The perimeter of a sector is a constant. If its area is to be maximum,the sectorial angle is:

If the pair of lines represented by $3 x^2 - 5 x y + P y^2 = 0$ and $6 x^2 - x y - 5 y^2 = 0$ have one line in common,then the sum of all possible values of $P$ is

In a transistor circuit,when the base current is increased by $50 \mu A$ keeping the collector voltage fixed at $2 \ V$,the collector current increases by $1 \ mA$. The current gain of the transistor is

The pair$(s)$ of diamagnetic ions is$(are)$
$(A) \ La ^{3+}, Ce ^{4+}$ $(B) \ Yb ^{2+}, Lu ^{3+}$ $(C) \ La ^{2+}, Ce ^{3+}$ $(D) \ Yb ^{3+}, Lu ^{2+}$

$A$ square matrix $[a_{ij}]$ in which $a_{ij} = 0$ for $i \neq j$ and $a_{ij} = k$ (constant) for $i = j$ is called a

An electrically charged particle enters a uniform magnetic field in a direction perpendicular to the field with a velocity $v$. Then,it travels