On dissolving sugar in water at room temperature
Question: On dissolving sugar in water at room temperature solution feels cool to touch. Under which of the following cases dissolution of sugar will be most rapid? (i) Sugar crystals in cold water. (ii) Sugar crystals in hot water. (iii) Powdered sugar in cold water. (iv) Powdered sugar in hot water. Solution: Option (iv)Powdered sugar in hot wateris the answer....
Read More →Find the domain and range of $R$.
Question: Let $R=\{(a, b): a, b \in N$ and $a+3 b=12\}$ Find the domain and range of $R$. Solution: $\operatorname{dom}(R)=\{3,6,9\}$ and range $(R)=\{3,2,1\}$...
Read More →Which of the following units is useful
Question: Which of the following units is useful in relating the concentration of a solution with its vapour pressure? (i) mole fraction (ii) parts per million (iii) mass percentage (iv) molality Solution: Option (i) mole fraction is the answer....
Read More →Let $R=(x, y): x+2 y=$ be are relation on $N$.
Question: Let $R=(x, y): x+2 y=$ be are relation on $N$. Write the range of $R$. Solution: $\{3,2,1\}$...
Read More →Solve this
Question: Let $R=\left\{\left(a, a^{3}\right): a\right.$ is a prime number less than 10$\}$. Find (i) R (ii) dom (R) (iii) range (R). Solution: (i) $R=\{(2,8),(3,27),(5,125),(7,343)\}$ (ii) $\operatorname{dom}(R)=\{2,3,5,7\}$ (iii) range $(R)=\{8,27,125,343\}$...
Read More →Find the value
Question: Let $R=\left\{\left(a, a^{3}\right): a\right.$ is a prime number less than 5$\} .$ Find the range of $R$. Solution: range $(R)=\{827\}$...
Read More →Find the domain and range of the relation
Question: Find the domain and range of the relation $R=\{(-1,1),(1,1),(-2,4),(2,4)\}$ Solution: dom $(R)=\{-1,1,-2,2\}$ and range $(R)=\{1,4\}$...
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{1}{2+\sin x+\cos x} d x$ Solution: Given I $=\int \frac{1}{2+\sin x+\cos x} d x$ We know that $\sin x=\frac{2 \tan \frac{x}{2}}{1+\tan ^{2} \frac{x}{2}}$ and $\cos x=\frac{1-\tan ^{2} \frac{x}{2}}{1+\tan ^{2} \frac{x}{2}}$ $\Rightarrow \int \frac{1}{2+\sin x+\cos x} d x=\int \frac{1}{2+\frac{2 \tan \frac{x}{2}}{1+\tan \frac{2}{2}}+\frac{1-\tan \frac{2}{2}}{1+\tan \frac{2}{2} \frac{x}{2}}} d x$ $=\int \frac{1+\tan ^{2} \frac{x}{2}}{2+2 \tan ...
Read More →Why does the electrical conductivity
Question: Why does the electrical conductivity of semiconductors increase with a rise in temperature? Solution: The energy gap between the valence band and conduction band is small, at room temperature they do not conduct electricity but raised the electrons to get enough amount of energy to excite from valence band to conduction band. This is called thermodynamic conduction in intrinsic semiconductors...
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{1}{5-4 \cos x} d x$ Solution: Given $I=\int \frac{1}{5-4 \cos x} d x$ We know that $\cos \mathrm{X}=\frac{1-\tan ^{2} \frac{x}{2}}{1+\tan ^{2} \frac{x}{2}}$ $\Rightarrow \int \frac{1}{5-4 \cos x} d x=\int \frac{1}{5-4\left(\frac{1-\tan ^{2} \frac{x}{2}}{1+\tan ^{2} \frac{x}{2}}\right)} d x$ $=\int \frac{1+\tan ^{2} \frac{x}{2}}{5\left(1+\tan ^{2} \frac{x}{2}\right)-4\left(1-\tan ^{2} \frac{x}{2}\right)} d x$ Replacing $1+\tan ^{2} x / 2$ in...
Read More →Why does white ZnO (s) become
Question: Why does white ZnO (s) become yellow upon heating? Solution: When ZnO is heated, it gives Zn2+ electrons. The excess Zn ions get trapped in the interstitial site and vacant sites also. The yellow colour is due to this electron and electrical conductivity in crystals....
Read More →Why is FeO (s) not formed in stoichiometric
Question: Why is FeO (s) not formed in stoichiometric composition? Solution: The composition of Fe2+ and O2 ions is not 1:1 it is 0.95:1. This can be obtained if and only if a small number of Fe2+ ions are replaced by two-third of Fe3+ in OH sites...
Read More →Why does table salt, NaCl,
Question: Why does table salt, NaCl, sometimes appear yellow? Solution: This is due to the metal excess defect. The unpaired electrons get trapped in anion vacancies. When the electrons absorb energy, it gets excited and falls on the crystals. Thus the colour becomes yellow....
Read More →Despite long-range order in the arrangement
Question: Despite long-range order in the arrangement of particles why are the crystals usually not perfect? Solution: The crystallization process will be faster so that the particle may not get enough time to arrange in perfect order. That is why crystals have the long-range arrangement of particles but not perfect....
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{1}{\sin x+\cos x} d x$ Solution: Given $I=\int \frac{1}{\sin x+\cos x} d x$ We know that $\sin x=\frac{2 \tan \frac{x}{2}}{1+\tan ^{2} \frac{x}{2}}$ and $\cos x=\frac{1-\tan ^{2} \frac{x}{2}}{1+\tan ^{2} \frac{2}{2}}$ $\Rightarrow \int \frac{1}{\sin x+\cos x} d x=\int \frac{1}{\frac{2 \tan \frac{x}{2}}{1+\tan \frac{2}{2}}+\frac{1-\tan \frac{2}{2}}{1+\tan \frac{2}{2}}} d x$ $=\int \frac{1+\tan ^{2} \frac{x}{2}}{2 \tan \frac{x}{2}+1-\tan ^{2}...
Read More →Why are solids incompressible?
Question: Why are solids incompressible? Solution: Solids are incompressible because their intermolecular distance between the molecules is very less. There will be a large repulsive force between the electron clouds....
Read More →Why are liquids and gases categorised
Question: Why are liquids and gases categorised as fluids? Solution: They both have the property to flow. The molecules of liquid and gases can move fast from one to another. That is why they are categorized as fluids....
Read More →Which of the following defects decrease
Question: Which of the following defects decrease the density? (i) Interstitial defect (ii) Vacancy defect (iii) Frankel defect (iv) Schottky defect Solution: Option (ii)Vacancy defect and (iv)Schottky defect are the answers....
Read More →Frenkel defect is also known as ________.
Question: Frenkel defect is also known as ________. (i) stoichiometric defect (ii) dislocation defect (iii) impurity defect (iv) non-stoichiometric defect Solution: Option (i)stoichiometric defect and (ii)dislocation defectare the answers....
Read More →In which of the following arrangements
Question: In which of the following arrangements octahedral voids are formed? (i) hcp (ii) bcc (iii) simple cubic (iv) fcc Solution: Option (i)hcpand (iv) fcc are the answers....
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{1}{\cos -\sin x} d x$ Solution: Given $I=\int \frac{1}{\cos x-\sin x} d x$ We know that $\sin x=\frac{2 \tan \frac{x}{2}}{1+\tan \frac{2}{2}}$ and $\cos x=\frac{1-\tan ^{2} \frac{x}{2}}{1+\tan ^{2} \frac{x}{2}}$ $\Rightarrow \int \frac{1}{-\sin x+\cos x} d x=\int \frac{1}{-\frac{2 \tan \frac{x}{2}}{1+\tan \frac{2 x}{2}}+\frac{1-\tan \frac{2 x}{2}}{1+\tan \frac{2 x}{2}}} d x$ $=\int \frac{1+\tan ^{2} \frac{x}{2}}{-2 \tan \frac{x}{2}+1-\tan ^...
Read More →Which of the following cannot be regarded
Question: Which of the following cannot be regarded as molecular solid? (i) SiC (Silicon carbide) (ii) AlN (iii) Diamond (iv) I2 Solution: Option (i)SiC (Silicon carbide), (ii)AlN and (iii)Diamondare the answers....
Read More →Which of the following features are not
Question: Which of the following features are not shown by quartz glass? (i) This is a crystalline solid. (ii) Refractive index is the same in all the directions. (iii) This has a definite heat of fusion. (iv) This is also called supercooled liquid. Solution: Option (i) and (iii) are the answers....
Read More →Which of the following statements are correct?
Question: Which of the following statements are correct? (i) Ferrimagnetic substances lose ferrimagnetism on heating and become paramagnetic. (ii) Ferrimagnetic substances do not lose ferrimagnetism on heating and remain ferrimagnetic. (iii) Antiferromagnetic substances have domain structures similar to ferromagnetic substances and their magnetic moments are not cancelled by each other. (iv) In ferromagnetic substances, all the domains get oriented in the direction of the magnetic field and rema...
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{1}{13+3 \cos x+4 \sin x} d x$ Solution: Given I $=\int \frac{1}{13+3 \cos x+4 \sin x} d x$ We know that $\sin x=\frac{2 \tan \frac{x}{2}}{1+\tan \frac{x}{2}}$ and $\cos x=\frac{1-\tan ^{2} \frac{x}{2}}{1+\tan 2 \frac{x}{2}}$ $\Rightarrow \int \frac{1}{13+4 \sin x+3 \cos x} d x=\int \frac{1}{13+4\left(\frac{2 \tan \frac{x}{2}}{1+\tan \frac{2 x}{2}}\right)+3\left(\frac{1-\tan \frac{2 x}{2}}{1+\tan \frac{2 x}{2}}\right)} d x$ $=\int \frac{1+\t...
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