$A$ liquid cools from $50^{\circ}C$ to $45^{\circ}C$ in $5 \ minutes$ and from $45^{\circ}C$ to $41.5^{\circ}C$ in the next $5 \ minutes$. The temperature of the surrounding is ......... $^{\circ}C$.

The equation of the directrix of the parabola ${y^2} + 4y + 4x + 2 = 0$ is

$A$ car $P$ approaching a crossing at a speed of $10 \, m/s$ sounds a horn of frequency $700 \, Hz$ when $40 \, m$ in front of the crossing. The speed of sound in air is $340 \, m/s$. Another car $Q$ is at rest on a road which is perpendicular to the road on which car $P$ is reaching the crossing. The driver of car $Q$ hears the sound of the horn of car $P$ when he is $30 \, m$ in front of the crossing. The apparent frequency heard by the driver of car $Q$ is ...... $Hz$.

The plant body is differentiated into which of the following parts?

The equation of the common tangent to the circle $x^2 + y^2 = 2$ and the parabola $y^2 = 8x$ is

If one of the lines given by the pair of lines $3x^2 + axy - 2y^2 = 0$ makes an angle of $60^{\circ}$ with the $x$-axis,then $a = $