If $\tan A$ and $\tan B$ are the roots of the quadratic equation $x^2-px+q=0$,then $\sin^2(A+B)$ is equal to

If the cold junction is held at $0^{\circ} C$,the thermo emf $V$ of a thermocouple varies as $V = 10 \times 10^{-6} t - \frac{1}{40} \times 10^{-6} t^2$,where $t$ is the temperature of the hot junction in $^{\circ} C$. The neutral temperature and the maximum value of thermo emf are respectively:

If $f(x) = \frac{x}{1+|x|}$,for $x \in \mathbb{R}$,then $f^{\prime}(0)$ is equal to :

Consider the following reactions at $1000\,^oC$:
$(I)$ $Zn_{(s)} + \frac{1}{2}O_{2(g)} \rightarrow ZnO_{(s)}; \Delta G^o = -360\,kJ\,mol^{-1}$
$(II)$ $C_{(s)} + \frac{1}{2}O_{2(g)} \rightarrow CO_{(g)}; \Delta G^o = -460\,kJ\,mol^{-1}$
Choose the correct statement at $1000\,^oC$.

$A$ current-carrying coil is placed with its axis perpendicular to the $N-S$ direction. Let the horizontal component of the earth's magnetic field be $H_0$ and the magnetic field inside the loop be $H$. If a magnet is suspended inside the loop,it makes an angle $\theta$ with $H$. Then $\theta =$

$A$ ball of mass $0.5\, kg$ moving with a velocity of $2\, m/s$ strikes a wall normally and bounces back with the same speed. If the time of contact between the ball and the wall is $1\, ms$,the average force exerted by the wall on the ball is ........ $N$.