Solved papers for JCECE Engineering JCECE Engineering Solved Paper-2003

done JCECE Engineering Solved Paper-2003

  • question_answer1) The internal resistance of a cell is the resistance of:

    A) electrolyte used in cell

    B) electrodes of the cell

    C) material used in cell

    D) vessel of the cell

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  • question_answer2) A device for generating an alternating current of d desired frequency is known as:

    A) an oscillator

    B) an amplifier

    C) a rectifier

    D) none of these

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  • question_answer3) The angle of minimum deviation for a thin prism with respect to air and when dipped in water will be:\[\left( _{a}{{\mu }_{g}}=\frac{3}{2},\,{{\,}_{a}}{{\mu }_{w}}=\frac{4}{3} \right)\]

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

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

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

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

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  • question_answer4) Escape velocity of a body when projected from the earth's surface is \[11.2\,\,km/s\]. If it is projected at an angle of \[{{50}^{o}}\] from the horizontal, the escape velocity is:

    A) \[11.8\,\,km/s\]

    B) \[16.5\,\,km/s\]

    C) \[11.2\,\,km/s\]

    D) \[14.5\,\,km/s\]

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  • question_answer5) A diamagnetic substance is brought near a strong magnet, then it is:

    A) attracted by a magnet

    B) repelled by a magnet

    C) repelled by north pole and attracted by south pole

    D) attracted by north pole and repelled by south pole

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  • question_answer6) The ratio of intensities of two waves is \[9:16\]. If they interfere, the ratio of maximum to minimum intensity will be:

    A) \[4:1\]

    B) \[1:25\]

    C) \[1:3\]

    D) \[49:1\]

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  • question_answer7) The sun emits a light with maximum wavelength\[510\,\,nm\] while another star emits a light with maximum wavelength of \[350\,\,nm\]. The ratio of surface temperature of sun and the star will be:

    A) \[0.69\]

    B) \[0.46\]

    C) \[1.45\]

    D) \[2.1\]

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  • question_answer8) If the equation of Motion of standing wave is\[y=0.3\sin (314t-1.57x)\], then the velocity of standing wave is:

    A) \[400\,\,unit\]

    B) \[350\,\,unit\]

    C) \[209\,\,unit\]

    D) \[200\,\,unit\]

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  • question_answer9) For driving current of \[2\,\,A\] for \[6\min \] in a circuit, \[1000\,\,J\] of work is to be done. The emf-of the source in the circuit is:

    A) \[2.03\,\,V\]

    B) \[2.54\,\,V\]

    C) \[1.25\,\,V\]

    D) \[1.39\,\,V\]

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  • question_answer10) The moment of momentum for an electron in second orbit of hydrogen atom as per Bohr's model is:

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

    B) \[2\pi h\]

    C) \[\frac{2h}{\pi }\]

    D) \[\frac{\pi }{h}\]

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  • question_answer11) The latent heat of vaporisation of water is\[2250\,\,J/kg\]. If the work done in the process of vaporisation of \[1\,\,kg\] is \[168\,\,J\], then increase in internal energy will be:

    A) \[1904\,\,J\]

    B) \[1984\,\,J\]

    C) \[3202\,\,J\]

    D) \[2082\,\,J\]

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  • question_answer12) Huygen's wave theory of light could not explain:

    A) photoelectric effect

    B) interference

    C) diffraction

    D) polarization

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  • question_answer13) In a triode valve, when the plate potential is increased from \[200\,\,V\] to \[220\,\,V\] and-grid potential is decreased from \[-0.5\,\,V\] to \[-\text{ }1.3\,\,V,\] there is no change in plate current. The amplification factor of the triode is:

    A) \[25\]

    B) \[14\]

    C) \[11\]

    D) \[73\]

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  • question_answer14) A bar magnet of magnetic moment \[220\,\,A{{m}^{2}}\] is suspended in a magnetic field of intensity\[0.25\,\,N/Am\]. The couple required to deflect it through \[{{30}^{o}}\] is:

    A) \[27.5\,\,Nm\]

    B) \[20.25\,\,Nm\]

    C) \[47.63\,\,Nm\]

    D) \[12\,\,Nm\]

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  • question_answer15) A plano-convex lens has refractive index \[1.5\] and radius of curvature \[50\,\,cm\]. What is focal length of lens?

    A) \[100\,\,cm\]

    B) \[200\,\,cm\]

    C) \[178\,\,cm\]

    D) \[150\,\,cm\]

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  • question_answer16) A source and an observer move away from each other, with a velocity of \[20\,\,m/s\]. If the apparent frequency heard by the observer is \[1840\,\,Hz\], the actual frequency of the source is: (Velocity of sound in\[=340\,\,m/s)\]:

    A) \[2486\,\,Hz\]

    B) \[2070\,\,Hz\]

    C) \[2134\,\,Hz\]

    D) \[1872\,\,Hz\]

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  • question_answer17) The speed of wave in a medium is \[650\,\,m/s\]. If \[3500\] waves are passing through a point in the medium in \[1.67\,\,\min \], then its wavelength will be:

    A) \[16.25\,\,m\]

    B) \[14.29\,\,m\]

    C) \[18.57\,\,m\]

    D) \[20.50\,\,m\]

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  • question_answer18) The body is projected at such angle that the horizontal range is three times the greatest height. The angle of projection is:

    A) \[{{43}^{o}}8'\]

    B) \[{{25}^{o}}8'\]

    C) \[{{33}^{o}}7'\]

    D) \[{{53}^{o}}1'\]

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  • question_answer19) On the horizontal surface of a truck, a block of mass \[1\,\,kg\] is placed \[(\mu =0.6)\] and truck is moving with acceleration \[5m/{{s}^{2}}\]. The frictional force acting on the block will be: \[(g=10\,\,m/{{s}^{2}})\]

    A) \[6\,\,N\]

    B) \[5.88\,\,N\]

    C) \[7\,\,N\]

    D) \[9\,\,N\]

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  • question_answer20) Calculate the work done when a force\[\overset{\to }{\mathop{\mathbf{F}}}\,=2\widehat{\mathbf{i}}+3\widehat{\mathbf{j}}-5\widehat{\mathbf{k}}\]. units acts on a body producing a displacement \[\overset{\to }{\mathop{\mathbf{s}}}\,=2\widehat{\mathbf{i}}+4\widehat{\mathbf{j}}+3\widehat{\mathbf{k}}\] units:

    A) \[1\,\,unit\]

    B) \[20\,\,unit\]

    C) \[5\,\,unit\]

    D) \[zero\]

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  • question_answer21) The efficiency of Carnot engine is, \[50%\] and temperature of sink is \[500\,\,K\]. If the temperature of source is kept constant and its efficiency is to be raised to \[60%\], then the required temperature of the sink will be:

    A) \[600\,\,K\]

    B) \[400\,\,K\]

    C) \[500\,\,K\]

    D) \[100\,\,K\]

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  • question_answer22) What happens to the internal energy of a gas during isothermal expansion?

    A) Internal energy will decrease

    B) Internal energy will increase

    C) Internal energy will become zero

    D) Internal energy will remain same

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  • question_answer23) \[100\,\,g\] ice is mixed with \[100\,\,g\] of water at \[{{100}^{o}}C\]. What will be the final temperature of the mixture?

    A) \[{{10}^{o}}C\]

    B) \[{{27}^{o}}C\]

    C) \[{{14}^{o}}C\]

    D) none of these

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  • question_answer24) Black hole consists of:

    A) ozone layer

    B) super dense planetary material

    C) upper surface of atmosphere

    D) none of the above

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  • question_answer25) Three resistors \[2\,\,\Omega ,\,\,\,3\,\,\Omega \] and \[4\,\,\Omega \] are connected as shown in the given diagram. The equivalent resistance will be:

    A) \[\frac{12}{13}\]

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

    C) \[2\]

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

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  • question_answer26) If an electron jumps from first orbit to third orbit of hydrogen atom it will:

    A) not loose energy

    B) release energy

    C) absorb energy

    D) not gain energy

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  • question_answer27) A body of mass \[10\,\,kg\] moving with velocity \[10\,\,m/s\] collides with a stationary body of mass\[5\,\,kg\]. After collision both bodies stick to each other, velocity of the joint body after collision is:

    A) \[\frac{3}{10}m/s\]

    B) \[20\,\,m/s\]

    C) \[\frac{20}{3}m/s\]

    D) \[15\,\,m/s\]

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  • question_answer28) If a body starts from rest and travels \[110\,\,cm\] in the \[9th\] second, then acceleration of the body is:

    A) \[0.13m/{{s}^{2}}\]

    B) \[0.16m/{{s}^{2}}\]

    C) \[0.18m/{{s}^{2}}\]

    D) \[0.34m/{{s}^{2}}\]

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  • question_answer29) It the momentum of a particle is doubled, then its de-Broglie wavelength will:

    A) become four times

    B) become half

    C) become two times

    D) remain unchanged

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  • question_answer30) Dimensions of torque are:

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

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

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

    D) \[[M{{L}^{0}}{{T}^{-2}}]\]

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  • question_answer31) Two vectors have magnitudes \[3\] and \[5\]. If angle between them is \[{{60}^{o}}\], then the dot product of two vectors will be:

    A) \[7.5\]

    B) \[6.5\]

    C) \[8.4\]

    D) \[7.9\]

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  • question_answer32) The kinetic energy of \[1\,\,g\] molecule of a gas, at normal temperature and pressure is:\[(R=8.321\,\,J/mol\text{-}K)\]

    A) \[1.2\times {{10}^{2}}J\]

    B) \[3.4\times {{10}^{3}}J\]

    C) \[1.66\times {{10}^{4}}J\]

    D) \[2.97\times {{10}^{4}}J\]

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  • question_answer33) If the coefficient of cubical expansion is \[x\] times of the coefficient of superficial expansion, then value of \[x\] is:

    A) \[2.7\]

    B) \[2\]

    C) \[1.5\]

    D) \[9.5\]

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  • question_answer34) \[X-\]ray will not show the phenomenon of:

    A) interference

    B) deflection by electric field

    C) diffraction

    D) polarisation

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  • question_answer35) Bernoulli's theorem is based on:

    A) conservation of mass, energy and momentum

    B) conservation of mass

    C) conservation of momentum

    D) conservation of energy

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  • question_answer36) In bringing an electron towards another electron, the electrostatic potential energy of the system:

    A) decreases

    B) increases

    C) remains same

    D) becomes zero

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  • question_answer37) The half-life of radium is \[1600\,\,yr\]. What is the mean life and disintegration constant of radium?

    A) \[2309\,\,yr,\,\,\frac{1}{2309}/yr\]

    B) \[3309\,\,yr,\,\,\frac{1}{3309}/yr\]

    C) \[1309\,\,yr,\,\,\frac{1}{1309}/yr\]

    D) none of the above

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  • question_answer38) Energy obtained when \[1\,\,mg\] mass is completely converted in to energy will be:

    A) \[9\times {{10}^{13}}J\]

    B) \[3\times {{10}^{8}}J\]

    C) \[3\times {{10}^{15}}J\]

    D) \[9\times {{10}^{15}}J\]

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  • question_answer39) A ray of light is incident on a surface of a plate of glass of refractive index \[1.5\] at polarising angle. The angle of refraction of the ray will be:

    A) \[{{53.7}^{o}}\]

    B) \[{{43.7}^{o}}\]

    C) \[{{33.7}^{o}}\]

    D) none of these

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  • question_answer40) A closed organ pipe and an open organ pipe are tuned to the same fundamental frequency. The ratio of their lengths is:

    A) \[1:2\]

    B) \[4:1\]

    C) \[1:4\]

    D) \[2:1\]

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  • question_answer41) A particle is moving along a circular path of radius \[5\,\,m\] with uniform speed \[5\,\,m/s\]. What will be the average acceleration when the particle completes half revolution?

    A) \[\frac{10}{\pi }m/{{s}^{2}}\]

    B) \[10\,\,m/{{s}^{2}}\]

    C) \[10\pi \,\,m/{{s}^{2}}\]

    D) \[Zero\]

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  • question_answer42) A body of mass \[m\] is attached between two springs of force constants \[{{k}_{1}}\] and \[{{k}_{2}}\] as Shown in figure. The other ends of the springs are fixed to firm supports. The frequency of the oscillation is:

    A) \[n=\frac{1}{2\pi }\sqrt{\frac{{{k}_{1}}-{{k}_{2}}}{m}}\]

    B) \[n=\frac{1}{2\pi }\sqrt{\frac{{{k}_{1}}{{k}_{2}}}{m}}\]

    C) \[n=\frac{1}{2\pi }\sqrt{\frac{{{k}_{1}}+{{k}_{2}}}{m}}\]

    D) none of the above

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  • question_answer43) In a \[p-\]type semicoriductor, germanium is doped with:

    A) boron

    B) gallium

    C) aluminium

    D) all of these

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  • question_answer44) In a full wave rectifier circuit operating from \[50\,\,Hz\] mains frequency, what is the fundamental frequency in the ripple?

    A) \[50\,\,Hz\]

    B) \[100\,\,Hz\]

    C) \[25\,\,Hz\]

    D) \[70\,\,Hz\]

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  • question_answer45) An ideal gas at \[{{27}^{o}}C\] is compressed adiabatically to \[\frac{8}{27}\] of its original volume. The rise in temperature will be\[\left( \gamma =\frac{5}{3} \right)\].

    A) \[{{480}^{o}}C\]

    B) \[{{275}^{o}}C\]

    C) \[{{450}^{o}}C\]

    D) \[{{375}^{o}}C\]

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  • question_answer46) When you make ice cubes, entropy of water:

    A) does not change

    B) increases

    C) decreases

    D) may either increase or decrease depending on the process used

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  • question_answer47) The focal length of the objective lens and eye-piece of an astronomical telescope are \[2\,\,m\] and\[0.05\,\,m\]. Find the length of the telescope.

    A) \[2.05\,\,m\]

    B) \[1.16\,\,m\]

    C) \[1.05\,\,m\]

    D) \[2.9\,\,m\]

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  • question_answer48) Two identical batteries, each of emf \[2\,\,V\] and internal resistance \[1\Omega \] pass a current through external, resistance\[R=0.5\Omega \]. The maximum power that can be developed across \[R\] using these batteries is:

    A) \[3.2\,\,W\]

    B) \[8.2\,\,W\]

    C) \[4\,\,W\]

    D) \[2\,\,W\]

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  • question_answer49) At what height from the earth's surface, the acceleration due to gravity will be half the value of \[g\] at surface? \[(R=6400\,\,km)\]

    A) \[6400\,\,km\]

    B) \[8200\,\,km\]

    C) \[4800\,\,km\]

    D) \[1600\,\,km\]

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  • question_answer50) In a semiconducting material the motilities of electrons and holes are \[{{\mu }_{e}}\] and \[{{\mu }_{h}}\] respectively which of the following is true?

    A) \[{{\mu }_{e}}>{{\mu }_{h}}\]

    B) \[{{\mu }_{e}}<{{\mu }_{h}}\]

    C) \[{{\mu }_{e}}={{\mu }_{h}}\]

    D) \[{{\mu }_{e}}<0,\,\,{{\mu }_{h}}>0\]

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  • question_answer51) Tyndall effect is shown by:

    A) solution

    B) precipitate

    C) sol

    D) none of these

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  • question_answer52) In reaction,\[MnO_{4}^{-}+{{H}^{+}}+{{C}_{2}}O_{4}^{2-}\xrightarrow{{}}M{{n}^{2+}}\]\[+{{H}_{2}}O+C{{O}_{2}}\]What is happening?

    A) Reduction of\[Mn\]

    B) Reduction of\[{{C}_{2}}O_{4}^{2-}\]

    C) Oxidation of\[Mn\]

    D) None of these

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  • question_answer53) In which of the following ionic bond is present?

    A) \[B{{F}_{3}}\]

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

    C) \[HCl\]

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

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  • question_answer54) Deficiency of vitamin \[E\] causes:

    A) scurvy

    B) beri-beri

    C) sterility

    D) xerophthalmia

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  • question_answer55) The reaction of Lucas reagent is fast with:

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

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

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

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

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  • question_answer56) \[IUPAC\] name of the compound is: \[H-\overset{\begin{smallmatrix} O \\ || \end{smallmatrix}}{\mathop{C}}\,-C{{H}_{2}}-C{{H}_{2}}-COOH\]

    A) 3-oxo-butanoic acid

    B) 4-oxo-propanoic acid

    C) 3-formyl-propanoic acid

    D) none of the above

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  • question_answer57) Tollen's reagent is:

    A) alkaline \[CuS{{O}_{4}}\] solution

    B) ammoniacal cuproxide solution

    C) aqueous solution of sodium cupritartarate

    D) ammoniacal \[AgN{{O}_{3}}\] solution

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  • question_answer58) Epsom salt is:

    A) \[MgS{{O}_{4}}\cdot 2{{H}_{2}}O\]

    B) \[BaS{{O}_{4}}\cdot 2{{H}_{2}}O\]

    C) \[MgS{{O}_{4}}\cdot 7{{H}_{2}}O\]

    D) \[CaS{{O}_{4}}\cdot 2{{H}_{2}}O\]

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  • question_answer59) Which of the following carbonate decompose most easily on heating?

    A) \[R{{b}_{2}}C{{O}_{3}}\]

    B) \[{{K}_{2}}C{{O}_{3}}\]

    C) \[N{{a}_{2}}C{{O}_{3}}\]

    D) \[MgC{{O}_{3}}\]

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  • question_answer60) In an isothermal expansion of an ideal gas:

    A) \[W=0\]

    B) \[\Delta E=0\]

    C) \[q=0\]

    D) \[\Delta V=0\]

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  • question_answer61) The degree of hydrolysis of \[0.01\,\,M\,\,N{{H}_{4}}Cl\] is:\[({{K}_{h}}=2.5\times {{10}^{-9}})\]

    A) \[5\times {{10}^{-5}}\]

    B) \[5\times {{10}^{-4}}\]

    C) \[5\times {{10}^{-3}}\]

    D) \[5\times {{10}^{-7}}\]

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  • question_answer62) The number of gram equivalent of \[{{H}_{2}}S{{O}_{4}}\] in \[1000\,\,mL\,\,3M\] solution, is:

    A) \[3\]

    B) \[6\]

    C) \[4\]

    D) \[1.5\]

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  • question_answer63) The radioactive isotope used in cancer therapy, is:

    A) \[{{I}^{128}}\]

    B) \[C{{o}^{60}}\]

    C) \[C{{o}^{59}}\]

    D) \[{{p}^{32}}\]

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  • question_answer64) The expression of angular momentum of an electron in a Bohr's orbit is:

    A) \[\frac{n\,\,h}{3\,\,\pi }\]

    B) \[\frac{n\,\,h}{2\,\,\pi }\]

    C) \[\frac{h}{4\pi }\]

    D) \[\sqrt{l(l+1)}\cdot \frac{h}{2\pi }\]

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  • question_answer65) Which of the following is called Hofmann's bromamide reaction?

    A) \[C{{H}_{3}}CHN+2{{H}_{2}}O\xrightarrow{{}}C{{H}_{3}}COO+N{{H}_{3}}\]

    B) \[C{{H}_{3}}CN+4H\xrightarrow{Na/ErOH}C{{H}_{3}}C{{H}_{2}}N{{H}_{2}}\]

    C) \[C{{H}_{3}}CON{{H}_{2}}\xrightarrow{B{{r}_{2}}/NaOH}C{{H}_{3}}N{{H}_{2}}\]

    D) \[C{{H}_{3}}COCl+C{{H}_{3}}OH\xrightarrow{{}}\]\[C{{H}_{3}}COOC{{H}_{3}}+HCl\]

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  • question_answer66) Which one among the following contains a phenolic \[-OH\] group?

    A) Oxalic acid

    B) Formic acid

    C) Picric acid

    D) Citric acid

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  • question_answer67) In the reaction, product \['X'\] is: \[C{{H}_{3}}-C\equiv CH+{{H}_{2}}O\xrightarrow{{{H}^{+}}/H{{g}^{2+}}}X\]

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

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

    C) \[C{{H}_{3}}-C(OH)=CHOH\]

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

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  • question_answer68) Which is an amphoteric oxide?

    A) \[MgO\]

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

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

    D) \[CuO\]

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  • question_answer69) The oxidation number of \[S\] in\[{{H}_{2}}{{S}_{2}}{{O}_{8}}\] is:

    A) \[+6\]

    B) \[-6\]

    C) \[+4\]

    D) \[+8\]

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  • question_answer70) Bleaching powder is obtained by treating chlorine with:

    A) \[CaC{{O}_{3}}\]

    B) \[Ca{{(OH)}_{2}}\]

    C) \[CaO\]

    D) none of these

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  • question_answer71) For reaction,\[PC{{l}_{3}}(g)+C{{l}_{2}}(g)PC{{l}_{5}}(g)\]the value of\[{{K}_{c}}\]at\[{{250}^{o}}C\]is\[26\]. At the same temperature, the value of \[{{K}_{p}}\] is:

    A) \[0.46\]

    B) \[0.61\]

    C) \[0.95\]

    D) \[0.73\]

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  • question_answer72) The volume of a gas is reduced to \[1.0\,\,L\] at \[{{25}^{o}}C\] and \[1\,\,atm\] pressure. Its pressure at \[{{35}^{o}}C\] would be:

    A) \[0.96\,\,atm\]

    B) \[1.03\,\,atm\]

    C) \[2.04\,\,atm\]

    D) \[3.08\,\,atm\]

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  • question_answer73) The strongest acid among the following is:

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

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

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

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

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  • question_answer74) The compressibility factor for an ideal gas is:

    A) \[<1\]

    B) \[=1\]

    C) \[>1\]

    D) always\[2\]

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  • question_answer75) The standard reduction potential of\[L{{i}^{+}},\,B{{a}^{2+}},\,\,N{{a}^{+}}\]and\[M{{g}^{2+}}\]are\[-3.05,\,\,-2.73,\]\[-2.71\] and \[-2.37\] volts respectively. Which one is the strongest reducing agent?

    A) \[Li\]

    B) \[Na\]

    C) \[Mg\]

    D) \[Ba\]

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  • question_answer76) The unit of rate constant for 1st order reaction is:

    A) \[mol\,\,{{L}^{-1}}{{s}^{-1}}\]

    B) \[mo{{l}^{-1}}L{{s}^{-1}}\]

    C) \[{{s}^{-1}}\]

    D) \[mo{{l}^{2}}{{L}^{-2}}{{s}^{-1}}\]

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  • question_answer77) In which of the following, the dipole moment is zero?

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

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

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

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

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  • question_answer78) The bond order of\[O_{2}^{+}\]is:

    A) \[2\]

    B) \[2.5\]

    C) \[1.5\]

    D) \[0.5\]

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  • question_answer79) Addition of \[HgC{{l}_{2}}\] to \[SnC{{l}_{2}}\] gives a black colour due to:

    A) oxidation of\[Sn\]

    B) reduction of\[HgC{{l}_{2}}\]

    C) formation of amalgam

    D) oxidation of\[Hg\]

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  • question_answer80) Which one of the following is a trihydric alcohol containing only secondary hydroxyl group?

    A) \[C{{H}_{3}}-\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\overset{\begin{smallmatrix} C{{H}_{3}} \\ | \end{smallmatrix}}{\mathop{C}}}\,-\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{C}}\,H-C{{H}_{2}}OH\]

    B) \[\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{C}}\,{{H}_{2}}-\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{C}}\,H-\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{C}}\,{{H}_{2}}\]

    C) \[C{{H}_{3}}-\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{C}}\,H-\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{C}}\,H-\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{C}}\,H-C{{H}_{3}}\]

    D) None of the above

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  • question_answer81) How, many sigma and it-bonds are there in the following compound? \[C{{H}_{2}}=CH-C\equiv C-\overset{\begin{smallmatrix} C{{H}_{3}} \\ | \end{smallmatrix}}{\mathop{C}}\,=C{{H}_{2}}\]

    A) \[11\sigma ,\,\,4\pi \]

    B) \[12\sigma ,\,\,3\pi \]

    C) \[14\sigma ,\,\,4\pi \]

    D) \[15\sigma ,\,\,4\pi \]

    View Answer play_arrow
  • question_answer82) In the nitration of benzene, the reactive species is:

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

    B) \[NO_{2}^{+}\]

    C) \[NO_{2}^{-}\]

    D) \[N{{O}^{-}}\]

    View Answer play_arrow
  • question_answer83) Reaction of phenol with\[CC{{l}_{4}}\]and\[NaOH\], followed by hydrolysis is likely to give:

    A)

    B)

    C)

    D)

    View Answer play_arrow
  • question_answer84) In the reaction, \[_{92}{{U}^{238}}{{\xrightarrow{{}}}_{82}}P{{b}^{206}}\], the number of \[\alpha \] and \[\beta -\]particles emitted are:

    A) \[7\alpha ,\,\,5\beta \]

    B) \[6\alpha ,\,\,4\beta \]

    C) \[4\alpha ,\,\,3\beta \]

    D) \[8\alpha ,\,\,6\beta \]

    View Answer play_arrow
  • question_answer85) Which is the correct Gibb's Helmholtz equation?

    A) \[\Delta H=\Delta G=T\cdot \Delta S\]

    B) \[\Delta S=\frac{1}{T}[\Delta G-\Delta H]\]

    C) \[\Delta S=\frac{1}{T}[\Delta H-\Delta G]\]

    D) \[-\Delta G=\Delta H-T\cdot \Delta S\]

    View Answer play_arrow
  • question_answer86) Vinegar is:

    A) \[8-10%\] acetic acid

    B) \[6-10%\] ethyl alcohol'

    C) glacial acetic acid

    D) \[10%\] formic acid

    View Answer play_arrow
  • question_answer87) Decreasing order of electron affinity of halogens is:

    A) \[Cl>Br>F>I\]

    B) \[Cl>F>Br>I\]

    C) \[Br>Cl>F>I\]

    D) \[F>Cl>Br>I\]

    View Answer play_arrow
  • question_answer88) Which of the following is an acidic salt?

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

    B) \[Pb(OH)Cl\]

    C) \[BaC{{l}_{2}}\]

    D) \[N{{a}_{2}}HP{{O}_{4}}\]

    View Answer play_arrow
  • question_answer89) Which one is the Lewis acid?

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

    B) \[AlC{{l}_{3}}\]

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

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

    View Answer play_arrow
  • question_answer90) \[720\,\,g\] water contain the number of moles:

    A) \[2\]

    B) \[190\]

    C) \[40\]

    D) \[55\]

    View Answer play_arrow
  • question_answer91) \[2HCHO\xrightarrow{50%NaOH}C{{H}_{3}}OH+HCOONa\] This reaction is called:

    A) aldol condensation

    B) Tischenko reaction

    C) Cannizaro reaction

    D) Reimer Tiemann reaction

    View Answer play_arrow
  • question_answer92) The geometry of the molecule having \[s\] and \[p-\]characters equal to \[25%\] and \[75%\] respectively, is:

    A) trigonal

    B) linear

    C) tetrahedral

    D) octahedral

    View Answer play_arrow
  • question_answer93) Impossible configuration is:

    A) \[1{{s}^{2}},\,\,2{{s}^{2}}2{{p}^{2}},\,\,3{{s}^{2}}\]

    B) \[1{{s}^{2}},\,\,2{{s}^{2}}\]

    C) \[1{{s}^{2}},\,\,2{{s}^{2}}2{{p}^{6}}\]

    D) None of these

    View Answer play_arrow
  • question_answer94) The solubility product of \[PbB{{r}_{2}}\] is \[10.8\times {{10}^{-5}}\]. It, is \[70%\] dissociated in saturated solution. The solubility of salt is:

    A) \[4.18\times {{10}^{-2}}\]

    B) \[6.76\times {{10}^{-3}}\]

    C) \[3.4\times {{10}^{-4}}\]

    D) \[5.44\times {{10}^{-2}}\]

    View Answer play_arrow
  • question_answer95) The latent heat of vaporisation of water is \[540\,\,cal\,\,{{g}^{-1}}\] at \[{{100}^{o}}C\]. What will be the entropy increase when one mole of water is evaporated at\[{{100}^{o}}C?\]

    A) \[28\,\,cal\,\,{{K}^{-1}}mo{{l}^{-1}}\]

    B) \[26\,\,cal\,\,{{K}^{-1}}mo{{l}^{-1}}\]

    C) \[540\,\,cal\,\,{{K}^{-1}}mo{{l}^{-1}}\]

    D) \[1.82\,\,cal\,\,{{K}^{-1}}mo{{l}^{-1}}\]

    View Answer play_arrow
  • question_answer96) The brown ring in the test of nitrate is formed due to:

    A) \[{{[Fe{{({{H}_{2}}O)}_{5}}N{{O}_{2}}]}^{2+}}\]

    B) \[Fe{{(N{{O}_{3}})}_{3}}\]

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

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

    View Answer play_arrow
  • question_answer97) The corrosive sublimate is :

    A) \[Hg\]

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

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

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

    View Answer play_arrow
  • question_answer98) The half-life of radium is\[1580\,\,yr\]. Its average life is:

    A) \[2.275\times {{10}^{3}}yr\]

    B) \[3.735\times {{10}^{2}}yr\]

    C) \[1.62\times {{10}^{3}}yr\]

    D) \[7.28\times {{10}^{2}}yr\]

    View Answer play_arrow
  • question_answer99) Cobalt is present in:

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

    B) vitamin\[{{B}_{6}}\]

    C) vitamin\[{{B}_{2}}\]

    D) vitamin\[{{B}_{1}}\]

    View Answer play_arrow
  • question_answer100) Adipic acid and hexamethylene diamine, on polymerisation gives:

    A) nylon\[-6\]

    B) Dacron

    C) nylon\[-66\]

    D) bakelite

    View Answer play_arrow
  • question_answer101) If \[z=x+iy\], then the area of a triangle whose vertices are points \[z,\,\,iz\] and \[z+iz\] is:

    A) \[2|z{{|}^{2}}\]

    B) \[\frac{1}{2}|z{{|}^{2}}\]

    C) \[|z{{|}^{2}}\]

    D) \[\frac{3}{2}|z{{|}^{2}}\]

    View Answer play_arrow
  • question_answer102) If the-complex number \[{{z}_{1}},\,\,{{z}_{2}}\] and \[{{z}_{3}}\] represent the vertices of an equilateral triangle such that \[|{{z}_{1}}|=|{{z}_{2}}|=|{{z}_{3}}|\], then \[{{z}_{1}}+{{z}_{2}}+{{z}_{3}}\] is equal to:

    A) \[0\]

    B) \[1\]

    C) \[-1\]

    D) none of these

    View Answer play_arrow
  • question_answer103) If\[{{i}^{2}}=-1\], then the value of\[\sum\limits_{n=1}^{200}{{{i}^{n}}}\]is:

    A) \[50\]

    B) \[-50\]

    C) \[0\]

    D) \[100\]

    View Answer play_arrow
  • question_answer104) The sum to infinity of the series\[2+\frac{1}{2}+\frac{1}{3}+\frac{1}{{{2}^{2}}}+\frac{1}{{{3}^{2}}}+\frac{1}{{{2}^{3}}}+\frac{1}{{{3}^{3}}}+...\]

    A) \[3\]

    B) \[4\]

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

    D) \[\frac{9}{2}\]

    View Answer play_arrow
  • question_answer105) If\[x>1,\,\,y>1,\,\,z>1\]are in\[GP\], then\[\frac{1}{1+\log x},\,\,\frac{1}{1+\log y},\,\,\frac{1}{1+\log z}\]are in:

    A) \[AP\]

    B) \[HP\]

    C) \[GP\]

    D) none of these

    View Answer play_arrow
  • question_answer106) If\[{{x}^{2}}-3x+2\]be a factor of\[{{x}^{4}}-p{{x}^{2}}+q\], then \[(p,\,\,q)\]is equal to:

    A) \[(3,\,\,4)\]

    B) \[(4,\,\,5)\]

    C) \[(4,\,\,3)\]

    D) \[(5,\,\,4)\]

    View Answer play_arrow
  • question_answer107) If\[a{{x}^{2}}+bx+c=0\]and\[b{{x}^{2}}+cx+a=0\], then a common root and\[a\ne 0\], then\[\frac{{{a}^{3}}+{{b}^{3}}+{{c}^{3}}}{abc}\]is equal to:

    A) \[1\]

    B) \[2\]

    C) \[3\]

    D) \[4\]

    View Answer play_arrow
  • question_answer108) If\[^{15}{{C}_{3r}}{{=}^{15}}{{C}_{r+3}}\], then the value of\[r\]is:

    A) \[3\]

    B) \[4\]

    C) \[5\]

    D) \[8\]

    View Answer play_arrow
  • question_answer109) The number of divisors of \[9600\] including \[1\] and \[9600\] are:

    A) \[60\]

    B) \[58\]

    C) \[48\]

    D) \[46\]

    View Answer play_arrow
  • question_answer110) If\[{{a}_{n}}=\sum\limits_{r=0}^{n}{\frac{1}{^{n}{{C}_{r}}}}\], then\[\sum\limits_{r=0}^{n}{\frac{r}{^{n}{{C}_{r}}}}\]is equal to:

    A) \[(n-1){{a}_{n}}\]

    B) \[n{{a}_{n}}\]

    C) \[\frac{1}{2}n{{a}_{n}}\]

    D) none of these

    View Answer play_arrow
  • question_answer111) 6th term in expansion of\[{{\left( 2{{x}^{2}}-\frac{1}{3{{x}^{2}}} \right)}^{10}}\]is:

    A) \[\frac{4580}{17}\]

    B) \[-\frac{896}{27}\]

    C) \[\frac{5580}{17}\]

    D) none of these

    View Answer play_arrow
  • question_answer112) In the expansion of\[{{(1+x)}^{m}}{{(1-x)}^{n}}\], the coefficient of \[x\] and\[{{x}^{2}}\]are \[3\] and \[-6\] respectively, then \[m\] is equal to:

    A) \[6\]

    B) \[9\]

    C) \[12\]

    D) \[24\]

    View Answer play_arrow
  • question_answer113) \[(1+3){{\log }_{e}}3+\frac{1+{{3}^{2}}}{2!}{{({{\log }_{e}}3)}^{2}}\]\[+\frac{1+{{3}^{3}}}{3!}{{({{\log }_{e}}3)}^{3}}+...\infty \]is equal to:

    A) \[28\]

    B) \[30\]

    C) \[25\]

    D) \[0\]

    View Answer play_arrow
  • question_answer114) The sum of\[\frac{1}{2}+\frac{1}{3}+\frac{1}{{{2}^{3}}}+\frac{1}{5}\cdot \frac{1}{{{2}^{5}}}+...\infty \]is:

    A) \[{{\log }_{e}}\sqrt{\frac{3}{2}}\]

    B) \[{{\log }_{e}}\sqrt{3}\]

    C) \[{{\log }_{e}}\sqrt{\frac{7}{2}}\]

    D) \[{{\log }_{e}}3\]

    View Answer play_arrow
  • question_answer115) \[\left| \begin{matrix} 1 & a & {{a}^{2}}-bc \\ 1 & b & {{b}^{2}}-ac \\ 1 & c & {{c}^{2}}-ac \\ \end{matrix} \right|\]is equal to:

    A) \[0\]

    B) \[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}-3abc\]

    C) \[3abc\]

    D) \[{{(a+b+c)}^{3}}\]

    View Answer play_arrow
  • question_answer116) \[x+ky-z=0\],\[3x-ky-z=0\]and\[x-3y+z=0\] has non-zero solution for \[k\] is equal to:

    A) \[-1\]

    B) \[0\]

    C) \[1\]

    D) \[2\]

    View Answer play_arrow
  • question_answer117) If\[A=\left| \begin{matrix} 1 & -2 & 3 \\ 0 & -1 & 4 \\ -2 & 2 & 1 \\ \end{matrix} \right|\], then\[{{(A')}^{-1}}\] is equal to:

    A) \[\left[ \begin{matrix} -9 & -8 & -2 \\ 8 & 7 & 2 \\ -5 & -4 & -1 \\ \end{matrix} \right]\]

    B) \[\left[ \begin{matrix} 1 & -1 & -2 \\ -2 & -1 & 2 \\ 3 & 4 & 1 \\ \end{matrix} \right]\]

    C) \[\left[ \begin{matrix} -9 & 8 & 5 \\ -8 & 7 & -4 \\ 2 & 2 & -1 \\ \end{matrix} \right]\]

    D) \[\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{matrix} \right]\]

    View Answer play_arrow
  • question_answer118) Inverse matrix of\[\left[ \begin{matrix} 4 & 7 \\ 1 & 2 \\ \end{matrix} \right]\]is equal to:

    A) \[\left[ \begin{matrix} 2 & -7 \\ -1 & 4 \\ \end{matrix} \right]\]

    B) \[\left[ \begin{matrix} 2 & -1 \\ -7 & 4 \\ \end{matrix} \right]\]

    C) \[\left[ \begin{matrix} -2 & 7 \\ 1 & -4 \\ \end{matrix} \right]\]

    D) \[\left[ \begin{matrix} -2 & 1 \\ 7 & -4 \\ \end{matrix} \right]\]

    View Answer play_arrow
  • question_answer119) If \[A\] lies in the second quadrant and\[3\tan A+4=0\], then value of\[2\cot A-5\cos A+\sin A\]is equal to:

    A) \[-53/10\]

    B) \[-7/10\]

    C) \[7/10\]

    D) \[23/10\]

    View Answer play_arrow
  • question_answer120) If\[\sin \theta +\cos \theta =1\], then the general value of\[\theta \]is:

    A) \[2n\pi \]

    B) \[n\pi +{{(-1)}^{n}}\frac{\pi }{4}-\frac{\pi }{4}\]

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

    D) none of these

    View Answer play_arrow
  • question_answer121) \[\cos \left[ 2{{\cos }^{-1}}\frac{1}{5}+{{\sin }^{-1}}\frac{1}{5} \right]\]is equal to:

    A) \[\frac{2\sqrt{6}}{5}\]

    B) \[\frac{-2\sqrt{6}}{5}\]

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

    D) \[\frac{-1}{5}\]

    View Answer play_arrow
  • question_answer122) From a roof of a \[15\,\,m\] high house the angle of elevation of a point located \[15\,\,m\] distant to the base of the house is:

    A) \[{{45}^{o}}\]

    B) \[{{30}^{o}}\]

    C) \[{{60}^{o}}\]

    D) \[{{90}^{o}}\]

    View Answer play_arrow
  • question_answer123) If \[A\] and \[B\] are two fixed point and \[P\] is a variable point such that\[PA+PB=4\], then the locus of \[P\] is a/an:

    A) parabola

    B) ellipse

    C) hyperbola

    D) none of these

    View Answer play_arrow
  • question_answer124) A line passes through \[(2,\,\,2)\] and is perpendicular to the line \[3x+y=3\], its \[y-\]intercept is:

    A) \[1/3\]

    B) \[2/3\]

    C) \[1\]

    D) \[4/3\]

    View Answer play_arrow
  • question_answer125) The angle between the pair of straight lines \[{{x}^{2}}-{{y}^{2}}-2xy-1=0\]is :

    A) \[{{90}^{o}}\]

    B) \[{{60}^{o}}\]

    C) \[{{75}^{o}}\]

    D) \[{{36}^{o}}\]

    View Answer play_arrow
  • question_answer126) The point of intersection of the line \[4x-3y-10=0\] and the circle \[{{x}^{2}}+{{y}^{2}}-2x+4y-20=0\] are:

    A) \[(-2,\,\,-6),\,\,(4,\,\,2)\]

    B) \[(2,\,\,6),\,\,(-4,\,\,-2)\]

    C) \[(-2,\,\,6),\,\,(-4,\,\,2)\]

    D) none of the above

    View Answer play_arrow
  • question_answer127) The focus of the parabola\[{{y}^{2}}=4y-4x\]is:

    A) \[(0,\,\,2)\]

    B) \[(1,\,\,2)\]

    C) \[(2,\,\,0)\]

    D) \[(2,\,\,1)\]

    View Answer play_arrow
  • question_answer128) The eccentricity of the ellipse\[4{{x}^{2}}+9{{y}^{2}}+8x+36y+4=0\]is:

    A) \[5/6\]

    B) \[3/5\]

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

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

    View Answer play_arrow
  • question_answer129) The angle of intersection of the curves\[{{y}^{2}}=2x/\pi \]and\[y=\sin x\]is:

    A) \[{{\cot }^{-1}}(-1/\pi )\]

    B) \[{{\cot }^{-1}}\pi \]

    C) \[{{\tan }^{-1}}(-\pi )\]

    D) \[{{\cot }^{-1}}\left( \frac{1}{\pi } \right)\]

    View Answer play_arrow
  • question_answer130) The projection of any line on coordinate axes be respectively \[3,\,\,\,4,\,\,\,5,\] then its length is:

    A) \[12\]

    B) \[50\]

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

    D) none of these

    View Answer play_arrow
  • question_answer131) If the direction ratios of a line are \[1,\,\,-3,\,\,2,\] then the direction cosines of the line are :

    A) \[\frac{1}{\sqrt{14}},\,\,\frac{-3}{\sqrt{14}},\,\,\frac{2}{\sqrt{14}}\]

    B) \[\frac{1}{\sqrt{14}},\,\,\frac{2}{\sqrt{14}},\,\,\frac{3}{\sqrt{14}}\]

    C) \[\frac{-1}{\sqrt{14}},\,\,\frac{3}{\sqrt{14}},\,\frac{-2}{\sqrt{14}}\]

    D) \[\frac{-1}{\sqrt{14}},\,\,\frac{-2}{\sqrt{14}},\,\,\frac{-3}{\sqrt{14}}\]

    View Answer play_arrow
  • question_answer132) The area of triangle whose vertices are\[A(1,\,\,-1,\,\,2),\,\,\,B(2,\,\,1,\,\,-1)\]and\[C(3,\,\,-1,\,\,2)\]is:

    A) \[13\,\,sq\,\,unit\]

    B) \[\sqrt{13}\,\,sq\,\,unit\]

    C) \[56\,\,sq\,\,unit\]

    D) \[\sqrt{6}\,\,sq\,\,unit\]

    View Answer play_arrow
  • question_answer133) \[|(\overset{\to }{\mathop{\mathbf{a}}}\,\times \overset{\to }{\mathop{\mathbf{b}}}\,)\cdot \overset{\to }{\mathop{\mathbf{c}}}\,|=|\overset{\to }{\mathop{\mathbf{a}}}\,||\overset{\to }{\mathop{\mathbf{b}}}\,||\overset{\to }{\mathop{\mathbf{c}}}\,|\]if:

    A) \[\overset{\to }{\mathop{\mathbf{a}}}\,\cdot \overset{\to }{\mathop{\mathbf{b}}}\,=\overset{\to }{\mathop{\mathbf{b}}}\,\cdot \overset{\to }{\mathop{\mathbf{c}}}\,=0\]

    B) \[\overset{\to }{\mathop{\mathbf{b}}}\,\cdot \overset{\to }{\mathop{\mathbf{c}}}\,=\overset{\to }{\mathop{\mathbf{c}}}\,\cdot \overset{\to }{\mathop{\mathbf{a}}}\,=0\]

    C) \[\overset{\to }{\mathop{\mathbf{c}}}\,\cdot \overset{\to }{\mathop{\mathbf{a}}}\,=\overset{\to }{\mathop{\mathbf{a}}}\,\cdot \overset{\to }{\mathop{\mathbf{b}}}\,=0\]

    D) \[\overset{\to }{\mathop{\mathbf{a}}}\,\cdot \overset{\to }{\mathop{\mathbf{b}}}\,=\overset{\to }{\mathop{\mathbf{b}}}\,\cdot \overset{\to }{\mathop{\mathbf{c}}}\,=\overset{\to }{\mathop{\mathbf{c}}}\,\cdot \overset{\to }{\mathop{\mathbf{a}}}\,=0\]

    View Answer play_arrow
  • question_answer134) The angle between the vectors \[(2\widehat{\mathbf{i}}+6\widehat{\mathbf{j}}+3\widehat{\mathbf{k}})\] and\[(12\widehat{\mathbf{i}}-4\widehat{\mathbf{j}}+3\widehat{\mathbf{k}})\]is:

    A) \[{{\cos }^{-1}}\left( \frac{1}{10} \right)\]

    B) \[{{\cos }^{-1}}\left( \frac{9}{11} \right)\]

    C) \[{{\cos }^{-1}}\left( \frac{9}{91} \right)\]

    D) \[{{\cos }^{-1}}\left( \frac{1}{9} \right)\]

    View Answer play_arrow
  • question_answer135) Domain of the function\[\sin \log \left( \frac{\sqrt{4-{{x}^{2}}}}{1-x} \right)\]is:

    A) \[[-2,\,\,1]\]

    B) \[(-2,\,\,1)\]

    C) \[[-2,\,\,1)\]

    D) \[(-2,\,\,1]\]

    View Answer play_arrow
  • question_answer136) If\[f(9)=9,\,\,f'(9)=4\]and\[\underset{x\to 9}{\mathop{\lim }}\,\frac{f(x)-9}{x-9}=4\]then \[\underset{x\to 9}{\mathop{\lim }}\,\frac{\sqrt{f(x)}-3}{\sqrt{x}-3}\]is equal to:

    A) \[2\]

    B) \[4\]

    C) \[-2\]

    D) \[-4\]

    View Answer play_arrow
  • question_answer137) Let \[f(x)\] be defined for all \[x>0\] and be continuous, let \[f(x)\] satisfy\[f\left( \frac{x}{y} \right)=f(x)-f(y)\]for all \[x,\,\,y,\] then:

    A) \[f(x)=\log x\]

    B) \[f(x)\]is bounded

    C) \[f\left( \frac{1}{2} \right)\to 0\]as\[x\to 0\]

    D) \[x\,\,f(x)\to 1\]as\[x\to 0\]

    View Answer play_arrow
  • question_answer138) The domain of the function\[y=\frac{1}{\sqrt{|x|-x}}\]is:

    A) \[(-\infty ,\,\,0)\]

    B) \[(+\infty ,\,\,0)\]

    C) \[(-\infty ,\,\,-1)\]

    D) \[(-\infty ,\,\,\infty )\]

    View Answer play_arrow
  • question_answer139) Differential coefficient of \[{{\sin }^{-1}}\frac{1-x}{1+x}\] with respect to\[\sqrt{x}\]is:

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

    B) \[\frac{\sqrt{x}}{\sqrt{1-x}}\]

    C) \[1\]

    D) none of these

    View Answer play_arrow
  • question_answer140) The number that exceeds its square by the greatest number is:

    A) \[-1\]

    B) \[0\]

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

    D) \[1\]

    View Answer play_arrow
  • question_answer141) \[\int{\frac{{{\sin }^{8}}x-{{\cos }^{8}}x}{1-2{{\sin }^{2}}x{{\cos }^{2}}x}dx}\]is equal to:

    A) \[\sin 2x+c\]

    B) \[-\frac{1}{2}\sin 2x+c\]

    C) \[\frac{1}{2}\sin 2x+c\]

    D) \[-\sin 2x+c\]

    View Answer play_arrow
  • question_answer142) If\[f(x)=A\sin \left( \frac{\pi x}{2} \right)+B,\,\,\,f'\left( \frac{1}{2} \right)=\sqrt{2}\]and\[\int_{0}^{1}{f(x)}dx=\frac{2A}{\pi }\], then the constants \[A\] and \[B\] are respectively:

    A) \[\frac{\pi }{2}\]and\[\frac{\pi }{2}\]

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

    C) \[\frac{4}{\pi }\]and\[0\]

    D) \[0\]and\[\frac{-4}{\pi }\]

    View Answer play_arrow
  • question_answer143) Let\[f(x)=x-[x]\]for all real number, where\[[x]\]is the integral part of\[x\], then\[\int_{-1}^{1}{f(x)}dx\]is equal to:

    A) \[1\]

    B) \[2\]

    C) \[0\]

    D) \[1/2\]

    View Answer play_arrow
  • question_answer144) A solution of the differential equation\[{{\left( \frac{dy}{dx} \right)}^{2}}-x\frac{dy}{dx}+y=0\]is:

    A) \[y=2\]

    B) \[y=2x\]

    C) \[y=2x-4\]

    D) \[y=2{{x}^{2}}-4\]

    View Answer play_arrow
  • question_answer145) If \[A\] and \[B\] are two independent events, then \[P(A+B)\] is equal to:

    A) \[P(A)+P(B)-P(A)P(B)\]

    B) \[P(A)-P(B)\]

    C) \[P(A)+P(B)\]

    D) \[P(A)+P(B)+P(A)P(B)\]

    View Answer play_arrow
  • question_answer146) A bag contains \[6\] red, \[5\] white and \[4\] black balls, two balls are drawn the probability that none of them is red, is:

    A) \[12/35\]

    B) \[6/35\]

    C) \[4/35\]

    D) none of these

    View Answer play_arrow
  • question_answer147) If\[P(A)=0.65,\,\,P(B)=0.15\], then\[P(\bar{A})+P(\bar{B})\]is equal to:

    A) \[1.5\]

    B) \[1.2\]

    C) \[0.8\]

    D) none of these

    View Answer play_arrow
  • question_answer148) If the regression equations of the variables \[x\]and \[y\] be \[x=19.13-0.83y\] and\[y=11.64-0.50x\], then the correlation coefficient between x and y is:

    A) \[0.66\]

    B) \[-0.64\]

    C) \[0.001\]

    D) \[-0.001\]

    View Answer play_arrow
  • question_answer149) The roots of \[x+{{\log }_{10}}x=3.375\] is approximately:

    A) \[2.09\]

    B) \[2.909\]

    C) \[2.990\]

    D) \[3.003\]

    View Answer play_arrow
  • question_answer150) After second iteration of Newton-Raphson method, the positive root of equation \[{{x}^{2}}=3\](taking initial approximation\[\frac{3}{2}):\]

    A) \[3/2\]

    B) \[7/4\]

    C) \[97/56\]

    D) \[347/200\]

    View Answer play_arrow

   



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