$A$ microscope consists of an objective of focal length $1.9 \ cm$ and an eyepiece of focal length $5 \ cm$. The two lenses are kept at a distance of $10.5 \ cm$. If the image is to be formed at the least distance of distinct vision $(25 \ cm)$,the distance at which the object is to be placed before the objective is: (in $cm$)

If the circle $x^2+y^2=a^2$ intersects the hyperbola $xy=c^2$ in four points $(x_i, y_i)$,for $i=1, 2, 3, 4$,then $y_1+y_2+y_3+y_4$ equals

When $X$ amperes of current is passed through molten $AlCl_3$ for $96.5 \ s$,$0.09 \ g$ of aluminium is deposited. What is the value of $X$?

Two cylinders $A$ and $B$ fitted with pistons contain equal number of moles of an ideal monoatomic gas at $400 ~K$. The piston of $A$ is free to move while that of $B$ is held fixed. Same amount of heat energy is given to the gas in each cylinder. If the rise in temperature of the gas in $A$ is $42 ~K$,the rise in temperature of the gas in $B$ is (in $~K$)

The coordinate axes are rotated through an angle $135^{\circ}$. If the coordinates of a point $P$ in the new system are known to be $(4, -3)$,then the coordinates of $P$ in the original system are

Heroin is chemically known as $.........$.