Let $a, b, c \in R$. If $f(x) = ax^2 + bx + c$ is such that $a + b + c = 3$ and $f(x + y) = f(x) + f(y) + xy$ for all $x, y \in R$,then $\sum_{n=1}^{10} f(n)$ is equal to:

Which of the following oxides is amphoteric?

Two cylinders $A$ and $B$ fitted with pistons,contain equal number of moles of an ideal monoatomic gas at $400 ~K$. The piston of $A$ is free to move while that of $B$ is held fixed. Same amount of heat energy is given to the gas in each cylinder. If the rise in temperature of the gas in $A$ is $42 ~K$,the rise in temperature of the gas in $B$ is $(\gamma = 5/3)$. (in $~K$)

$HCl$ is added to the following oxides,which one would give $H_2O_2$?

Which of the following statements is true for an $N$-type semiconductor?

An inductor $L$,a resistance $R$ and two identical bulbs $B_1$ and $B_2$ are connected to a battery through a switch $S$ as shown in the figure. The resistance of the coil having inductance $L$ is also $R$. Which of the following statements gives the correct description of the happenings when the switch $S$ is closed?