At a certain place,the angle of dip is $60^{\circ}$ and the horizontal component of the earth's magnetic field $(B_H)$ is $0.8 \times 10^{-4} ~T$. The earth's overall magnetic field is

If the transformed equation of the equation $2x^2+3xy-2y^2-17x+6y+8=0$ after translating the coordinate axes to a new origin $(\alpha, \beta)$ is $aX^2+2hXY+bY^2+c=0$,then $3\alpha+c=$

An iron load of $2 \ kg$ is suspended in air from the free end of a sonometer wire of length $1 \ m$. $A$ tuning fork of frequency $256 \ Hz$ is in resonance with $\frac{1}{\sqrt{7}}$ times the length of the sonometer wire. If the load is immersed in water,the length of the wire in metres that will be in resonance with the same tuning fork is (Specific gravity of iron $= 8$)

When alcohol vapor is passed over heated reduced copper $(Cu)$,the alcohol is converted into an alkene. Which type of alcohol is this?

The velocity of a particle which starts from rest is given by the following table. The total distance travelled (in metre) by the particle in $10 \ s$,using the Trapezoidal rule is given by:

$t$ (in second)	$0$	$2$	$4$	$6$	$8$	$10$
$v$ (in m/s)	$0$	$12$	$16$	$20$	$35$	$60$

$KMnO_4$ reacts with $KI$ in basic medium to form $I_2$ and $MnO_2$. When $250 \ mL$ of $0.1 \ M \ KI$ solution is mixed with $250 \ mL$ of $0.02 \ M \ KMnO_4$ in basic medium,what is the number of moles of $I_2$ formed?