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Solved papers for JCECE Engineering JCECE Engineering Solved Paper-2004

done JCECE Engineering Solved Paper-2004

  • question_answer1) The direction of vector \[\overset{\to }{\mathop{\mathbf{A}}}\,\] is reversed. What are the values of \[\Delta \overset{\to }{\mathop{\mathbf{A}}}\,\]A and\[\Delta |\overset{\to }{\mathop{\mathbf{A}}}\,|\]?

    A) \[+2\overset{\to }{\mathop{\mathbf{A}}}\,,\,\,0\]

    B) \[+\overset{\to }{\mathop{\mathbf{A}}}\,,\,\,0\]

    C) \[-\overset{\to }{\mathop{\mathbf{A}}}\,,\,\,0\]

    D) \[-2\overset{\to }{\mathop{\mathbf{A}}}\,,\,\,0\]

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  • question_answer2) The velocity of a body moving with uniform acceleration at a given instant of time \[t\] is\[10\,\,m/s\]. After \[5\,\,s\] its velocity is \[20\,\,m/s\]. Distance travelled in that time is:

    A) \[300\,\,m\]

    B) \[400\,\,m\]

    C) \[150\,\,m\]

    D) \[75\,\,m\]

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  • question_answer3) A stone falls freely such that the distance covered by it in the last second of its motion is equal to the distance covered by it in the first\[5\,\,s\]. It is in air for:

    A) \[26\,\,s\]

    B) \[25\,\,s\]

    C) \[13\,\,s\]

    D) \[12\,\,s\]

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  • question_answer4) A child is swinging a swing. Minimum and maximum heights of swing from earth's surface are \[0.75\,\,m\] and \[2\,\,m\] respectively. The maximum velocity of this swing is:

    A) \[5\,\,m/s\]

    B) \[10\,\,m/s\]

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

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

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  • question_answer5) An object is thrown along a direction making an angle \[{{45}^{o}}\] with the horizontal direction. The horizontal range of the object is equal to:

    A) twice the vertical height

    B) vertical height

    C) four times the vertical height

    D) three times the vertical height

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  • question_answer6) A fireman wants to slide down a rope. The breaking load for the rope is \[\frac{3}{4}th\] of the weight of the man. With what acceleration should the fireman slide down? (Acceleration due to gravity is\[g)\]

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

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

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

    D) \[zero\]

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  • question_answer7) A body of mass \[1\,\,kg\] is rotating in a vertical circle of radius \[1\,\,m\]. What will be the difference in kinetic energy at the top and at the bottom of the circle? (Take\[g=10\,\,m/{{s}^{2}})\]

    A) \[50\,\,J\]

    B) \[30\,\,J\]

    C) \[20\,\,J\]

    D) \[10\,\,J\]

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  • question_answer8) A circular ring of mass m and radius r is rolling on a smooth horizontal surface with speed \[v\]. Its kinetic energy is:

    A) \[\frac{1}{8}m{{v}^{2}}\]

    B) \[\frac{1}{4}m{{v}^{2}}\]

    C) \[\frac{1}{3}m{{v}^{2}}\]

    D) \[m{{v}^{2}}\]

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  • question_answer9) A satellite is evolving around the earth in a circular orbit of radius 4 times that of the parking orbit, The time period of the satellite is:

    A) \[16\,\,days\]

    B) \[2\,\,days\]

    C) \[4\,\,days\]

    D) \[8\,\,days\]

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  • question_answer10) As shown, in figure, a planet revolves in elliptical orbit around the sun. Where is \[KE\] of the planet maximum?

    A) At\[{{P}_{4}}\]

    B) At\[{{P}_{1}}\]

    C) At\[{{P}_{2}}\]

    D) At\[{{P}_{3}}\]

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  • question_answer11) If the condenser shown in the circuit is charged to \[5\,\,V\] and left in the circuit, in \[12\,\,s\] the charge on the condenser will become:

    A) \[\frac{10}{e}coulomb\]

    B) \[\frac{{{e}^{2}}}{10}coulomb\]

    C) \[\frac{10}{{{e}^{2}}}coulomb\]

    D) \[\frac{e}{10}coulomb\]

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  • question_answer12) A sings with a frequency \[(n)\] and \[B\] sings with a frequency \[1/8\] that of \[A\]. If the energy remains the same and the amplitude of \[A\] is \[a,\] the amplitude of \[B\] will be:

    A) \[2a\]

    B) \[8a\]

    C) \[4a\]

    D) \[a\]

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  • question_answer13) Reactance of a capacitor of capacitance \[C\,\,\mu F\] for \[AC\] frequency \[\frac{400}{\pi }Hz\] is \[25\Omega \], the value of \[C\] is:

    A) \[75\,\,\mu F\]

    B) \[100\,\,\mu F\]

    C) \[25\,\,\mu F\]

    D) \[50\,\,\mu F\]

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  • question_answer14) An electron and a proton have same de-Broglie wavelength, then kinetic energy of the electron is:

    A) greater than \[KE\] of proton

    B) zero

    C) equal to \[KE\] of proton

    D) infinite

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  • question_answer15) Relative permeability of iron is \[5500\]. Its magnetic susceptibility is:

    A) \[5499\]

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

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

    D) \[5501\]

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  • question_answer16) A force of \[7\widehat{\mathbf{i}}+6\widehat{\mathbf{k}}\] makes a body to move on a plane with the velocity \[3\widehat{\mathbf{j}}+4\widehat{\mathbf{k}}\]. The power developed is:

    A) \[\sqrt{45}\]

    B) \[45\]

    C) \[24\]

    D) \[\sqrt{24}\]

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  • question_answer17) The variation of \[PV\] with \[V\] of a fixed mass of an ideal gas at constant temperature is graphically represented by as shown in figure:

    A)

    B)

    C)

    D)

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  • question_answer18) The number of oxygen molecules in a cylinder of volume \[1\,\,{{m}^{3}}\] at a temperature of \[{{27}^{o}}C\] and pressure of \[13.8\,\,Pa\] is: (Boltzmann's constant\[k=1.38\times {{10}^{-23}}J\,\,{{K}^{-1}})\]

    A) \[6.13\times {{10}^{26}}\]

    B) \[0.3\times {{10}^{28}}\]

    C) \[3.3\times {{10}^{21}}\]

    D) none of these

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  • question_answer19) The minimum magnifying power of a telescope is \[M\]. If the focal length of the eye lens is halved, the magnifying power will become:

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

    B) \[3\,\,M\]

    C) \[2\,\,M\]

    D) \[4\,\,M\]

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  • question_answer20) The surface temperature is maximum for:

    A) blue star

    B) yellow star

    C) green star

    D) red star

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  • question_answer21) A convergent doublet of separated lens, corrected for spherical aberration, are separated by \[2\,\,cm\] and has an equivalent focal length of \[10\,\,cm\]. The focal length of its component lenses are:

    A) \[{{f}_{1}}=18\,\,cm,\,\,{{f}_{2}}=10\,\,cm\]

    B) \[{{f}_{1}}=20\,\,cm,\,\,{{f}_{2}}=28\,\,cm\]

    C) \[{{f}_{1}}=20\,\,cm,\,\,{{f}_{2}}=18\,\,cm\]

    D) \[{{f}_{1}}=24\,\,cm,\,\,{{f}_{2}}=18\,\,cm\]

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  • question_answer22) In Young's experiment using light of wavelength \[6000\overset{\text{o}}{\mathop{\text{A}}}\,\], fringe width obtained at distance \[2.5\,\,m\] is \[0.8\,\,mm\]. If the entire apparatus is immersed in a liquid of refractive index \[1.6\], the fringe width will be:

    A) \[0.2\,\,mm\]                   

    B) \[0.4\,\,mm\]

    C) \[0.5\,\,mm\]                   

    D) \[0.6\,\,mm\]

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  • question_answer23) In double slit experiment, the angular width of interference fringes with sodium light \[(\lambda =5890\overset{\text{o}}{\mathop{\text{A}}}\,)\] is \[{{0.20}^{o}}\]. The change in wavelength required to increase the angular width by \[10%\] will be:

    A)  zero

    B)  increased by \[6479\overset{\text{o}}{\mathop{\text{A}}}\,\]  

    C)  increased by \[589\overset{\text{o}}{\mathop{\text{A}}}\,\]

    D)  decreased by \[589\overset{\text{o}}{\mathop{\text{A}}}\,\]

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  • question_answer24) \[SHM\] is executed by a particle of mass \[m\]. The displacement of the particle is \[\left( \frac{1}{\sqrt{2}} \right)\] times the amplitude. What fraction of the total energy is kinetic at this displacement?

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

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

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

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

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  • question_answer25) The period of SHM of a particle is 12 s. The phase difference between the positions at\[t=3\,\,s\]and\[t=4\,\,s\]will be:

    A) \[\pi /4\]

    B) \[3\pi /5\]

    C) \[\pi /6\]

    D) \[\pi /2\]

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  • question_answer26) The volume of a metal sphere increases by \[0.15%\] when its temperature is raised by\[{{24}^{o}}C\]. The coefficient of linear expansion of metal is:

    A) \[2.5\times {{10}^{-5}}{{/}^{o}}C\]

    B) \[2.0\times {{10}^{-5}}{{/}^{o}}C\]

    C) \[1.5\times {{10}^{-5}}{{/}^{o}}C\]

    D) \[1.2\times {{10}^{-5}}{{/}^{o}}C\]

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  • question_answer27) The radii of two soap bubbles are \[{{r}_{1}}\] and \[{{r}_{2}}\] \[({{r}_{2}}>{{r}_{1}})\]. When they come into contact, the radius of their common interface is:

    A) \[{{r}_{2}}-{{r}_{1}}\]

    B) \[\sqrt{r_{1}^{2}-r_{2}^{2}}\]

    C) \[\frac{{{r}_{1}}+{{r}_{2}}}{2}\]

    D) \[\frac{{{r}_{1}}{{r}_{2}}}{{{r}_{1}}-{{r}_{2}}}\]

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  • question_answer28) A ray of light is incident on the surface of a glass slab at \[{{60}^{o}}\]. The refractive index of glass, if the reflected and refracted rays are mutually perpendicular to each other, will be:

    A) \[1.5\]

    B) \[4.16\]

    C) \[2.25\]

    D) \[1.73\]

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  • question_answer29) A stretched string is \[1\,\,m\] long. It?s mass per unit length is \[0.5\,\,g/m\]. It is stretched with a force of \[20\,\,N\]. It is plucked at a distance of \[25\,\,cm\] from one end. The frequency of note emitted by it will be:

    A) \[400\,\,Hz\]

    B) \[300\,\,Hz\]

    C) \[200\,\,Hz\]

    D) \[100\,\,Hz\]

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  • question_answer30) A transverse wave is given by \[y=A\sin 2\pi (f\,\,t-x/\lambda )\] . The maximum particle velocity is \[4\] times the wave velocity when:

    A) \[\lambda =2\pi A\]

    B) \[\lambda =\pi A\]

    C) \[\lambda =\pi A/2\]

    D) \[\lambda =\pi A/4\]

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  • question_answer31) The energy in \[eV\] of red light of wavelength \[\lambda =6560\overset{\text{o}}{\mathop{\text{A}}}\,\] is:

    A) \[1.89\,\,eV\]                   

    B) \[2.89\,\,eV\]

    C) \[3.89\,\,eV\]                   

    D) \[4.89\,\,eV\]

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  • question_answer32) The wavelength of first member of Lyman series is \[1215\overset{\text{o}}{\mathop{\text{A}}}\,\]. The wavelength of \[{{H}_{\alpha }}\] line is:

    A) \[6561\overset{\text{o}}{\mathop{\text{A}}}\,\]

    B) \[5464\overset{\text{o}}{\mathop{\text{A}}}\,\]

    C) \[800\overset{\text{o}}{\mathop{\text{A}}}\,\]     

    D) \[4840\overset{\text{o}}{\mathop{\text{A}}}\,\]

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  • question_answer33) When silver is irradiated by ultraviolet light of \[1000\overset{\text{o}}{\mathop{\text{A}}}\,\], potential of \[7.7\,\,V\] is required to stop the photo electrons. The work function of silver will be:

    A) \[3.72\,\,eV\]                   

    B) \[6.72\,\,eV\]

    C) \[5.72\,\,eV\]                   

    D) \[4.67\,\,eV\]

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  • question_answer34) Maximum kinetic energy \[{{E}_{k}}\] of a photoelectron varies with the frequency \[v\] of the incident radiation as:

    A)

    B)

    C)

    D)

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  • question_answer35) A radioactive element has half-life period\[1600\,\,yr\]. After \[6400\,\,yr\], what part of element will remain?

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

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

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

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

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  • question_answer36) For a transistor \[{{I}_{E}}=25\,\,mA\] and \[{{I}_{B}}=1\,\,mA\], the value of current gain \[\alpha \] will be:

    A) \[\frac{25}{24}\]

    B) \[\frac{24}{25}\]

    C) \[\frac{25}{26}\]

    D) \[\frac{26}{25}\]

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  • question_answer37) When two semiconductors of \[p\] and \[n\] type are brought into contact, they form a \[p-n\] junction which acts like a:

    A) rectifier

    B) amplifier

    C) oscillator

    D) conductor

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  • question_answer38) The de-Broglie wavelength of \[1\,\,kg\] mass moving with a velocity of \[10\,\,m/s\], will be:

    A) \[6.626\times {{10}^{-35}}m\]

    B) \[6.626\times {{10}^{-34}}m\]

    C) \[6.626\times {{10}^{-33}}m\]

    D) none of these

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  • question_answer39) Radioactive nuclei that are injected into a patient collected at certain sites within its body, undergoing radioactive decay and emitting electromagnetic radiation. These radiations can then be recorded by a detector. This procedure provides an important diagnostic tools called:

    A) gamma camera

    B) CAT scan

    C) radiotracer technique

    D) gamma ray spectroscopy

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  • question_answer40) If \[R,\,\,\,C\] and \[L\] denote resistance, capacitance and inductance. Which of the following will not have the dimensions of frequency?

    A) \[R{{L}^{-1}}\]

    B) \[{{R}^{-1}}{{C}^{-1}}\]

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

    D) \[RCL\]

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  • question_answer41) A \[10\mu F\] capacitor is connected across a\[200\,\,V,\] \[50\,\,Hz\,\,AC\] supply. The peak current through the circuit is:

    A) \[0.6\sqrt{2}A\]

    B) \[0.6\,\,A\]

    C) \[\frac{0.6\pi }{2}A\]

    D) \[\frac{0.6}{\sqrt{2}}A\]

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  • question_answer42) What is the energy stored in \[50\,\,mH\] inductor carrying a current of\[4\,\,A?\]

    A) \[0.2\,\,J\]

    B) \[0.4\,\,J\]

    C) \[0.05\,\,J\]

    D) \[0.1\,\,J\]

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  • question_answer43) In an ammeter, \[4%\] of the main current is passing through galvanometer. If the galvanometer is shunted with a \[5\Omega \] resistance, the resistance of the galvanometer is:

    A) \[120\Omega \]

    B) \[20\Omega \]

    C) \[5\Omega \]

    D) \[4\Omega \]

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  • question_answer44) If \[100\,\,kWh\] of energy is consumed at \[33\,\,V\] in a copper voltameter, what is the mass of copper liberated? (Electrochemical equivalent of copper is\[0.33\times {{10}^{-6}}kg/C)\]

    A) \[1\,\,mg\]

    B) \[3.6\,\,kg\]

    C) \[3.3\,\,kg\]

    D) \[1\,\,kg\]

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  • question_answer45) Four identical resistors when connected in series dissipate \[5\,\,W\] power. If they are connected in parallel, the power dissipated will be:

    A) \[80\,\,W\]

    B) \[60\,\,W\]

    C) \[40\,\,W\]

    D) \[20\,\,W\]

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  • question_answer46) What is the magnitude of the point charge due to which the electric field 30 cm away has the magnitude of\[2N/C?\] \[\left( \frac{1}{4\pi {{\varepsilon }_{0}}}=9\times {{10}^{9}}N{{m}^{2}}/{{C}^{2}} \right)\]

    A) \[4\times {{10}^{-11}}C\]

    B) \[2\times {{10}^{-11}}C\]

    C) \[5.4\times {{10}^{-11}}C\]

    D) \[7.5\times {{10}^{-11}}C\]

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  • question_answer47) A parallel plate capacitor is immersed in an oil of dielectric constant 2. The field between the plates is:

    A) decreased, by a factor of\[\frac{1}{\sqrt{2}}\]

    B) increased, by a factor of\[\sqrt{2}\]

    C) increased, by a factor of\[\frac{1}{2}\]

    D) decreased, by a factor of\[2\]

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  • question_answer48) A triode valve has an amplification factor of \[20\] and its plate is given a potential of \[300\,\,V\]. The grid voltage to reduce the plate current to zero is:

    A) \[25\,\,V\]

    B) \[15\,\,V\]

    C) \[12\,\,V\]

    D) \[10\,\,V\]

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  • question_answer49) In an ideal parallel \[LC\] circuit, the capacitor is charged by connecting it to a \[DC\,\] source which is then disconnected. The current in the circuit:

    A) becomes zero instantaneously

    B) grows monotonically

    C) decays monotonically

    D) oscillates instantaneously

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  • question_answer50) For a satellite moving in an orbit around the earth, the ratio of kinetic to potential energy is:

    A) \[1:2\]

    B) \[2:1\]

    C) \[1:1\]

    D) \[4:1\]

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  • question_answer51) Which of the following statements, about zero order reaction is not true?

    A) Its rate constant unit is\[{{s}^{-1}}\]

    B) The graph between time and rate of reaction is a straight line

    C) Rate of reaction is independent of concentration of reactants

    D) None of the above

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  • question_answer52) The amount of \[{{H}_{2}}S\], required to precipitate \[1.69\,\,g\,\,BaS\] from \[BaC{{l}_{2}}\] solution is:

    A) \[3.4\,\,g\]

    B) \[0.034\,\,g\]

    C) \[0.34\,\,g\]

    D) \[0.17\,\,g\]

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  • question_answer53) Which of the following is not a protein?

    A) Testosterone

    B) Lipase

    C) Keratin

    D) Haemoglobin

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  • question_answer54) The reaction,\[C{{H}_{3}}COC{{H}_{3}}\xrightarrow[(ii)\,\,KOH,\,\,glycol]{(i)\,\,N{{H}_{2}}N{{H}_{2}}}C{{H}_{3}}C{{H}_{2}}C{{H}_{3}}\]is known as:

    A) Clemmensen's reduction

    B) Blanc's reduction

    C) Birch reduction

    D) Wolff-Kishner reduction

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  • question_answer55) \[pH-\]scale was proposed by:

    A) Arrhenius

    B) Sorenson

    C) Pierre de Coubertin

    D) none of the above

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  • question_answer56) Thomas slag is:

    A) \[C{{a}_{3}}{{(P{{O}_{4}})}_{2}}\cdot 2{{H}_{2}}O\]

    B) \[C{{a}_{3}}{{(P{{O}_{4}})}_{2}}\cdot CaSi{{O}_{3}}\]

    C) \[MgSi{{O}_{3}}\]

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

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  • question_answer57) Mohr's salt is:

    A) \[N{{a}_{2}}S{{O}_{4}}\cdot A{{l}_{2}}{{(S{{O}_{4}})}_{3}}\cdot 24{{H}_{2}}O\]

    B) \[CuS{{O}_{4}}\cdot A{{l}_{2}}{{(S{{O}_{4}})}_{3}}\cdot 24{{H}_{2}}O\]

    C) \[FeS{{O}_{4}}\cdot {{(N{{H}_{4}})}_{2}}S{{O}_{4}}\cdot 6{{H}_{2}}O\]

    D) \[{{K}_{2}}S{{O}_{4}}\cdot F{{e}_{2}}{{(S{{O}_{4}})}_{3}}\cdot 2{{H}_{2}}O\]

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  • question_answer58) Which of the following has maximum ionisation energy?

    A) Caesium

    B) Fluorine

    C) Xenon

    D) Nitrogen

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  • question_answer59) Which of the following give ammonia, on heating with\[NaOH?\]

    A) Ethyl amine

    B) Ethane nitrile

    C) Nitroethane

    D) Ethanamide

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  • question_answer60) Which of the following is poisonous?

    A) Methanol

    B) Ethanol

    C) Glycerol

    D) Castor oil

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  • question_answer61) Which of the following fraction of coal tar distillation is obtained at\[{{270}^{o}}-{{360}^{o}}C?\]

    A) Light oil

    B) Middle oil

    C) Green oil

    D) Heavy oil

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  • question_answer62) The amount of oxalic acid, required to prepare \[300\,\,mL\,\,2.5\,\,M\] solution, is:

    A) \[67.5\,\,g\]

    B) \[9.45\,\,g\]

    C) \[6.75\,\,g\]

    D) \[94.5\,\,g\]

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  • question_answer63) The carbon di-oxide gas does not follow gaseous laws at all ranges of pressure and temperature because:

    A) it is triatomic gas

    B) its internal energy is quite high

    C) there is attraction between its, molecules

    D) it solidify at low temperature

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  • question_answer64) The bond-angle in \[As{{H}_{3}}\] is greater than that in:

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

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

    C) \[BC{{l}_{3}}\]

    D) none of these

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  • question_answer65) Which of the following gas, diffuse, most slowly?

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

    B) \[{{C}_{2}}{{H}_{4}}\]

    C) \[C{{H}_{4}}\]

    D) All of these diffuse at equal rate

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  • question_answer66) Oxidation number of fluorine is \[+1\] in:

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

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

    C) both [a] and [b]

    D) none of these

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  • question_answer67) Which radioisotope is used in the treatment of Leukeamia?

    A) \[P-32\]

    B) \[Na-24\]

    C) \[I-128\]

    D) \[Co-59\]

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  • question_answer68) A metal having higher value of\[{{E}^{o}}\], can:

    A) replace hydrogen from dilute\[{{H}_{2}}S{{O}_{4}}\]

    B) replace hydrogen from concentrate\[{{H}_{2}}S{{O}_{4}}\]

    C) act as oxidising agent

    D) all of the above

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  • question_answer69) The method, which is used to purify colloidal solution is:

    A) electrophoresis

    B) dialysis

    C) chromatography

    D) peptisation

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  • question_answer70) Four gases ethane, ethene, ethyne and propene are passed into a wolf bottle containing ammoniacal \[AgN{{O}_{3}}\] solution. Which gas will come out of wolf bottle?

    A) Only ethyne

    B) Ethane and ethyne

    C) Ethane and ethane

    D) Ethane, ethene and propene

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  • question_answer71) How many conformers are known of ethane?

    A) Two

    B) Three

    C) \[>3\]

    D) Ethane cannot show conformation

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  • question_answer72) Interfering radicals interfere in the usual test of:

    A) acid radicals

    B) basic radicals

    C) both [a] and [b]

    D) none of these

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  • question_answer73) Flux in the smelting process is added to:

    A) decrease the solubility of impurities

    B) increase the fusion temperature of roasted ore

    C) convert impurities into slag

    D) all of the above

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  • question_answer74) The heat of formation of \[MgO,\,\,A{{l}_{2}}O\] and \[Si{{O}_{2}}\] are \[-692,\,\,\,-1676,\,\,\,-911,\,\,\,kJ\,\,mo{{l}^{-1}}\]. Most stable oxide is:

    A) \[MgO\]

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

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

    D) cannot be predicted

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  • question_answer75) Which of the following reaction, will be favoured by low pressure?

    A) \[PC{{l}_{5}}PC{{l}_{3}}+C{{l}_{2}}\]

    B) \[{{N}_{2}}+3{{H}_{2}}2N{{H}_{3}}\]

    C) \[{{H}_{2}}+\frac{1}{2}{{O}_{2}}{{H}_{2}}O\]

    D) \[2NO+{{O}_{2}}2N{{O}_{2}}\]

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  • question_answer76) In III group of basic radical analysis, \[N{{H}_{4}}Cl\] is added before group reagent \[N{{H}_{4}}OH\]. This is done to:

    A) increase the solubility product of \[III\] group salts

    B) decrease the solubility product of \[III\] group salts

    C) increase the ionic product of \[O{{H}^{-}}\] and \[III\] group radicals

    D) decrease the degree of ionisation of group reagent

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  • question_answer77) Representative elements are:

    A) \[s-\]block elements

    B) \[p-\]block elements

    C) both [a] and [b]

    D) none of these

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  • question_answer78) Which of the following equation is used in Pauling's scale of electronegativity?

    A) \[{{x}_{A}}=0.187(IE+EA)+0.17\]

    B) \[{{x}_{A}}-{{x}_{B}}=0.182\] \[{{[{{E}_{A-B}}-\sqrt{({{E}_{A-A}}\times {{E}_{B-B}})}]}^{1/2}}\]

    C) \[{{x}_{A}}=\frac{0.359\,\,{{Z}_{eff}}}{r_{A}^{2}}+0.744\]

    D) None of the above

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  • question_answer79) Which hybridisation has sulphur in\[S{{O}_{2}}\]?

    A) \[s{{p}^{2}}\]

    B) \[s{{p}^{3}}{{d}^{2}}\]

    C) \[s{{p}^{3}}\]

    D) \[sp\]

    View Answer play_arrow
  • question_answer80) The energy of last electron of Li will be:

    A) \[-30.6\,\,eV\]

    B) \[-13.6\,\,eV\]

    C) \[-24.6\,\,eV\]

    D) \[-28.6\,\,eV\]

    View Answer play_arrow
  • question_answer81) Benzaldehyde, in presence of \[dil.\,\,NaOH,\]changes into benzyl alcohol and sodium benzoate. This reaction is an example of:

    A) rearrangement

    B) oxidation

    C) disproportionation

    D) hone of the above

    View Answer play_arrow
  • question_answer82) Which of the following is the strongest acid?

    A) \[o-\]nitro benzoic acid

    B) \[m-\]nitro benzoic acid

    C) \[m-\]chloro benzoic acid

    D) \[m-\]cyano benzoic acid

    View Answer play_arrow
  • question_answer83) What is the product \['X'\] in the reaction\[,\]\[C{{H}_{3}}COCl\xrightarrow{C{{H}_{3}}COONa}X\]?

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

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

    C) \[C{{H}_{3}}COC{{H}_{2}}COO{{C}_{2}}{{H}_{5}}\]

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

    View Answer play_arrow
  • question_answer84) A \[0.5\,\,g/L\] solution of glucose is found to be isotonic with a \[2.5\,\,g/L\] solution of an organic compound. What will be the molecular weight of that organic compound?

    A) \[300\]

    B) \[600\]

    C) \[925\]

    D) \[1200\]

    View Answer play_arrow
  • question_answer85) Which of the following ion does not follow \[EAN\] rule?

    A) \[{{[Fe{{(CN)}_{6}}]}^{4-}}\]

    B) \[{{[Ag{{(CN)}_{2}}]}^{-}}\]

    C) \[{{[PtC{{l}_{6}}]}^{2-}}\]

    D) None of these

    View Answer play_arrow
  • question_answer86) Potassium, on burning in oxygen atmosphere gives:

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

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

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

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

    View Answer play_arrow
  • question_answer87) Which method is employed to prepare copper sol?

    A) Peptisation

    B) Bredig's arc method

    C) Double decomposition

    D) Reduction of\[CuC{{l}_{2}}\]

    View Answer play_arrow
  • question_answer88) How much copper will be deposited at cathode on passing 4 coulomb charge in \[15\min ?\]

    A) \[0.0195\,\,g\]

    B) \[0.0013\,\,g\]

    C) \[0.020\,\,g\]

    D) \[0.0020\,\,g\]

    View Answer play_arrow
  • question_answer89) If \[50%\] of a radioactive substance dissociates in \[15\min \], then the time taken by substance to dissociate \[99%\] will be:

    A) \[50\,\,\min \]

    B) \[100\,\,\min \]

    C) \[99\,\,\min \]

    D) \[150\,\,\min \]

    View Answer play_arrow
  • question_answer90) Which of the following alcohol give positive iodo form test?

    A) Methanol

    B) Ethyl carbinol

    C) Pentanol\[-3\]

    D) Methyl carbinol

    View Answer play_arrow
  • question_answer91) Human body is an example of:

    A) open system

    B) closed system

    C) isolated system

    D) none of these

    View Answer play_arrow
  • question_answer92) The atomic size of cerium and promethium is quite close, due to:

    A) they are in same period in periodic table

    B) their electronic configuration is same

    C) \[f-\]electrons have poor shielding effect

    D) nuclear charge is higher on cerium than promethium

    View Answer play_arrow
  • question_answer93) Brown glass and cement have, which element common in them?

    A) \[Fe\]

    B) \[Al\]

    C) \[Na\]

    D) All of these

    View Answer play_arrow
  • question_answer94) The most common isomerism found in ethers, is:

    A) chain isomerism

    B) tautomerism

    C) metamerism

    D) optical isomerism

    View Answer play_arrow
  • question_answer95) \[t-\]butyl chloride preferably undergo hydrolysis by:

    A) \[{{S}_{N}}1\] mechanism

    B) \[{{S}_{N}}2\] mechanism

    C) any of [b] and [b]

    D) none of the above

    View Answer play_arrow
  • question_answer96) Which of the following has lowest boiling point?

    A) \[NaCl\]

    B) \[CuCl\]

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

    D) \[CsCl\]

    View Answer play_arrow
  • question_answer97) Which of the following is true for the reaction\[CO(g)+\frac{1}{2}{{O}_{2}}(g)C{{O}_{2}}(g)\]

    A) \[{{K}_{p}}>{{K}_{c}}\]

    B) \[{{K}_{p}}<{{K}_{c}}\]

    C) \[{{K}_{p}}={{K}_{c}}\]

    D) \[{{K}_{p}}\ge {{K}_{c}}\]

    View Answer play_arrow
  • question_answer98) Which of the following is not a buffer solution?

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

    B) \[{{H}_{3}}B{{O}_{3}}+N{{a}_{3}}B{{O}_{3}}\]

    C) \[HCl{{O}_{4}}+NaCl{{O}_{4}}\]

    D) \[N{{H}_{4}}OH+{{(N{{H}_{4}})}_{2}}S{{O}_{4}}\]

    View Answer play_arrow
  • question_answer99) Which of the following ore is concentrated by both, magnetic and gravimetric separation?

    A) Dolomite

    B) Tin stone

    C) Galena

    D) Bauxite

    View Answer play_arrow
  • question_answer100) Which of the following is not a polymer?

    A) RNA

    B) Oxytocin

    C) Cholesterol

    D) Amylose

    View Answer play_arrow
  • question_answer101) The minimum value of \[{{x}^{2}}+\frac{1}{1+{{x}^{2}}}\] is at:

    A) \[x=0\]

    B) \[x=4\]

    C) \[x=1\]

    D) \[x=3\]

    View Answer play_arrow
  • question_answer102) If \[\overrightarrow{\mathbf{a}},\,\,\overrightarrow{\mathbf{b}},\,\,\overrightarrow{\mathbf{c}}\]are the non-coplanar vectors, then the value of\[\frac{\overset{\to }{\mathop{\mathbf{a}}}\,\cdot (\overset{\to }{\mathop{\mathbf{b}}}\,\times \overset{\to }{\mathop{\mathbf{c}}}\,)}{(\overset{\to }{\mathop{\mathbf{c}}}\,\times \overset{\to }{\mathop{\mathbf{a}}}\,)\cdot \overset{\to }{\mathop{\mathbf{b}}}\,}+\frac{\overset{\to }{\mathop{\mathbf{b}}}\,(\overset{\to }{\mathop{\mathbf{a}}}\,\times \overset{\to }{\mathop{\mathbf{c}}}\,)}{\overset{\to }{\mathop{\mathbf{c}}}\,\cdot (\overset{\to }{\mathop{\mathbf{a}}}\,\times \overset{\to }{\mathop{\mathbf{b}}}\,)}\]is:

    A) \[1\]

    B) \[2\]

    C) \[0\]

    D) None of these

    View Answer play_arrow
  • question_answer103) If\[x-2y=4\], the minimum value of\[xy\]is:

    A) \[-2\]

    B) \[0\]

    C) \[0\]

    D) \[-3\]

    View Answer play_arrow
  • question_answer104) If\[z=x+iy\]and\[\left| \frac{1-iz}{z-i} \right|=1\], the locus of\[z\]is:

    A) \[x-\]axis

    B) \[y-\]axis

    C) circle with unity radius

    D) none of the above

    View Answer play_arrow
  • question_answer105) The vertex of an equilateral triangle is \[(2,\,\,-1)\] and the equation of its base is \[x+2y=1\], the length of its sides is:

    A) \[2/\sqrt{15}\]

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

    C) \[1/\sqrt{5}\]

    D) \[4/\sqrt{15}\]

    View Answer play_arrow
  • question_answer106) The resultant of two forces \[P\] and \[Q\] is \[R\]. If the direction of \[P\] is reversed keeping the direction \[Q\] same, the resultant remains unaltered. The angle between \[P\] and \[Q\] is:

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

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

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

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

    View Answer play_arrow
  • question_answer107) The distance \[s\] (in cm) travelled by a particle in\[t\] seconds is given by\[,\] \[s={{t}^{3}}+2{{t}^{2}}+t\]. The speed of the particle after \[1\,\,s\] will be:

    A) \[2\,\,cm/s\]

    B) \[8\,\,cm/s\]

    C) \[6\,\,cm/s\]

    D) None of these

    View Answer play_arrow
  • question_answer108) The roots of\[|x-2{{|}^{2}}+|x-2|-6=0\]are:

    A) \[4,\,\,2\]

    B) \[0,\,\,4\]

    C) \[-1,\,\,3\]

    D) \[5,\,\,1\]

    View Answer play_arrow
  • question_answer109) The height of a tower is\[7848\,\,cm\]. A particle is thrown from the top of the tower with the horizontal velocity of \[1784\,\,cm/s\]. The time taken by the particle to reach the ground is (g \[=981\,\,cm/{{s}^{2}})\]:

    A) \[\sqrt{8}\,\,s\]

    B) \[2\,\,s\]

    C) \[4\,\,s\]

    D) \[8\,\,s\]

    View Answer play_arrow
  • question_answer110) The directrix of the hyperbola\[\frac{{{x}^{2}}}{9}-\frac{{{y}^{2}}}{4}=1\]is:

    A) \[y=6/\sqrt{13}\]

    B) \[x=6/\sqrt{13}\]

    C) \[y=9/\sqrt{13}\]

    D) \[x=\pm 9/\sqrt{13}\]

    View Answer play_arrow
  • question_answer111) The value of\[{{\cos }^{-1}}\left( \cos \frac{5\pi }{3} \right)+{{\sin }^{-1}}\left( \cos \frac{5\pi }{3} \right)\]is:

    A) \[10\pi /3\]

    B) \[0\]

    C) \[\pi /2\]

    D) \[5\pi /3\]

    View Answer play_arrow
  • question_answer112) If\[f(x)=\log \left( \frac{1+x}{1-x} \right)\], then\[f\left( \frac{2x}{1+{{x}^{2}}} \right)\]will be equal to:

    A) \[2f({{x}^{2}})\]

    B) \[f({{x}^{2}})\]

    C) \[2f(2x)\]

    D) \[2f(x)\]

    View Answer play_arrow
  • question_answer113) If\[{{(1+x-2{{x}^{2}})}^{6}}=1+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+...+{{a}_{12}}{{x}^{12}}\] then the value of\[{{a}_{2}}+{{a}_{4}}+...+{{a}_{12}}\]is:

    A) \[31\]

    B) \[32\]

    C) \[64\]

    D) \[1024\]

    View Answer play_arrow
  • question_answer114) \[2{{x}^{3}}-6x+5\]is an increasing function, if:

    A) \[0<x<1\]

    B) \[-1<x<1\]

    C) \[x<-1\]or\[x>1\]

    D) \[-1<x<-\frac{1}{2}\]

    View Answer play_arrow
  • question_answer115) Two trains are \[2\,\,km\] apart their lengths are \[200\,\,m\] and \[300\,\,m\]. They are approaching towards each other with speed of \[20\,\,m/s\] and \[30\,\,m/s\] respectively. After how much time will they cross each other?

    A) \[150\,\,s\]

    B) \[100\,\,s\]

    C) \[50\,\,s\]

    D) \[\frac{25}{3}s\]

    View Answer play_arrow
  • question_answer116) \[\frac{{{d}^{3}}y}{d{{x}^{3}}}+\left[ 1+\frac{{{d}^{2}}y}{d{{x}^{2}}} \right]=1\], has degree and order as:

    A) \[3,\,\,1\]

    B) \[3,\,\,2\]

    C) \[1,\,\,3\]

    D) \[2,\,\,3\]

    View Answer play_arrow
  • question_answer117) The value of\[I=\int_{0}^{1}{x\left| x-\frac{1}{2} \right|\,}dx\]is:

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

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

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

    D) none of these

    View Answer play_arrow
  • question_answer118) If\[A=\left[ \begin{matrix} 4 & 2 \\ 3 & 4 \\ \end{matrix} \right]\],\[|adj\,\,A|\]is equal to:

    A) \[6\]

    B) \[16\]

    C) \[10\]

    D) none of these

    View Answer play_arrow
  • question_answer119) \[\overset{\to }{\mathop{\mathbf{a}}}\,\cdot (\overset{\to }{\mathop{\mathbf{b}}}\,+\overset{\to }{\mathop{\mathbf{c}}}\,)\times (\overset{\to }{\mathop{\mathbf{a}}}\,+\overset{\to }{\mathop{\mathbf{b}}}\,+\overset{\to }{\mathop{\mathbf{c}}}\,)\]is equal to:

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

    B) \[3[\overset{\to }{\mathop{\mathbf{a}}}\,\overset{\to }{\mathop{\mathbf{b}}}\,\overset{\to }{\mathop{\mathbf{c}}}\,]\]

    C) \[0\]

    D) \[2[\overset{\to }{\mathop{\mathbf{a}}}\,\overset{\to }{\mathop{\mathbf{b}}}\,\overset{\to }{\mathop{\mathbf{c}}}\,]\]

    View Answer play_arrow
  • question_answer120) A block weighing \[w\], is supported on an inclined surface with the help of a horizontal force \[P\]. The same block can be supported with the help of another force \[Q\] acting parallel to the inclined surface, then \[\frac{1}{{{p}^{2}}}+\frac{1}{{{w}^{2}}}\] is equal to:

    A) \[w\sin \alpha \]

    B) \[1\]

    C) \[1/Q\]

    D) \[1/{{Q}^{2}}\]

    View Answer play_arrow
  • question_answer121) \[\int_{0}^{2}{|x-1}|dx\]is equal to:

    A) \[0\]

    B) \[1/2\]

    C) \[1\]

    D) \[2\]

    View Answer play_arrow
  • question_answer122) Two cards are drawn one by one from a pack of cards. The probability of getting first card an ace and second a coloured one is (before drawing second card first card is not placed again in the pack):

    A) \[4/13\]

    B) \[1/26\]

    C) \[5/52\]

    D) \[5/221\]

    View Answer play_arrow
  • question_answer123) A particle is displaced from the point\[A(5,\,\,-5,\,\,-7)\]to the point\[B(6,\,\,2,\,\,-2)\]under the influence of the forces\[{{P}_{1}}=10\widehat{\mathbf{i}}-\widehat{\mathbf{j}}+11\widehat{\mathbf{k}}\],\[{{P}_{2}}=4\widehat{\mathbf{i}}+5\widehat{\mathbf{j}}+6\widehat{\mathbf{k}}\]\[{{P}_{3}}=-2\widehat{\mathbf{i}}+\widehat{\mathbf{j}}-9\widehat{\mathbf{k}}\], the work done is:

    A) \[87\,\,unit\]

    B) \[85\,\,unit\]

    C) \[81\,\,unit\]

    D) none of these

    View Answer play_arrow
  • question_answer124) If\[\sin x+\cos x=\frac{1}{5}\], then\[\tan 2x\]is:

    A) \[\frac{25}{17}\]

    B) \[\frac{24}{7}\]

    C) \[\frac{7}{25}\]

    D) \[\frac{25}{7}\]

    View Answer play_arrow
  • question_answer125) In \[\text{a}\] \[\Delta ABC,\,\,\angle B=\pi /3\]and\[\angle C=\pi /4\]. If\[D\]divides \[BC\] internally in ratio \[1:3\], then\[\frac{\sin \angle BAD}{\sin \angle CAD}\]is equal to:

    A) \[1/\sqrt{3}\]

    B) \[1/\sqrt{6}\]

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

    D) \[1/3\]

    View Answer play_arrow
  • question_answer126) If\[|\overset{\to }{\mathop{\mathbf{a}}}\,\times \overset{\to }{\mathop{\mathbf{b}}}\,|=|\overset{\to }{\mathop{\mathbf{a}}}\,\cdot \overset{\to }{\mathop{\mathbf{b}}}\,|\] then the angle between\[\overset{\to }{\mathop{\mathbf{a}}}\,\]and\[\overset{\to }{\mathop{\mathbf{b}}}\,\]is:

    A) \[\pi \]

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

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

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

    View Answer play_arrow
  • question_answer127) Let \[A,\,\,B\] and \[C\] are the angles of a plain triangle and\[\tan \left( \frac{A}{2} \right)=\frac{1}{3},\,\,\tan \left( \frac{B}{2} \right)=\frac{2}{3}\]. Then\[\tan \left( \frac{C}{2} \right)\] is equal to:

    A) \[1/3\]

    B) \[2/3\]

    C) \[2/9\]

    D) \[7/9\]

    View Answer play_arrow
  • question_answer128) The value\[\underset{x\to 1}{\mathop{\lim }}\,(1-x)\tan \left( \frac{\pi }{2}x \right)\]:

    A) \[3\pi /4\]

    B) \[2\pi /3\]

    C) \[2/\pi \]

    D) \[\pi /4\]

    View Answer play_arrow
  • question_answer129) If\[f(x)={{\left( \frac{1}{x} \right)}^{x}}\], then the maximum value of\[f(x)\]is:

    A) \[e\]

    B) \[{{(e)}^{1/e}}\]

    C) \[{{\left( \frac{1}{e} \right)}^{e}}\]

    D) none of these

    View Answer play_arrow
  • question_answer130) The volume of the solid formed by rotating, the area enclosed between the curve \[y={{x}^{2}}\] and the line \[y=1\] about \[y=1\] is (in cubic unit):

    A) \[9\pi /5\]

    B) \[2\pi /5\]

    C) \[8\pi /3\]

    D) \[7\pi /5\]

    View Answer play_arrow
  • question_answer131) \[\int_{8}^{15}{\frac{dx}{(x-3)\sqrt{x+1}}}\]is equal to:

    A) \[\frac{1}{2}\log \frac{5}{3}\]

    B) \[\frac{1}{3}\log \frac{5}{3}\]

    C) \[\frac{1}{5}\log \frac{3}{5}\]

    D) \[\frac{1}{2}\log \frac{3}{5}\]

    View Answer play_arrow
  • question_answer132) Area of the square formed by\[|x|+|y|\,\,=1\]is:

    A) \[0\,\,sq\,\,unit\]

    B) \[1\,\,sq\,\,unit\]

    C) \[2\,\,sq\,\,unit\]

    D) \[4\,\,sq\,\,unit\]

    View Answer play_arrow
  • question_answer133) If\[x=3+i\], then\[{{x}^{3}}-3{{x}^{2}}-8x+15\]is equal to:

    A) \[45\]

    B) \[-15\]

    C) \[10\]

    D) \[6\]

    View Answer play_arrow
  • question_answer134) The function\[f(x)=\log (x+\sqrt{{{x}^{2}}+1})\]is:

    A) even function

    B) odd function

    C) neither even nor odd

    D) periodic function

    View Answer play_arrow
  • question_answer135) The locus of the intersection point of\[x\cos \alpha +y\sin \alpha =a\]and\[x\sin \alpha -y\cos \alpha =b\]is:

    A) parabola

    B) ellipse

    C) hyperbola

    D) none of these

    View Answer play_arrow
  • question_answer136) If\[|\overset{\to }{\mathop{\mathbf{a}}}\,|\,\,=\,\,|\overset{\to }{\mathop{\mathbf{b}}}\,|\,\,=\,\,|\overset{\to }{\mathop{\mathbf{c}}}\,|\,\,=1\]and\[\overset{\to }{\mathop{\mathbf{a}}}\,+\overset{\to }{\mathop{\mathbf{b}}}\,+\overset{\to }{\mathop{\mathbf{c}}}\,=0\], then the value of\[\overset{\to }{\mathop{\mathbf{a}}}\,\cdot \overset{\to }{\mathop{\mathbf{b}}}\,+\overset{\to }{\mathop{\mathbf{b}}}\,\cdot \overset{\to }{\mathop{\mathbf{c}}}\,+\overset{\to }{\mathop{\mathbf{c}}}\,\cdot \overset{\to }{\mathop{\mathbf{a}}}\,\]is:

    A) \[0\]

    B) \[-1\]

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

    D) \[3\]

    View Answer play_arrow
  • question_answer137) If\[x={{\log }_{b,}}a,\,\,y={{\log }_{c}}b,\,\,z={{\log }_{a}}c\], then\[xyz\]is:

    A) \[0\]

    B) \[1\]

    C) \[3\]

    D) none of these

    View Answer play_arrow
  • question_answer138) The value of the determinant\[\left| \begin{matrix} 1 & \cos (\alpha -\beta ) & \cos \alpha \\ \cos (\alpha -\beta ) & 1 & \cos \beta \\ \cos \alpha & \cos \beta & 1 \\ \end{matrix} \right|\]is

    A) \[0\]

    B) \[1\]

    C) \[{{\alpha }^{2}}-{{\beta }^{2}}\]

    D) \[{{\alpha }^{2}}+{{\beta }^{2}}\]

    View Answer play_arrow
  • question_answer139) If \[P(A)=P(B)=x\] and\[P(A\cap B)=P(A'\cap B')=\frac{1}{3}\], then \[x\] is equal to:

    A) \[1/2\]

    B) \[1/4\]

    C) \[1/3\]

    D) \[1/6\]

    View Answer play_arrow
  • question_answer140) If \[p\] and \[q\] are the roots of the equation\[{{x}^{2}}+px+q=0\], thus:

    A) \[p=1\]or\[0\]

    B) \[p=-2\]or\[0\]

    C) \[p=-2\]

    D) \[p=1\]

    View Answer play_arrow
  • question_answer141) If a dice is thrown twice, the probability of occurrence of \[4\] atleast once, is:

    A) \[11/36\]

    B) \[35/36\]

    C) \[7/12\]

    D) none of these

    View Answer play_arrow
  • question_answer142) The value of \[\int_{0}^{8}{|x-5|}\,\,dx\]is:

    A) \[9\]

    B) \[12\]

    C) \[17\]

    D) \[18\]

    View Answer play_arrow
  • question_answer143) The value of\[\int_{0}^{\pi }{|{{\sin }^{3}}\theta |d\theta }\]is:

    A) \[0\]

    B) \[\pi \]

    C) \[4/3\]

    D) \[3/8\]

    View Answer play_arrow
  • question_answer144) A ball weighing \[2\,\,kg\]and speed\[6\,\,m/s\]collides with another ball of \[4\,\,kg\] moving in opposite direction with speed of \[3\,\,m/s\]. They combine after the collision. The speed of this combined mass in \[m/s\] is:

    A) \[4\]

    B) \[2\]

    C) \[0\]

    D) \[3\]

    View Answer play_arrow
  • question_answer145) If\[\alpha ,\,\,\beta ,\,\,\gamma \]are the roots of the equation\[{{x}^{3}}+4x+1=0\]then\[{{(\alpha +\beta )}^{-1}}+{{(\beta +\gamma )}^{-1}}+{{(\gamma +\alpha )}^{-1}}\]is equal to:

    A) \[2\]

    B) \[3\]

    C) \[4\]

    D) \[5\]

    View Answer play_arrow
  • question_answer146) If\[\cos \theta +\cos 2\theta +\cos 3\theta =0\], the general value of\[\theta \]is:

    A) \[\theta =2m\pi \pm \pi /4\]

    B) \[\theta =m\pi +{{(-1)}^{n}}2\pi /3\]

    C) \[\theta =m\pi +{{(-1)}^{n}}\pi /3\]

    D) \[\theta =2m\pi \pm 2\pi /3\]

    View Answer play_arrow
  • question_answer147) Forces \[P\] and \[Q\] acting at a point \[O\] make an angle \[{{150}^{o}}\] between them. Their resultant acts at \[O\], has magnitude \[2\] unit and is perpendicular to \[P\]. Then in the same unit, the magnitudes of \[P\] and \[Q\] are:

    A) \[2\sqrt{3},\,\,4\]

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

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

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

    View Answer play_arrow
  • question_answer148) A person observes the angle of depression of a building as \[{{30}^{o}}\]. The person proceeds towards the building with a speed of \[25(\sqrt{3}-1)m/h\]. After two hours, he observes the angle of elevation as \[{{45}^{o}}\]. The height of the building (in \[m)\] is:

    A) \[50(\sqrt{3}-1)\]

    B) \[50(\sqrt{3}+1)\]

    C) \[50\]

    D) \[100\]

    View Answer play_arrow
  • question_answer149) The value of\[\underset{x\to \infty }{\mathop{\lim }}\,{{\left( \frac{x+3}{x+1} \right)}^{x+2}}\]is:

    A) \[0\]

    B) \[1\]

    C) \[{{e}^{2}}\]

    D) \[{{e}^{4}}\]

    View Answer play_arrow
  • question_answer150) If\[A+B+C={{270}^{o}}\], then \[\cos 2A+\cos 2B\]\[+\cos 2C+4\sin A\sin B\sin C\]is equal to:

    A) \[0\]

    B) \[1\]

    C) \[2\]

    D) \[3\]

    View Answer play_arrow

   



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