Two substances $A$ and $B$ of equal mass $m$ are heated at a uniform rate of $6 \, cal \, s^{-1}$ under similar conditions. $A$ graph between temperature and time is shown in the figure. The ratio of heat absorbed $H_A/H_B$ by them for complete fusion is

The locus of the centre of the circle,which cuts the circle $x^2+y^2-20x+4=0$ orthogonally and touches the line $x=2$,is

If $5x - 12y + 10 = 0$ and $12y - 5x + 16 = 0$ are two tangents to a circle,then the radius of the circle is

$A$ container of mass $m$ is pulled by a constant force $F$. Inside the container,a second block of the same mass $m$ is placed,connected to the wall by a massless spring of constant $k$. Initially,the spring is at its natural length. Find the velocity of the container at the instant when the compression in the spring is maximum for the first time.

The area of the region bounded by the curve $y=2x-x^2$ and the $X$-axis is

The number of solutions for the equation $x^2 - 5|x| + 6 = 0$ is