You are provided with a fine white
Question: You are provided with a fine white coloured powder which is either sugar or salt. How would you identify it without tasting? Solution: Dissolve both sugar and salt separately in water taken in two glass beakers. Pass electric current through both. In case, solution is conducting, it represents a salt dissolved in water. If it fails to conduct electricity, it represents a sugar solution....
Read More →Solve the following equations
Question: If $A=\left[\begin{array}{ll}x 1 \\ 1 0\end{array}\right]$ and $A^{2}$ is the identity matrix, then $x=$ ____________ Solution: The given matrix is $A=\left[\begin{array}{ll}x 1 \\ 1 0\end{array}\right]$. It is given that, $A^{2}=I$ $\therefore\left[\begin{array}{ll}x 1 \\ 1 0\end{array}\right]\left[\begin{array}{ll}x 1 \\ 1 0\end{array}\right]=\left[\begin{array}{ll}1 0 \\ 0 1\end{array}\right]$ $\Rightarrow\left[\begin{array}{cc}x^{2}+1 x \\ x 1\end{array}\right]=\left[\begin{array}{...
Read More →Classify each of the following on the basis of their atomicity.
Question: Classify each of the following on the basis of their atomicity. Solution: (a) 2 (b) 3 (c) 3 (d) 8 (e) 4 (f) 4 (g) 14 (h) 3 (i) 2 (j) 5 (k) 1 (I) $1 .$...
Read More →Does the solubility of a substance change
Question: Does the solubility of a substance change with temperature? Explain with the help of an example. Solution: In most of the cases, the solubility of a substance in a particular solvent such as water increases with the rise in temperature. For example, more of sugar can dissolve in a particular volume of water by increasing the temperature. ....
Read More →What is the fraction of mass of water
Question: What is the fraction of mass of water $\left(\mathrm{H}_{2} \mathrm{O}\right)$ due to neutrons? Solution: Molecular mass of $\mathrm{H}_{2} \mathrm{O}=2 \times 1+16=18 \mathrm{u}$ Total number of neutrons $=2 \times 0+8=8$ Mass of neutrons $=8 \mathrm{u}$ Fraction of mass due to neutrons $=\frac{\text { Mass of neutrons }}{\text { Molecular mass of } \mathrm{H}_{2} \mathrm{O}}=\frac{(8 \mathrm{u})}{(18 \mathrm{u})}$ $=\frac{8}{18}=\frac{4}{9}$ or $4: 9$...
Read More →Solve this problem
Question: $\left[\begin{array}{c}1 \\ -1 \\ 2\end{array}\right]\left[\begin{array}{lll}2 1 -1\end{array}\right]=$ _________ Solution: The order of matrix $\left[\begin{array}{c}1 \\ -1 \\ 2\end{array}\right]$ is $3 \times 1$ and the order of matrix $\left[\begin{array}{lll}2 1 -1\end{array}\right]$ is $1 \times 3$. So, $\left[\begin{array}{c}1 \\ -1 \\ 2\end{array}\right]\left[\begin{array}{lll}2 1 -1\end{array}\right]$ is a matrix of order $3 \times 3$. $\left[\begin{array}{c}1 \\ -1 \\ 2\end{a...
Read More →Solve this problem
Question: $\left[\begin{array}{c}1 \\ -1 \\ 2\end{array}\right]\left[\begin{array}{lll}2 1 -1\end{array}\right]=$______ Solution: The order of matrix $\left[\begin{array}{c}1 \\ -1 \\ 2\end{array}\right]$ is $3 \times 1$ and the order of matrix $\left[\begin{array}{lll}2 1 -1\end{array}\right]$ is $1 \times 3$. So, $\left[\begin{array}{c}1 \\ -1 \\ 2\end{array}\right]\left[\begin{array}{lll}2 1 -1\end{array}\right]$ is a matrix of order $3 \times 3$. $\left[\begin{array}{c}1 \\ -1 \\ 2\end{array...
Read More →State the number of atoms present in each of the following chemical species:
Question: State the number of atoms present in each of the following chemical species: (a) $\mathrm{CO}_{3}{ }^{2-}$ (b) $\mathrm{PO}_{4}{ }^{3-}$ (c) $\mathrm{P}_{2} \mathrm{O}_{5}$ (d) CO. Solution: (a) Four (b) Five (c) Seven (d) Two....
Read More →Give the chemical formulae for the following compounds
Question: Give the chemical formulae for the following compounds and compute the ratio by mass of the combining elements in each one of them. (a) Ammonia (b) Carbon monoxide (c) Hydogen chloride (d) Aluminium fluoride (e) Magnesium sulphide. Solution:...
Read More →Which of the following symbols of elements are incorrect?
Question: Which of the following symbols of elements are incorrect? Give their correct symbols: (a) Cobalt Co (b) Carbon C (c) Aluminium $\mathrm{Al}$ (d) Helium He (e) Sodium So Solution: (a) Incorrect; correct symbol is Co (b) Incorrect; correct symbol is $C$ (c) Incorrect; correct symbol is Al (e) Incorrect; correct symbol is $\mathrm{Na}$....
Read More →Give the formulae of the compounds formed from the following sets of elements :
Question: Give the formulae of the compounds formed from the following sets of elements : (a) Calcium and fluorine (b) Hydrogen and sulphur (c) Nitrogen and hydrogen (d) Carbon and chlorine (e) Sodium and oxygen (f) Carbon and oxygen. Solution: (a) $\mathrm{CaF}_{2}$ (b) $\mathrm{H}_{2} \mathrm{~S}$ (c) $\mathrm{NH}_{3}$ (d) $\mathrm{CCl}_{4}$ (e) $\mathrm{Na}_{2} \mathrm{O}$ (f) $\mathrm{CO}$ and $\mathrm{CO}_{2}$....
Read More →Write the cations and anions present (if any) in the following compounds :
Question: Write the cations and anions present (if any) in the following compounds : (a) $\mathrm{CH}_{3} \mathrm{COONa}$ (b) $\mathrm{NaCl}$ (c) $\mathrm{H}_{2}$ (d) $\mathrm{NH}_{4} \mathrm{NO}_{3}$. Solution: (a) $\mathrm{CH}_{3} \mathrm{O}^{-}$(anion), $\mathrm{Na}^{+}$(cation) (b) $\mathrm{Na}^{+}$(cation), $\mathrm{Cl}^{-}$(anion) (c) Molecular compound (no ions) (d) $\mathrm{NH}_{4}^{+}$(cation), $\mathrm{NO}_{3}^{-}$(anion)....
Read More →If A = diag (2, –1, 3), B = diag (–1, 3, 2),
Question: If $A=\operatorname{diag}(2,-1,3), B=\operatorname{diag}(-1,3,2)$, then $A^{2} B=$______ Solution: The given matrices are $A=\operatorname{diag}(2,-1,3), B=\operatorname{diag}(-1,3,2)$. Now, $A^{2}=A \cdot A=\left[\begin{array}{ccc}2 0 0 \\ 0 -1 0 \\ 0 0 3\end{array}\right]\left[\begin{array}{ccc}2 0 0 \\ 0 -1 0 \\ 0 0 3\end{array}\right]=\left[\begin{array}{ccc}4+0+0 0+0+0 0+0+0 \\ 0+0+0 0+1+0 0+0+0 \\ 0+0+0 0+0+0 0+0+9\end{array}\right]=\left[\begin{array}{lll}4 0 0 \\ 0 1 0 \\ 0 0 9...
Read More →If A = 30°, verify that:
Question: IfA= 30, verify that: (i) $\sin 2 A=\frac{2 \tan A}{1+\tan ^{2} A}$ (ii) $\cos 2 A=\frac{1-\tan ^{2} A}{1+\tan ^{2} A}$ (iii) $\tan 2 A=\frac{2 \tan A}{1-\tan ^{2} A}$ Solution: A= 30o $\Rightarrow 2 A=2 \times 30^{\circ}=60^{\circ}$ (i) $\sin 2 A=\sin 60^{\circ}=\frac{\sqrt{3}}{2}$ $\frac{2 \tan A}{1+\tan ^{2} A}=\frac{2 \tan 30^{\circ}}{1+\tan ^{2} 30^{\circ}}=\frac{2 \times\left(\frac{1}{\sqrt{3}}\right)}{1+\left(\frac{1}{\sqrt{3}}\right)^{2}}=\frac{\left(\frac{2}{\sqrt{3}}\right)}{...
Read More →Write the chemical formulae of all the compounds that
Question: Write the chemical formulae of all the compounds that can be formed by the combination of following ions: $\mathrm{Cu}^{2+}, \mathrm{Na}^{+}, \mathrm{Fe}^{3+}, \mathrm{Cl}^{-}, \mathrm{SO}_{4}{ }^{2-} ; \mathrm{PO}_{4}{ }^{3-}$. Solution: For $\mathrm{Cu}^{2+}$ ion : $\mathrm{CuCl}_{2}, \mathrm{CuSO}_{4}, \mathrm{Cu}_{3}\left(\mathrm{PO}_{4}\right)_{2}$ For $\mathrm{Na}^{+}$ion : $\mathrm{NaCl}, \mathrm{Na}_{2} \mathrm{SO}_{4}, \mathrm{Na} 3 \mathrm{PO}_{4}$ For $\mathrm{Fe}^{3+}$ um :...
Read More →Write the chemical formulae for the following compounds :
Question: Write the chemical formulae for the following compounds : (a) Copper (II) bromide (b) Aluminium (III) nitrate (c) Calcium (II) phosphate (d) Iron (III) Sulphide (e) Mercury (II) chloride (f) Magnesium (II) acetate. Solution: (a) CuBr 2 (b) $\mathrm{Al}\left(\mathrm{NO}_{3}\right)_{3}$ (c) $\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}$ (d) $\mathrm{Fe}_{2} \mathrm{~S}_{3}$ (e) $\mathrm{HgCl}_{2}$ (f) $\mathrm{Mg}\left(\mathrm{CH}_{2} \mathrm{COO}\right)_{2}$....
Read More →Solve this
Question: If $A=\left[\begin{array}{lll}3 0 0 \\ 0 3 0 \\ 0 0 3\end{array}\right]$, then $A^{4}=$_______ Solution: The given matrix is $A=\left[\begin{array}{lll}3 0 0 \\ 0 3 0 \\ 0 0 3\end{array}\right]$. Now, $A^{2}=A \cdot A=\left[\begin{array}{lll}3 0 0 \\ 0 3 0 \\ 0 0 3\end{array}\right]\left[\begin{array}{lll}3 0 0 \\ 0 3 0 \\ 0 0 3\end{array}\right]=\left[\begin{array}{lll}3 \times 3+0 \times 0+0 \times 0 3 \times 0+0 \times 3+0 \times 0 3 \times 0+0 \times 0+0 \times 3 \\ 0 \times 3+3 \t...
Read More →Solve this
Question: If $A=\left[\begin{array}{lll}3 0 0 \\ 0 3 0 \\ 0 0 3\end{array}\right]$, then $A^{4}=$_______ Solution: The given matrix is $A=\left[\begin{array}{lll}3 0 0 \\ 0 3 0 \\ 0 0 3\end{array}\right]$. Now, $A^{2}=A \cdot A=\left[\begin{array}{lll}3 0 0 \\ 0 3 0 \\ 0 0 3\end{array}\right]\left[\begin{array}{lll}3 0 0 \\ 0 3 0 \\ 0 0 3\end{array}\right]=\left[\begin{array}{lll}3 \times 3+0 \times 0+0 \times 0 3 \times 0+0 \times 3+0 \times 0 3 \times 0+0 \times 0+0 \times 3 \\ 0 \times 3+3 \t...
Read More →Which of the following represents a correct chemical formula?
Question: Which of the following represents a correct chemical formula? Name it. (a) $\mathrm{CaCl}$ (b) $\mathrm{BiPO}_{4}$ (c) $\mathrm{NaSO}_{4}$ (d) NaS. Solution: (b). Both Bi and $\mathrm{PO}_{4}$ are trivalent ion $\left(\mathrm{Bi}^{3+}\right.$ and $\left.\mathrm{PO}_{4}{ }^{3-}\right)$. It is known as bismuth phosphate....
Read More →If A = 45°, verify that:
Question: IfA= 45, verify that:(i) sin 2A= 2 sinAcosA(ii) cos 2A= 2 cos2A 1 = 1 2 sin2A Solution: $A=45^{\circ}$ $\Rightarrow 2 A=2 \times 45^{\circ}=90^{\circ}$ (i) $\sin 2 A=\sin 90^{\circ}=1$ $2 \sin A \cos A=2 \sin 45^{\circ} \cos 45^{\circ}=2 \times \frac{1}{\sqrt{2}} \times \frac{1}{\sqrt{2}}=1$ sin 2A= 2 sinAcosA (ii) cos 2A= cos 90o= 0 $2 \cos ^{2} A-1=2 \cos ^{2} 45^{\circ}-1=2 \times\left(\frac{1}{\sqrt{2}}\right)^{2}-1=2 \times \frac{1}{2}-1=1-1=0$ Now, $1-2 \sin ^{2} A=1-2 \times\lef...
Read More →A change in the physical state can be brought about:
Question: A change in the physical state can be brought about: (a) only when energy is given to the system (b) only when energy is taken out from the system (c) when energy is either given to, or taken out from the system (d) without any energy change. Solution: (c) when energy is either given to, or taken out from the system...
Read More →Solve this
Question: If $A=\left[\begin{array}{ccc}0 2 0 \\ 0 0 3 \\ -2 2 0\end{array}\right]$ and $B=\left[\begin{array}{ccc}1 2 3 \\ 3 4 5 \\ 5 -4 0\end{array}\right]$, then $(A B)_{33}=$______ Solution: The given matrices are $A=\left[\begin{array}{ccc}0 2 0 \\ 0 0 3 \\ -2 2 0\end{array}\right]$ and $B=\left[\begin{array}{ccc}1 2 3 \\ 3 4 5 \\ 5 -4 0\end{array}\right]$. $\therefore A B=\left[\begin{array}{ccc}0 2 0 \\ 0 0 3 \\ -2 2 0\end{array}\right]\left[\begin{array}{ccc}1 2 3 \\ 3 4 5 \\ 5 -4 0\end{...
Read More →3.42g of sucrose are dissolved in
Question: $3.42 \mathrm{~g}$ of sucrose are dissolved in $18 \mathrm{~g}$ of water in a beaker. The number of oxygen atoms in the solution are (a) $6.68 \times 10^{23}$ (b) $6.09 \times 102^{22}$ (c) $6.022 \times 10^{23}$ (d) $6.022 \times 10^{21}$ Solution: (a). No. of moles of sucrose in $3.42 \mathrm{~g}=\frac{(3.42 \mathrm{~g})}{\left(342 \mathrm{gmol}^{-1}\right)}$ $=0.01 \mathrm{~mol}$ No. of oxygen atoms in 1 mole of sucrose $=0.01 \times 11 \times N_{A}=0.11 \mathrm{~N}_{A}$ No. of oxyg...
Read More →Verify each of the following:
Question: Verify each of the following:(i) sin 60 cos 30 cos 60 sin 30 = sin 30(ii) cos 60 cos 30 + sin 60 sin 30 = cos 30(iii) 2 sin 30 cos 30 = sin 60(iv) 2 sin 45 cos 45 = sin 90 Solution: (i) sin 60ocos 30o cos 60osin 30o $=\left(\frac{\sqrt{3}}{2}\right) \times\left(\frac{\sqrt{3}}{2}\right)-\left(\frac{1}{2}\right) \times\left(\frac{1}{2}\right)=\frac{3}{4}-\frac{1}{4}=\frac{2}{4}=\frac{1}{2}$ Also, $\sin 30^{\circ}=\frac{1}{2}$ sin60ocos30ocos60osin30o= sin 30o(ii) cos 60ocos 30o+ sin 60o...
Read More →If A is an m × n matrix and B is a matrix such that both AB and BA
Question: If $A$ is an $m \times n$ matrix and $B$ is a matrix such that both $A B$ and $B A$ are defined, then the order of $B$ is______ Solution: Let $X=\left[x_{i j}\right]_{m \times n}$ and $Y=\left[y_{i j}\right]_{p \times q}$ be two matrices of order $m \times n$ and $p \times q$. The multiplication of matrices $X$ and $Y$ is defined if number of columns of $X$ is same as the number of rows of $Y$ i.e. $n=p$. Also, $X Y$ is a matrix of order $m \times q$. It is given that, $A$ is an $m \ti...
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