Find the value$(s)$ of $k$ such that the distance between the two parallel lines represented by $(x-2y)^2 + k(x-2y) = 0$ is $3$ units.

If $(1, a)$ and $(b, 2)$ are conjugate points with respect to the circle $x^2+y^2=25$,then $4a+2b$ is equal to

When an object of height $12 \ cm$ is placed at a distance from a convex lens, an image of height $18 \ cm$ is formed on a screen. Without changing the positions of the object and the screen, if the lens is moved towards the screen, another clear image is formed on the screen. The height of this image is (in $cm$)

Two identical bodies have temperatures $277^{\circ} C$ and $67^{\circ} C$. If the surroundings temperature is $27^{\circ} C$, the ratio of loss of heats of the two bodies during the same interval of time is (approximately) (in $19 : 1$)

Two particles $A$ and $B$ initially at rest move towards each other under a mutual force of attraction. At the instant when the speed of $A$ is $v$ and the speed of $B$ is $2v$,the speed of the centre of mass of the system is:

Which of the following sets of variables gives a straight line with a negative slope when plotted? ($P =$ vapour pressure,$T =$ Temperature in $K$)