Beryllium and magnesium do not give colour to flame whereas other alkaline earth metals do so.
Question: Beryllium and magnesium do not give colour to flame whereas other alkalineearth metals do so. Why? Solution: When an alkaline earth metal is heated, the valence electrons get excited to a higher energy level. When this excited electron comes back to its lower energy level, it radiates energy, which belongs to the visible region. Hence, the colour is observed. In Be and Mg, the electrons are strongly bound. The energy required to excite these electrons is very high. Therefore, when the ...
Read More →Expand the expression
Question: Expand the expression $\left(\frac{2}{x}-\frac{x}{2}\right)^{5}$ Solution: By using Binomial Theorem, the expression $\left(\frac{2}{x}-\frac{x}{2}\right)^{5}$ can be expanded as $\left(\frac{2}{x}-\frac{x}{2}\right)^{5}={ }^{5} C_{0}\left(\frac{2}{x}\right)^{5}-{ }^{5} C_{1}\left(\frac{2}{x}\right)^{4}\left(\frac{x}{2}\right)+{ }^{5} C_{2}\left(\frac{2}{x}\right)^{3}\left(\frac{x}{2}\right)^{2}$ $-{ }^{5} C_{3}\left(\frac{2}{x}\right)^{2}\left(\frac{x}{2}\right)^{3}+{ }^{5} C_{4}\left...
Read More →Find the inverse of each of the matrices, if it exists.
Question: Find the inverse of each of the matrices, if it exists. $\left[\begin{array}{ll}3 1 \\ 5 2\end{array}\right]$ Solution: Let $A=\left[\begin{array}{ll}3 1 \\ 5 2\end{array}\right]$ We know thatA=AI $\therefore\left[\begin{array}{ll}3 1 \\ 5 2\end{array}\right]=A\left[\begin{array}{ll}1 0 \\ 0 1\end{array}\right]$ $\Rightarrow\left[\begin{array}{ll}1 1 \\ 1 2\end{array}\right]=A\left[\begin{array}{ll}1 0 \\ -2 1\end{array}\right] \quad\left(\mathrm{C}_{1} \rightarrow \mathrm{C}_{1}-2 \ma...
Read More →When an alkali metal dissolves in liquid ammonia the solution can acquire different colours.
Question: When an alkali metal dissolves in liquid ammonia the solution can acquire different colours. Explain the reasons for this type of colour change. Solution: When an alkali metal is dissolved in liquid ammonia, it results in the formation of a deep blue coloured solution. $\mathrm{M}+(x+y) \mathrm{NH}_{3} \longrightarrow \mathrm{M}^{+}\left(\mathrm{NH}_{3}\right)_{x}+\mathrm{e}^{-1}\left(\mathrm{NH}_{3}\right)_{y}$ The ammoniated electrons absorb energy corresponding to red region of visi...
Read More →Obtain the answers (a) to (b) in Exercise 7.13 if the circuit is connected to a high frequency supply
Question: Obtain the answers (a) to (b) in Exercise 7.13 if the circuit is connected to a high frequency supply (240 V, 10 kHz). Hence, explain the statement that at very high frequency, an inductor in a circuit nearly amounts to an open circuit. How does an inductor behave in a dc circuit after the steady state? Solution: Inductance of the inductor,L= 0.5 Hz Resistance of the resistor,R= 100 Ω Potential of the supply voltages,V= 240 V Frequency of the supply,=10 kHz = 104Hz Angular frequency,= ...
Read More →Obtain the answers (a) to (b) in Exercise 7.13 if the circuit is connected to a high frequency supply
Question: Obtain the answers (a) to (b) in Exercise 7.13 if the circuit is connected to a high frequency supply (240 V, 10 kHz). Hence, explain the statement that at very high frequency, an inductor in a circuit nearly amounts to an open circuit. How does an inductor behave in a dc circuit after the steady state? Solution: Inductance of the inductor,L= 0.5 Hz Resistance of the resistor,R= 100 Ω Potential of the supply voltages,V= 240 V Frequency of the supply,=10 kHz = 104Hz Angular frequency,= ...
Read More →Why are potassium and cesium, rather than lithium used in photoelectric cells?
Question: Why are potassium and cesium, rather than lithium used in photoelectric cells? Solution: All the three, lithium,potassium, and cesium, are alkali metals. Still, K and Cs are used in the photoelectric cell and not Li. This is because as compared to Cs and K, Li is smaller in size and therefore, requires high energy to lose an electron. While on the other hand, K and Cs have low ionization energy. Hence, they can easily lose electrons. This property of K and Cs is utilized in photoelectr...
Read More →Expand the expression (1– 2x)5
Question: Expand the expression $(1-2 x)^{5}$ Solution: By using Binomial Theorem, the expression $(1-2 x)^{5}$ can be expanded as $(1-2 x)^{5}$ $={ }^{5} C_{0}(1)^{5}-{ }^{5} C_{1}(1)^{4}(2 x)+{ }^{3} C_{2}(1)^{3}(2 x)^{2}-{ }^{5} C_{3}(1)^{2}(2 x)^{3}+{ }^{5} C_{4}(1)^{1}(2 x)^{4}-{ }^{5} C_{5}(2 x)^{5}$ $=1-5(2 x)+10\left(4 x^{2}\right)-10\left(8 x^{3}\right)+5\left(16 x^{4}\right)-\left(32 x^{5}\right)$ $=1-10 x+40 x^{2}-80 x^{3}+80 x^{4}-32 x^{5}$...
Read More →Explain why alkali and alkaline earth metals cannot be obtained by chemical reduction methods?
Question: Explain why alkali and alkaline earth metals cannot be obtained by chemical reduction methods? Solution: In the process of chemical reduction, oxides of metals are reduced using a stronger reducing agent. Alkali metals and alkaline earth metals are among the strongest reducing agents and the reducing agents that are stronger than them are not available. Therefore, they cannot be obtained by chemical reduction of their oxides....
Read More →Find the inverse of each of the matrices, if it exists.
Question: Find the inverse of each of the matrices, if it exists. $\left[\begin{array}{ll}2 5 \\ 1 3\end{array}\right]$ Let $A=\left[\begin{array}{ll}2 5 \\ 1 3\end{array}\right]$ Solution: Let $A=\left[\begin{array}{ll}2 5 \\ 1 3\end{array}\right]$ We know thatA=IA $\therefore\left[\begin{array}{ll}2 5 \\ 1 3\end{array}\right]=\left[\begin{array}{ll}1 0 \\ 0 1\end{array}\right] A$ $\Rightarrow\left[\begin{array}{ll}1 \frac{5}{2} \\ 1 3\end{array}\right]=\left[\begin{array}{ll}\frac{1}{2} 0 \\ 0...
Read More →A coil of inductance 0.50 H and resistance 100 Ω is connected to a 240 V,
Question: A coil of inductance 0.50 H and resistance 100 Ω is connected to a 240 V, 50 Hz ac supply. (a)What is the maximum current in the coil? (b)What is the time lag between the voltage maximum and the current maximum? Solution: Inductance of the inductor,L= 0.50 H Resistance of the resistor,R= 100 Ω Potential of the supply voltage,V= 240 V Frequency of the supply,= 50 Hz (a)Peak voltage is given as: $V_{0}=\sqrt{2} V$ $=\sqrt{2} \times 240=339.41 \mathrm{~V}$ Angular frequency of the supply,...
Read More →In how many ways can the letters of the word ASSASSINATION be arranged so that all the S’s are together?
Question: In how many ways can the letters of the word ASSASSINATION be arranged so that all the Ss are together? Solution: In the given word ASSASSINATION, the letter A appears 3 times, S appears 4 times, I appears 2 times, N appears 2 times, and all the other letters appear only once. Since all the words have to be arranged in such a way that all the Ss are together, SSSS is treated as a single object for the time being. This single object together with the remaining 9 objects will account for...
Read More →In what ways lithium shows similarities to magnesium in its chemical behaviour?
Question: In what ways lithium shows similarities to magnesium in its chemical behaviour? Solution: Similarities between lithium andmagnesium are as follows. (i)Both Li and Mg react slowly with cold water. (ii)The oxides of both Li and Mg are much less soluble in water and their hydroxides decompose at high temperature. $2 \mathrm{LiOH} \stackrel{\text { heat }}{\longrightarrow} \mathrm{Li}_{2} \mathrm{O}+\mathrm{H}_{2} \mathrm{O}$ $\mathrm{Mg}(\mathrm{OH})_{2} \stackrel{\text { heat }}{\longrig...
Read More →Find the inverse of each of the matrices, if it exists.
Question: Find the inverse of each of the matrices, if it exists. $\left[\begin{array}{ll}2 1 \\ 7 4\end{array}\right]$ Solution: Let $A=\left[\begin{array}{ll}2 1 \\ 7 4\end{array}\right]$ We know that $A=I A$ $\therefore\left[\begin{array}{ll}2 1 \\ 7 4\end{array}\right]=\left[\begin{array}{ll}1 0 \\ 0 1\end{array}\right] A$ $\Rightarrow\left[\begin{array}{ll}1 \frac{1}{2} \\ 7 4\end{array}\right]=\left[\begin{array}{ll}\frac{1}{2} 0 \\ 0 1\end{array}\right] A \quad\left(\mathrm{R}_{1} \righta...
Read More →From a class of 25 students, 10 are to be chosen for an excursion party.
Question: From a class of 25 students, 10 are to be chosen for an excursion party. There are 3 students who decide that either all of them will join or none of them will join. In how many ways can the excursion party be chosen? Solution: From the class of 25 students, 10 are to be chosen for an excursion party. Since there are 3 students who decide that either all of them will join or none of them will join, there are two cases. Case I: All the three students join. Then, the remaining 7 students...
Read More →It is required to seat 5 men and 4 women in a row so that the women occupy the even places.
Question: It is required to seat 5 men and 4 women in a row so that the women occupy the even places. How many such arrangements are possible? Solution: 5 men and 4 women are to be seated in a row such that the women occupy the even places. The 5 men can be seated in 5! ways. For each arrangement, the 4 women can be seated only at the cross marked places (so that women occupy the even places). $\mathrm{M} \times \mathrm{M} \times \mathrm{M} \times \mathrm{M} \times \mathrm{M}$ Therefore, the wom...
Read More →Compare the alkali metals and alkaline earth metals with respect to
Question: Compare the alkali metals and alkaline earth metals with respect to (i) ionization enthalpy (ii) basicity of oxides and (iii) solubility of hydroxides. Solution:...
Read More →An LC circuit contains a 20 mH inductor and a 50 μF capacitor with an initial charge of 10 mC.
Question: AnLCcircuit contains a 20 mH inductor and a 50 F capacitor with an initial charge of 10 mC. The resistance of the circuit is negligible. Let the instant the circuit is closed bet= 0. (a)What is the total energy stored initially? Is it conserved duringLCoscillations? (b)What is the natural frequency of the circuit? (c)At what time is the energy stored (i) completely electrical (i.e., stored in the capacitor)? (ii) completely magnetic (i.e., stored in the inductor)? (d)At what times is t...
Read More →Explain why is sodium less reactive than potassium?
Question: Explain why is sodium less reactive than potassium? Solution: In alkali metals, on moving down the group, the atomic size increases and the effective nuclear charge decreases. Because of these factors, the outermost electron in potassium can be lost easily as compared to sodium. Hence, potassium is more reactive than sodium....
Read More →Determine the number of 5-card combinations
Question: Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king. Solution: From a deck of 52 cards, 5-card combinations have to be made in such a way that in each selection of 5 cards, there is exactly one king. In a deck of 52 cards, there are 4 kings. 1 king can be selected out of 4 kings in ${ }^{4} \mathrm{C}_{1}$ ways. 4 cards out of the remaining 48 cards can be selected in ${ }^{48} \mathrm{C}_{4}$ ways. Thus, the required ...
Read More →An LC circuit contains a 20 mH inductor and a 50 μF capacitor with an initial charge of 10 mC.
Question: AnLCcircuit contains a 20 mH inductor and a 50 F capacitor with an initial charge of 10 mC. The resistance of the circuit is negligible. Let the instant the circuit is closed bet= 0. (a)What is the total energy stored initially? Is it conserved duringLCoscillations? (b)What is the natural frequency of the circuit? (c)At what time is the energy stored (i) completely electrical (i.e., stored in the capacitor)? (ii) completely magnetic (i.e., stored in the inductor)? (d)At what times is t...
Read More →Find the oxidation state of sodium in Na2O2.
Question: Find the oxidation state of sodium in $\mathrm{Na}_{2} \mathrm{O}_{2}$. Solution: Let the oxidation state of Na bex. The oxidation state of oxygen, in case of peroxides, is 1. Therefore, $2(x)+2(-1)=0$ $2 x-2=0$ $2 x=2$ $x=+1$ Therefore, the oxidation sate of sodium is +1....
Read More →Why are alkali metals not found in nature?
Question: Why are alkali metals not found in nature? Solution: Alkali metals include lithium, sodium, potassium, rubidium, cesium, and francium. These metals have only one electron in their valence shell, which they lose easily, owing to their low ionization energies. Therefore, alkali metals are highly reactive and are not found in nature in their elemental state....
Read More →In an examination, a question paper consists of 12 questions divided into two parts i.e.
Question: In an examination, a question paper consists of 12 questions divided into two parts i.e., PartIand PartII, containing 5 and 7 questions, respectively. A student is required to attempt 8 questions in all, selecting at least 3 from each part. In how many ways can a student select the questions? Solution: It is given that the question paper consists of 12 questions divided into two parts PartIand PartII, containing 5 and 7 questions, respectively. A student has to attempt 8 questions, sel...
Read More →The English alphabet has 5 vowels and 21 consonants.
Question: The English alphabet has 5 vowels and 21 consonants. How many words with two different vowels and 2 different consonants can be formed from the alphabet? Solution: 2 different vowels and 2 different consonants are to be selected from the English alphabet. Since there are 5 vowels in the English alphabet, number of ways of selecting 2 different vowels from the alphabet $={ }^{5} \mathrm{C}_{2}=\frac{5 !}{2 ! 3 !}=10$ Since there are 21 consonants in the English alphabet, number of ways ...
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