In India,electricity is supplied for domestic use at $220 \,V$. It is supplied at $110 \,V$ in the $USA$. If the resistance of a $60 \,W$ bulb for use in India is $R$,what will be the resistance of a $60 \,W$ bulb for use in the $USA$?
- A$R$
- B$2 R$
- C$\frac{R}{4}$
- D$\frac{R}{2}$
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Match List-$I$ with List-$II$ :
List-$I$ (Defects) List-$II$ (Shown by) $a$. Frenkel defect $i$. Non-ionic solids and density of the solid decreases $b$. Schottky defect $ii$. Non-ionic solids and density of the solid increases $c$. Vacancy defect $iii$. Ionic solids and density of the solid decreases $d$. Interstitial defect $iv$. Ionic solids and density of the solid remains constant
Choose the correct answer from the options given below :
| List-$I$ (Defects) | List-$II$ (Shown by) |
| $a$. Frenkel defect | $i$. Non-ionic solids and density of the solid decreases |
| $b$. Schottky defect | $ii$. Non-ionic solids and density of the solid increases |
| $c$. Vacancy defect | $iii$. Ionic solids and density of the solid decreases |
| $d$. Interstitial defect | $iv$. Ionic solids and density of the solid remains constant |
Choose the correct answer from the options given below :
The wavelengths of light used in an optical instrument are ${\lambda _1} = 4000\,\mathring{A}$ and ${\lambda _2} = 5000\,\mathring{A}$. The ratio of their respective resolving powers (corresponding to ${\lambda _1}$ and ${\lambda _2}$) is:
$A$ straight line which makes equal intercepts on positive $X$ and $Y$ axes and which is at a distance of $1$ unit from the origin intersects the straight line $y = 2x + 3 + \sqrt{2}$ at $(x_0, y_0)$. Then $2x_0 + y_0$ is equal to
The weight in grams of a non-volatile solute (mol. wt. $60$) to be dissolved in $90 \ g$ of water to produce a relative lowering of vapour pressure of $0.02$ is
The value of $x$,where $x>0$ and $\tan \left(\sec ^{-1}\left(\frac{1}{x}\right)\right)=\sin \left(\tan ^{-1} 2\right)$ is
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