The point $P$ is equidistant from $A(1, 3)$,$B(-3, 5)$,and $C(5, -1)$. Then $PA =$

$A$ bimetallic strip consists of metals $A$ and $B$. It is mounted rigidly at the base as shown. The metal $A$ has a higher coefficient of expansion compared to that of metal $B$. When the bimetallic strip is placed in a cold bath,it will:

$A$ coil of circular cross-section having $1000$ turns and $4 \, cm^2$ face area is placed with its axis parallel to a magnetic field which decreases by $10^{-2} \, Wb \, m^{-2}$ in $0.01 \, s$. The $e.m.f.$ induced in the coil is......$mV$

$A$ series combination of resistor $(R)$ and capacitor $(C)$ is connected to an $A$.$C$. source of angular frequency $\omega$. Keeping the voltage same,if the frequency is changed to $\omega / 3$,the current becomes half of the original current. Then the ratio of the capacitive reactance and resistance at the former frequency is

When one end of a capillary tube is dipped in water,the height of the water column is $h$. The upward force of $105 \text{ dyne}$ due to surface tension is balanced by the force due to the weight of the water column. What is the inner circumference of the capillary (in $\text{ cm}$)? (Surface tension of water $= 7 \times 10^{-2} \text{ N m}^{-1}$)

Match the following columns:

Column-$I$	Column-$II$
$(A)$ Blue-green algae	$(i)$ Spirogyra
$(B)$ Unicellular algae	$(ii)$ Nostoc
$(C)$ Filamentous algae	$(iii)$ Volvox
$(D)$ Colonial algae	$(iv)$ Chlamydomonas