The length of the $x$-intercept made by the pair of lines $2x^2 + xy - 6y^2 - 2x + 17y - 12 = 0$ is

The oxoacid of sulphur which contains two sulphur atoms in different oxidation states is

If $\int \frac{\cos x-\sin x}{\sqrt{8-\sin 2 x}} d x=a \sin ^{-1}\left(\frac{\sin x+\cos x}{b}\right)+c$ where $c$ is a constant of integration,then the ordered pair $(a, b)$ is equal to

$AgNO_3 \xrightarrow{\Delta} (W) + (X) + O_2$
$(X) + H_2O \to HNO_2 + HNO_3$
$(W) + HNO_3 \to (Y) + NO + H_2O$
$(Y) + Na_2S_2O_3 (\text{excess}) \to (Z) + NaNO_3$
Identify $(W)$ to $(Z)$.

Which of the following is a class of $Bryophytes$?

Current $I$ flows through a long conducting wire bent at right angles as shown in the figure. The magnetic field at a point $P$ on the right bisector of the angle $XOY$ at a distance $r$ from $O$ is