Which of the following hydrides is the least stable?

If the area of the triangle formed by the pair of lines $8x^2 - 6xy + y^2 = 0$ and the line $2x + 3y = a$ is $7$,then $a$ is equal to

Let $P(6, 3)$ be a point on the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$. If the normal at point $P$ intersects the $x$-axis at $(9, 0)$,then the eccentricity of the hyperbola is:

If \(x_1\) be the size of the magnified image and \(x_2\) the size of the diminished image in Lens Displacement Method, then the size of the object is :

The amplitude of a damped oscillator decreases to $0.9$ times its original magnitude in $5\,s$. In another $10\,s$ it will decrease to $\alpha$ times its original magnitude,where $\alpha$ equals

The objective and eyepiece of an astronomical telescope are double convex lenses with refractive index $1.5$. When the telescope is adjusted to infinity,the separation between the two lenses is $16 ~cm$. If the space between the lenses is now filled with water (refractive index $4/3$) and the telescope is again adjusted for infinity,then the present separation between the lenses is: (in $~cm$)