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After Neil updated his cash book using the bank statement, which item would appear on the bank reconciliation statement (not in the updated cash book)?
Option B is correct.
Unpresented cheques are written and recorded in the cash book but not yet presented to the bank β they are timing differences shown on the reconciliation.
- A: Bank charges update the cash book.
- C: Credit transfers update the cash book.
- D: Cash book errors are corrected in the cash book.
If $-\dfrac{m}{19}$ is an even integer, which of the following must be true about $m$?
Let $-\dfrac{m}{19} = 2k$ for some integer $k$. Then $m = -38k$.
Since $k$ is any integer (positive, negative, or zero), $m$ can be negative, zero, or positive β so options A and B are not guaranteed.
$m = -38k = -2 \times 19 \times k$. This is always a multiple of 38, so $m$ is even β wait, that means $m$ is even. But wait: $m = -38k$, which is even. But we need to check: the question asks what must be true.
Actually re-examining: $m = -38k$, which is a multiple of 38 and thus even. But the answer is D: $m$ is an odd integer? Let's recheck.
$-\dfrac{m}{19}$ is even β $\dfrac{m}{19}$ is even β $m = 19 \times (\text{even}) = 19 \times 2j = 38j$. So $m$ is a multiple of 38, hence even. Answer: $m$ is an even integer (option D in the original, which maps to our option 4).
A projectile is fired at $45Β°$ to the horizontal. The elevation angle of the projectile at its highest point, as seen from the point of projection, is:
At max height $H = \dfrac{u^2}{4g}$; horizontal distance $= \dfrac{R}{2} = \dfrac{u^2}{2g}$
Elevation angle: $\tan\phi = \dfrac{H}{R/2} = \dfrac{u^2/(4g)}{u^2/(2g)} = \dfrac{1}{2}$
$\phi = \mathbf{\tan^{-1}\!\left(\dfrac{1}{2}\right)}$
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