Complete the following reactions:
Question: Complete the following reactions: Solution:...
Read More →A short bar magnet placed with its axis at 30º with a uniform external magnetic field of 0.25 T
Question: A short bar magnet placed with its axis at 30 with a uniform externalmagnetic field of 0.25 T experiences a torque of magnitude equal to4.5 102J. What is the magnitude of magnetic moment of the magnet? Solution: Magnetic field strength,B= 0.25 T Torque on the bar magnet,T= 4.5102J Angle between the bar magnet and the external magnetic field,= 30 Torque is related to magnetic moment (M) as: T=MBsin $\therefore M=\frac{T}{B \sin \theta}$ $=\frac{4.5 \times 10^{-2}}{0.25 \times \sin 30^{\...
Read More →Solve the inequality 6 ≤ –3(2x – 4) < 12
Question: Solve the inequality63(2x 4) 12 Solution: $6 \leq-3(2 x-4)12$ $\Rightarrow 2 \leq-(2 x-4)4$ $\Rightarrow-2 \geq 2 x-4-4$ $\Rightarrow 4-2 \geq 2 x4-4$ $\Rightarrow 2 \geq 2 x0$ $\Rightarrow 1 \geq x0$ Thus,the solution set for the given inequalityis (0, 1]....
Read More →Answer the following questions:
Question: Answer the following questions: (a)The earths magnetic field varies from point to point in space. Does it also change with time? If so, on what time scale does it change appreciably? (b)The earths core is known to contain iron. Yet geologists do not regard this as a source of the earths magnetism. Why? (c)The charged currents in the outer conducting regions of the earths core are thought to be responsible for earths magnetism. What might be the battery (i.e., the source of energy) to s...
Read More →Solve the inequality 2 ≤ 3x – 4 ≤ 5
Question: Solve the inequality 23x 45 Solution: 23x 45 ⇒2 + 43x 4 + 45 + 4 ⇒63x9 ⇒2x3 Thus, all the real numbers,x, which are greater than or equal to 2 but less than or equal to 3, are the solutions of the given inequality. The solution set for the given inequalityis [2, 3]....
Read More →Describe the bulk preparation of dihydrogen by electrolytic method
Question: Describe the bulk preparation of dihydrogen by electrolytic method. What is therole of an electrolyte in this process? Solution: Dihydrogen is prepared by the electrolysis of acidified or alkaline water using platinum electrodes. Generally, $15-20 \%$ of an acid $\left(\mathrm{H}_{2} \mathrm{SO}_{4}\right)$ or a base $(\mathrm{NaOH})$ is used. Reduction of water occurs at the cathode as: $2 \mathrm{H}_{2} \mathrm{O}+2 \mathrm{e}^{-} \longrightarrow 2 \mathrm{H}_{2}+2 \mathrm{OH}^{-}$ A...
Read More →Solve the following system of inequalities graphically: x + 2y ≤ 10, x + y ≥ 1, x – y ≤ 0, x ≥ 0, y ≥ 0
Question: Solve the following system of inequalities graphically:x+ 2y10,x+y1,xy0,x0, y0 Solution: $x+2 y \leq 10 \ldots$ (1) $x+y \geq 1 \ldots$ (2) $x-y \leq 0 \ldots$ (3) The graph of the lines,x+ 2y= 10,x+y= 1, andxy= 0, are drawn in the figure below. Inequality (1) represents the region below the line,x+ 2y= 10 (including the linex+ 2y= 10). Inequality (2) represents the region above the line,x+y= 1 (including the linex+y= 1). Inequality (3) represents the region above the line,xy= 0 (inclu...
Read More →Solve the following system of inequalities graphically: 3x + 2y ≤ 150, x + 4y ≤ 80,
Question: Solve the following system of inequalities graphically:3x+ 2y150,x+ 4y80,x15,y0,x0 Solution: $3 x+2 y \leq 150$ $x+4 y \leq 80 \ldots$ $x \leq 15 \ldots$ (3) The graph of the lines, 3x+ 2y= 150,x+ 4y= 80, andx= 15, are drawn in the figure below. Inequality (1) represents the region below the line, 3x+ 2y= 150 (including the line 3x+ 2y= 150). Inequality (2) represents the region below the line,x+ 4y= 80 (including the linex+ 4y= 80). Inequality (3) represents the region on the left han...
Read More →How can the production of dihydrogen, obtained from ‘coal gasification’, be increased?
Question: How can the production of dihydrogen, obtained from coal gasification, beincreased? Solution: Dihydrogenis produced by coal gasification method as: The yield of dihydrogen (obtained from coal gasification) can be increased by reacting carbon monoxide (formed during the reaction) with steam in the presence of iron chromate as a catalyst. This reaction is calledthe water-gas shift reaction. Carbon dioxide is removed by scrubbing it with a solution of sodium arsenite....
Read More →Answer the following questions regarding earth’s magnetism:
Question: Answer the following questions regarding earths magnetism: (a)A vector needs three quantities for its specification. Name the three independent quantities conventionally used to specify the earths magnetic field. (b)The angle of dip at a location in southern India is about 18. Would you expect a greater or smaller dip angle in Britain? (c)If you made a map of magnetic field lines at Melbourne in Australia, would the lines seem to go into the ground or come out of the ground? (d)In whic...
Read More →Solve the following system of inequalities graphically:
Question: Solve the following system of inequalities graphically: 4x+ 3y 60,y 2x,x 3,x,y 0 Solution: $4 x+3 y \leq 60 \ldots(1)$ $y \geq 2 x \ldots$ (2) $x \geq 3 \ldots$ (3) The graph of the lines, 4x+ 3y= 60,y= 2x, andx= 3, are drawn in the figure below. Inequality (1) represents the region below the line, 4x+ 3y= 60 (including the line 4x+ 3y= 60). Inequality (2) represents the region above the line,y= 2x(including the liney= 2x). Inequality (3) represents the region on the right hand side of...
Read More →Answer the following questions regarding earth’s magnetism:
Question: Answer the following questions regarding earths magnetism: (a)A vector needs three quantities for its specification. Name the three independent quantities conventionally used to specify the earths magnetic field. (b)The angle of dip at a location in southern India is about 18. Would you expect a greater or smaller dip angle in Britain? (c)If you made a map of magnetic field lines at Melbourne in Australia, would the lines seem to go into the ground or come out of the ground? (d)In whic...
Read More →Simplify
Question: Simplify $\cos \theta\left[\begin{array}{rr}\cos \theta \sin \theta \\ -\sin \theta \cos \theta\end{array}\right]+\sin \theta\left[\begin{array}{cc}\sin \theta -\cos \theta \\ \cos \theta \sin \theta\end{array}\right]$ Solution: $\cos \theta\left[\begin{array}{rr}\cos \theta \sin \theta \\ -\sin \theta \cos \theta\end{array}\right]+\sin \theta\left[\begin{array}{lr}\sin \theta -\cos \theta \\ \cos \theta \sin \theta\end{array}\right]$ $=\left[\begin{array}{lc}\cos ^{2} \theta \cos \the...
Read More →Why does hydrogen occur in a diatomic form rather than in a monoatomic form under normal conditions?
Question: Why does hydrogen occur in a diatomic form rather than in a monoatomic form under normal conditions? Solution: The ionization enthalpy of hydrogen atom is very high (1312 kJ mol1). Hence, it is very hard to remove its only electron. As a result, its tendency to exist in the monoatomic form is rather low. Instead, hydrogen forms a covalent bond with another hydrogen atom and exists as a diatomic (H2) molecule....
Read More →Solve the following system of inequalities graphically:
Question: Solve the following system of inequalities graphically: x 2y 3, 3x+ 4y 12,x 0,y 1 Solution: $x-2 y \leq 3 \ldots(1)$ $3 x+4 y \geq 12 \ldots(2)$ $y \geq 1 \ldots(3)$ The graph of the lines,x 2y= 3, 3x+ 4y= 12, andy= 1, are drawn in the figure below. Inequality (1) represents the region above the line,x 2y= 3 (including the linex 2y= 3). Inequality (2) represents the region above the line, 3x+ 4y= 12 (including the line 3x+ 4y= 12). Inequality (3) represents the region above the line,y=...
Read More →Write the names of isotopes of hydrogen.
Question: Write the names of isotopes of hydrogen. What is the mass ratio of these isotopes? Solution: Hydrogen has three isotopes. They are: 1. Protium, ${ }_{1}^{1} \mathrm{H}$, 2. Deuterium, ${ }_{1}^{2} \mathrm{H}$ or $\mathrm{D}$, and 3. Tritium, ${ }_{1}^{3} \mathrm{H}$ or $\mathrm{T}$ The mass ratio of protium, deuterium and tritium is $1: 2: 3$....
Read More →If andthen compute.
Question: If $A=\left[\begin{array}{ccc}\frac{2}{3} 1 \frac{5}{3} \\ \frac{1}{3} \frac{2}{3} \frac{4}{3} \\ \frac{7}{3} 2 \frac{2}{3}\end{array}\right]$ and $B=\left[\begin{array}{ccc}\frac{2}{5} \frac{3}{5} 1 \\ \frac{1}{5} \frac{2}{5} \frac{4}{5} \\ \frac{7}{5} \frac{6}{5} \frac{2}{5}\end{array}\right]$ then compute $3 A-5 B$ Solution: $3 A-5 B=3\left[\begin{array}{ccc}\frac{2}{3} 1 \frac{5}{3} \\ \frac{1}{3} \frac{2}{3} \frac{4}{3} \\ \frac{7}{3} 2 \frac{2}{3}\end{array}\right]-5\left[\begin{...
Read More →Solve the following system of inequalities graphically: 2x + y≥ 4, x + y ≤ 3, 2x – 3y ≤ 6
Question: Solve the following system of inequalities graphically:2x+y4,x+y3, 2x 3y6 Solution: $2 x+y \geq 4 \ldots(1)$ $x+y \leq 3 \ldots(2)$ $2 x-3 y \leq 6$$\ldots(3)$ The graph of the lines, 2x+y= 4,x+y= 3, and 2x 3y= 6, are drawn in the figure below. Inequality (1) represents the region above the line, 2x+y= 4 (including the line 2x+y= 4). Inequality (2) represents the region below the line, x+y= 3 (including the linex+y= 3). Inequality (3) represents the region above the line, 2x 3y= 6 (inc...
Read More →Solve the following system of inequalities graphically: 3x + 4y ≤ 60, x + 3y ≤ 30, x ≥ 0, y ≥ 0
Question: Solve the following system of inequalities graphically:3x+ 4y60,x+ 3y30,x0,y0 Solution: $3 x+4 y \leq 60 \ldots(1)$ $x+3 y \leq 30 \ldots(2)$ The graph of the lines, 3x+ 4y= 60 andx+ 3y= 30, are drawn in the figure below. Inequality (1) represents the region below the line, 3x+ 4y= 60 (including the line 3x+ 4y= 60), and inequality (2) represents the region below the line,x+ 3y= 30 (including the linex+ 3y= 30). Sincex0 andy0, every point in the common shaded region in the first quadra...
Read More →A galvanometer coil has a resistance of 15 Ω and the metre shows full scale deflection for a current of 4 mA.
Question: A galvanometer coil has a resistance of 15 Ω and the metre shows full scale deflection for a current of 4 mA. How will you convert the metre into an ammeter of range 0 to 6 A? Solution: Resistance of the galvanometer coil,G= 15 Ω Current for which the galvanometer shows full scale deflection, $I_{\mathrm{g}}=4 \mathrm{~mA}=4 \times 10^{-3} \mathrm{~A}$ Range of the ammeter is 0, which needs to be converted to 6 A. $\therefore$ Current, $I=6 \mathrm{~A}$ A shunt resistor of resistanceSi...
Read More →Justify the position of hydrogen in the periodic table on the basis of its electronic configuration.
Question: Justify the position of hydrogen in the periodic table on the basis of its electronicconfiguration. Solution: Hydrogen is the first element of the periodic table. Its electronic configuration is $\left[1 s^{1}\right]$. Due to the presence of only one electron in its $1 s$ shell, hydrogen exhibits a dual behaviour, i.e., it resembles both alkali metals and halogens. Resemblance with alkali metals: 1. Like alkali metals, hydrogen contains one valence electron in its valency shell. $\math...
Read More →then compute and. Also, verify that
Question: If $A=\left[\begin{array}{rrr}1 2 -3 \\ 5 0 2 \\ 1 -1 1\end{array}\right], B=\left[\begin{array}{rrr}3 -1 2 \\ 4 2 5 \\ 2 0 3\end{array}\right]$, and $C=\left[\begin{array}{rrr}4 1 2 \\ 0 3 2 \\ 1 -2 3\end{array}\right]$, then compute $(A+B)$ and $(B-C)$. Also, verify that $A+(B-C)=(A+B)-C$ Solution: $A+B=\left[\begin{array}{rrr}1 2 -3 \\ 5 0 2 \\ 1 -1 1\end{array}\right]+\left[\begin{array}{rrr}3 -1 2 \\ 4 2 5 \\ 2 0 3\end{array}\right]$ $=\left[\begin{array}{ccc}1+3 2-1 -3+2 \\ 5+4 0...
Read More →Solve the following system of inequalities graphically: 5x + 4y ≤ 20, x ≥ 1, y ≥ 2
Question: Solve the following system of inequalities graphically:5x+ 4y20,x1,y2 Solution: $5 x+4 y \leq 20$(1) $x \geq 1 \ldots(2)$ $y \geq 2 \ldots(3)$ The graph of the lines, 5x+ 4y= 20,x= 1, andy= 2, are drawn in the figure below. Inequality (1) represents the region below the line, 5x+ 4y= 20 (including the line 5x+ 4y= 20). Inequality (2) represents the region on the right hand side of the line,x= 1 (including the linex= 1). Inequality (3) represents the region above the line,y= 2 (includin...
Read More →A galvanometer coil has a resistance of 12 Ω and the metre shows full scale deflection for a current of 3 mA.
Question: A galvanometer coil has a resistance of 12 Ω and the metre shows full scale deflection for a current of 3 mA. How will you convert the metre into a voltmeter of range 0 to 18 V? Solution: Resistance of the galvanometer coil,G= 12 Ω Current for which there is full scale deflection, $I_{g}=3 \mathrm{~mA}=3 \times 10^{-3} \mathrm{~A}$ Range of the voltmeter is 0, which needs to be converted to 18 V. $\therefore V=18 \mathrm{~V}$ Let a resistor of resistanceRbe connected in series with the...
Read More →Solve the following system of inequalities graphically: x + y ≤ 9, y > x, x ≥ 0
Question: Solve the following system of inequalities graphically:x+y9,yx,x0 Solution: $x+y \leq 9 \quad \ldots(1)$ $yx \quad \ldots(2)$ $x \geq 0$ (3) The graph of the lines,x+y= 9 andy=x, are drawn in the figure below. Inequality (1) represents the region below the line,x+y= 9 (including the linex+y= 9). It is observed that (0, 1) satisfies the inequality,yx. [1 0] Therefore, inequality (2) represents the half plane corresponding to the line,y=x, containing the point (0, 1) [excluding the liney...
Read More →