A solution is to be kept between 68°F and 77°F.
Question: A solution is to be kept between 68F and 77F. What is the range in temperature in degree Celsius (C) if the Celsius/Fahrenheit (F) conversion formula is given by $\mathrm{F}=\frac{9}{8} \mathrm{C}+32 ?$ Solution: Since the solution is to be kept between $68^{\circ} \mathrm{F}$ and $77^{\circ} \mathrm{F}$, $68F77$ Putting $\mathrm{F}=\frac{9}{5} \mathrm{C}+32$, we obtain $68\frac{9}{5} \mathrm{C}+3277$ $\Rightarrow 68-32\frac{9}{5} \mathrm{C}77-32$ $\Rightarrow 36\frac{9}{5} \mathrm{C}4...
Read More →What do you understand by the term “non-stoichiometric hydrides”?
Question: What do you understand by the term non-stoichiometric hydrides? Do youexpect this type of the hydrides to be formed by alkali metals? Justify your answer. Solution: Non-Stoichiometric hydrides are hydrogen-deficient compounds formed by the reaction of dihydrogen with $d$-block and $f$-block elements. These hydrides do not follow the law of constant composition. For example: $\mathrm{LaH}_{2.87}, \mathrm{YbH}_{2.55}, \mathrm{TiH}_{1.5-1.8}$ etc. Alkali metals form stoichiometric hydride...
Read More →Solve the inequalities and represent the solution graphically on number line: 5(2x – 7) – 3(2x + 3) ≤ 0, 2x + 19 ≤ 6x + 47
Question: Solve the inequalities and represent the solution graphically on number line:5(2x 7) 3(2x+ 3)0, 2x+ 196x+ 47 Solution: $5(2 x-7)-3(2 x+3) \leq 0$ $\Rightarrow 10 x-35-6 x-9 \leq 0$ $\Rightarrow 4 x-44 \leq 0$ $\Rightarrow 4 x \leq 44$ $\Rightarrow x \leq 11 \ldots(1)$ $2 x+19 \leq 6 x+47$ $\Rightarrow 19-47 \leq 6 x-2 x$ $\Rightarrow-28 \leq 4 x$ $\Rightarrow-7 \leq x \ldots(2)$ From (1) and (2),it can be concluded that the solution set for the given system of inequalities is [7, 11]. ...
Read More →Find x and y, if
Question: Findxandy, if$2\left[\begin{array}{ll}1 3 \\ 0 x\end{array}\right]+\left[\begin{array}{ll}y 0 \\ 1 2\end{array}\right]$$=\left[\begin{array}{ll}5 6 \\ 1 8\end{array}\right]$ Solution: $2\left[\begin{array}{ll}1 3 \\ 0 x\end{array}\right]+\left[\begin{array}{ll}y 0 \\ 1 2\end{array}\right]=\left[\begin{array}{ll}5 6 \\ 1 8\end{array}\right]$ $\Rightarrow\left[\begin{array}{ll}2 6 \\ 0 2 x\end{array}\right]+\left[\begin{array}{ll}y 0 \\ 1 2\end{array}\right]=\left[\begin{array}{ll}5 6 \\...
Read More →Do you expect the carbon hydrides of the type
Question: Do you expect the carbon hydrides of the type $\left(\mathrm{C}_{n} \mathrm{H}_{2 n+2}\right)$ to act as 'Lewis' acid or base? Justify your answer. Solution: For carbon hydrides of type $\mathrm{C}_{n} \mathrm{H}_{2 n+2}$, the following hydrides are possible for $n=1 \Rightarrow \mathrm{CH}_{4}$ $n=2 \Rightarrow \mathrm{C}_{2} \mathrm{H}_{6}$ $n=3 \Rightarrow \mathrm{C}_{3} \mathrm{H}_{8}$ For a hydride to act as a Lewis acid i.e., electron accepting, it should be electron-deficient. A...
Read More →Solve the following inequalities and represent the solution graphically on number line:
Question: Solve the following inequalities and represent the solution graphically on number line: $3 x-72(x-6), 6-x11-2 x$ Solution: $3 x-72(x-6)$ $\Rightarrow 3 x-72 x-12$ $\Rightarrow 3 x-2 x-12+7$ $\Rightarrow x-5 \ldots(1)$ $6-x11-2 x$ $\Rightarrow-x+2 x11-6$ $\Rightarrow x5 \ldots(2)$ From (1) and (2), it can be concluded that the solution set for the given system of inequalities is. The solution of the given system of inequalities can be represented on number line as...
Read More →A closely wound solenoid of 2000 turns and area of cross-section
Question: A closely wound solenoid of 2000 turns and area of cross-section1.6104m2, carrying a current of 4.0 A, is suspended through its centre allowing it to turn in a horizontal plane. (a) What is the magnetic moment associated with the solenoid? (b) What is the force and torque on the solenoid if a uniform horizontal magnetic fieldof 7.5 102T is set up at an angle of 30 with the axis of the solenoid? Solution: Number of turns onthe solenoid,n= 2000 Area of cross-section of the solenoid,A= 1....
Read More →Find the largest number which divides 615 and 963 leaving remainder 6 in each case.
Question: Find the largest number which divides 615 and 963 leaving remainder 6 in each case. Solution: We need to find the largest number which divides 615 and 963 leaving remainder 6 in each case. The required number when divides 615 and 963 , leaves remainder 6 , this means $615-6=609$ and $963-6=957$ are completely divisible by the number. Therefore, The required number = H.C.F. of 609 and 957. By applying Euclids division lemma $957=609 \times 1+348$ $609=348 \times 1+261$ $348=216 \times 1...
Read More →Solve the inequalities and represent the solution graphically on number line: 2(x – 1) < x + 5, 3(x + 2) > 2 – x
Question: Solve the inequalities and represent the solution graphically on number line:2(x 1) x+ 5, 3(x+ 2) 2 x Solution: $2(x-1)x+5$ $\Rightarrow 2 x-2x+5$ $\Rightarrow 2 x-x5+2$ $\Rightarrow x7 \ldots(1)$ $3(x+2)2-x$ $\Rightarrow 3 x+62-x$ $\Rightarrow 3 x+x2-6$ $\Rightarrow 4 x-4$ $\Rightarrow x-1 \ldots(2)$ From (1) and (2),it can be concluded that the solution set for the given system of inequalities is (1, 7). The solution of the given system of inequalities can be represented on number li...
Read More →Find X, if
Question: Find $X$, if $Y$$Y=\left[\begin{array}{ll}3 2 \\ 1 4\end{array}\right]$ and $2 X+Y=\left[\begin{array}{rr}1 0 \\ -3 2\end{array}\right]$ Solution: $2 X+Y=\left[\begin{array}{rr}1 0 \\ -3 2\end{array}\right]$ $\Rightarrow 2 X+\left[\begin{array}{ll}3 2 \\ 1 4\end{array}\right]=\left[\begin{array}{rr}1 0 \\ -3 2\end{array}\right]$ $\Rightarrow 2 X=\left[\begin{array}{cc}1 0 \\ -3 2\end{array}\right]-\left[\begin{array}{ll}3 2 \\ 1 4\end{array}\right]=\left[\begin{array}{ll}1-3 0-2 \\ -3-...
Read More →A bar magnet of magnetic moment
Question: A bar magnet of magnetic moment 1.5 J T1lies aligned with the direction of a uniform magnetic field of 0.22 T. (a)What is the amount of work required by an external torque to turn the magnet so as to align its magnetic moment: (i) normal to the field direction, (ii) opposite to the field direction? (b)What is the torque on the magnet in cases (i) and (ii)? Solution: (a)Magnetic moment,M= 1.5 J T1 Magnetic fieldstrength,B= 0.22 T (i)Initial angle between the axis and the magnetic field,...
Read More →Solve the inequalities and represent the solution graphically on number line:
Question: Solve the inequalities and represent the solution graphically on number line:$5 x+1-24,5 x-124$ Solution: $5 x+1-24$ $\Rightarrow 5 x-25$ $\Rightarrow x-5 \ldots(1)$ $5 x-124$ $\Rightarrow 5 x25$ $\Rightarrow x5 \ldots(2)$ From (1) and (2),it can be concluded that the solution set for the given system of inequalities is (5, 5). The solution of the given system of inequalities can be represented on number line as...
Read More →A bar magnet of magnetic moment
Question: A bar magnet of magnetic moment 1.5 J T1lies aligned with the direction of a uniform magnetic field of 0.22 T. (a)What is the amount of work required by an external torque to turn the magnet so as to align its magnetic moment: (i) normal to the field direction, (ii) opposite to the field direction? (b)What is the torque on the magnet in cases (i) and (ii)? Solution: (a)Magnetic moment,M= 1.5 J T1 Magnetic fieldstrength,B= 0.22 T (i)Initial angle between the axis and the magnetic field,...
Read More →What characteristics do you expect from an electron-deficient hydride
Question: What characteristics do you expect from an electron-deficient hydride with respectto its structure and chemical reactions? Solution: An electron-deficient hydride does not have sufficient electrons to form a regular bond in which two electrons are shared by two atoms e.g., $\mathrm{B}_{2} \mathrm{H}_{6}, \mathrm{Al}_{2} \mathrm{H}_{6}$ etc. These hydrides cannot be represented by conventional Lewis structures. $\mathrm{B}_{2} \mathrm{H}_{6}$, for example, contains four regular bonds an...
Read More →Solve the inequality
Question: Solve the inequality$7 \leq \frac{(3 x+11)}{2} \leq 11$ Solution: $7 \leq \frac{(3 x+11)}{2} \leq 11$ $\Rightarrow 14 \leq 3 x+11 \leq 22$ $\Rightarrow 14-11 \leq 3 x \leq 22-11$ $\Rightarrow 3 \leq 3 x \leq 11$ $\Rightarrow 1 \leq x \leq \frac{11}{3}$ Thus, the solution set for the given inequalityis $\left[1, \frac{11}{3}\right]$....
Read More →Solve the inequality
Question: Solve the inequality$-124-\frac{3 x}{-5} \leq 2$ Solution: $-124-\frac{3 x}{-5} \leq 2$ $\Rightarrow-12-4\frac{-3 x}{-5} \leq 2-4$ $\Rightarrow-16\frac{3 x}{5} \leq-2$ $\Rightarrow-803 x \leq-10$ Thus, the solution set for the given inequalityis $\left(\frac{-80}{3}, \frac{-10}{3}\right]$. $\Rightarrow \frac{-80}{3}x \leq \frac{-10}{3}$...
Read More →Find the HCF of the following pairs of integers and express it as a linear combination of them.
Question: Find the HCF of the following pairs of integers and express it as a linear combination of them. (i) 963 and 657 (ii) 592 and 252 (iii) 506 and 1155 (iv) 1288 and 575 Solution: (i) We need to find the H.C.F. of 963 and 657 and express it as a linear combination of 963 and 657. By applying Euclid's division lemma $963=657 \times 1+306$. Since remainder $\neq 0$, apply division lemma on divisor 657 and remainder 306 $657=306 \times 2+45$ Since remainder $\neq 0$, apply division lemma on d...
Read More →What do you understand by
Question: What do you understand by (i) electron-deficient, (ii) electron-precise, and (iii)electron-rich compounds of hydrogen? Provide justification with suitable examples. Solution: Molecular hydrides are classified on the basis of the presence of the total number of electrons and bonds in their Lewis structures as: 1. Electron-deficient hydrides 2. Electron-precise hydrides 3. Electron-rich hydrides An electron-deficient hydride has very few electrons, less than that required for representin...
Read More →Find X, if
Question: Find $X$ and $Y$, if (i) $X+Y$$=\left[\begin{array}{ll}7 0 \\ 2 5\end{array}\right]$ and $X-Y=\left[\begin{array}{ll}3 0 \\ 0 3\end{array}\right]$ (ii) $2 X+3 Y$$=\left[\begin{array}{ll}2 3 \\ 4 0\end{array}\right]$ and $3 X+2 Y=\left[\begin{array}{rr}2 -2 \\ -1 5\end{array}\right]$ Solution: (i) $X+Y=\left[\begin{array}{ll}7 0 \\ 2 5\end{array}\right] \quad \ldots(1)$....(1) $X-Y=\left[\begin{array}{ll}3 0 \\ 0 3\end{array}\right]$....(2) Adding equations (1) and (2), we get: $2 X=\le...
Read More →If the solenoid in Exercise 5.5 is free to turn
Question: If the solenoid in Exercise 5.5 is free to turn about the vertical direction and a uniform horizontal magnetic field of 0.25 T is applied, what is the magnitude of torque on the solenoid when its axis makes an angle of 30 with the direction of applied field? Solution: Magnetic field strength,B= 0.25 T Magnetic moment,M= 0.6 T1 The angle, between the axis of the solenoid and the direction of the applied field is 30. Therefore, the torque acting on the solenoid is given as: $\tau=M B \si...
Read More →A closely wound solenoid of 800 turns and area of cross section
Question: A closely wound solenoid of 800 turns and area of cross section2.5 104m2carries a current of 3.0 A. Explain the sense in which the solenoid acts like a bar magnet. What is its associated magnetic moment? Solution: Number of turns in the solenoid,n= 800 Area of cross-section,A= 2.5104m2 Current in the solenoid,I= 3.0 A A current-carrying solenoid behaves as a bar magnet because a magnetic field develops along its axis, i.e., along its length. The magneticmoment associated with the given...
Read More →Solve the inequality
Question: Solve the inequality $-15\frac{3(x-2)}{5} \leq 0$ Solution: $-15\frac{3(x-2)}{5} \leq 0$ $\Rightarrow-753(x-2) \leq 0$ $\Rightarrow-25x-2 \leq 0$ $\Rightarrow-25+2x \leq 2$ $\Rightarrow-23x \leq 2$ Thus,the solution set for the given inequalityis (23, 2]....
Read More →A short bar magnet of magnetic moment m
Question: A short bar magnet of magnetic moment m = 0.32 JT1is placed in a uniform magnetic field of 0.15 T. If the bar is free to rotate in the plane of the field, which orientation would correspond to its (a) stable, and (b) unstable equilibrium? What is the potential energy of the magnet in each case? Solution: Moment of the bar magnet,M= 0.32J T1 External magnetic field,B= 0.15 T (a)The bar magnet is aligned along the magnetic field. This system is considered as being in stable equilibrium. ...
Read More →Discuss the consequences of high enthalpy of H–H bond in terms of chemical reactivity of dihydrogen.
Question: Discuss the consequences of high enthalpy of HH bond in terms of chemical reactivity of dihydrogen. Solution: The ionization enthalpy of $\mathrm{H}-\mathrm{H}$ bond is very high $\left(1312 \mathrm{~kJ} \mathrm{~mol}^{-1}\right)$. This indicates that hydrogen has a low tendency to form $\mathrm{H}^{+}$ions. Its ionization enthalpy value is comparable to that of halogens. Hence, it forms diatomic molecules $\left(\mathrm{H}_{2}\right)$, hydrides with elements, and a large number of cov...
Read More →Solve the inequality
Question: Solve the inequality$-3 \leq 4-\frac{7 x}{2} \leq 18$ Solution: $-3 \leq 4-\frac{7 x}{2} \leq 18$ $\Rightarrow-3-4 \leq-\frac{7 x}{2} \leq 18-4$ $\Rightarrow-7 \leq-\frac{7 x}{2} \leq 14$ $\Rightarrow 7 \geq \frac{7 x}{2} \geq-14$ $\Rightarrow 1 \geq \frac{x}{2} \geq-2$ $\Rightarrow 2 \geq x \geq-4$ Thus, the solution set for the given inequalityis $[-4,2]$....
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