Needles $N_1, N_2$ and $N_3$ are made of a ferromagnetic,a paramagnetic and a diamagnetic substance respectively. $A$ magnet when brought close to them will

When metal $X$ is treated with sodium hydroxide,a white precipitate $(A)$ is obtained,which is soluble in excess of $NaOH$ to give soluble complex $(B)$. Compound $(A)$ is soluble in dilute $HCl$ to form compound $(C)$. The compound $(A)$ when heated strongly gives $(D)$,which is used to extract metal. Identify $(X), (A), (B), (C)$ and $(D)$. Write suitable equations to support their identities.

If the range of a random variable $X$ is $\{0, 1, 2, 3, 4, \ldots\}$ with $P(X=k) = \frac{(k+1)a}{3^k}$ for $k \geq 0$, then $a$ is equal to

Work done to increase the temperature of one mole of an ideal gas by $30^{\circ} C$,if it is expanding under the condition $V \propto T^{2/3}$ is,$(R = 8.314 \ J/mol \cdot K)$ (in $J$)

$A$ cell of $emf$ $E$ and internal resistance $r$ is connected in series with an external resistance $nr$. Then,the ratio of the terminal potential difference to $emf$ is

The equation of the circle with radius $5$ and touching the coordinate axes in the third quadrant is