If $0.5 \ mol$ of $CaBr_2$ is mixed with $0.2 \ mol$ of $K_3PO_4$,then the maximum number of moles of $Ca_3(PO_4)_2$ obtained will be:

The differential equation obtained by eliminating the arbitrary constants $a$ and $b$ from $xy = ae^x + be^{-x}$ is

Inbreeding depression is primarily associated with which of the following?

If $z_1 = a + ib$ and $z_2 = c + id$ are complex numbers such that $|z_1| = |z_2| = 1$ and $R(z_1\overline{z_2}) = 0$,then the pair of complex numbers $w_1 = a + ic$ and $w_2 = b + id$ satisfies

Let $\alpha$ and $\beta$ be the roots of the equation $x^2-x-1=0$. If $p_{k}=(\alpha)^{k}+(\beta)^{k}, k \geq 1$,then which one of the following statements is not true?

For the parabola $y^2+6y-2x+5=0$:
$(I)$ The vertex is $(-2,-3)$
$(II)$ The directrix is $y+3=0$
Which of the following is correct?