At what time between 10,,O'clock and 11,, | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(b)

Exactly at $10\,O'clock$ the hour hand has travelled $300^{\circ}$ from $120^{\prime}$ 'clock.

One hour $=60$ minute.

One minute

Vedclass · Accepted Answer

$10h \,9m \,14s$

Vedclass · Answer

(b)

Exactly at $10\,O'clock$ the hour hand has travelled $300^{\circ}$ from $120^{\prime}$ 'clock.

One hour $=60$ minute.

One minute hand moves $1^{\circ}$ and hour clock hand move $\left(\frac{30}{360}ight)^{\circ}=\left(\frac{1}{12}ight)^{\circ}$

Assuming we have made it to 10 O'clock and now the hour and the minute hand start moving spontaneously.

If the hands of the watch are symmetric with vertical line.

Supposing this happens when $x$ minutes have passed $x$ minutes $=(6 x)^{\circ}$ have been covered our hour hand would cover.

On subtracting this from $360^{\circ}$ to find the angle from 12 O'clock anti-clockwise, we get

$360^{\circ}-\left(300+\frac{x}{2}ight)^{\circ}=\left(60-\frac{x}{2}ight)^{\circ}$

So, they are symmetric.

$	herefore \quad 60-\frac{x}{2}=6 x$

$\Rightarrow \quad x=\left(\frac{120}{13}ight)^{\circ}=9min\,13.8s$

$	herefore 	ext { Time }=10 h\,9m\,14s$

At what time between $10\,\,O'clock$ and $11\,\,O 'clock$ are the two hands of a clock symmetric with respect to the vertical line (give the answer to the nearest second)?

Similar Questions

If the arcs of the same lengths in two circles subtend angles $65^{\circ}$ and $110^{\circ}$ at the centre, find the ratio of their radii.

Find the value of the trigonometric function $\sin 765^{\circ}$

If $\cot x=-\frac{5}{12}, x$ lies in second quadrant, find the values of other five trigonometric functions.

If $A + B + C = \pi $ and $\cos A = \cos B\,\cos C,$ then $\tan B\,\,\tan C$ is equal to

If $\tan A + \cot A = 4,$ then ${\tan ^4}A + {\cot ^4}A$ is equal to