Solved papers for BCECE Engineering BCECE Engineering Solved Paper-2009

done BCECE Engineering Solved Paper-2009

  • question_answer1) A rectangular coil of 100 turns and size \[0.1\times 0.05\] m is placed perpendicular to a magnetic field of 0.1 T. The induced emf when the field drops to 0.05 T in 0.05 s is

    A) 0.5 V

    B) 1.0 V

    C) 1.5 V

    D) 2.0 V

    View Answer play_arrow
  • question_answer2) A paramagnetic substance is placed in a weak magnetic field and its absolute temperature T is increased. As a result, its magnetization

    A) increases in proportion to T

    B) decreases in proportion to \[\frac{1}{T}\]

    C) increases in proportion to\[{{T}^{2}}\]

    D) decreases in proportion to \[\frac{1}{{{T}^{2}}}\]

    View Answer play_arrow
  • question_answer3) The current through n bulb is increased by. Assuming that the resistance of the filament remains unchanged the power of the bulb will

    A) increase by 1%

    B) decrease by 1%

    C) increase by 2%

    D) decrease by 2%

    View Answer play_arrow
  • question_answer4) You are given two resistances \[{{R}_{1}}\] and\[{{R}_{2}}\] By using them singly in series and In parallel you can obtain four resistances of \[1.5\,\Omega ,\,2\,\Omega ,\,6\,\Omega \] and 8 \[\Omega .\] The values of \[{{R}_{1}}\] and \[{{R}_{2}}\] are

    A) \[1\,\,\Omega ,\,7\,\Omega \]

    B) \[1.5\,\,\Omega ,\,6.5\,\Omega \]

    C) \[3\,\,\Omega ,\,5\,\Omega \]

    D) \[2\,\,\Omega ,\,6\,\Omega \]

    View Answer play_arrow
  • question_answer5) A wire often the \[l\] carrying a current \[I\] A is bent into a circle. The magnitude of the magnetic moment is

    A) \[\frac{l{{I}^{2}}}{2\pi }\]

    B) \[\frac{l{{I}^{2}}}{4\pi }\]

    C) \[\frac{{{l}^{2}}I}{2\pi }\]

    D) \[\frac{{{l}^{2}}I}{4\pi }\]

    View Answer play_arrow
  • question_answer6) A parallel beam of white light is reflected from a thin wedge-shaped film. The colour of the fringe the edge of the wedge will be

    A) white

    B) red

    C) black

    D) violet

    View Answer play_arrow
  • question_answer7) An object is placed at the focus of a convex mirror. If its focal length is 20 cm, the distance of mirror is

    A) 20 cm

    B) 10 cm

    C) 40 cm

    D) None of these

    View Answer play_arrow
  • question_answer8) A convex lens of glass (\[\mu =1\] of 8 cm when place in has a focal length of lens when air. What is the focal \[\left( \mu =\frac{4}{3} \right)?\]

    A) \[4cm\]

    B) \[8\,cm\]

    C) \[16\,cm\]

    D) \[32\,cm\]

    View Answer play_arrow
  • question_answer9) An LCR series circuit, connected to a source E, is resonance. Then

    A) the voltage across R is zero

    B) the voltage across R equals applied voltage

    C) the voltage across C is zero

    D) the voltage across L equals applied voltage

    View Answer play_arrow
  • question_answer10) What will be the colour of the sky as seen from the earth if there were no atmosphere?

    A) Black

    B) Blue

    C) Orange

    D) Red

    View Answer play_arrow
  • question_answer11) In a single slit diffraction experiment, the width of the slit is made double its original width. Then the central maximum on the diffraction pattern will become

    A) narrower and fainter

    B) narrower and brighter

    C) broader and fainter

    D) broader and brighter

    View Answer play_arrow
  • question_answer12) An \[\alpha -\]particle and a deuteron projected with equal kinetic energies describe circular paths or radii \[{{r}_{1}}\] and\[{{r}_{2}}\] respectively in a uniform magnetic field. The ratio\[{{\text{r}}_{\text{1}}}\text{/}{{\text{r}}_{\text{2}}}\] is

    A) 1

    B) 2

    C) \[\frac{1}{\sqrt{2}}\]

    D) \[\sqrt{2}\]

    View Answer play_arrow
  • question_answer13) The energy in monochromatic X-rays of wavelength \[1\,\overset{\text{o}}{\mathop{\text{A}}}\,\] is roughly equal to

    A) \[\text{2 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-15}}}\text{J}\]

    B) \[\text{2 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-16}}}\text{J}\]

    C) \[\text{2 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-17}}}\text{J}\]

    D) \[\text{2 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-18}}}\text{J}\]

    View Answer play_arrow
  • question_answer14) The de-Broglie wavelength of a neutron at 927?C is \[\lambda \]. What will be its wavelength at 27?C?

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

    B) \[\lambda \]

    C) \[2\lambda \]

    D) None of these

    View Answer play_arrow
  • question_answer15) A telescope has an objective of focal length 100 cm and an eye-piece of focal length 5 cm. What is the magnifying power of the telescope when it is in normal adjustment?

    A) 0.2

    B) 2.0

    C) 20

    D) 200

    View Answer play_arrow
  • question_answer16) An isotropic source of 2 candela produces a light flux equal to

    A) \[2\pi \] lumen

    B) \[4\pi \] lumen

    C) \[6\pi \] lumen

    D) \[8\pi \] lumen

    View Answer play_arrow
  • question_answer17) No photoelectrons are emitted from a metal if the wavelength of the light exceeds 600 nm. The work function of the metal is approximately equal to

    A) \[\text{3 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-16}}}\text{J}\]

    B) \[\text{3 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-19}}}\text{J}\]

    C) \[\text{3 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-20}}}\text{J}\]

    D) \[\text{3 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-22}}}\text{J}\]

    View Answer play_arrow
  • question_answer18) In Rutherfords\[\alpha -\]particle experiment with thin gold foil, 8100 scintillations per minute are observed at an angle of 60?. The number of scintillations per minute at an angle of 120? will be

    A) 900

    B) 2025

    C) 32400

    D) 4050

    View Answer play_arrow
  • question_answer19) Which of the following gates has the truth table

    A B X
    0 0 1
    1 0 1
    0 1 1
    1 1 0
     

    A) NAND                                 

    B) NOR

    C) XOR                     

    D) AND

    View Answer play_arrow
  • question_answer20) Which of the junction diodes shown below are forward biased?

    A)

    B)

    C)

    D)

    View Answer play_arrow
  • question_answer21) A uniform rod or mass m and length l is held \[{{60}^{\text{o}}}\] with the vertical. . What will be the potential this position?

    A) Zero

    B) \[\frac{mgl}{4}\]

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

    D) \[mgl\]

    View Answer play_arrow
  • question_answer22) A sphere roils down an inclined plane without slipping. What fraction of its total energy is rotational?

    A) \[\frac{2}{7}\]

    B) \[\frac{3}{7}\]

    C) \[\frac{4}{7}\]

    D) \[\frac{5}{7}\]

    View Answer play_arrow
  • question_answer23) 23. From the top of a building 40 m tall, a boy projects a Stone vertically upwards with an initial velocity \[10\,m{{s}^{-1}}\] such that it eventually falls to the ground. After how long will the stone strike the ground? Take \[g=10\,m{{s}^{-2}}\]

    A) 1 s

    B) 2 s

    C) 3 s

    D) 4 s

    View Answer play_arrow
  • question_answer24) A 150 m long train is travelling from east to west at a speed of \[20\,m{{s}^{-1}}\]. A bird is flying from west to east at a speed of \[5\,m{{s}^{-1}}\]. How long wilt the bird take to cross the train?

    A) 6 s

    B) 7.5 s

    C) 10 s

    D) 30 s

    View Answer play_arrow
  • question_answer25) An elastic spring has a length \[{{l}_{1}}\] when it is stretched with a force of 2 N and a length of \[{{l}_{2}}\] when it is stretched with a force of 3N. What will be the length of the spring if it is stretched with force of 5N?

    A) \[(l{{  }_{1}}+{{l}_{2}})\]            

    B) \[\frac{1}{2}(l{{  }_{1}}+{{l}_{2}})\]   

    C) \[(3l{{  }_{2}}-2{{l}_{1}})\]        

    D) \[(3l{{  }_{1}}-2{{l}_{2}})\]

    View Answer play_arrow
  • question_answer26) The density of water at the surface of ocean is \[\rho \] If the bulk modulus of water is B, what is the density of ocean water at a depth where the pressure is\[n{{p}_{0,}}\] where\[{{p}_{0,}}\] is the atmospheric pressure?

    A) \[\frac{\rho B}{B-(n-1){{P}_{0}}}\]

    B) \[\frac{\rho B}{B+(n-1)P0}\]

    C) \[\frac{\rho B}{B-n{{P}_{0}}}\]

    D) \[\frac{\rho B}{B+n{{P}_{0}}}\]

    View Answer play_arrow
  • question_answer27) What is the torque of force \[\mathbf{\hat{F}}=-3\mathbf{\hat{i}}+\mathbf{\hat{j}}+5\mathbf{\hat{k}}\] acting at point whose position vector is\[\mathbf{\vec{r}}=7\mathbf{\hat{i}}+3\mathbf{\hat{j}}+\mathbf{\hat{k}}?\]

    A) \[14\mathbf{\hat{i}}-38\mathbf{\hat{j}}+16\mathbf{\hat{k}}\]

    B) \[4\mathbf{\hat{i}}+4\mathbf{\hat{j}}+6\mathbf{\hat{k}}\]

    C) \[-14\mathbf{\hat{i}}+38\mathbf{\hat{j}}-6\mathbf{\hat{k}}\]

    D) \[-21\mathbf{\hat{i}}+3\mathbf{\hat{j}}+5\mathbf{\hat{k}}\]

    View Answer play_arrow
  • question_answer28) Two satellites of masses 3M and M orbit the earth in circular orbits of radii r and 3r respectively. The ratio of their speeds is

    A) 1 : 1

    B) \[\sqrt{3}\]: 1

    C) 3 : 1

    D) 9 : 1

    View Answer play_arrow
  • question_answer29) The dimensions of Reynoldss constant are

    A) \[\text{ }\!\![\!\!\text{ }{{\text{M}}^{\text{o}}}{{\text{L}}^{\text{o}}}{{\text{T}}^{\text{o}}}\text{ }\!\!]\!\!\text{ }\]

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

    C) \[\text{ }\!\![\!\!\text{ M}{{\text{L}}^{-1}}{{\text{T}}^{-2}}\text{ }\!\!]\!\!\text{ }\]

    D) \[\text{ }\!\![\!\!\text{ M}{{\text{L}}^{-2}}{{\text{T}}^{-2}}\text{ }\!\!]\!\!\text{ }\]

    View Answer play_arrow
  • question_answer30) The surface tension of soap solution is \[\sigma \]. What is the work done in blowing soap bubble of radius r?

    A) \[\pi {{r}^{2}}\sigma \]

    B) \[2\pi {{r}^{2}}\sigma \]

    C) \[4\pi {{r}^{2}}\sigma \]

    D) \[8\pi {{r}^{2}}\sigma \]

    View Answer play_arrow
  • question_answer31) The ratio of nns speed of \[{{O}_{2}}\] to \[{{H}_{2}}\] is

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

    B) 4

    C) 2

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

    View Answer play_arrow
  • question_answer32) Two rods A and B of different materials are welded together as shown in figure. If their thermal conductivities are \[{{K}_{1}}\] and\[{{K}_{2}}\] the thermal conductivity of the composite rod will be

    A) \[2({{K}_{1}}+{{K}_{2}})\]

    B) \[\frac{3}{2}({{K}_{1}}+{{K}_{2}})\]

    C) \[({{K}_{1}}+{{K}_{2}})\]

    D) \[\frac{1}{2}({{K}_{1}}+{{K}_{2}})\]

    View Answer play_arrow
  • question_answer33) The wavelength of the radiation emitted by a body depends upon

    A) the nature of its surface

    B) the area of its surface

    C) the temperature of its surface

    D) All the above factors

    View Answer play_arrow
  • question_answer34) An ideal monoatomic gas is taken around the cycle ABCDA as shown in the p- V diagram. The work done during the cycle is given by

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

    B) \[pV\]                  

    C) \[2pV\]               

    D) \[4pV\]

    View Answer play_arrow
  • question_answer35) An ideal gas at pressure p is adiabaticalty compressed so that its density becomes n times the initial value. The final pressure of the gas will be\[\left( \gamma =\frac{{{C}_{P}}}{{{C}_{V}}} \right)\]

    A) \[{{n}^{\gamma }}P\]

    B) \[{{n}^{-\gamma }}P\]

    C) \[{{n}^{(-\gamma -1)}}P\]

    D) \[{{n}^{(1-\gamma )}}P\]

    View Answer play_arrow
  • question_answer36) The displacement of a travelling wave is given by\[y=2\,\cos \,2\pi \,(10t-\,0.008\,x\,+\,.35)\] where, x and y are in centimetre and t in second. What is the phase difference between oscillatory motion at two points separated by a distance of 4 m?

    A) \[2\pi \]

    B) \[4\pi \]

    C) \[6\pi \]

    D) \[8\pi \]

    View Answer play_arrow
  • question_answer37) A bimetallic strip consists of brass and iron when it is heated it bends into an arc with brass on the convex and iron on the concave side of the arc. This happens because

    A) brass has a higher specific heat capacity than iron

    B) density of brass is more than that of iron

    C) it is easier to bend an iron strip than a brass strip of the same size

    D) brass has a higher coefficient of linear expansion than iron

    View Answer play_arrow
  • question_answer38) Three sound waves of equal amplitudes have frequencies (v -1), v, (v + 1). They superpose to give beats. The number of beats produced per second will be

    A) v

    B) v/2

    C) 2

    D) 1

    View Answer play_arrow
  • question_answer39) Which of the following functions does not represent a stationary wave? Here a, b and c are constants.

    A) \[y=a\,\cos bx\,\sin ct\]

    B) \[y=a\sin bx\,\cos \,ct\]

    C) \[y=a\,\sin (bx+ct)\]

    D) \[y=a\sin (bx+ct)\,+a\,\sin \,(bx-ct)\]

    View Answer play_arrow
  • question_answer40) The velocity of sound is greatest in

    A) water

    B) air

    C) vacuum

    D) steel

    View Answer play_arrow
  • question_answer41) Due to Doppler effect, the shift in wavelength observed is \[0.1\,\overset{\text{o}}{\mathop{\text{A}}}\,,\] for a star producing wavelength \[6000\overset{\text{o}}{\mathop{\text{A}}}\,\]. The velocity of recession of star will be

    A) \[2.5\,km{{s}^{-1}}\]

    B) \[10\,km{{s}^{-1}}\]

    C) \[5\,km{{s}^{-1}}\]

    D) \[20\,km{{s}^{-1}}\]

    View Answer play_arrow
  • question_answer42) A body executing linear simple harmonic motion has a velocity of \[3\,m{{s}^{-1}}\] when its displacement is 4 cm and a velocity of \[4\,m{{s}^{-1}}\] when its displacement is 3 cm. What is the amplitude of oscillation?

    A) 5 cm

    B) 7.5 cm

    C) 10 cm

    D) 12.5 cm

    View Answer play_arrow
  • question_answer43) Two masses \[{{m}_{1}}\] and\[{{m}_{2}}\] are suspended together by a massless spring of force constant k, as shown in figure. When the masses are in equilibrium, mass \[{{m}_{1}}\]is removed without disturbing the system. The angular frequency of oscillation of mass \[{{m}_{2}}\] is

    A) \[\sqrt{\frac{k}{{{m}_{2}}}}\]

    B) \[\sqrt{\frac{k}{{{m}_{1}}}}\]

    C) \[\sqrt{\frac{k{{m}_{1}}}{m\,_{2}^{2}}}\]

    D) \[\sqrt{\frac{k{{m}_{2}}}{m_{1}^{2}\,}}\]

    View Answer play_arrow
  • question_answer44) The intensity level of a sound wave is defined by an arbitrary scale. The zero of the scale is taken at the sound wave intensity

    A) \[\text{1 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-10}}}\,\text{W}{{\text{m}}^{\text{-2}}}\]

    B) \[\text{1 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-12}}}\,\text{W}{{\text{m}}^{\text{-2}}}\]

    C) \[\text{1 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-14}}}\,\text{W}{{\text{m}}^{\text{-2}}}\]

    D) \[\text{1 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-16}}}\,\text{W}{{\text{m}}^{\text{-2}}}\]

    View Answer play_arrow
  • question_answer45) A pendulum bob of mass m carrying a charge q is at rest with its string making an angle \[\theta \] with the vertical in a uniform horizontal electric field E. The tension in the siring is

    A) \[\frac{\text{mg}}{\text{sin}}\text{and}\frac{\text{qE}}{\text{cos}\,}\]

    B) \[\frac{\text{mg}}{\text{cos}}\text{and}\frac{\text{qE}}{\sin \,}\]

    C) \[\frac{\text{qE}}{mg}\]

    D) \[\frac{mg}{\text{qE}}\]

    View Answer play_arrow
  • question_answer46) A galvanometer of resistance 10 \[\Omega \] gives full-scale deflection when 1 mA current passes through it. The resistance required to convert it into a voltmeter reading upto 2.5 V is

    A) \[24.9\,\Omega \]

    B) \[249\,\Omega \]

    C) \[2490\,\Omega \]

    D) \[24900\,\Omega \]

    View Answer play_arrow
  • question_answer47) The current inside an electrolytic cell is carried by

    A) positive ions

    B) negative ions

    C) both positive and negative ions

    D) electrons

    View Answer play_arrow
  • question_answer48) The electric potential V (in volt) varies with x (in metre) according to the relation \[V=(5+4{{x}^{2}})\]. The force experienced by a negative charge of 2x10-6C located at a =0.5 m is

    A) \[\text{2 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-6}}}\text{N}\]

    B) \[\text{4 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-6}}}\text{N}\]

    C) \[\text{6 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-6}}}\text{N}\]

    D) \[\text{8 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-6}}}\text{N}\]

    View Answer play_arrow
  • question_answer49) A parallel plate capacitor of plate area A has a charge Q. The force on each plate of the capacitor is

    A) \[\frac{2{{Q}^{2}}}{{{\varepsilon }_{0}}A}\]

    B) \[\frac{{{Q}^{2}}}{{{\varepsilon }_{0}}A}\]

    C) \[\frac{{{Q}^{2}}}{2{{\varepsilon }_{0}}A}\]

    D) Zero

    View Answer play_arrow
  • question_answer50) In Millikans oil drop experiment, an oil drop is observed to move vertically upwards. The upward motion of the drop is due to

    A) gravity

    B) viscosity

    C) buoyancy

    D) electric field

    View Answer play_arrow
  • question_answer51) Which one of these is an important polysaccharide present in plants?

    A) Glucose

    B) Glycogen

    C) Sucrose

    D) Starch

    View Answer play_arrow
  • question_answer52) Cannizaro reaction would be given by

    A) \[{{C}_{6}}{{H}_{5}}CHO\]

    B) \[C{{H}_{3}}COC{{H}_{3}}\]

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

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

    View Answer play_arrow
  • question_answer53) \[C{{H}_{3}}C\equiv CH\xrightarrow[+H{{g}^{2+}},60{{\,}^{o}}C]{{{H}_{2}}S{{O}_{4}}}\]?

    A) \[C{{H}_{3}}CHO\]

    B) \[C{{H}_{3}}COOH\]

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

    D) \[C{{H}_{3}}C{{H}_{2}}COOH\]

    View Answer play_arrow
  • question_answer54) In which of the following can peroxide effect operate?

    A) \[C{{H}_{3}}C{{H}_{2}}CH=C{{H}_{2}}+HCl\]

    B) \[C{{H}_{3}}C{{H}_{2}}CH=C{{H}_{2}}+HBr\]

    C) \[C{{H}_{3}}CH=CH.C{{H}_{3}}+HBr\]

    D) \[C{{H}_{3}}C{{H}_{2}}CH=C{{H}_{2}}+HI\]

    View Answer play_arrow
  • question_answer55) The term quaternary structure is used in the context of

    A) carbohydrates

    B) vitamins

    C) proteins

    D) nucleic acids

    View Answer play_arrow
  • question_answer56) Aspirin is

    A) antibiotic

    B) sedative

    C) tranquilizer

    D) antipyretic

    View Answer play_arrow
  • question_answer57) The following is a coordination compound of iron

    A) chlorophyll

    B) Mohrs salt

    C) haemoglobin

    D) vitamin \[{{B}_{12}}\]

    View Answer play_arrow
  • question_answer58) This metal is extracted from its ore by formation of a cyanide complex

    A) \[Ag\]

    B) \[Cu\]

    C) \[Al\]

    D) \[Zn\]

    View Answer play_arrow
  • question_answer59) Smoke is an example of

    A) emulsion

    B) aerosol

    C) gel

    D) foam

    View Answer play_arrow
  • question_answer60) Propan-2-ol + ethanoic acid\[\xrightarrow{{}}\]

    A) \[{{(C{{H}_{3}})}_{2}}CHCOOC{{H}_{3}}\]

    B) \[C{{H}_{3}}COOCH{{(C{{H}_{3}})}_{2}}\]

    C) \[C{{H}_{3}}COOC{{H}_{2}}C{{H}_{3}}\]

    D) \[{{(C{{H}_{3}})}_{2}}CHCOOC{{H}_{2}}C{{H}_{3}}\]

    View Answer play_arrow
  • question_answer61) Which of the following gives RNC when treated with \[CHC{{l}_{3}}\]and KOH?

    A) \[RN{{H}_{2}}\]

    B) \[{{R}_{2}}NH\]

    C) \[{{R}_{4}}{{N}^{+}}C{{l}^{-}}\]

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

    View Answer play_arrow
  • question_answer62) Which of the following is a soap?

    A) Sodium acetate

    B) Magnesium butyrate

    C) Sodium palmitate

    D) Palmitic acid

    View Answer play_arrow
  • question_answer63) The C-C bond dissociation energy in kcal/mol is

    A) 8.1

    B) 0.81

    C) 81

    D) 810

    View Answer play_arrow
  • question_answer64) A compound has four \[s{{p}^{3}}\]hybridized covalent bonds. Its shape is

    A) linear

    B) square planar

    C) octahedral

    D) tetrahedral

    View Answer play_arrow
  • question_answer65) The resonance energy of benzene in kcal/mol is about

    A) \[\approx 20\]

    B) \[\approx 40\]

    C) \[\approx 60\]

    D) \[\approx 80\]

    View Answer play_arrow
  • question_answer66) 1 mole of \[\text{C}{{\text{O}}_{\text{2}}}\]contains

    A) \[6\times {{10}^{23}}\]atoms of C

    B) \[6\times {{10}^{23}}\]atoms of O

    C) \[18\times {{10}^{23}}\]molecules of \[C{{O}_{2}}\]

    D) 3 g-atoms of \[C{{O}_{2}}\]

    View Answer play_arrow
  • question_answer67) Rutherfords famous experiment with \[\alpha -\]particles used this metal

    A) Ni

    B) Au

    C) Fe

    D) Zn

    View Answer play_arrow
  • question_answer68) The charge on an electron in Coulombs is

    A) \[1.602\times {{10}^{-19}}\]

    B) \[1.062\times {{10}^{-19}}\]

    C) \[1.620\times {{10}^{-19}}\]

    D) \[1.006\times {{10}^{-19}}\]

    View Answer play_arrow
  • question_answer69) The number of subshells for a shell with principal quantum number \[n\] is

    A) \[n\]

    B) \[~n+1\]

    C) \[n-1\]

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

    View Answer play_arrow
  • question_answer70) Which of the following pairs of atomic numbers represents s-block elements?

    A) 7, 15

    B) 6, 12

    C) 9, 17

    D) 3, 11

    View Answer play_arrow
  • question_answer71) For a system in equilibrium

    A) \[\Delta G=0\]

    B) \[\Delta G>0\]

    C) \[\Delta G<0\]

    D) \[\Delta H=0\]

    View Answer play_arrow
  • question_answer72) Which of the following will produce the highest rise in temperature?

    A) \[\text{64}\,\text{mL}\,\text{1M}\,\text{NaOH}\,\text{+}\,\text{33}\,\text{mL}\]of \[\text{0}\text{.5}\,\text{M}\,{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}\]

    B) \[\text{33}\,\text{mL}\]of \[\text{1}\,\text{M}\,\text{NaOH}\,\text{+}\,\text{67}\,\text{mL}\,\]of \[\text{0}\text{.5}\,\text{M}\,{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}\]

    C) \[\text{40}\,\text{mL}\]of \[\text{1}\,\text{M}\,\text{NaOH}\,\text{+}\,\text{60}\,\text{mL}\]of \[\text{0}\text{.5}\,\text{M}\,{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}\]

    D) \[\text{50}\,\text{mL}\]of \[\text{1}\,\text{M}\,\text{NaOH}\,\text{+}\,\text{50}\,\text{mL}\]of \[\text{0}\text{.5}\,\text{M}\,{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}\]

    View Answer play_arrow
  • question_answer73) The standard for atomic mass is

    A) \[_{1}^{1}H\]

    B) \[_{6}^{12}C\]

    C) \[_{6}^{14}C\]

    D) \[_{8}^{16}O\]

    View Answer play_arrow
  • question_answer74) Which of the following involves absorption of energy?

    A) \[Cl+{{e}^{-}}\xrightarrow{{}}C{{l}^{-}}\]

    B) \[{{O}^{-}}+{{e}^{-}}\xrightarrow{{}}{{O}^{2-}}\]

    C) \[O+{{e}^{-}}\xrightarrow{{}}{{O}^{-}}\]

    D) \[S+{{e}^{-}}\xrightarrow{{}}{{S}^{-}}\]

    View Answer play_arrow
  • question_answer75) The successive ionization energies of an element are 800, 2,000, 3,600, 25,000 and 32,000 kJ/mol. The number of valence electrons are

    A) 5

    B) 2

    C) 3

    D) 4

    View Answer play_arrow
  • question_answer76) The first order rate constant for the decomposition of \[{{\text{N}}_{\text{2}}}{{\text{O}}_{\text{5}}}\]is \[6.2\times {{10}^{-4}}{{s}^{-1}}.\] The half-life in seconds is nearly

    A) 1117.7

    B) 111.7

    C) 223

    D) 160

    View Answer play_arrow
  • question_answer77) The rate constant of a reaction is \[1\times {{10}^{-2}}mo{{l}^{-2}}{{L}^{2}}{{s}^{-1}}.\] The order of the reaction is

    A) 0

    B) 1

    C) 2

    D) 3

    View Answer play_arrow
  • question_answer78) The oxidation number of O in \[\text{O}{{\text{F}}_{\text{2}}}\]is

    A) \[-2\]

    B) \[+\,1\]

    C) \[+\,2\]

    D) \[-1\]

    View Answer play_arrow
  • question_answer79) The correct relationship is

    A) \[{{K}_{C}}=n\times {{K}_{p}}\]

    B) \[{{K}_{p}}={{K}_{C}}{{(RT)}^{\Delta {{n}_{g}}}}\]

    C) \[{{K}_{p}}=n\times {{K}_{C}}\]

    D) \[{{K}_{C}}-{{K}_{p}}={{(RT)}^{\Delta N}}\]

    View Answer play_arrow
  • question_answer80) W. For the reaction, \[2B+AC,\] the equilibrium constant is

    A) \[\frac{[A]{{[B]}^{3}}}{[C]}\]

    B) \[\frac{[C]}{[A][2B]}\]

    C) \[\frac{[C]}{[A]{{[B]}^{2}}}\]

    D) \[\frac{[A][B]}{[C]}\]

    View Answer play_arrow
  • question_answer81) A buffer contains equal concentrations of \[{{X}^{-}}\] and HX. The \[{{K}_{a}}\]for HX is \[{{10}^{-8}}.\] The pH of the buffer is

    A) 3

    B) 8

    C) 7

    D) 11

    View Answer play_arrow
  • question_answer82) The metal which gives \[{{\text{H}}_{\text{2}}}\]on treatment with acid as well as \[NaOH\] is

    A) Fe

    B) Cu

    C) Zn

    D) Hg

    View Answer play_arrow
  • question_answer83) Which is isoelectronic with hydride ion?

    A) He

    B) \[\text{H}{{\text{e}}^{+}}\]

    C) Li

    D) \[{{H}^{+}}\]

    View Answer play_arrow
  • question_answer84) A solution of Na in liquid\[\text{N}{{\text{H}}_{\text{3}}}\] is

    A) green

    B) blue

    C) pink

    D) yellow

    View Answer play_arrow
  • question_answer85) The oxide which gives \[{{\text{H}}_{\text{2}}}{{\text{O}}_{\text{2}}}\]on treatment with dilute acid is

    A) \[Pb{{O}_{2}}\]

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

    C) \[Mn{{O}_{2}}\]

    D) \[N{{a}_{2}}{{O}_{2}}\]

    View Answer play_arrow
  • question_answer86) During the electrolysis of fused \[NaCl,\] this happens at cathode

    A) oxidation of\[N{{a}^{+}}\]

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

    C) reduction of \[C{{l}^{-}}\]

    D) oxidation of \[C{{l}^{-}}\]

    View Answer play_arrow
  • question_answer87) Which of the following-s a colored gas?

    A) \[{{N}_{2}}O\]

    B) \[NO\]

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

    D) \[N{{O}_{2}}\]

    View Answer play_arrow
  • question_answer88) This compound gives off \[{{\text{O}}_{\text{2}}}\]on moderate heating

    A) \[HgO\]

    B) \[ZnO\]

    C) \[CaO\]

    D) \[A{{l}_{2}}{{O}_{3}}\]

    View Answer play_arrow
  • question_answer89) Plaster of Paris is hardened by

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

    B) hydration

    C) dehydration

    D) changing into \[CaC{{O}_{3}}\]

    View Answer play_arrow
  • question_answer90) The least ionic chloride is formed by

    A) Mg

    B) Ca

    C) Be

    D) Sr

    View Answer play_arrow
  • question_answer91) Aluminium bronze has

    A) 90% Cu

    B) 50% Ni

    C) 90% Sn

    D) 50% Cu

    View Answer play_arrow
  • question_answer92) In the thermite welding, this is used

    A) Ca

    B) Al + Fe

    C) Fe

    D) \[Al+F{{e}_{2}}{{O}_{3}}\]

    View Answer play_arrow
  • question_answer93) \[{{\text{K}}_{\text{2}}}\text{C}{{\text{O}}_{\text{3}}}\]cannot be prepared by Solvay-ammonia process because

    A) \[{{\text{K}}_{\text{2}}}\text{C}{{\text{O}}_{\text{3}}}\]is fairly soluble in water

    B) it has no water of crystallization

    C) \[\text{KHC}{{\text{O}}_{\text{3}}}\] is highly soluble in water

    D) \[{{\text{K}}_{\text{2}}}\text{C}{{\text{O}}_{\text{3}}}\]decomposes in \[{{\text{H}}_{\text{2}}}\text{O}\]

    View Answer play_arrow
  • question_answer94) Glaubers salt is

    A) \[N{{a}_{2}}S{{O}_{4}}.10{{H}_{2}}O\]

    B) \[FeS{{O}_{4}}.7{{H}_{2}}O\]

    C) \[ZnS{{O}_{4}}.7{{H}_{2}}O\]

    D) \[MgS{{O}_{4}}.7{{H}_{2}}O\]

    View Answer play_arrow
  • question_answer95) The salt responsible for permanent hardness of \[{{\text{H}}_{\text{2}}}\text{O}\]is

    A) \[N{{a}_{2}}S{{O}_{4}}\]

    B) \[MgHC{{O}_{3}}\]

    C) \[NaCl\]

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

    View Answer play_arrow
  • question_answer96) Which of the following carbonium ion is most stable?

    A) \[{{C}_{6}}{{H}_{5}}\overset{+}{\mathop{C}}\,{{H}_{2}}\]

    B) \[{{(C{{H}_{3}})}_{3}}\overset{+}{\mathop{C}}\,\]

    C) \[{{(C{{H}_{3}})}_{2}}\overset{+}{\mathop{C}}\,H\]

    D) \[C{{H}_{3}}\overset{+}{\mathop{C}}\,{{H}_{2}}\]

    View Answer play_arrow
  • question_answer97) Which of the following reacts in presence of anhydrpus \[\text{AlC}{{\text{l}}_{\text{3}}}\]to give acetophenone?

    A) \[{{C}_{6}}{{H}_{6}}+C{{H}_{3}}COC{{H}_{3}}\]

    B) \[{{C}_{6}}{{H}_{5}}OH+C{{H}_{3}}COC{{H}_{3}}\]

    C) \[{{C}_{6}}{{H}_{5}}OH+C{{H}_{3}}COOH\]

    D) \[{{C}_{6}}{{H}_{6}}+C{{H}_{3}}COCl\]

    View Answer play_arrow
  • question_answer98) The isomers which can be interconverted through rotation around a single bond are

    A) conformers

    B) diastereoisomers

    C) enantiomers

    D) position isomers

    View Answer play_arrow
  • question_answer99) Phenol is the component of this fraction upon fractional distillation of petroleum

    A) light oil

    B) middle oil

    C) heavy oil

    D) pitch

    View Answer play_arrow
  • question_answer100) Ethyl chloride on treatment with alcoholic alkali gives

    A) \[{{C}_{2}}{{H}_{6}}\]

    B) \[C{{H}_{3}}CHO\]

    C) \[{{C}_{2}}{{H}_{5}}OH\]

    D) \[C{{H}_{2}}=C{{H}_{2}}\]

    View Answer play_arrow
  • question_answer101) The area of the figure bounded by \[{{y}^{2}}=2x+1\] and \[x-y=1\]is

    A) \[\frac{2}{3}\]

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

    C) \[\frac{8}{3}\]

    D) \[\frac{11}{3}\]

    View Answer play_arrow
  • question_answer102) The order of the differential equation of all tangent lines to the parabola \[y={{x}^{2}}\]is

    A) 1

    B) 2

    C) 3

    D) 4

    View Answer play_arrow
  • question_answer103) \[\int_{{}}^{{}}{\frac{dx}{\sqrt{(1-x)(x-2)}}}\]is equal to

    A) \[{{\sin }^{-1}}(2x-3)+C\]

    B) \[{{\sin }^{-1}}(2x+5)+C\]

    C) \[{{\sin }^{-1}}(3-2x)+C\]

    D) \[{{\sin }^{-1}}(5-2x)+C\]

    View Answer play_arrow
  • question_answer104) \[\int_{{}}^{{}}{\frac{({{\sec }^{2}}x-7)}{{{\sin }^{7}}x}}dx\]is equal to

    A) \[\frac{\tan x}{{{\sin }^{7}}x}+C\]

    B) \[\frac{\cos x}{{{\sin }^{7}}x}+C\]

    C) \[\frac{\sin x}{{{\cos }^{7}}x}+C\]

    D) \[\frac{\sin x}{{{\tan }^{7}}x}+C\]

    View Answer play_arrow
  • question_answer105) \[\int_{-3}^{2}{\{|x+1|+|x+2|+||x-1|\}}\,dx\]is equal to

    A) \[\frac{31}{2}\]

    B) \[\frac{35}{2}\]

    C) \[\frac{37}{2}\]

    D) \[\frac{39}{2}\]

    View Answer play_arrow
  • question_answer106) The variance of first \[n\]natural numbers is

    A) \[\frac{{{n}^{2}}+1}{12}\]

    B) \[\frac{{{n}^{2}}-1}{12}\]

    C) \[\frac{(n+1)(2n+1)}{6}\]

    D) \[{{\left[ \frac{n(n+1)}{2} \right]}^{2}}\]

    View Answer play_arrow
  • question_answer107) A particular solution of \[\log \left( \frac{dy}{dx} \right)=3x+4y,y(0)=0\]is

    A) \[{{e}^{3x}}+3{{e}^{-4y}}=4\]

    B) \[4{{e}^{3x}}-3{{e}^{-4y}}=3\]

    C) \[3{{e}^{3x}}+4{{e}^{-4y}}=7\]

    D) \[4{{e}^{3x}}+3{{e}^{-4y}}=7\]

    View Answer play_arrow
  • question_answer108) The equation of the curve whose subnormal is equal to a constant a is

    A) \[y=ax+b\]

    B) \[{{y}^{2}}=2ax+2b\]

    C) \[a{{y}^{2}}-{{x}^{3}}=a\]

    D) None of these

    View Answer play_arrow
  • question_answer109) If the standard deviation of a variable X is \[\sigma ,\]then the standard deviation of \[\sigma ,\](a, b, c are constants) is

    A) \[\frac{a}{c}\sigma \]

    B) \[\left| \frac{a}{c} \right|\sigma \]

    C) \[\left| \frac{c}{a} \right|\sigma \]

    D) \[\frac{c}{a}\sigma \]

    View Answer play_arrow
  • question_answer110) If \[\sin \alpha ,\cos \alpha \]are the roots of the equation\[a{{x}^{2}}+bx+c=0,(c\ne 0),\]the

    A) \[{{a}^{2}}-{{b}^{2}}+2ac=0\]

    B) \[{{(a+c)}^{2}}={{b}^{2}}-{{c}^{2}}\]

    C) \[{{a}^{2}}+{{b}^{2}}-2ac=0\]

    D) \[{{(a-c)}^{2}}={{b}^{2}}+{{c}^{2}}\]

    View Answer play_arrow
  • question_answer111) If \[\alpha ,\beta ,\gamma \]are such that \[\alpha +\beta +\gamma =2,\]\[{{\alpha }^{2}}+{{\beta }^{2}}+{{\gamma }^{2}}=6,\]\[{{\alpha }^{3}}+{{\beta }^{3}}+{{\gamma }^{3}}=8,\]then \[{{\alpha }^{4}}+{{\beta }^{4}}+{{\gamma }^{4}}\]is equal to

    A) 7

    B) 12

    C) 18

    D) 36

    View Answer play_arrow
  • question_answer112) The equation \[\bar{z}=\bar{a}+\frac{{{r}^{2}}}{(z-a)},r>0\] represents

    A) an ellipse

    B) a parabola

    C) a circle

    D) _ a straight line through point \[\bar{a}\]

    View Answer play_arrow
  • question_answer113) If \[\frac{3}{2+\cos \theta +i\sin \theta }=a+ib,\]then \[[{{(a-2)}^{2}}+{{b}^{2}}]\]is equal to

    A) 0

    B) 1

    C) \[-1\]

    D) 2

    View Answer play_arrow
  • question_answer114) The value of \[4+5{{\left( -\frac{1}{2}+\frac{i\sqrt{3}}{2} \right)}^{334}}+3{{\left( -\frac{1}{2}+\frac{i\sqrt{3}}{2} \right)}^{365}}\]is

    A) \[1-i\sqrt{3}\]

    B) \[-1+i\sqrt{3}\]

    C) \[i\sqrt{3}\]

    D) \[-i\sqrt{3}\]

    View Answer play_arrow
  • question_answer115) If in the expansion of \[{{(a-2b)}^{n}},\] the sum of 4th and 5th term is zero, then the value of\[\frac{a}{b}\] is

    A) \[\frac{n-4}{5}\]

    B) \[\frac{2(n-4)}{5}\]

    C) \[\frac{5}{n-4}\]

    D) \[\frac{5}{2(n-4)}\]

    View Answer play_arrow
  • question_answer116) If\[A=\left[ \begin{matrix} a & b \\ c & d \\ \end{matrix} \right]\]is such that \[|A|=0\] and\[{{A}^{2}}-(a+d)A+kI=0,\] then \[k\]is equal to

    A) \[b+c\]

    B) \[a+d\]

    C) \[ab+cd\]

    D) zero

    View Answer play_arrow
  • question_answer117) The sum of series\[1+\frac{3}{2}+\frac{7}{4}+\frac{15}{8}+\frac{31}{16}+...\]is equal to

    A) \[2(n-1)+\frac{1}{{{2}^{n-1}}}\]

    B) \[2n-\frac{1}{{{2}^{n}}}\]

    C) \[2+\frac{1}{{{2}^{n}}}\]

    D) \[2n-1+\frac{1}{{{2}^{n}}}\]

    View Answer play_arrow
  • question_answer118) The number of meaningful solutions of \[{{\log }_{4}}(x-1)={{\log }_{2}}(x-3)\]is

    A) 3

    B) 2

    C) 1

    D) zero

    View Answer play_arrow
  • question_answer119) The number of ways of arranging letters of the word HAVANA so that V and N do not appear together is

    A) 60

    B) 80

    C) 100

    D) 120

    View Answer play_arrow
  • question_answer120) A man is known to speak the truth 3 out of 4 times. He throws a die and reports that it is a six. The probability that it is actually a six is

    A) \[\frac{3}{8}\]

    B) \[\frac{1}{5}\]

    C) \[\frac{3}{4}\]

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

    View Answer play_arrow
  • question_answer121) The expression \[{{\cos }^{2}}(A-B)+co{{s}^{2}}B-2\cos (A-B)cos\,A\,cos\,B\]is independent of

    A) A

    B) B

    C) both A and B

    D) neither A nor B

    View Answer play_arrow
  • question_answer122) If the system of equations \[ax+y=3,\]\[x+2y=3,3x+4y=7\]is consistent, then value of a is equal to

    A) 2

    B) 1

    C) -1

    D) 0

    View Answer play_arrow
  • question_answer123) If \[\left| \begin{matrix} x-1 & 5x & 7 \\ {{x}^{2}}-1 & x-1 & 8 \\ 2x & 3x & 0 \\ \end{matrix} \right|=a{{x}^{3}}+b{{x}^{2}}+cx+d,\]then c is equal to

    A) \[-1\]

    B) 12

    C) 15

    D) 17

    View Answer play_arrow
  • question_answer124) If \[a,b,c>0,\]the minimum value of \[\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}\]is

    A) 1

    B) \[\frac{3}{2}\]

    C) 2

    D) \[\frac{5}{2}\]

    View Answer play_arrow
  • question_answer125) If \[\tan {{1}^{o}}\tan {{2}^{o}}...tan{{2}^{o}}....\tan {{89}^{o}}={{x}^{2}}-8,\]then the value of \[x\]can be

    A) \[\pm \,1\]

    B) \[\pm \,\,2\]

    C) \[\pm \,\,3\]

    D) \[\pm \,\,4\]

    View Answer play_arrow
  • question_answer126) If \[\sin (x+3\alpha )=3\sin (\alpha -x),\]then

    A) \[\tan \,x=\tan \alpha \]

    B) \[\tan \,x={{\tan }^{2}}\alpha \]

    C) \[\tan x={{\tan }^{3}}\alpha \]

    D) \[\tan x=3\tan \alpha \]

    View Answer play_arrow
  • question_answer127) In a \[\Delta ABC,2{{a}^{2}}+4{{b}^{2}}+{{c}^{2}}=4ab+2ac,\]then \[\cos \,B\]is equal to

    A) 0

    B) \[\frac{1}{8}\]

    C) \[\frac{3}{8}\]

    D) \[\frac{7}{8}\]

    View Answer play_arrow
  • question_answer128) Let A and B be two events such that \[P(A)=0.3\]and \[p(A\cup B)=0.8.\]If A and B are independent events, then \[P(B)\] is

    A) \[\frac{3}{7}\]

    B) \[\frac{4}{7}\]

    C) \[\frac{5}{7}\]

    D) \[\frac{6}{7}\]

    View Answer play_arrow
  • question_answer129) A bag contains 4 brown and 5 white balls. A man pulls two balls at random without replacement. The probability that the man gets both the balls of the same colour is

    A) \[\frac{5}{108}\]

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

    C) \[\frac{5}{18}\]

    D) \[\frac{4}{9}\]

    View Answer play_arrow
  • question_answer130) The value of expression\[\frac{1}{\cos {{290}^{o}}}+\frac{1}{\sqrt{3}\sin {{250}^{o}}}\] is equal to

    A) \[\frac{\sqrt{3}}{4}\]

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

    C) \[\frac{2}{\sqrt{3}}\]

    D) \[\frac{\sqrt{3}}{2}\]

    View Answer play_arrow
  • question_answer131) An equation of a line through the point (1, 2) whose distance from the point (3, 1) has the greatest value is

    A) \[y=2x\]

    B) \[y=x+1\]

    C) \[x+2y=5\]

    D) \[y=3x-1\]

    View Answer play_arrow
  • question_answer132) A line is drawn through the point P(3,11) to cut the circle \[{{x}^{2}}+{{y}^{2}}=9\]at A and B. Then, \[PA.PB\]is equal to

    A) 9

    B) 121

    C) 205

    D) 139

    View Answer play_arrow
  • question_answer133) If the tangent at point P on the circle \[{{x}^{2}}+{{y}^{2}}+6x+6y-2=0\] meets the straight line \[5x-2y+6=0\] at a point Q on the. \[y-\]axis, then length PQ is

    A) 4

    B) \[2\sqrt{5}\]

    C) 5

    D) \[3\sqrt{5}\]

    View Answer play_arrow
  • question_answer134) In a triangle ABC, \[a:\text{ }b:\text{ }c\text{ }=\text{ }4:\text{ }5:\text{ }6.\]The ratio of the radius of the circumcircle to that of the incircle is

    A) \[\frac{15}{4}\]

    B) \[\frac{11}{5}\]

    C) \[\frac{16}{7}\]

    D) \[\frac{16}{3}\]

    View Answer play_arrow
  • question_answer135) If \[4{{\sin }^{-1}}x+{{\cos }^{-1}}x=\pi ,\]then \[x\]is equal to

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

    B) 0

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

    D) 1

    View Answer play_arrow
  • question_answer136) The Value of \[\cos \left( \frac{1}{2}{{\cos }^{-1}}\frac{1}{8} \right)\] is equal to

    A) \[\frac{3}{4}\]

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

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

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

    View Answer play_arrow
  • question_answer137) The vectors \[\vec{a}=\hat{i}+\hat{j}+m\hat{k},\]\[\vec{b}=\hat{i}+\hat{j}+(m+1)\hat{k}\] and \[\vec{c}=\hat{i}-\hat{j}+m\hat{k}\] are coplanar, if \[m\]is equal to

    A) 1

    B) 4

    C) 3

    D) no value of m for which vectors are coplanar

    View Answer play_arrow
  • question_answer138) If|\[|\vec{a}|=2,|\vec{b}|=3,|\vec{c}|=4\]and \[\vec{a}+\vec{b}+\vec{c}=0,\] then the value of \[\vec{b}.\vec{c}+\vec{c}.\vec{a}+\vec{a}+\vec{a}.\vec{b}\]is equal to

    A) \[\frac{19}{2}\]

    B) \[-\frac{19}{2}\]

    C) \[\frac{29}{2}\]

    D) \[-\frac{29}{2}\]

    View Answer play_arrow
  • question_answer139) The line \[x+y=6\]is a normal to the parabola \[{{y}^{2}}=8x\]at the point

    A) \[(18,-12)\]

    B) \[(4,2)\]

    C) \[(2,4)\]

    D) \[(8,8)\]

    View Answer play_arrow
  • question_answer140) If\[{{F}_{1}}=(3,0),{{F}_{2}}=(-3,0)\] and P is any point on the curve \[16{{x}^{2}}+25{{y}^{2}}=400,\] then \[P{{F}_{1}}+P{{F}_{2}}\]is equal to

    A) 6

    B) 8

    C) 10

    D) 12

    View Answer play_arrow
  • question_answer141) If e and\[{{e}_{1}}\]are the eccentricities of a hyperbola and its conjugate, then\[\frac{1}{{{e}^{2}}}+\frac{1}{e_{1}^{2}}\] is equal to

    A) \[-1\]

    B) 0

    C) 1

    D) 2

    View Answer play_arrow
  • question_answer142) \[\underset{x\to 0}{\mathop{\lim }}\,\frac{1-{{\cos }^{3}}x}{x\sin \cos x}\]is equal to

    A) \[\frac{2}{5}\]

    B) \[\frac{3}{5}\]

    C) \[\frac{3}{2}\]

    D) \[\frac{3}{4}\]

    View Answer play_arrow
  • question_answer143) If \[y={{\cos }^{-1}}(\cos \,x),\]then \[y(x)\]is equal to

    A) 1 for all \[x\]

    B) \[-1\]for all \[x\]

    C) 1 in 2nd and 3rd quadrant

    D) \[-1\]in 3rd and 4th quadrant

    View Answer play_arrow
  • question_answer144) If the vectors \[\overrightarrow{AB}=3\hat{i}+4\hat{k}\] and =\[\overrightarrow{AC}=5\hat{i}-2\hat{j}+4\hat{k}\]are the sides of a \[\Delta ABC,\] then the length of the median through A is

    A) \[\sqrt{14}\]

    B) \[\sqrt{18}\]

    C) \[\sqrt{29}\]

    D) 4

    View Answer play_arrow
  • question_answer145) The period of the function\[f(x)=\cos e{{c}^{2}}3x+\cot 4x\]is

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

    B) \[\frac{\pi }{4}\]

    C) \[\frac{\pi }{6}\]

    D) \[\pi \]

    View Answer play_arrow
  • question_answer146) The graph of the function\[f(x)={{\log }_{a}}(x+\sqrt{{{x}^{2}}+1})\] is symmetric about

    A) \[x-\]axis

    B) origin

    C) \[y-\]axis

    D) the line \[y=x\]

    View Answer play_arrow
  • question_answer147) The difference between the greatest and least values of the function\[f(x)=\cos x+\frac{1}{2}\cos 2x-\frac{1}{3}\cos 3x\]is

    A) \[\frac{2}{3}\]

    B) \[\frac{8}{7}\]

    C) \[\frac{3}{8}\]

    D) \[\frac{9}{4}\]

    View Answer play_arrow
  • question_answer148) \[f(x)=\left\{ \begin{matrix} a{{x}^{2}}+b, & b\ne 0,x\le 1 \\ b{{x}^{2}}+ax+c, & x>1 \\ \end{matrix} \right.\] then\[f(x)\] is continuous and differentiable at \[x=1\]if

    A) \[c=0,\,a=2b\]

    B) \[a=b,\,c\in R\]

    C) \[a=b,c=0\]

    D) \[a=b,c\ne 0\]

    View Answer play_arrow
  • question_answer149) Let \[g(x)\]be the inverse of function \[f(x)\] and \[f(x)=\frac{1}{1+{{x}^{3}}},\] then \[g(x)\]is equal to

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

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

    C) \[1+{{\{g(x)\}}^{3}}\]

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

    View Answer play_arrow
  • question_answer150) If \[\theta \] is the semi vertical angle of a cone of maximum volume and given slant height, then\[\tan \,\theta \]is given by

    A) 2

    B) 1

    C) \[\sqrt{2}\]

    D) \[\sqrt{3}\]

    View Answer play_arrow

   

You need to login to perform this action.
You will be redirected in 3 sec spinner

Free
Videos