What will happen during the electrolysis
Question: What will happen during the electrolysis of an aqueous solution of CuSO4 by using platinum electrodes? (i) Copper will deposit at the cathode. (ii) Copper will deposit at the anode. (iii) Oxygen will be released at anode. (iv) Copper will dissolve at the anode. Solution: Option (i)Copper will deposit at the cathode and (iii)Oxygen will be released at anode are the answers....
Read More →Find the value
Question: Let $A=(1,2,3,4)$ and $R=\{(1,1),(2,2),(3,3),(4,4),(1,2),(1,3),(3,2)\} .$ Show that $R$ is reflexive and transitive but not symmetric. Solution: Given that, $A=\{1,2,3\}$ and $R=\{1,1),(2,2),(3,3),(4,4),(1,2),(1,3),(3,2)\}$ Now, $\mathrm{R}$ is reflexive $\because(1,1),(2,2),(3,3),(4,4) \in \mathrm{R}$ $\mathrm{R}$ is not symmetric $\because(1,2),(1,3),(3,2) \in \mathrm{R}$ but $(2,1),(3,1),(2,3) \notin \mathrm{R}$ $\mathrm{R}$ is transitive $\because(1,3) \in \mathrm{R}$ and $(3,2) \i...
Read More →Find the value
Question: Let $A=\{1,2,3\}$ and $R=\{(1,1),(2,2),(3,3),(1,2),(2,3)\}$ Show that $R$ is reflexive but neither symmetric nor transitive. Solution: Given that, $A=\{1,2,3\}$ and $R=\{1,1),(2,2),(3,3),(1,2),(2,3)\}$ Now, $\mathrm{R}$ is reflexive $\because(1,1),(2,2),(3,3) \in \mathrm{R}$ $\mathrm{R}$ is not symmetric $\because(1,2),(2,3) \in \mathrm{R}$ but $(2,1),(3,2) \notin \mathrm{R}$ $\mathrm{R}$ is not transitive $\because(1,2) \in \mathrm{R}$ and $(2,3) \in \mathrm{R} \Rightarrow(1,3) \notin...
Read More →˄0m(H2O) is equal to ______________.
Question: ˄0m(H2O)is equal to ______________. (i) ˄0m(HCl)+ ˄0m(NaOHl) ˄0m(NaCl) (ii) ˄0m(HNO3)+ ˄0m(NaNO3) ˄0m(NaOH) (iii) ˄0m(HNO3)+ ˄0m(NaOH) ˄0m(NaNO3) (iv) ˄0m(NH4OH)+ ˄0m(HCl) ˄0m(NH4Cl) Solution: Option (i)˄0m(HCl)+ ˄0m(NaOHl) ˄0m(NaCl) and (iii)˄0m(HNO3)+ ˄0m(NaOH) ˄0m(NaNO3) are the answer...
Read More →Show that the relation
Question: Show that the relation $R=\{(a, b): ab\}$ on $N$ is transitive but neither reflexive nor symmetric. Solution: We have, $R=\{(a, b): ab\}$ relation defined on $N$. Now, We observe that, any element a $\in N$ cannot be greater than itself. $\Rightarrow(a, a) \notin R \forall a \in N$ $\Rightarrow R$ is not reflexive. Let $(a, b) \in R \forall a, b \in N$ $\Rightarrow \mathrm{a}$ is greater than $\mathrm{b}$ But $b$ cannot be greater than $a$ if $a$ is greater than $b$. $\Rightarrow(b, a)...
Read More →Conductivity of an electrolytic solution depends
Question: Conductivity of an electrolytic solution depends on ____________. (i) nature of electrolyte. (ii) the concentration of electrolyte. (iii) power of AC source. (iv) distance between the electrodes. Solution: Option (i) and (ii) are the answers....
Read More →E°Cell = 1.1V for Daniel cell.
Question: ECell = 1.1V for Daniel cell. Which of the following expressions are correct description of state of equilibrium in ths cell? (i) 1.1 = Kc (ii) 2.303RT/2F logKc = 1.1 (iii) log Kc = 2.2/0.059 (iv) log Kc = 1.1 Solution: Option (ii) and (iii) are the answers....
Read More →E°Cell for some half cell reactions
Question: ECell for some half cell reactions are given below. Based on these mark the correct answer. (a) H+(aq) + e 1/2H2(g) ; Ecell = 0.00V (b) 2H2O (l) O2 (g) + 4H+(aq) + 4e: Ecell = 1.23V (c) 2SO42 (aq) S2O82 (aq) + 2e ; Ecell = 1.96V (i) In dilute sulphuric acid solution, hydrogen will be reduced at the cathode. (ii) In concentrated sulphuric acid solution, water will be oxidised at the anode. (iii) In dilute sulphuric acid solution, water will be oxidised at the anode. (iv) In dilute sulph...
Read More →Evaluate the integral
Question: Evaluate the integral $\int \frac{1}{3+4 \cot x} d x$ Solution: Ideas required to solve the problems: * Integration by substitution: A change in the variable of integration often reduces an integral to one of the fundamental integration. If derivative of a function is present in an integration or if chances of its presence after few modification is possible then we apply integration by substitution method. * Knowledge of integration of fundamental functions like sin, cos, polynomial, l...
Read More →The positive value of the standard electrode potential
Question: The positive value of the standard electrode potential of Cu2+/Cu indicates that ____________. (i) this redox couple is a stronger reducing agent than the H+/H2 couple. (ii) this redox couple is a stronger oxidising agent than H+/H2. (iii) Cu can displace H2 from acid. (iv) Cu cannot displace H2 from acid. Solution: Option (ii) and (iv) are the answers....
Read More →Solve this
Question: Let $R=\left\{(a, b): a=b^{2}\right\}$ for $a l l a, b \in N$. Show that R satisfies none of reflexivity, symmetry and transitivity. Solution: We have, $R=\left\{(a, b): a=b^{2}\right\}$ relation defined on $N$. Now, We observe that, any element a $\in \mathrm{N}$ cannot be equal to its square except 1 . $\Rightarrow(a, a) \notin R \forall a \in N$ For e.g. $(2,2) \notin R \because 2 \neq 2^{2}$ $\Rightarrow \mathrm{R}$ is not reflexive. Let $(a, b) \in R \forall a, b \in N$ $\Rightarr...
Read More →In the electrolysis of aqueous sodium chloride
Question: In the electrolysis of aqueous sodium chloride solution which of the half cell reaction will occur at anode? (i) Na+(aq) + e Na (s); ECell = 2.71V (ii) 2H2O (l) O2(g) + 4H+(aq) + 4e : ECell = 1.23V (iii) H+(aq) + e1/2H2 (g); ECell = 0.00V (iv) Cl(aq) 1/2Cl2(g) + e ; ECell = 1.36V Solution: Option (iv)Cl(aq) 1/2Cl2(g) + e ; ECell = 1.36V is the answer....
Read More →˄0m(NH4OH) is equal to ______________.
Question: ˄0m(NH4OH)is equal to ______________. (i) ˄0m(NH4OH)+ ˄0m(NH4Cl) ˄0(HCl) (ii) ˄0m(NH4Cl)+ ˄0m(NaOH) ˄0(NaCl) (iii) ˄0m(NH4Cl)+ ˄0m(NaCl) ˄0(NaOH) (iv) ˄0m(NaOH)+ ˄0m(NaCl) ˄0(NH4Cl) Solution: Option (ii)˄0m(NH4Cl)+ ˄0m(NaOH) ˄0(NaCl) is the answer....
Read More →While charging the lead storage battery
Question: While charging the lead storage battery ______________. (i) PbSO4 anode is reduced to Pb. (ii) PbSO4 cathode is reduced to Pb. (iii) PbSO4 cathode is oxidised to Pb. (iv) PbSO4 anode is oxidised to PbO2 Solution: Option (i)PbSO4 anode is reduced to Pbis the answer....
Read More →The cell constant of a conductivity cell _____________.
Question: The cell constant of a conductivity cell _____________. (i) changes with the change of electrolyte. (ii) changes with the change of concentration of electrolyte. (iii) changes with the temperature of the electrolyte. (iv) remains constant for a cell. Solution: Option (iv)remains constant for a cell is the answer....
Read More →The quantity of charge required to obtain
Question: The quantity of charge required to obtain one mole of aluminium from Al2O3 is ___________. (i) 1F (ii) 6F (iii) 3F (iv) 2F Solution: Option (iii)3F is the answer....
Read More →find out the most stable oxidised species.
Question: find out the most stable oxidised species. EᶱCr2O72-/Cr3+= 1.33V EᶱMnO4/Mn2+= 1.51V EᶱCl2/Cl= 1.36V EᶱCr3+/Cr = -0.74V (i) Cr3+ (ii) MnO4 (iii) Cr2O72 (iv) Mn2+ Solution: Option (i) is the answer....
Read More →Let S be the set of all real numbers. Show that the relation
Question: Let $\mathrm{S}$ be the set of all real numbers. Show that the relation $\mathrm{R}=\left\{(\mathrm{a}, \mathrm{b}): \mathrm{a}^{2}+\mathrm{b}^{2}=1\right\}$ is symmetric but neither reflexive nor transitive. Solution: Given that, $\forall a, b \in S, R=\left\{(a, b): a^{2}+b^{2}=1\right\}$ Now, $\underline{R}$ is Reflexive if $(a, a) \in \underline{R} \underline{\forall} \underline{a} \in \underline{S}$ For any $a \in S$, we have $a^{2}+a^{2}=2 a^{2} \neq 1$ $\Rightarrow(a, a) \notin ...
Read More →find out the most stable ion in its reduced form.
Question: find out the most stable ion in its reduced form. EᶱCr2O72-/Cr3+= 1.33V EᶱMnO4/Mn2+= 1.51V EᶱCl2/Cl= 1.36V EᶱCr3+/Cr = -0.74V (i) Cl (ii) Cr3+ (iii) Cr (iv) Mn2+ Solution: Option (iv) is the answer....
Read More →Let S be the set of all points in a plane and let R be a relation in S defined by R
Question: Let $S$ be the set of all points in a plane and let $R$ be a relation in $S$ defined by $R=\{(A, B): d(A, B)2$ units $\}$, where $d(A, B)$ is the distance between the points $A$ and $B$. Show that $\mathrm{R}$ is reflexive and symmetric but not transitive. Solution: Given that, $\forall A, B \in S, R=\{(A, B): d(A, B)2$ units $\} .$ Now, $\underline{R}$ is Reflexive if $(A, A) \in \underline{R} \forall \underline{A} \in \underline{S}$ For any $A \in S$, we have $\mathrm{d}(\mathrm{A}, ...
Read More →Let S be the set of all real numbers and let
Question: Let $\mathrm{S}$ be the set of all real numbers and let $\mathrm{R}=\{(\mathrm{a}, \mathrm{b}): \mathrm{a}, \mathrm{b} \in \mathrm{S}$ and $\mathrm{a}=\pm \mathrm{b}\}$ Show that $R$ is an equivalence relation on $S$. Solution: In order to show $R$ is an equivalence relation we need to show $R$ is Reflexive, Symmetric and Transitive. Given that, $\forall a, b \in S, R=\{(a, b): a=\pm b\}$ Now, $\underline{R}$ is Reflexive if $(a, a) \in \underline{R} \underline{\forall} \underline{a} \...
Read More →Evaluate the integral
Question: Evaluate the integral $\int \frac{2 \sin x+3 \cos x}{3 \sin x+4 \cos x} d x$ Solution: Ideas required to solve the problems: * Integration by substitution: A change in the variable of integration often reduces an integral to one of the fundamental integration. If derivative of a function is present in an integration or if chances of its presence after few modification is possible then we apply integration by substitution method. * Knowledge of integration of fundamental functions like ...
Read More →Show that the relation
Question: Show that the relation $\mathrm{R}$ on $\mathrm{N} \times \mathrm{N}$, defined by $(a, b) R(c, d) \Leftrightarrow a+d=b+c$ is an equivalent relation. Solution: In order to show $R$ is an equivalence relation we need to show $R$ is Reflexive, Symmetric and Transitive. Given that, $R$ be the relation in $N \times N$ defined by $(a, b) R(c, d)$ if $a+d=b+c$ for $(a, b),(c, d)$ in $N \times N$. $\underline{R}$ is Reflexive if $(a, b) R(a, b)$ for $(a, b)$ in $N \times N$ Let $(a, b) R(a, b...
Read More →which option the order of reducing
Question: which option the order of reducing power is correct. EᶱCr2O72-/Cr3+= 1.33V EᶱMnO4/Mn2+= 1.51V EᶱCl2/Cl= 1.36V EᶱCr3+/Cr = -0.74V (i) Cr3+ Cl Mn2+ Cr (ii) Mn2+ Cl Cr3+ Cr (iii) Cr3+ Cl Cr2O72 MnO4\ (iv) Mn2+ Cr3+ Cl Cr Solution: Option (ii) is the answer....
Read More →Use the data given in Q.8 and find out
Question: Use the data given in Q.8 and find out which of the following is the strongest oxidising agent. (i) Cl (ii) Mn2+ (iii) MnO4 (iv) Cr3+ Solution: Option (iii)MnO4 is the answer....
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