Answers posted by yamini.v

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Solve the equation : $\;\sqrt{3}x^{2}-\sqrt{2}x+3\sqrt{3}=0\;$

answered Apr 11, 2014

Answer : $\;\large\frac{\sqrt{2} \pm \sqrt{34} i}{2 \sqrt{3}}$Explanation :The given quadratic equa...

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Solve the equation : $\;\sqrt{2}x^{2}+x+\sqrt{2}=0\;$

answered Apr 11, 2014

Answer : $\; \large\frac{-1 \pm \sqrt{7} i}{2 \sqrt{2}}$Explanation :The given quadratic equation ...

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Solve the equation : $\;x^{2}-x+2=0\;$

answered Apr 11, 2014

Answer : $\;\large\frac{1 \pm \sqrt{7} i}{2}$Explanation :The given quadratic equation is $\;x^2-x+...

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Solve the equation : $\;x^{2}+3x+5=0\;$

answered Apr 11, 2014

Answer : $\;\large\frac{-3\pm \sqrt{11} i}{2}$Explanation :The given quadratic equation is $\;x^2+3...

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Solve the equation : $\;-x^{2}+x-2=0\;$

answered Apr 11, 2014

Answer : $\;\large\frac{-1 \pm \sqrt{7} i}{-2}$Explanation :The given quadratic equation is $\;-x^2...

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Solve the equation : $\;x^{2}+3x+9=0\;$

answered Apr 11, 2014

Answer : $\;\large\frac{-3 \pm 3 \sqrt{3}i}{2}$Explanation :The given quadratic equation is $\;x^2+...

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Solve the equation : $\;2x^{2}+x+1=0\;$

answered Apr 10, 2014

Answer : $\;\large\frac{-1\pm \sqrt{7} i}{4}$Explanation :The given quadratic equation is $\;2x^2+...

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Solve the equation : $\;x^{2}+3=0\;$

answered Apr 10, 2014

Answer : $\;\pm \sqrt{3} i$Explanation :The given quadratic equation is $\;x^2+3=0$On comparing the...

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Convert the given complex number in polar form :$\;i\;$

answered Apr 10, 2014

Answer : $\;cos (\large\frac{\pi}{2})+i\;sin(\large\frac{\pi}{2})$Explanation :$i\;$ Let $\;r cos \...

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Convert the given complex number in polar form :$\;\sqrt{3}+i\;$

answered Apr 10, 2014

Answer : $\;2\;[cos(\large\frac{\pi}{6})+i\; sin(\large\frac{\pi}{6})]$Explanation :$\;\sqrt{3}+i\;...

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Convert the given complex number in polar form :$\;-3$

answered Apr 10, 2014

Answer : $\;3[cos \pi + i sin \pi]$Explanation :$\;-3\;$ Let $\;r cos \theta =-3 \;$ and $\;r sin \...

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Convert the given complex number in polar form :$\;-1-i\;$

answered Apr 10, 2014

Answer : $\;\sqrt{2}\;[cos (-\large\frac{3\pi}{4})+i \;sin(-\large\frac{3\pi}{4})]$Explanation :$\...

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Convert the given complex number in polar form :$\;-1+i\;$

answered Apr 10, 2014

Answer : $\;\sqrt{2}\;[cos (\large\frac{3\pi}{4})+i \;sin(\large\frac{3\pi}{4})]$Explanation :$\;-...

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Convert the given complex number in polar form :$\;1-i\;$

answered Apr 10, 2014

Answer : $\;\sqrt{2}\;[cos (-\large\frac{\pi}{4})+i \;sin(-\large\frac{\pi}{4})]$Explanation :$\;1...

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Find the modulus and the argument of the complex number $\;z=-\normalsize \sqrt{3} + \normalsize i$

answered Apr 10, 2014

Answer : $\;\large\frac{5 \pi}{6}$Explanation :Let $\;z=-\normalsize \sqrt{3} + \normalsize i$$r cos...

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Find the modulus and the argument of the complex number $\;z=-\normalsize 1- \normalsize i\sqrt{3}$

answered Apr 10, 2014

Answer : $\;-\large\frac{2 \pi}{3}$Explanation :Let$\;z=-\normalsize 1- \normalsize i\sqrt{3}$Let $...

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Express the following expression in the form $\;\normalsize a + \normalsize ib : \large\frac{(\normalsize 3 + \normalsize i \sqrt{5})(\normalsize 3 - \normalsize i \sqrt{5})}{(\normalsize \sqrt{3} + \normalsize i \sqrt{2})-(\normalsize \sqrt{3} - \normalsize i \sqrt{2})}$

answered Apr 10, 2014

Answer : $\;-\large\frac{7\sqrt{2}}{2} \normalsize i$Explanation :$\large\frac{(\normalsize 3 + \n...

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Find the multiplicative inverse of the complex number $\;\normalsize -i\;$

answered Apr 10, 2014

Answer : $\; \normalsize i$Explanation :Let$\;z= \normalsize - i$Then , $\;\overline{z}=\normalsize...

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Find the multiplicative inverse of the complex number $\;\sqrt{5} +3 \normalsize i\;$

answered Apr 10, 2014

Answer : $\;\normalsize \large\frac{\sqrt{5}}{14}- \normalsize \large\frac{3}{14} \normalsize i$Exp...

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Find the multiplicative inverse of the complex number $\;\normalsize 4-\normalsize 3 \normalsize i\;$

answered Apr 10, 2014

Answer : $ \;\normalsize \large\frac{4}{25}+\normalsize \large\frac{3}{25} \normalsize i$Explanatio...

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Express the given complex number in the form $\;a+ib : (-2-\large\frac{1}{3} \normalsize i)^{3}$

answered Apr 9, 2014

Answer : $\;-\large\frac{22}{3} \normalsize-\large\frac{107}{27} \normalsize i$Explanation :$(-2-\...

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Express the given complex number in the form $\;a+ib : (\large\frac{1}{3}$$+3i)^{3}$

answered Apr 9, 2014

Answer : $\;-\large\frac{242}{27} -26i$Explanation :$(\large\frac{1}{3}$$+3i)^{3} = (\large\frac{1}...

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Express the given complex number in the form $\;a+ib : (1-i)^{4}$

answered Apr 9, 2014

Answer : $\;-4$Explanation :$(1-i)^{4} = [(1-i)^2]^2$$ = [1^2 + i^2-2i]^2$$= (-2i)^2$$= (-2i) \time...

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Express the given complex number in the form $\;a+ib :\;[( \normalsize \large\frac{1}{3} +\normalsize i \normalsize \large\frac{7}{3}) + (\normalsize 4 + \normalsize i \normalsize \large\frac{1}{3})-( \normalsize -\large\frac{4}{3}+ \normalsize i)]$

answered Apr 9, 2014

Answer : $\;\large\frac{17}{3} +i \large\frac{5}{3}$Explanation :$(\large\frac{1}{3}+i\large\frac{7...

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Express the complex number $(\large\frac{1}{5} + i\large\frac{2}{5})-(4 + i (\large\frac{5}{2}))$ in the form $a+ib$

answered Apr 9, 2014

Answer : $\;- \large\frac{19}{5} - \large\frac{21}{10}i$Explanation :$ (\large\frac{1}{5} +i \larg...

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Express the complex number $(1-i)-(-1+6i)$ in the form $a+ib$

answered Apr 9, 2014

Answer : $\;2-7i$Explanation :$(1-i) - (-1+i6) =1 -i +1-6i $$= 2-7i\;.$

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Express the complex number $3(7+i7) + i(7 + i7)$ in the form $a+ib$

answered Apr 9, 2014

Answer : $\;14+28i$Explanation :$3 (7+i7) +i(7+i7) = 21 + 21 i + 7i + 7i^{2}$$ = 21+28i +7 \times...

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Express the complex number $i^{-39}$ in the form $a+ib$

answered Apr 9, 2014

Answer : $\;i$Explanation :$i^{-39} = i^{-4 \times 9-3}$$= (i^{4})^{-9} \;. i^{-3}$$ = (1)^{-9} \;...

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Express the complex number $i^{9}+i^{19}$ in the form $a+bi$

answered Apr 9, 2014

Answer : 0Explanation :$i^{9} + i^{19} = i^{4\times 2 + 1 } + i^{4 \times 4 + 3}$$= (i^4)^{2}\;.i +(...

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An ideal gas initially at a state $\;(P_{1},V_{1})\;$ is allowed to expand isothermally to a state $\;(P_{2},V_{2})\;$ . Then the gas is compressed adiabatically to its initial volume $\;V_{1}\;$ . Let the final pressure be $\;p_{3}\;$ and the workdone by the gas be W , Then

answered Apr 9, 2014

Answer : $\;P_{3} > P_{1} \;and \; W <0$Explanation :AB - isothermal expansion BC - adiaba...

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A sample of an ideal gas is taken through the process ABCA shown . It rejects 50 J of heat during part AB , does not absorb or reflect heat during BC and accepts 70 J of heat during CA . Forty joules of work is done on the gas during the part BC . The internal energies at B and C respectively will be $\;(u_{A} =1500\;J)$

answered Apr 9, 2014

Answer : $\;1450\;J\;and\;1490\;J$Explanation :$A \to B \;$ is an isochoric process$\bigtriangleup...

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Logarithms of readings of pressure and volume from ideal gas were plotted on a graph as shown . By measuring the gradient , it can be shown that the gas may be

answered Apr 9, 2014

Answer : Diatomic and undergoing an adiabatic changeExplanation : Answer : Diatomic and undergoing...

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An ideal gas is filled in a closed rigid and thermally insulated container . A coil of 100 oms resistor carrying a current of 1 A for 5 minutes supplies heat to the gas . The change in the internal energy of the gas is

answered Apr 9, 2014

Answer : $30\;KJ$Explanation :Heat supplied : $\; \bigtriangleup Q = I^2 R t$$= 1 \times 100 \tim...

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An ideal gas is taken through the cycle $\;A \to B \to C \to A \;$ as shown in the figure . If the net heat supplied to the gas in the cycle is 5 J , the work done by the gas is the process $\;C \to A\;$ is

answered Apr 9, 2014

Answer : $\;-5\;J$Explanation :In the cyclic process : $\; \bigtriangleup W =0$$\bigtriangleup Q ...

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Starting from the same initial conditions , an ideal gas expands from volume $\;V_{1}\;$ to $\;V_{2}\;$ in three different ways . The work done by the gas is $\;W_{1}\;$ if the process is purely isothermal , $\;W_{2}\;$ if purely isobaric and $\;W_{3}\;$ if purely adiabatic . Then :

answered Apr 9, 2014

Answer : $\;W_{2} >W_{1} >W_{3}$Explanation :Curve 1 - isobaric process Curve 2 - isothermal ...

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A thermodynamics ideal gas , initially at temperature $\;T_{1}\;$ ia enclosed in a cylinder fitted with a friction less piston . The gas is allowed to expand adiabatically to a temperature $\;T_{2}\;$ by releasing the piston suddenly . If $\;L_{1}\;$ and $\;L_{2}\;$ are the lengths of gas column before and after expansion respectively , then $\;\large\frac{T_{1}}{T_{2}}\;$ is given by

answered Apr 9, 2014

Answer : $\;(\large\frac{L_{2}}{L_{1}})^{\large\frac{2}{3}}$Explanation :For an adiabatic process$P...

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A thermodynamic process , the pressures and volumes corresponding to some points in the figure are $\;P_{A} = 3 \times 10^{4}\;pa \;,V_{A} = 2 \times 10^{-3} \;m^3\;$ . $\;P_{B}=8 \times 10^{4}\;pa\;V_{D} = 5 \times 10^{-3}\;m^3\;$. In the process AB , 600 J of heat and in the process BC , 200 J of heat is added to the system . The change in internal energy in process AC would be

answered Apr 9, 2014

Answer : $\;560\;J$Explanation :For process AB , W=0 , $\; \bigtriangleup Q =\bigtriangleup u $The...

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Volume $\;V_{S}\;$ Temperature graph of two moles of helium gas is show in figure . The ratio of heat absorbed and the work done by the gas in process 1 - 2 is

answered Apr 9, 2014

Answer : 3Explanation :Since $\;V \; \propto \;T\;$ , or $\;\large\frac{V}{T}\;$ = Constant$\b...

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A copper disc at $\;0^{0}C\;$ has a diameter of 50 cm and a hole is cut in the center with a diameter 5 cm . The diameter of the hole at $\;100^{0}C\;$ will be $\;(\alpha = 0.00016/^{0}C)\;$

answered Apr 8, 2014

Answer : $\;5.08\;cm$Explanation :$d_{h} = d_{h} \;at\;0^{0}C\;(1+\alpha_{cu} \bigtriangleup t)$$ =...

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A composite bar of length $\;(l_{1} + l_{2})\;$ is made from two bars of length $\;l_{1}\;$ and $\;l_{2}\;$ . Their coefficients of linear expansion $\;\alpha_{1}\;$ and $\;\alpha_{2}\;$ respectively . The effective linear coefficient of composite bar

answered Apr 8, 2014

Answer : $\;\large\frac{l_{1} \alpha_{1} + l_{2} \alpha_{2}}{l_{1}+l_{2}}$Explanation :$\bigtrian...

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When a block of iron floats in mercury at $\;0^{0}C\;$ , a fraction $\;K_{1}\;$ of its volume is submerged. While at the temperature $\;60^{0}C\;$ , a fraction $\;K_{2}\;$ is seen submerged . If the coefficient of volume expansion of iron is $\;r_{Fe}\;$ and that of mercury is $\;r_{Hg}\;$ , then the ratio $\;\large\frac{K_{1}}{K_{2}}\;$ can be expanded as

answered Apr 8, 2014

Answer : $\;\large\frac{1+60 r_{Fe}}{1+60 r_{Hg}}$Explanation :Since iron block in floating weight...

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The apparent expansion of a liquid when heated in a copper vessel is C and when heated in a silver vessel is S . If A is coefficient of linear expansion of silver is

answered Apr 8, 2014

Answer : $\;\large\frac{C+3A-S}{3}$Explanation :$r_{real} = r_{app} + r_{container}$$real = r_{ap...

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$\;l_{1}\;$ and $\;l_{2}\;$ are the lengths of two rods at $\;0^{0}C\;$ and have coefficients of linear expansion $\;\alpha_{1}\;$ and $\;\alpha_{2}\;$ respectively . If the difference between the lengths X is the same at all temperatures then $\;l_{1}\;$ is

answered Apr 8, 2014

Answer : $\;\large\frac{\alpha_{2}\;x}{\alpha_{1} -\alpha_{2}}$Explanation :$l_{1}^{'} = l_{1} \;...

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A wire of length 60 cm is bent into a circle with a gap of 1 cm at its ends . On heating by by $\;100^{0}C\;$ , If the length of the gap increases to 1.02 cm , $\;\alpha\;$ of the material of the wire is

answered Apr 8, 2014

Answer : $\;2 \times 10^{-4}/^{0}C$Explanation :Arc length at $\;100^{0}C\;$ = Arc length at $\;0...

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The brass scale of a barometer is correct at $\;0^{0}C\;$ and it reads 755 mm at $\;25^{0}C\;$ , Its reading at $\;0^{0}C\;$ is $\;r_{mercury} = 0.00018/^{0}C\;,r_{brass} =0.00021/^{0}C$

answered Apr 8, 2014

Answer : $755.2\;mm$Explanation :Correct length of mercury column at $\;25^{0}C\;$ = observed le...

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If the temperature of metal sphere increases by $\;\bigtriangleup t\;$ , the fractional change in its moment of inertia is $\;(\alpha \;= Coefficient\; of\; linear \;expansion )$

answered Apr 8, 2014

Answer : $\;2 \alpha \bigtriangleup t$Explanation :$I_{0} = \large\frac{2}{5} mr_{0}^2$$I^{'} = \l...

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The wavelength $\;\lambda_{m}\;$ of maximum intensity of emission of solar radiation is $\;\lambda_{m}=14\; \mu m\;$. The surface temperatures of sun and moon are (given $ b= 2.898 \times 10^{-3} \; metre/Kelvin $).

answered Apr 8, 2014

Answer : $\;6097\;K ,207\;K$

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A metal ball having surface area of $\;2 \times 10^{-2}\;m^2\;$ and at 900 K is kept in an enclosure at 300 K . If the surface emissivity of metal is 0.4 , find the rate of which heat is lost by the ball

answered Apr 8, 2014

Answer : $\;293\;W$Explanation :Stefan Boltzman law$\large\frac{dE}{dt} = eA \sigma\; [T_{0}^{4}-T_...

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A steel rod of length 20 cm and cross sectional area 3 $cm^{2}$ is heated at one end to $\;300^{0}C\;$ and the other end is in ice . Assuming no loss of heat , the mass of ice that melts in 10 minutes if $\;K_{steel} = 0.16 \;C.G.S\;$ units .

answered Apr 8, 2014

Answer : $\;54\;grams$Explanation : Rate of heat flow = $\large\frac{KA (T_{1}-T_{2})}{L}$$= \la...

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The temperature of a solid falls from $\;77^{0}C\;$ to $\;73^{0}C\;$ in 3 minutes and $\;73^{0}C\;$ to $\;69^{0}C\;$ in 4 minutes . What is the room temperature ?

answered Apr 8, 2014

Answer : 59Explanation :$\large\frac{dT}{dt} = K (\large\frac{\theta_{1}+\theta_{2}}{2} - \theta_{s...

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