This is a $1^\infty$ indeterminate form. Take logarithm:

$\ln p = \lim_{x\to0^+}\dfrac{\ln(1+\tan^2\sqrt{x})}{2x}$

Let $t=\sqrt{x}$, so $x=t^2$, $x\to0^+$ means $t\to0^+$:

$= \lim_{t\to0^+}\dfrac{\ln(1+\tan^2 t)}{2t^2} = \lim_{t\to0^+}\dfrac{\tan^2 t}{2t^2} = \dfrac{1}{2}$

(using $\ln(1+u)\approx u$ for small $u$ and $\lim_{t\to0}\frac{\tan t}{t}=1$)

By time-reversal symmetry: the last $t$ seconds of ascent is equivalent to free fall from rest for $t$ seconds.

Distance $= \dfrac{1}{2}gt^2$

To solve this, you have to break it down into the same "Select then Arrange" flow:

1. Selection ($C$): * We need 3 Physics books. Since P1 is mandatory, we only need to choose 2 more from the remaining 4. Calculation: $\binom{4}{2} = 6$.

   • We need 2 Math books from 4. Calculation: $\binom{4}{2} = 6$.

   • Total selection combinations: $6 \times 6 = 36$.

2. Arrangement ($P$): * We have 5 books (3 Physics, 2 Math).

   • The "Gap Method" is best for the constraint "Math books not together."

   • First, arrange the 3 Physics books: $3! = 6$ ways.

   • This creates 4 possible gaps ( _ P _ P _ P _ ).

   • We must place the 2 Math books into these 4 gaps: $^4P_2 = 12$ ways.

   • Total arrangements per selection: $6 \times 12 = 72$.

3. Final Calculation:

   • $36 \text{ (selections)} \times 72 \text{ (arrangements)} = 2592$.

Correct Answer: D (1200 or more)

The apparent dip $\delta'$ is the angle of dip observed when the dip circle is not oriented in the magnetic meridian (tilted at angle $\phi$ from the meridian).

The relationship is: $\tan\delta' = \frac{\tan\delta}{\cos\phi}$, where $\delta$ is the true dip.

Since $\cos\phi \leq 1$: $\tan\delta' \geq \tan\delta$, so $\delta' \geq \delta$.

Therefore true dip is always less than or equal to apparent dip. They are equal only when $\phi = 0°$ (dip circle in the meridian).