{x}{a}+\frac{y}{b}=\]

    A) \[ab\]

    B) \[4ab\]

    C) \[4({{a}^{2}}-{{b}^{2}})\]

    D) \[4({{a}^{2}}+{{b}^{2}})\]

    View Answer play_arrow
  • question_answer151) The derivative of \[{{\sin }^{-1}}\left( \frac{2x}{1+{{x}^{2}}} \right)\] w.r.t.\[{{\cos }^{-1}}\left( \frac{1-{{x}^{2}}}{1+{{x}^{2}}} \right)\]is:

    A) \[-1\]

    B) \[1\]

    C) 2

    D) 4

    View Answer play_arrow
  • question_answer152) If R is the radius of circum circle of the\[\Delta ABC\] and \[\Delta \]is its area, then:

    A) \[R=\frac{a+b+c}{\Delta }\]

    B) \[R=\frac{a+b+c}{4\Delta }\]

    C) \[R=\frac{abc}{4\Delta }\]

    D) \[R=\frac{abc}{\Delta }\]

    View Answer play_arrow
  • question_answer153) \[\int_{{}}^{{}}{\frac{(x+3){{e}^{x}}}{{{(x+4)}^{2}}}}dx\]

    A) \[\frac{1}{{{(x+4)}^{2}}}+c\]

    B) \[\frac{{{e}^{x}}}{{{(x+4)}^{2}}}+c\]

    C) \[\frac{{{e}^{x}}}{x+4}+c\]

    D) \[\frac{{{e}^{x}}}{x+3}+c\]

    View Answer play_arrow
  • question_answer154) \[\int_{0}^{2a}{\frac{f(x)}{f(x)+f(2a-x)}dx}\]

    A) \[\pi /4\]

    B) \[\pi /2\]

    C) \[a\]

    D) \[2a\]

    View Answer play_arrow
  • question_answer155) The differential equation obtained on eliminating A and B from the equation \[y=A\cos \omega t+B\sin \omega t\]

    A) \[y''=-{{\omega }^{2}}y\]

    B) \[y''+y=0\]

    C) \[y''+y'=0\]

    D) none of these

    View Answer play_arrow
  • question_answer156) The solution of \[\frac{dy}{dx}={{2}^{y-x}}\]is:

    A) \[{{2}^{x}}+{{2}^{y}}=c\]

    B) \[{{2}^{x}}-{{2}^{y}}=c\]

    C) \[\frac{1}{{{2}^{x}}}-\frac{1}{{{2}^{y}}}=c\]

    D) \[\frac{1}{{{2}^{x}}}+\frac{1}{{{2}^{y}}}=c\]

    View Answer play_arrow
  • question_answer157) \[\int_{{}}^{{}}{\frac{\sin xdx}{3+4{{\cos }^{2}}x}}\]

    A) \[\log (3+4{{\cos }^{2}}x)+c\]

    B) \[-\frac{1}{2\sqrt{3}}{{\tan }^{-1}}\left( \frac{\cos x}{\sqrt{3}} \right)+c\]

    C) \[-\frac{1}{2\sqrt{3}}{{\tan }^{-1}}\left( \frac{2\cos x}{\sqrt{3}} \right)+c\]

    D) \[\frac{1}{2\sqrt{3}}{{\tan }^{-1}}\left( \frac{2\cos x}{\sqrt{3}} \right)+c\]

    View Answer play_arrow
  • question_answer158) The value of\[\int_{-1}^{3}{\left[ {{\tan }^{-1}}\left( \frac{x}{{{x}^{2}}+1} \right)+{{\tan }^{-1}}\left( \frac{{{x}^{2}}+1}{x} \right) \right]dx}\]is

    A) \[2\pi \]

    B) \[\pi \]

    C) \[\pi /2\]

    D) \[\pi /4\]

    View Answer play_arrow
  • question_answer159) \[\int_{0}^{\pi /2}{\log (\tan x)dx}\]

    A) zero

    B) 2

    C) \[\pi /3\]

    D) \[\pi /4\]

    View Answer play_arrow
  • question_answer160) \[\int_{0}^{\pi /4}{\log (1+\tan x)\,dx}\]

    A) \[\frac{\pi }{4}\log 2\]

    B) \[\frac{\pi }{8}\log 2\]

    C) \[\frac{\pi }{4}\log \tan x\]

    D) zero

    View Answer play_arrow
  • question_answer161) The maximum value of \[\frac{{{\log }_{e}}x}{x}\]in\[0<x<\infty \]is:

    A) \[e\]

    B) \[{{\log }_{x}}e\]

    C) \[1/e\]

    D) \[e/2\]

    View Answer play_arrow
  • question_answer162) If \[{{x}_{r}}=\cos \frac{\pi }{{{2}^{r}}}+i\sin \frac{\pi }{{{2}^{r}}},\]then\[{{x}_{1}},{{x}_{2}},{{x}_{3...\infty }}\]is equal to:

    A) zero

    B) 1

    C) \[\pi \]

    D) \[-1\]

    View Answer play_arrow
  • question_answer163) Which of the following is the empty set:

    A) [\[x:x\]is a real number and\[{{x}^{2}}-1=0\,\]}

    B) [\[x:x\]is a real number and \[{{x}^{2}}+1=0\]}

    C) [\[x:x\]is a real number and\[{{x}^{2}}-9=0\]}

    D) [\[x:x\]is a real number and\[{{x}^{2}}=x+2\]}

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  • question_answer164) If \[A=\{1,2\}\]and \[B=(0,1)\]then \[A\times B\]is:

    A) \[\{(1,0),(1,1),(2,0),(2,1)\}\]

    B) \[\{(1,0),(2,1)\}\]

    C) \[\{(1,1),(1,2),(0,1),(0,2)\}\]

    D) none of these

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  • question_answer165) \[f:R\to R\]is a function defined by\[f(x)=10x-7.\]If \[g={{f}^{-1}}\]then \[g(x)=\]

    A) \[\frac{1}{10{{x}^{-7}}}\]

    B) \[\frac{1}{10x+7}\]

    C) \[\frac{x+7}{10}\]

    D) \[\frac{x-7}{10}\]

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  • question_answer166) The identity element for the binary operation * defined by \[a*b=\frac{ab}{2},a,b\in {{Q}_{0}}\] (the set of all non-zero rational number) is:

    A) 1

    B) zero

    C) 2

    D) none of these

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  • question_answer167) The curve represented by\[\operatorname{Im}({{z}^{2}})=K,\]where K is a non-zero real number is:

    A) a pair of straight lines

    B) an ellipse

    C) a parabola

    D) a hyperbola

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  • question_answer168) The value of \[{{i}^{i}}\]is:

    A) \[\omega \]

    B) \[-{{\omega }^{2}}\]

    C) \[\pi /2\]

    D) none of these

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  • question_answer169) If 7th and 13th terms of an AP be 34 and 64 respectively, then its 18th term is:

    A) 87

    B) 88

    C) 89

    D) 90

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  • question_answer170) If \[\alpha ,\beta \]are the roots of the equation x2 + x +1 \[{{x}^{2}}+x+1=0\]and \[\alpha /\beta ,\beta /\alpha \]are roots of the equation \[{{x}^{2}}+px+q=0\]then p equals:

    A) \[-1\]

    B) \[1\]

    C) \[-2\]

    D) \[2\]

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  • question_answer171) The number of ways to arrange the letters of word CHEESE are:

    A) 120

    B) 240

    C) 720

    D) 6

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  • question_answer172) The coefficient of\[{{x}^{4}}\]in the expansion of \[{{(1+x+{{x}^{2}}+{{x}^{3}})}^{11}}\]is:

    A) 900

    B) 909

    C) 990

    D) 999

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  • question_answer173) If A and B are two matrices such that \[AB=B\]and \[BA=A\]then \[{{A}^{2}}+{{B}^{2}}=\]

    A) \[2AB\]

    B) \[2BA\]

    C) \[A\div B\]

    D) \[AB\]

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  • question_answer174) The value of the determinant\[\left| \begin{matrix} 1 & {{\omega }^{2}} & {{\omega }^{5}} \\ {{\omega }^{2}} & 1 & {{\omega }^{4}} \\ {{\omega }^{5}} & {{\omega }^{4}} & 1 \\ \end{matrix} \right|\]where \[\omega \]is an imaginary cube root of unity is:

    A) \[{{(1-\omega )}^{2}}\]

    B) 3

    C) \[-3\]

    D) zero

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  • question_answer175) The line \[x+y=4\]divides the line joining\[(-1,1)\] and \[(5,7)\] in the ratio\[\lambda :1,\] then the value of\[\lambda \] is:

    A) 2

    B) \[1/2\]

    C) 3

    D) none of these

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  • question_answer176) Four distinct points \[(2K,3K),(1,0),(0,1)\] and (0, 0) lie on a circle for:

    A) all integral value of K

    B) \[0<K<1\]

    C) \[K<0\]

    D) for two values of K

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  • question_answer177) The equation to the ellipse referred to its axes as the axes of\[x\]and \[y\]respectively) whose foci are \[(\pm \,2,0)\] and eccentricity 1/2 is:

    A) \[\frac{{{x}^{2}}}{12}+\frac{{{y}^{2}}}{16}=1\]

    B) \[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{12}=1\]

    C) \[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{8}=1\]

    D) none of these

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  • question_answer178) If \[f(x)=\frac{x-1}{x+1},\]then \[f(2x)\]is:

    A) \[\frac{f(x)+1}{f(x)+3}\]

    B) \[\frac{3f(x)+1}{f(x)+3}\]

    C) \[\frac{f(x)+3}{f(x)+1}\]

    D) \[\frac{f(x+3)}{3f(x)+1}\]

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  • question_answer179) The degree of the differential equation \[{{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{2}}+{{\left( \frac{dy}{dx} \right)}^{2}}=x\sin \left( \frac{{{d}^{2}}y}{dx} \right)\]is:

    A) 1

    B) 2

    C) 3

    D) none of these

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  • question_answer180) In any group the number of improper subgroups is:

    A) 2

    B) 3

    C) Depends on the given group

    D) 1

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