$A$ metal nitrate reacts with $KI$ to give a black precipitate which on addition of excess of $KI$ converts into an orange-colored solution. The cation of the metal nitrate is

The displacement $x$ of a particle varies with time $t$ as $x = a e^{-\alpha t} + b e^{\beta t}$,where $a, b, \alpha$,and $\beta$ are positive constants. The velocity of the particle will:

Let $a \neq 0$ and $p(x)$ be a polynomial of degree greater than $2$. If $p(x)$ leaves remainders $a$ and $-a$ when divided respectively by $x+a$ and $x-a$,then the remainder when $p(x)$ is divided by $x^2-a^2$ is:

Which of the following statements is incorrect regarding saline hydrides?

Select the two correct statements out of the four $(i-iv)$ given below about the lac operon.
$i.$ Glucose or galactose may bind with the repressor and inactivate it.
$ii.$ In the absence of lactose,the repressor binds with the operator region.
$iii.$ The $z$-gene codes for permease.
$iv.$ This was elucidated by Francois Jacob and Jacques Monod.

Observe the following statements:
$(I)$ In $\triangle ABC, b \cos^2 \frac{C}{2} + c \cos^2 \frac{B}{2} = s$
$(II)$ In $\triangle ABC, \cot \frac{A}{2} = \frac{b+c}{a} \Rightarrow B = 90^{\circ}$
Which of the following is correct?