$A$ pair of perpendicular lines passes through the origin and also through the points of intersection of the curve $x^2+y^2=4$ with $x+y=a$,where $a>0$. Then $a$ is equal to

The potential energy of a particle of mass $m$ is given by,$U(x) = \begin{cases} E_0 & 0 \leqslant x \leqslant 1 \\ 0 & x > 1 \end{cases}$. $\lambda_1$ and $\lambda_2$ are the de-Broglie wavelengths of the particle when $0 \leqslant x \leqslant 1$ and $x > 1$ respectively. If the total energy of the particle is $2 E_0$,the ratio $\frac{\lambda_1}{\lambda_2}$ will be

If the best and the worst paper never appear together,then in how many ways can six examination papers be arranged?

For the given figure,if the block remains in an equilibrium position,find the frictional force between the block and the wall in $N$.

The curve satisfying the differential equation,$ydx - (x + 3y^2) dy = 0$ and passing through the point $(1, 1)$,also passes through the point

For $x \in \mathbb{R}$,the least value of $\frac{x^2-6x+5}{x^2+2x+1}$ is