When a weight of $10\, kg$ is suspended from a copper wire of length $3\, m$ and diameter $0.4\, mm$,its length increases by $2.4\, cm$. If the diameter of the wire is doubled,then the extension in its length will be ........ $cm$.

Let $P(a\sec \theta, b\tan \theta)$ and $Q(a\sec \varphi, b\tan \varphi)$,where $\theta + \varphi = \frac{\pi}{2}$,be two points on the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$. If $(h, k)$ is the point of intersection of the normals at $P$ and $Q$,then $k$ is equal to

Which of the following would produce a buffer solution when mixed in equal volumes?

$A$ wire elongates by $l \, mm$ when a load $W$ is hung from it. If the wire goes over a pulley and two weights $W$ each are hung at the two ends,the elongation of the wire will be (in $mm$)

If the lines $x^2+2xy-35y^2-4x+44y-12=0$ and $5x+\lambda y-8=0$ are concurrent,then $\lambda$ equals

When the momentum of a proton is changed by an amount $P_0$,the corresponding change in the de-Broglie wavelength is found to be $0.25\%$. Then,the original momentum of the proton was