If $a \neq 0, b \neq 0, c \neq 0, a \times b = 0$ and $b \times c = 0$, then $a \times c$ is equal to

Two metal plates each of area $A$ form a parallel plate capacitor with air in between the plates. The distance between the plates is $d$. $A$ metal plate of thickness $d/2$ and of same area $A$ is inserted between the plates to form two capacitors of capacitances $C_1$ and $C_2$ as shown in the figure. If the effective capacitance of the two capacitors is $C^{\prime}$ and the capacitance of the capacitor initially is $C$,then $C^{\prime}/C$ is

If $f(x) = \frac{x^2-10x+25}{x^2-7x+10}$ and $f$ is continuous at $x = 5$, then $f(5)$ is equal to

The sum of the fourth powers of the roots of the equation $x^3+x+1=0$ is

Observe the following statements :
$I$. The circle $x^2+y^2-6x-4y-7=0$ touches the $y$-axis.
$II$. The circle $x^2+y^2+6x+4y-7=0$ touches the $x$-axis.
Which of the following is a correct statement?

Which of the following alkaline earth metals shows anomalous behavior and has an electronegativity similar to that of aluminum?