Several sodium compounds find use in industries.
Question: Several sodium compounds find use in industries. Which of the following compounds are used for textile industry? (i) Na2CO3 (ii) NaHCO3 (iii) NaOH (iv) NaCl Solution: Option (i)Na2CO3 and (iii)NaOHare the answers....
Read More →Metallic elements are described by their standard
Question: Metallic elements are described by their standard electrode potential, fusion enthalpy, atomic size, etc. The alkali metals are characterised by which of the following properties? (i) High boiling point (ii) High negative standard electrode potential (iii) High density (iv) Large atomic size Solution: Option (ii)High negative standard electrode potential and (iv)Large atomic sizeare the answers....
Read More →If A ( - 1, 6), B( - 3, - 9) and C(5, - 8) are the vertices of a ΔABC
Question: If $A(-1,6), B(-3,-9)$ and $C(5,-8)$ are the vertices of a $\triangle A B C$, find the equations of its medians. Solution: Construction: - Draw median from vertices $A, B$ and $C$ on lines $B C, A C$ and AC respectively .Let the mid - points of lines BC,AC and AB be L,M and N respectively. Now find the coordinate of L, M and N using mid - point theorem $(\mathrm{x}, \mathrm{y})=\left(\frac{\mathrm{x}_{1}+\mathrm{x}_{2}}{2}, \frac{\mathrm{y}_{1}+\mathrm{y}_{2}}{2}\right)$ coordinates of...
Read More →Find the slope of the normal
Question: Find the slope of the normal at the point ' $t$ ' on the curve $x=\frac{1}{t}, y=t$. Solution: Given that the curve $x=\frac{1}{t}, y=t$ $\frac{\mathrm{dx}}{\mathrm{dt}}=\frac{-1}{\mathrm{t}^{2}}, \frac{\mathrm{dy}}{\mathrm{dt}}=1$ $\therefore \frac{d y}{d x}=\frac{\frac{d y}{d t}}{\frac{d x}{d t}}=\frac{1}{\frac{-1}{t^{2}}}=-t^{2}$ Now, Slope of tangent $=-t^{2}$ Slope of normal $=\frac{-1}{\text { Slope of tangent }}=\frac{1}{t^{2}}$...
Read More →If the tangent line at a point (x, y) on the curve
Question: If the tangent line at a point $(x, y)$ on the curve $y=f(x)$ is parallel to $y$-axis, find the value of $\frac{d x}{d y}$. Solution: Slope of the $y$-axis $=\infty$ $\therefore$ Slope of the tangent $\frac{\mathrm{dy}}{\mathrm{dx}}=\infty$ $\frac{\mathrm{dx}}{\mathrm{dy}}=\frac{1}{\infty}=0$...
Read More →If the tangent line at a point (x, y) on the curve
Question: If the tangent line at a point $(x, y)$ on the curve $y=f(x)$ is parallel to $y$-axis, find the value of $\frac{d x}{d y}$. Solution: Given that the tangent line at a point $(x, y)$ on the curve $y=f(x)$ is $\|$ to $y$-axis. Slope of the $y$-axis $=\infty$ $\therefore$ Slope of the tangent $\frac{d y}{d x}=\infty$ $\frac{\mathrm{dx}}{\mathrm{dy}}=\frac{1}{\infty}=0$...
Read More →Dehydration of hydrates of halides of calcium,
Question: Dehydration of hydrates of halides of calcium, barium and strontium i.e., CaCl26H2O, BaCl2.2H2O, SrCl2.2H2O, can be achieved by heating. These become wet on keeping in air. Which of the following statements is correct about these halides? (i) act as dehydrating agent (ii) can absorb moisture from the air (iii) The tendency to form hydrate decreases from calcium to barium (iv) All of the above Solution: Option (iv)All of the aboveis the answer....
Read More →If the tangent to a curve at a point
Question: If the tangent to a curve at a point $(x, y)$ is equally inclined to the coordinate axes, then write the value of $\frac{d y}{d x}$. Solution: Given that the tangent to a curve at a point $(x, y)$ is equally inclined to the coordinate axes. $\Rightarrow$ The angle made by the tangent with the axes can be $\pm 45^{\circ} .$ $\therefore$ Slope of the tangent $\frac{\mathrm{dy}}{\mathrm{dx}}=\tan \pm 45^{\circ}=\pm 1$...
Read More →A chemical A is used for the preparation
Question: A chemical A is used for the preparation of washing soda to recover ammonia. When CO2 is bubbled through an aqueous solution of A, the solution turns milky. It is used in whitewashing due to disinfectant nature. What is the the chemical formula of A? (i) Ca (HCO3)2 (ii) Cao (iii) Ca(OH)2 (iv) CaCO3 Solution: Option (iii)Ca(OH)2 is the answer....
Read More →If A(0, 0), b(2, 4) and C(6, 4) are the vertices of a ΔABC,
Question: If A(0, 0), b(2, 4) and C(6, 4) are the vertices of a ΔABC, find the equations of its sides. Solution: Using two point form equation of lines AB, BC and AC can be find. Now A is origin so the lines passing through A (origin) are simply y = mx so we have to find slope of AB and AC. For line AB, $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \Rightarrow \frac{4-0}{2-0}=\frac{4}{2}$ $m=2$ So, the equation of line $A B$ is $y=2 x$. For line $A C$, $\mathrm{m}=\frac{\mathrm{y}_{2}-\mathrm{y}_{1}}{\math...
Read More →Which of the following statements
Question: Which of the following statements is true about Ca(OH)2? (i) It is used in the preparation of bleaching powder (ii) It is a light blue solid (iii) It does not possess disinfectant property. (iv) It is used in the manufacture of cement. Solution: Option (i)It is used in the preparation of bleaching powder is the answer....
Read More →Write the value
Question: Write the value of $\frac{d y}{d x}$, if the normal to the curve $y=f(x)$ at $(x, y)$ is parallel to $y$-axis. Solution: Given that the normal to the curve $y=f(x)$ at $(x, y)$ is parallel to $y$-axis. We know that the slope of the $y$-axis is $\infty$. $\because$ Slope of the normal = Slope of the $y$-axis $=\infty$ $\therefore$ Slope of the tangent $\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{-1}{\text { Slope of the normal }}=\frac{1}{\infty}=0$...
Read More →A substance which gives brick
Question: A substance which gives brick red flame and breaks down on heating to give oxygen and a brown gas is (i) Magnesium nitrate (ii) Calcium nitrate (iii) Barium nitrate (iv) Strontium nitrate Solution: Option (ii)Calcium nitrate is the answer....
Read More →The formula of soda ash is
Question: The formula of soda ash is (i) Na2CO3.10H2O (ii) Na2CO3.2H2O (iii) Na2CO3.H2O (iv) Na2CO3 Solution: Option (iv) Na2CO3is the answer....
Read More →If the tangent line at a point
Question: If the tangent line at a point $(x, y)$ on the curve $y=f(x)$ is parallel to $x$-axis, then write the value of $\frac{d y}{d x}$. Solution: Given curve $y=f(x)$ has a point $(x, y)$ which is parallel to $x$-axis. We know that the slope of the $x$-axis is $0 .$ $\because$ the point lies on the given curve $\therefore$ Slope of the tangent $\frac{d y}{d x}=0$...
Read More →If the tangent line at a point
Question: If the tangent line at a point $(x, y)$ on the curve $y=f(x)$ is parallel to $x$-axis, then write the value of $\frac{d y}{d x}$. Solution: Given curve $y=f(x)$ has a point $(x, y)$ which is parallel to $x$-axis. We know that the slope of the $x$-axis is $0 .$ $\because$ the point lies on the given curve $\therefore$ Slope of the tangent $\frac{d y}{d x}=0$...
Read More →Prove that the points A
Question: Prove that the points A(1, 4), B(3, - 2) and C(4, - 5) are collinear. Also, find the equation of the line on which these points lie. Solution: If two lines having the same slope pass through a common point, then two lines will coincide. Hence, if A, B and C are three points in the XY - plane, then they will lie on a line, i.e., three points are collinear if and only if slope of AB = slope of BC. Slope of AB = slope of BC $\frac{-2-4}{3-1}=\frac{-5-(-2)}{4-3} \Rightarrow \frac{-6}{2}=\f...
Read More →Find the slope of the tangent to the curve
Question: Find the slope of the tangent to the curve $x=t^{2}+3 t-8, y=2 t^{2}-2 t-5$ at $t=2$. Solution: Given that $x=t^{2}+3 t-8, y=2 t^{2}-2 t-5$ $\Rightarrow \frac{\mathrm{dx}}{\mathrm{dt}}=2 \mathrm{t}+3, \frac{\mathrm{dy}}{\mathrm{dt}}=4 \mathrm{t}-2$ $\therefore \frac{d y}{d x}=\frac{4 t-2}{2 t+3}$ Now, Slope of the tangent $($ at $t=2)=\frac{8-2}{4+3}=\frac{6}{7}$...
Read More →Which of the following elements does
Question: Which of the following elements does not form hydride by direct heating with dihydrogen? (i) Be (ii) Mg (iii) Sr (iv) Ba Solution: Option (i)Beis the answer....
Read More →Suspension of slaked lime in water
Question: Suspension of slaked lime in water is known as (i) lime water (ii) quick lime (iii) milk of lime (iv) an aqueous solution of slaked lime Solution: Option (iii) milk of lime is the answer....
Read More →Find the angle which the line joining the points
Question: Find the angle which the line joining the points $(1, \sqrt{3})$ and $(\sqrt{2}, \sqrt{6})$ makes with the $x$-axis. Solution: To find angle, we will find slope using two points $\mathrm{m}=\frac{\mathrm{y}_{2}-\mathrm{y}_{1}}{\mathrm{x}_{2}-\mathrm{x}_{1}} \Rightarrow \frac{(\sqrt{6})-(\sqrt{3})}{(\sqrt{2})-1}=\frac{(\sqrt{3})((\sqrt{2})-1)}{((\sqrt{2})-1)}$ $\mathrm{m}=\sqrt{3}$ Now as we have m = tan $\tan \theta=(\sqrt{3}) \Rightarrow \theta=60^{\circ}$ So, angle line makes with th...
Read More →Dead burnt plaster is
Question: Dead burnt plaster is (i) CaSO4 (ii) CaSO4.1/2 H2O (iii) CaSO4.H2O (iv) CaSO4.2H2O Solution: Option (i)CaSO4is the answer....
Read More →Find the point on the curve
Question: Find the point on the curve $y=x^{2}-2 x+3$, where the tangent is parallel to $x$-axis. Solution: Given curve $y=x^{2}-2 x+3$ We know that the slope of the $x$-axis is 0 . Let the required point be $(a, b)$. $\because$ the point lies on the given curve $\therefore b=a^{2}-2 a+3$ .....(1) Now, $y=x^{2}-2 x+3$ $\frac{\mathrm{dy}}{\mathrm{dx}}=2 \mathrm{x}-2$ Slope of the tangent at $(a, b)=2 a-2$ According to the question, $2 a-2=0$ $\Rightarrow a=1$ Putting this in (1), $b=1-2+3$ $\Righ...
Read More →By adding gypsum to cement
Question: By adding gypsum to cement (i) setting time of cement becomes less. (ii) setting time of cement increases. (iii) colour of cement becomes light. (iv) the shining surface is obtained. Solution: Option (ii)setting time of cement increasesis the answer....
Read More →Find the slope and the equation of the line passing through the points:
Question: Find the slope and the equation of the line passing through the points: $(a, b)$ and $(-a, b)$ Solution: The slope of the equation can be calculated using $\mathrm{m}=\frac{\mathrm{y}_{2}-\mathrm{y}_{1}}{\mathrm{x}_{2}-\mathrm{x}_{1}} \Rightarrow \frac{\mathrm{b}-\mathrm{b}}{-\mathrm{a}-\mathrm{a}}=0$ m = 0 (Horizontal line) Now using two point form of the equation of a line $\mathrm{y}-\mathrm{y}_{1}=\frac{\mathrm{y}_{2}-\mathrm{y}_{1}}{\mathrm{x}_{2}-\mathrm{x}_{1}}\left(\mathrm{x}-\...
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