A body cools from $100^\circ C$ to $60^\circ C$ in $20$ minutes, the temperature of the surroundings being $20^\circ C$. The total time taken (in minutes) for the body to cool down to $40^\circ C$ is ...
- A$60$
- B$40$
- C$50$
- D$30$
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For the components of a vector $\vec{A} = (3 \hat{i} + 4 \hat{j} - 5 \hat{k})$,match the following columns.
Column $I$ Column $II$ $(A)$ Component along $x$-axis $(p)$ $5 \text{ unit}$ $(B)$ Component along vector $(2 \hat{i} + \hat{j} + 2 \hat{k})$ $(q)$ $4 \text{ unit}$ $(C)$ Component along $(6 \hat{i} + 8 \hat{j} - 10 \hat{k})$ $(r)$ $0$ $(D)$ Component along $(-3 \hat{i} - 4 \hat{j} + 5 \hat{k})$ $(s)$ None
| Column $I$ | Column $II$ |
|---|---|
| $(A)$ Component along $x$-axis | $(p)$ $5 \text{ unit}$ |
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| $(C)$ Component along $(6 \hat{i} + 8 \hat{j} - 10 \hat{k})$ | $(r)$ $0$ |
| $(D)$ Component along $(-3 \hat{i} - 4 \hat{j} + 5 \hat{k})$ | $(s)$ None |
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