The area of the triangle formed by the lines ${y^2} - 9xy + 18{x^2} = 0$ and $y = 9$ is

If $p$ and $q$ are distinct prime numbers and if the equation $x^2 - px + q = 0$ has positive integers as its roots,then the roots of the equation are

$A$ glucose molecule reacts with $X$ number of molecules of phenylhydrazine to yield osazone. The value of $X$ is

Match List-$I$ with List-$II$ :

List-$I$ (Defects)	List-$II$ (Shown by)
$a$. Frenkel defect	$i$. Non-ionic solids and density of the solid decreases
$b$. Schottky defect	$ii$. Non-ionic solids and density of the solid increases
$c$. Vacancy defect	$iii$. Ionic solids and density of the solid decreases
$d$. Interstitial defect	$iv$. Ionic solids and density of the solid remains constant

Choose the correct answer from the options given below :

An electron moves with speed $2 \times 10^5 \ m/s$ along the positive $x$-direction in the presence of a magnetic field of induction $B = (\hat{i} + 4\hat{j} - 3\hat{k}) \ T$. The magnitude of the force experienced by the electron in newtons is (Charge on the electron $= 1.6 \times 10^{-19} \ C$)

If $X$ is a binomial variate with the range $\{0, 1, 2, 3, 4, 5, 6\}$ and $P(X=2) = 4 P(X=4)$, then the parameter $p$ of $X$ is