Solve the following
Question: The volume, in $\mathrm{mL}$, of $0.02 \mathrm{M} \mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}$ solution required to react with $0.288 \mathrm{~g}$ of ferrous oxalate in acidic medium is ______________(Molar mass of $\mathrm{Fe}=56 \mathrm{~g} \mathrm{~mol}^{-1}$ ) Solution: (50) M. eq. of $\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}=\mathrm{M}$. eq. of $\mathrm{FeC}_{2} \mathrm{O}_{4}$ $\mathrm{FeC}_{2} \mathrm{O}_{4}+\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-} \longrightarrow \mathrm{Fe}^...
Read More →A cube of metal is subjected to a hydrostatic pressure of 4 GPa.
Question: A cube of metal is subjected to a hydrostatic pressure of $4 \mathrm{GPa}$. The percentage change in the length of the side of the cube is close to : (Given bulk modulus of metal, $B=8 \times 10^{10} \mathrm{~Pa}$ )5$0.6$20$1.67$Correct Option: , 4 Solution: (4) Bulk modulus, $B=\frac{P}{\frac{\Delta V}{V}}$ $\Rightarrow \frac{\Delta V}{V}=\frac{P}{B}$ ...(i) If the side of cube is $L$ then $V=L^{3}$ $\frac{\Delta V}{V}=\frac{3 \Delta L}{L}=\frac{P}{B}$ $\Rightarrow \frac{\Delta L}{L}=...
Read More →If the distance between the plane
Question: If the distance between the plane, $23 x-10 y-2 z+48=0$ and the plane containing the lines $\frac{x+1}{2}=\frac{y-3}{4}=\frac{z+1}{3}$ and $\frac{x+3}{2}=\frac{y+2}{6}=\frac{z-1}{\lambda}(\lambda \in \mathrm{R})$ is equal to $\frac{k}{\sqrt{633}}$, then $k$ is equal to________. Solution: Since, the line $\frac{x+1}{2}=\frac{y-3}{4}=\frac{z+1}{3}$ contains the point $(-1,3,-1)$ and line $\frac{x+3}{2}=\frac{y+2}{6}=\frac{z-1}{\lambda}$ contains the point $(-3,-2,1)$ Then, the distance b...
Read More →Consider the following equations :
Question: Consider the following equations : $2 \mathrm{Fe}^{2+}+\mathrm{H}_{2} \mathrm{O}_{2} \rightarrow x \mathrm{~A}+y \mathrm{~B}$ (in basic medium) $2 \mathrm{MnO}_{4}^{-}+6 \mathrm{H}^{+}+5 \mathrm{H}_{2} \mathrm{O}_{2} \rightarrow x^{\prime} \mathrm{C}+y^{\prime} \mathrm{D}+z^{\prime} \mathrm{E}$ (in acidic medium) The sum of the stoichiometric coefficients $x, y, x^{\prime}, y^{\prime}$ and $z^{\prime}$ for products A, B, C, D and E, respectively, is ___________. Solution: (11) $2 \math...
Read More →The projection of the line segment joining
Question: The projection of the line segment joining the points $(1,-1,3)$ and $(2,-4,11)$ on the line joining the points $(-1,2,3)$ and $(3,-2,10)$ is______. Solution: Let $P(1,-1,3), Q(2,-4,11), R(-1,2,3)$ and $S(3,-2,10)$ Then, $\overrightarrow{P Q}=\hat{i}-3 \hat{j}+8 \hat{k}$ $\overrightarrow{R S}=4 \hat{i}-4 \hat{j}+7 \hat{k}$ Projection of $\overrightarrow{P Q}$ on $\overrightarrow{R S}$ $=\frac{\overrightarrow{P Q} \cdot \overrightarrow{R S}}{|\overrightarrow{R S}|}=\frac{4+12+56}{\sqrt{...
Read More →The length of metallic wire
Question: The length of metallic wire is $l_{1}$ when tension in it is $T_{1}$. It is $l_{2}$ when the tension is $T_{2}$. The original length of the wire will be :$\frac{l_{1}+l_{2}}{2}$$\frac{\mathrm{T}_{1} l_{1}-\mathrm{T}_{2} l_{2}}{\mathrm{~T}_{2}-\mathrm{T}_{1}}$$\frac{\mathrm{T}_{2} l_{1}+\mathrm{T}_{1} l_{2}}{\mathrm{~T}_{1}+\mathrm{T}_{2}}$$\frac{T_{2} l_{1}-T_{1} l_{2}}{T_{2}-T_{1}}$Correct Option: , 4 Solution: (4) From young's modulus relation $\left(\mathrm{y}=\frac{\frac{\mathrm{F}...
Read More →In mildly alkaline medium, thiosulphate ion is oxidized by
Question: In mildly alkaline medium, thiosulphate ion is oxidized by $\mathrm{MnO}_{4}^{-}$to "A". The oxidation state of sulphur in "A" is Solution: (6) $\mathrm{S}_{2} \mathrm{O}_{3}^{2-}+\mathrm{MnO}_{4}^{-} \frac{\text { Alkaliue }}{\text { Melium }} \mathrm{A}$ $A \rightarrow S O_{4}^{-2}$ $\therefore$ Oxidation no. of 'S' $=+6$ Ans....
Read More →Prove the following
Question: If for some $\alpha$ and $\beta$ in $\mathbf{R}$, the intersection of the following three planes $x+4 y-2 z=1$ $x+7 y-5 z=\beta$ $x+5 y+\alpha z=5$ is a line in $R^{3}$, then $\alpha+\beta$ is equal to: 0102$-10$Correct Option: , 2 Solution: $\Delta=0 \Rightarrow\left|\begin{array}{ccc}1 4 -2 \\ 1 7 -5 \\ 1 5 \alpha\end{array}\right|=0$ $\Rightarrow(7 \alpha+25)-(4 \alpha+10)+(-20+14)=0$ $\Rightarrow 3 \alpha+9=0 \Rightarrow \alpha=-3$ Also, $D_{z}=0 \Rightarrow\left|\begin{array}{lll}...
Read More →Consider titration of NaOH solution versus 1.25M oxalic acid solution.
Question: Consider titration of $\mathrm{NaOH}$ solution versus $1.25 \mathrm{M}$ oxalic acid solution. At the end point following burette readings were obtained. (i) $4.5 \mathrm{ml}$. (ii) $4.5 \mathrm{ml}$. (iii) $4.4 \mathrm{ml}$ (iv) $4.4 \mathrm{ml}$ (v) $4.4 \mathrm{ml}$ If the volume of oxalic acid taken was $10.0 \mathrm{ml}$. then the molarity of the $\mathrm{NaOH}$ solution is __________ M. (Rounded-off to the nearest integer) Solution: (6) Eq. of $\mathrm{NaOH}=$ Eq. of oxalic acid $...
Read More →The normal density of a material is $ ho$ and its bulk modulus of elasticity is
Question: The normal density of a material is $\rho$ and its bulk modulus of elasticity is $\mathrm{K}$. The magnitude of increase in density of material, when a pressure $\mathrm{P}$ is applied uniformly on all sides, will be :$\frac{\rho K}{P}$$\frac{\mathrm{K}}{\rho \mathrm{P}}$$\frac{\mathrm{PK}}{\rho}$$\frac{\rho P}{K}$Correct Option: , 4 Solution: (4) Bulk modulus $\mathrm{K}=\frac{-\Delta \mathrm{P}}{\frac{\Delta \mathrm{V}}{\mathrm{V}}}=\frac{-\Delta \mathrm{pV}}{\Delta \mathrm{V}}$ We k...
Read More →The mirror image of the point (1,2,3) in a plane is
Question: The mirror image of the point $(1,2,3)$ in a plane is $\left(-\frac{7}{3},-\frac{4}{3},-\frac{1}{3}\right)$. Which of the following points lies on this plane?$(1,1,1)$$(1,-1,1)$$(-1,-1,1)$$(-1,-1,-1)$Correct Option: , 2 Solution: $\vec{n}=\frac{-7}{3}-1, \frac{-4}{3}-2, \frac{-1}{3}-3$ $\vec{n}=\frac{10}{3}, \frac{10}{3}, \frac{10}{3}$ $D . r$ of normal to the plane $(1,1,1)$ Midpoint of $P$ and $Q$ is $\left(\frac{-2}{3}, \frac{1}{3}, \frac{4}{3}\right)$ $\therefore \quad$ Equation of...
Read More →Solve the following
Question: $0.4 \mathrm{~g}$ mixture of $\mathrm{NaOH}, \mathrm{Na}_{2} \mathrm{CO}_{3}$ and some inert impurities was first titrated with $\frac{\mathrm{N}}{10} \mathrm{HCl}$ using phenolphthalein as an indicator, $17.5 \mathrm{~mL}$ of $\mathrm{HCl}$ was required at the end point. After this methyl orange was added and titrated. $1.5 \mathrm{~mL}$ of same $\mathrm{HCl}$ was required for the next end point. The weight percentage of $\mathrm{Na}_{2} \mathrm{CO}_{3}$ in the mixture is ____________...
Read More →A uniform metallic wire is elongated by 0.04 m
Question: A uniform metallic wire is elongated by $0.04 \mathrm{~m}$ when subjected to a linear force $\mathrm{F}$. The elongation, if its length and diameter is doubled andsubjected to the same force will be $\mathrm{cm}$. Solution: $\mathrm{y}=\frac{\mathrm{F} / \mathrm{A}}{\Delta \ell / \ell}$ $\Rightarrow \frac{F}{A}=y \frac{\Delta \ell}{\ell}$ $\Rightarrow \frac{F}{A}=y \times \frac{0.04}{\ell} \quad \ldots(1)$ When length $\backslash \$ diameter is doubled. $\Rightarrow \frac{F}{4 A}=y \ti...
Read More →The formula of a gaseous hydrocarbon which requires 6 times of its own volume of
Question: The formula of a gaseous hydrocarbon which requires 6 times of its own volume of $\mathrm{O}_{2}$ for complete oxidation and produces 4 times its own volume of $\mathrm{CO}_{2}$ is $\mathrm{C}_{\mathrm{x}} \mathrm{H}_{\mathrm{y}}$. The value of $\mathrm{y}$ is Solution: (8) $\mathrm{C}_{\mathrm{x}} \mathrm{H}_{\mathrm{y}}+6 \mathrm{O}_{2} \longrightarrow 4 \mathrm{CO}_{2}+\frac{\mathrm{y}}{2} \mathrm{H}_{2} \mathrm{O}$ Applying POAC on 'O' atoms $6 \times 2=4 \times 2+y / 2 \times 1$ $...
Read More →The shortest distance between the lines
Question: The shortest distance between the lines $\frac{x-3}{3}=\frac{y-8}{-1}=\frac{z-3}{1}$ and $\frac{x+3}{-3}=\frac{y+7}{2}=\frac{z-6}{4} \mathrm{is}:$$2 \sqrt{30}$$\frac{7}{2} \sqrt{30}$$3 \sqrt{30}$3Correct Option: , 3 Solution: $\overrightarrow{A B}=6 \hat{i}+15 \hat{j}+3 \hat{k}$ $\vec{p}=\hat{i}+4 \hat{j}+22 \hat{k}$ $\vec{q}=\hat{i}+\hat{j}+7 \hat{k}$ $\vec{p} \times \vec{q}=\left|\begin{array}{rrr}i j k \\ 1 4 22 \\ 1 1 7\end{array}\right|=6 \hat{i}+15 \hat{j}-3 \hat{k}$ Shortest dis...
Read More →The reaction of sulphur in alkaline medium is given below:
Question: The reaction of sulphur in alkaline medium is given below: $\mathrm{S}_{8(\mathrm{~s})}+\mathrm{aOH}_{(\mathrm{aq})}^{-} \longrightarrow \mathrm{bS}_{(\mathrm{aq})}^{2-}+\mathrm{CS}_{2} \mathrm{O}_{3}^{2-}(\mathrm{aq})+\mathrm{dH}_{2} \mathrm{O}_{(\ell)}$ The values of 'a' is Solution: (12) $\mathrm{S}_{8}+\mathrm{aOH}^{-} \longrightarrow \mathrm{bs}^{-2}+\mathrm{CdS}_{2} \mathrm{O}_{3}^{-2}+\mathrm{dH}_{2} \mathrm{O}$ $\mathrm{S}_{8}+\mathrm{bOH}^{-} \longrightarrow 4 \mathrm{~S}^{-2}...
Read More →Solve this
Question: If $Y, K$ and $\eta$ are the values of Young's modulus, bulk modulus and modulus of rigidity of any material respectively. Choose the correct relation for these parameters.$\mathrm{K}=\frac{\mathrm{Y} \eta}{9 \eta-3 \mathrm{Y}} \mathrm{N} / \mathrm{m}^{2}$$\eta=\frac{3 Y K}{9 K+Y} N / m^{2}$$\mathrm{Y}=\frac{9 \mathrm{~K} \eta}{3 \mathrm{~K}-\eta} \mathrm{N} / \mathrm{m}^{2}$$\mathrm{Y}=\frac{9 \mathrm{~K} \eta}{2 \eta+3 \mathrm{~K}} \mathrm{~N} / \mathrm{m}^{2}$Correct Option: 1 Solut...
Read More →Let P be a plane passing through the points
Question: Let $P$ be a plane passing through the points $(2,1,0)$, $(4,1,1)$ and $(5,0,1)$ and $R$ be any point $(2,1,6)$. Then the image of $R$ in the plane $P$ is:$(6,5,2)$$(6,5,-2)$$(4,3,2)$$(3,4,-2)$Correct Option: , 2 Solution: Equation of plane is $x+y-2 z=3$ $\Rightarrow \frac{x-2}{1}=\frac{y-1}{1}=\frac{z-6}{-2}=\frac{-2(2+1-12-3)}{6}$ $\Rightarrow \quad(x, y, z)=(6,5,-2)$...
Read More →Choose the correct option.
Question: (A) $\mathrm{HOCl}+\mathrm{H}_{2} \mathrm{O}_{2} \rightarrow \mathrm{H}_{3} \mathrm{O}^{+}+\mathrm{Cl}^{-}+\mathrm{O}_{2}$ (B) $\mathrm{I}_{2}+\mathrm{H}_{2} \mathrm{O}_{2}+2 \mathrm{OH}^{-} \rightarrow 2 \mathrm{I}^{-}+2 \mathrm{H}_{2} \mathrm{O}+\mathrm{O}_{2}$ Choose the correct option. $\mathrm{H}_{2} \mathrm{O}_{2}$ act as oxidizing and reducing agent respectively in equations (A) and (B).$\mathrm{H}_{2} \mathrm{O}_{2}$ acts as oxidizing agent in equations (A) and (B).$\mathrm{H}_...
Read More →Two separate wires A and B are stretched
Question: Two separate wires $\mathrm{A}$ and $\mathrm{B}$ are stretched by $2 \mathrm{~mm}$ and $4 \mathrm{~mm}$ respectively, when they are subjected to a force of $2 \mathrm{~N}$. Assume that both the wires are made up of same material and the radius of wire B is 4 times that of the radius of wire A. The length of the wires $A$ and $B$ are in the ratio of $a: b$. Then $a / b$ can be expressed as $1 / \mathrm{x}$ where $\mathrm{x}$ is Solution: $(32)$ For $\mathrm{A} \frac{\mathrm{E}}{\pi \mat...
Read More →A plane P meets the coordinate axes at
Question: A plane $P$ meets the coordinate axes at $A, B$ and $C$ respectively. The centroid of $\triangle \mathrm{ABC}$ is given to be $(1,1,2)$. Then the equation of the line through this centroid and perpendicular to the plane $P$ is:$\frac{x-1}{2}=\frac{y-1}{1}=\frac{z-2}{1}$$\frac{x-1}{1}=\frac{y-1}{1}=\frac{z-2}{2}$$\frac{x-1}{2}=\frac{y-1}{2}=\frac{z-2}{1}$$\frac{x-1}{1}=\frac{y-1}{2}=\frac{z-2}{2}$Correct Option: , 3 Solution: $\therefore \alpha=3, \beta=3$ and $\gamma=6$ as $\mathrm{G}$...
Read More →Let L denote the line in the
Question: Let L denote the line in the $x y$-plane with $x$ and $y$ intercepts as 3 and 1 respectively. Then the image of the point $(-1,-4)$ in this line is:$\left(\frac{11}{5}, \frac{28}{5}\right)$$\left(\frac{29}{5}, \frac{8}{5}\right)$$\left(\frac{8}{5}, \frac{29}{5}\right)$$\left(\frac{29}{5}, \frac{11}{5}\right)$Correct Option: 1 Solution: The line in $x y$-plane is, $\frac{x}{3}+y=1 \Rightarrow x+3 y-3=0$ Let image of the point $(-1,-4)$ be $(\alpha, \beta)$, then $\frac{\alpha+1}{1}=\fra...
Read More →15mL of aqueous solution of
Question: $15 \mathrm{~mL}$ of aqueous solution of $\mathrm{Fe}^{2+}$ in acidic medium completely reacted with $20 \mathrm{~mL}$ of $0.03 \mathrm{M}$ aqueous $\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}$. The molarity of the $\mathrm{Fe}^{2+}$ solution is ________________.$\times 10^{-2} \mathrm{M}$ (Round off to the Nearest Integer). Solution: (24) $\mathrm{n}_{\mathrm{eq}} \mathrm{Fe}^{2+}=\mathrm{n}_{\mathrm{eq}} \mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}$ or, $\left(\frac{15 \times \mathrm{M}_{\mathrm{Fe}^...
Read More →The shortest distance between the lines
Question: The shortest distance between the lines $\frac{x-1}{0}=\frac{y+1}{-1}=\frac{z}{1}$ and $x+y+z+1=0,2 x-y+z+3=0$ is : 1$\frac{1}{\sqrt{3}}$$\frac{1}{\sqrt{2}}$$\frac{1}{2}$Correct Option: , 2 Solution: For line of intersection of planes $x+y+z+1=0$ and $2 x-y+z+3=0$ $\vec{b}_{2}=\left|\begin{array}{ccc}\hat{i} \hat{j} \hat{k} \\ 1 1 1 \\ 2 -1 1\end{array}\right|=2 \hat{i}+\hat{j}-3 \hat{k}$ Put $y=0$, we get $x=-2$ and $z=1$ $L_{2}: \bar{r}=(-2 \hat{i}+\hat{k})+\lambda(2 \hat{i}+\hat{j}-...
Read More →In order to determine the Young's Modulus of a wire of radius
Question: In order to determine the Young's Modulus of a wire of radius $0.2 \mathrm{~cm}$ (measured using a scale of least count $=0.001 \mathrm{~cm}$ ) and length $1 \mathrm{~m}$ (measured using a scale of least count $=1 \mathrm{~g}$ ) was hanged to get the elongation of $0.5 \mathrm{~cm}$ (measured using a scale of least count $0.001 \mathrm{~cm}$ ). What will be the fractional error in the value of Young's Modulus determined by this experiment?$0.14 \%$$0.9 \%$$9 \%$$1.4 \%$Correct Option: ...
Read More →