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If the tangent drawn at the point $P(3 \sqrt{2}, 4)$ on the hyperbola $\frac{x^2}{9}-\frac{y^2}{16}=1$ meets its directrix at $Q(\alpha, \beta)$ in fourth quadrant, then $\beta=$
A body of mass 500 g is falling from rest from a height of 3.2 m from the ground. If the body reaches the ground with a velocity of $6 \mathrm{~ms}^{-1}$, then the energy lost by the body due to air resistance is (Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )
The energy associated with electron in first orbit of hydrogen atom is $-2.18 \times 10^{-18} \mathrm{~J}$. The frequency of the light required (in Hz ) to excite the electron to fifth orbit is ( $h=6.6 \times 10^{-34} \mathrm{Js}$ )
If the equations $x^2+p x+2=0$ and $x^2+x+2 p=0$ have a common root, then the sum of the roots of the equation $x^2+2 p x+8=0$ is
If the length of a rod is measured as 830600 mm , then the number of significant figures in the measurement is
In $\mathrm{Sr}(Z=38)$, the number of electrons with $l=0$ is $x$, number of electrons with $l=2$ is $y \cdot(x-y)$ is equal to ( $l=$ Azimuthal quantum number)