The standard Gibbs energy for the given cell reaction in
Question: The standard Gibbs energy for the given cell reaction in $\mathrm{kJ}$ $\mathrm{mol}^{-1}$ at $298 \mathrm{~K}$ is: $\mathrm{Zn}(\mathrm{s})+\mathrm{Cu}^{2+}(\mathrm{aq}) \rightarrow \mathrm{Zn}^{2+}(\mathrm{aq})+\mathrm{Cu}(\mathrm{s})$ $\mathrm{E}^{\circ}=2 \mathrm{~V}$ at $298 \mathrm{~K}$ (Faraday's constant, $\mathrm{F}=96000 \mathrm{C} \mathrm{mol}^{-1}$ )$-384$384192$-192$Correct Option: 1 Solution: $\Delta \mathrm{G}^{\circ}=-\mathrm{nFE}_{\text {cell }}^{\circ}$ $=-2(96000) 2 ...
Read More →On the x-axis and at a distance $x$ from the origin, the gravitational field due to a mass distribution is given by
Question: On the $x$-axis and at a distance $x$ from the origin, the gravitational field due to a mass distribution is given by $\frac{A x}{\left(x^{2}+a^{2}\right)^{3 / 2}}$ in the $x$-direction. The magnitude of gravitational potential on the $x$-axis at a distance $x$, taking its value to be zero at infinity, is : (1) $\frac{A}{\left(x^{2}+a^{2}\right)^{1 / 2}}$(2) $\frac{A}{\left(x^{2}+a^{2}\right)^{3 / 2}}$(3) $A\left(x^{2}+a^{2}\right)^{1 / 2}$(4) $A\left(x^{2}+a^{2}\right)^{3 / 2}$Correct...
Read More →Calculate the standard cell potential (in V) of the cell in which following reaction takes place :
Question: Calculate the standard cell potential (in V) of the cell in which following reaction takes place : $\mathrm{Fe}^{2+}(\mathrm{aq})+\mathrm{Ag}^{+}(\mathrm{aq}) \rightarrow \mathrm{Fe}^{3+}(\mathrm{aq})+\mathrm{Ag}(\mathrm{s})$ Given that $\mathrm{E}_{\mathrm{Ag}^{+} / \mathrm{Ag}}^{0}=x \mathrm{~V}$ $\mathrm{E}_{\mathrm{Fe}^{2+} / \mathrm{Fe}}^{0}=y \mathrm{~V}$ $\mathrm{E}_{\mathrm{Fe}^{3+} / \mathrm{Fe}}^{0}=z \mathrm{~V}$$x-z$$x-y$$x+2 y-3 z$$x+y-z$Correct Option: , 3 Solution:...
Read More →For the system of linear equations:
Question: For the system of linear equations: $x-2 y=1, x-y+k z=-2, k y+4 z=6, k \in \mathbf{R}$ consider the following statements: (A) The system has unique solution if $k \neq 2, k \neq-2$. (B) The system has unique solution if $k=-2$. (C) The system has unique solution if $k=2$. (D) The system has no-solution if $k=2$. (E) The system has infinite number of solutions if $k \neq-2$. Which of the following statements are correct? (1) $(B)$ and $(E)$ only(2) $(C)$ and $(D)$ only(3) (A) and (D) on...
Read More →The mass density of a planet of radius $R$ varies with the
Question: The mass density of a planet of radius $R$ varies with the distance $r$ from its centre as $\rho(r)=\rho_{0}\left(1-\frac{r^{2}}{R^{2}}\right)$. Then the gravitational field is maximum at:(1) $r=\sqrt{\frac{3}{4}} R$(2) $r=R$(3) $r=\frac{1}{\sqrt{3}} R$(4) $r=\sqrt{\frac{5}{9}} R$Correct Option: , 4 Solution: Mass of small element of planet of radius $x$ and thickness $d x$. $d m=\rho \times 4 \pi x^{2} d x=\rho_{0}\left(1-\frac{x^{2}}{R^{2}}\right) \times 4 \pi x^{2} d x$ Mass of the ...
Read More →Solve the following
Question: Given that $\mathrm{E}_{\mathrm{O}_{2} / \mathrm{H}_{2} \mathrm{O}}^{\circ}=+1.23 \mathrm{~V}$; $\mathrm{E}_{\mathrm{S}_{2} \mathrm{O}_{8}^{2-} / / \mathrm{SO}_{4}^{2-}}^{2-}=2.05 \mathrm{~V}$ $\mathrm{E}_{\mathrm{Br}_{2} / \mathrm{Br}}^{\circ}=+1.09 \mathrm{~V}$ $\mathrm{E}_{\mathrm{Au}^{3+} / \mathrm{Au}}^{\circ}=+1.4 \mathrm{~V}$ The strongest oxidising agent is :$\mathrm{Au}^{3+}$$\mathrm{O}_{2}$$\mathrm{S}_{2} \mathrm{O}_{8}^{2-}$$\mathrm{Br}_{2}$Correct Option: , 3 Solution: More...
Read More →The sum of two natural numbers is 15 and the sum of their reciprocals is
Question: The sum of two natural numbers is 15 and the sum of their reciprocals is $\frac{3}{10}$. Find the numbers. Solution: Let the required natural numbers bexand (15 x).According to the given condition, $\frac{1}{x}+\frac{1}{15-x}=\frac{3}{10}$ $\Rightarrow \frac{15-x+x}{x(15-x)}=\frac{3}{10}$ $\Rightarrow \frac{15}{15 x-x^{2}}=\frac{3}{10}$ $\Rightarrow 15 x-x^{2}=50$ $\Rightarrow x^{2}-15 x+50=0$ $\Rightarrow x^{2}-10 x-5 x+50=0$ $\Rightarrow x(x-10)-5(x-10)=0$ $\Rightarrow(x-5)(x-10)=0$ ...
Read More →Amongst the following, the form of water with the lowest ionic conductance at
Question: Amongst the following, the form of water with the lowest ionic conductance at $298 \mathrm{~K}$ is : distilled watersaline water used for intravenous injectionwater from a wellsea waterCorrect Option: 1 Solution: In distilled water, there are only neutral water molecules therefore, it does not conduct electricity....
Read More →Solve the following
Question: $108 \mathrm{~g}$ of silver (molar mass $108 \mathrm{~g} \mathrm{~mol}^{-1}$ ) is deposited at cathode from $\mathrm{AgNO}_{3}(\mathrm{aq})$ solution by a certain quantity of electricity. The volume (in L) of oxygen gas produced at $273 \mathrm{~K}$ and 1 bar pressure from water by the same quantity of electricity is _______________ . Solution: (5.68) No. of moles of silver deposited. $=\frac{108}{108}=1 \mathrm{~mol}$ $\mathrm{Ag}^{+}+e^{-} \rightarrow \mathrm{Ag}$ $1 \mathrm{~F}$ cha...
Read More →Prove the following
Question: Let $M$ be any $3 \times 3$ matrix with entries from the set $\{0,1,2\}$. The maximum number of such matrices, for which the sum of diagonal elements of $\mathrm{M}^{\top} \mathrm{M}$ is seven, is Solution: $\left[\begin{array}{lll}a b c \\ d e f \\ g h i\end{array}\right]\left[\begin{array}{lll}a d g \\ b e h \\ c f i\end{array}\right]$ $a^{2}+b^{2}+c^{2}+d^{2}+e^{2}+f^{2}+g^{2}+h^{2}+i^{2}=7$ Case I : Seven (l's) and two (O's) ${ }^{9} \mathrm{C}_{2}=36$ Case II : One (2) and three (...
Read More →For an electrochemical cell
Question: For an electrochemical cell$\mathrm{Sn}(\mathrm{s})\left|\mathrm{Sn}^{2+}(a q, 1 \mathrm{M}) \| \mathrm{Pb}^{2+}(a q, 1 \mathrm{M})\right| \mathrm{Pb}(\mathrm{s})$ the ratio $\frac{\left[\mathrm{Sn}^{2+}\right]}{\left[\mathrm{Pb}^{2+}\right]}$ when this cell attains equilibrium is ________. (Given: $\mathrm{E}_{\mathrm{Sn}^{2+} \mid \mathrm{Sn}}^{0}=-0.14 \mathrm{~V}$,$\left.\mathrm{E}_{\mathrm{Pb}} \quad \mid \mathrm{Pb}=-0.13 \mathrm{~V}, \frac{2.303 \mathrm{RT}}{=0.06}\right)$ Solut...
Read More →Solve the following
Question: Let $P=\left[\begin{array}{ccc}3 -1 -2 \\ 2 0 \alpha \\ 3 -5 0\end{array}\right]$, where $\alpha \in R .$ Suppose $Q=\left[q_{i j}\right]$ is a matrix satisfying $P Q=k I_{3}^{[}$for some non-zero $\mathrm{k} \in \mathrm{R}$. If $\mathrm{q}_{23}=-\frac{\mathrm{k}}{8}$ and $|\mathrm{Q}|=\frac{\mathrm{k}^{2}}{2}$, then $\alpha^{2}+\mathrm{k}^{2}$ is equal to Solution: As $\mathrm{PQ}=\mathrm{KI} \Rightarrow \mathrm{Q}=\mathrm{kP}^{-1} \mathrm{I}$ Now $\mathrm{Q}=\frac{k}{|P|}(\operatorna...
Read More →What would be the electrode potential for the given half cell reaction at pH =5?
Question: What would be the electrode potential for the given half cell reaction at $\mathrm{pH}=5$ ? ______________. $2 \mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{O}_{2}+4 \mathrm{H}^{\oplus}+4 \mathrm{e}^{-} ; E_{\mathrm{red}}^{0}=1.23 \mathrm{~V}$ $\left(\mathrm{R}=8.314 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1} ;\right.$ Temp $=298 \mathrm{~K} ;$ oxygen under std. atm. pressure of 1 bar) Solution: (1.52) $\mathrm{E}=1.23-\frac{0.0591}{4} \log \left[\mathrm{H}^{+}\right]^{4}$ $=1.23+...
Read More →A satellite is moving in a low nearly circular orbit around the earth.
Question: A satellite is moving in a low nearly circular orbit around the earth. Its radius is roughly equal to that of the earth's radius $R_{e}$. By firing rockets attached to it, its speed is instantaneously increased in the direction of its motion so that it become $\sqrt{\frac{3}{2}}$ times larger. Due to this the farthest distance from the centre of the earth that the satellite reaches is $R$. Value of $R$ is :(1) $4 R_{e}$(2) $2.5 R_{e}$(3) $3 R_{e}$(4) $2 R_{e}$Correct Option: , 2 Soluti...
Read More →The system of linear equations
Question: The system of linear equations $3 x-2 y-k z=10$ $2 x-4 y-2 z=6$ $x+2 y-z=5 m$ is inconsistent if: (1) $\mathrm{k}=3, \mathrm{~m}=\frac{4}{5}$(2) $k \neq 3, m \in R$(3) $\mathrm{k} \neq 3, \mathrm{~m} \neq \frac{4}{5}$(4) $\mathrm{k}=3, \mathrm{~m} \neq \frac{4}{5}$Correct Option: , 4 Solution: $\Delta=\left|\begin{array}{ccc}3 -2 -k \\ 1 -4 -2 \\ 1 2 -1\end{array}\right|=0$ $3(4+4)+2(-2+2)-\mathrm{k}(4+4)=0$ $\Rightarrow \mathrm{k}=3$ $\Delta_{x}=\left|\begin{array}{ccc}10 -2 -3 \\ 6 -...
Read More →The sum of two natural numbers is 9 and the sum of their reciprocals is
Question: The sum of two natural numbers is 9 and the sum of their reciprocals is $\frac{1}{2}$. Find the numbers. Solution: Let the required natural numbers bexand (9 x).According to the given condition, $\frac{1}{x}+\frac{1}{9-x}=\frac{1}{2}$ $\Rightarrow \frac{9-x+x}{x(9-x)}=\frac{1}{2}$ $\Rightarrow \frac{9}{9 x-x^{2}}=\frac{1}{2}$ $\Rightarrow 9 x-x^{2}=18$ $\Rightarrow x^{2}-9 x+18=0$ $\Rightarrow x^{2}-6 x-3 x+18=0$ $\Rightarrow x(x-6)-3(x-6)=0$ $\Rightarrow(x-3)(x-6)=0$ $\Rightarrow x-3=...
Read More →The equation that is incorrect is:
Question: The equation that is incorrect is:$\left(\Lambda_{\mathrm{m}}^{0}\right)_{\mathrm{NaBr}}-\left(\Lambda_{\mathrm{m}}^{0}\right)_{\mathrm{Na}^{2} \mathrm{Cl}}=\left(\Lambda_{\mathrm{m}}^{0}\right)_{\mathrm{KBr}}-\left(\Lambda_{\mathrm{m}}^{0}\right)_{\mathrm{KCl}}$$\left(\Lambda_{\mathrm{m}}^{0}\right)_{\mathrm{KCl}}-\left(\Lambda_{\mathrm{m}}^{0}\right)_{\mathrm{NaCl}}=\left(\Lambda_{\mathrm{m}}^{0}\right)_{\mathrm{KBr}}-\left(\Lambda_{\mathrm{m}}^{0}\right)_{\mathrm{NaBr}}$$\left(\Lamb...
Read More →The height ' h ' at which the weight of a body
Question: The height ' $h$ ' at which the weight of a body will be the same as that at the same depth ' $h$ ' from the surface of the earth is (Radius of the earth is $R$ and effect of the rotation of the earth is neglected):(1) $\frac{\sqrt{5}}{2} R-R$(2) $\frac{R}{2}$(3) $\frac{\sqrt{5} R-R}{2}$(4) $\frac{\sqrt{3} R-R}{2}$Correct Option: , 3 Solution: (3) The acceleration due to gravity at a height $h$ is given by $g=\frac{G M}{(R+h)^{2}}$ Here, $G=$ gravitation constant $M=$ mass of earth Giv...
Read More →Let I be an identity matrix of order
Question: Let $\mathrm{I}$ be an identity matrix of order $2 \times 2$ and $\mathrm{P}=\left[\begin{array}{cc}2 -1 \\ 5 -3\end{array}\right]$. Then the value of $\mathrm{n} \in \mathrm{N}$ for which $\mathrm{P}^{\mathrm{n}}=5 \mathrm{I}-8 \mathrm{P}$ is equal to___________. Solution: $P=\left[\begin{array}{ll}2 -1 \\ 5 -3\end{array}\right]$ $5 I-8 P=\left[\begin{array}{ll}5 0 \\ 0 5\end{array}\right]-\left[\begin{array}{cc}16 -8 \\ 40 -24\end{array}\right]=\left[\begin{array}{ll}-11 8 \\ -40 29\...
Read More →Find two consecutive positive even integers whose product is 288.
Question: Find two consecutive positive even integers whose product is 288. Solution: Let the two consecutive positive even integers bexand (x+ 2).According to the given condition, $x(x+2)=288$ $\Rightarrow x^{2}+2 x-288=0$ $\Rightarrow x^{2}+18 x-16 x-288=0$ $\Rightarrow x(x+18)-16(x+18)=0$ $\Rightarrow(x+18)(x-16)=0$ $\Rightarrow x+18=0$ or $x-16=0$ $\Rightarrow x=-18$ or $x=16$ x= 16 (xis a positive even integer)Whenx= 16,x+ 2 = 16 + 2 = 18Hence, the required integers are 16 and 18....
Read More →Given that the standard potentials
Question: Given that the standard potentials $\left(\mathrm{E}^{0}\right)$ of $\mathrm{Cu}^{2+} / \mathrm{Cu}$ and $\mathrm{Cu}^{+} /$ $\mathrm{Cu}$ are $0.34 \mathrm{~V}$ and $0.522 \mathrm{~V}$ respectively, the $\mathrm{E}^{0}$ of $\mathrm{Cu}^{2+} /$ $\mathrm{Cu}^{+}$is:$+0.182 \mathrm{~V}$$+0.158 \mathrm{~V}$$-0.182 \mathrm{~V}$$-0.158 \mathrm{~V}$Correct Option: , 2 Solution: $\mathrm{Cu}^{2+}+2 e^{-} \longrightarrow \mathrm{Cu}, \Delta \mathrm{G}_{1}^{0}=-2 \mathrm{~F}(0.34) \ldots$ (i) $...
Read More →Given that the standard potentials
Question: Given that the standard potentials $\left(\mathrm{E}^{0}\right)$ of $\mathrm{Cu}^{2+} / \mathrm{Cu}$ and $\mathrm{Cu}^{+} /$ $\mathrm{Cu}$ are $0.34 \mathrm{~V}$ and $0.522 \mathrm{~V}$ respectively, the $\mathrm{E}^{0}$ of $\mathrm{Cu}^{2+} /$ $\mathrm{Cu}^{+}$is:$+0.182 \mathrm{~V}$$+0.158 \mathrm{~V}$$-0.182 \mathrm{~V}$$-0.158 \mathrm{~V}$Correct Option: Solution: $\mathrm{Cu}^{2+}+2 e^{-} \longrightarrow \mathrm{Cu}, \Delta \mathrm{G}_{1}^{0}=-2 \mathrm{~F}(0.34) \ldots$ (i) $\mat...
Read More →Let the system of linear equations
Question: Let the system of linear equations $4 x+\lambda y+2 z=0$ $2 x-y+z=0$ $\mu \mathrm{x}+2 \mathrm{y}+3 \mathrm{z}=0, \lambda, \mu \in \mathrm{R}$ has a non-trivial solution. Then which of the following is true?(1) $\mu=6, \lambda \in \mathrm{R}$(2) $\lambda=2, \mu \in \mathrm{R}$(3) $\lambda=3, \mu \in \mathrm{R}$(4) $\mu=-6, \lambda \in \mathrm{R}$Correct Option: 1 Solution: For non-trivial solution $\left|\begin{array}{ccc}4 \lambda 2 \\ 2 -1 1 \\ \mu 2 3\end{array}\right|=0$ $\Rightarr...
Read More →Find two consecutive positive odd integers whose product is 483.
Question: Find two consecutive positive odd integers whose product is 483. Solution: Let the two consecutive positive odd integers bexand (x+ 2).According to the given condition, $x(x+2)=483$ $\Rightarrow x^{2}+2 x-483=0$ $\Rightarrow x^{2}+23 x-21 x-483=0$ $\Rightarrow x(x+23)-21(x+23)=0$ $\Rightarrow(x+23)(x-21)=0$ $\Rightarrow x+23=0$ or $x-21=0$ $\Rightarrow x=-23$ or $x=21$ x= 21 (xis a positive odd integer)Whenx= 21,x+ 2 = 21 + 2 = 23Hence, the required integers are 21 and 23....
Read More →Solve the following
Question: Let $A+2 B=\left[\begin{array}{ccc}1 2 0 \\ 6 -3 3 \\ -5 3 1\end{array}\right]$ and $2 A-B=\left[\begin{array}{ccc}2 -1 5 \\ 2 -1 6 \\ 0 1 2\end{array}\right]$. If $\operatorname{Tr}(\mathrm{A})$ denotes the sum of all diagonal elements of the matrix $\mathrm{A}$, then $\operatorname{Tr}(A)-\operatorname{Tr}(B)$ has value equal to(1) 1(2) 2(3) 0(4) 3Correct Option: , 2 Solution: $A+2 B=\left(\begin{array}{ccl}1 2 0 \\ 6 -3 3 \\ -5 3 1\end{array}\right) \ldots(1)$ $2 \mathrm{~A}-\mathrm...
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