$A$ pair of perpendicular straight lines passes through the origin and also through the point of intersection of the curve $x^2+y^2=4$ with $x+y=a$. The set containing the value of $a$ is

The transformed equation of $x^2+y^2=r^2$ when the axes are rotated through an angle $36^{\circ}$ is

Graphite is a soft solid lubricant and is extremely difficult to melt. What is the reason for this behavior of graphite?

$A$ convex lens of focal length $0.15 \ m$ is made of a material of refractive index $\frac{3}{2}$. When it is placed in a liquid,its focal length increases by $0.225 \ m$. The refractive index of the liquid is

$A$ uniform rope of length $L$ and mass $m_1$ hangs vertically from a rigid support. $A$ block of mass $m_2$ is attached to the free end of the rope. $A$ transverse pulse of wavelength $\lambda_1$ is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is $\lambda_2$. The ratio $\lambda_2/\lambda_1$ is

Which of the following oxides reacts with both $HCl$ and $NaOH$?