If the tangent at point $(1, 2)$ on the curve $y = ax^2 + bx + \frac{1}{2}$ is parallel to the normal at $(-2, 2)$ on the curve $y = x^2 + 6x + 10$,then:

The quantum numbers $+1/2$ and $-1/2$ for the electron spin represent:

Which hormone is produced by the placenta?

$A$ Zener diode,having a breakdown voltage equal to $15\,V,$ is used in a voltage regulator circuit as shown in the figure. The current through the diode is ........ $mA$.

$A$ small fish $0.4\, m$ below the surface of a lake is viewed through a simple converging lens of focal length $3\, m$. The lens is kept at $0.2\, m$ above the water surface such that the fish lies on the optical axis of the lens. The image of the fish seen by the observer will be at (given $\mu_{water} = 4/3$):

The midpoint of the chord $4x - 3y = 5$ of the hyperbola $2x^2 - 3y^2 = 12$ is