Two identical square rods of metal are welded end to end as shown in figure $(a)$. $20 \text{ calories}$ of heat flows through them in $4 \text{ minutes}$. If the rods are welded as shown in figure $(b)$,the same amount of heat will flow through the rods in ...... $\text{min}$.

$A$ rod of length $20 \, cm$ is made of metal $A$. It expands by $0.075 \, cm$ when its temperature is raised from $0^{\circ}C$ to $100^{\circ}C$. Another rod of a different metal $B$ having the same length expands by $0.045 \, cm$ for the same change in temperature. $A$ third rod of the same length is composed of two parts,one of metal $A$ and the other of metal $B$. This rod expands by $0.060 \, cm$ for the same change in temperature. The portion made of metal $A$ has the length ........ $cm$.

Let $E$ be the ellipse $\frac{x^2}{9} + \frac{y^2}{4} = 1$ and $C$ be the circle $x^2 + y^2 = 9$. Let $P$ and $Q$ be the points $(1, 2)$ and $(2, 1)$ respectively. Then:

Among the nitrates of alkali metals,which one can be decomposed to its oxide on strong heating?

$A$ man wants to reach a certain destination. One-sixth of the total distance is muddy while half the distance is tar road. For the remaining distance,he takes a boat. His speed of travelling in mud,in water,and on tar road is in the ratio $3:4:5$. The ratio of the durations he requires to cross the patch of mud,stream,and tar road is

In the circuit,if the forward voltage drop for the diode is $0.5\, V$,the current will be.......$mA$.