The equation $16 x^2+y^2+8 x y-74 x-78 y+212=0$ represents:

If the direction cosines of two lines are such that $l+m+n=0$ and $l^2+m^2-n^2=0$,then the angle between them is:

Match the columns.

Column-$I$	Column-$II$
$(a)$ Parturition	$(p)$ Attachment of embryo to endometrium
$(b)$ Gestation	$(q)$ Release of egg from Graafian follicle
$(c)$ Ovulation	$(r)$ Delivery of Foetus from uterus
$(d)$ Implantation	$(s)$ Duration between pregnancy and birth
	$(t)$ Formation of zygote by fusion of egg and sperm

$A$ vessel contains oil (density $= 0.8 \, g/cm^3$) over mercury (density $= 13.6 \, g/cm^3$). $A$ homogeneous sphere floats with half of its volume immersed in mercury and the other half in oil. The density of the material of the sphere in $g/cm^3$ is

The cold junction of a thermocouple is maintained at $10\,^{\circ}C$. No thermo $e.m.f.$ is developed when the hot junction is maintained at $530\,^{\circ}C$. The neutral temperature is ................ $^{\circ}C$.

The value of the integral $\int_0^4 \frac{dx}{1+x^2}$ obtained by using the Trapezoidal rule with $h=1$ is