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

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

Question

(B) Let $x$ be the number of minutes past $10\,	ext{O'clock}$.At $10\,	ext{O'clock}$,the hour hand is at $300^{\circ}$ from the $12\,	ext{O'clock}$

Vedclass · Accepted Answer

$10\,	ext{h } 9\,	ext{m } 14\,	ext{s}$

Vedclass · Answer

(B) Let $x$ be the number of minutes past $10\,	ext{O'clock}$.At $10\,	ext{O'clock}$,the hour hand is at $300^{\circ}$ from the $12\,	ext{O'clock}$ position.In $x$ minutes,the minute hand moves $6x^{\circ}$ from the $12\,	ext{O'clock}$ position.The hour hand moves $\frac{x}{2}^{\circ}$ in $x$ minutes,so its position is $(300 + \frac{x}{2})^{\circ}$ from $12\,	ext{O'clock}$.For the hands to be symmetric with respect to the vertical line (the $12-6$ line),the angle of the minute hand from $12\,	ext{O'clock}$ (clockwise) must equal the angle of the hour hand from $12\,	ext{O'clock}$ (counter-clockwise).The angle of the hour hand from $12\,	ext{O'clock}$ (counter-clockwise) is $360^{\circ} - (300 + \frac{x}{2})^{\circ} = (60 - \frac{x}{2})^{\circ}$.Setting these equal: $6x = 60 - \frac{x}{2}$.$12x = 120 - x$ $\Rightarrow 13x = 120$ $\Rightarrow x = \frac{120}{13} \approx 9.2307\,	ext{minutes}$.$0.2307 	imes 60 \approx 13.84\,	ext{seconds}$,which rounds to $14\,	ext{seconds}$.Thus,the time is $10\,	ext{h } 9\,	ext{m } 14\,	ext{s}$.

At what time between $10\,\text{O'clock}$ and $11\,\text{O'clock}$ 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 algebraic sum of the distances from the points $(2,0)$, $(0,2)$, and $(1,1)$ to a variable straight line is zero, then the line passes through the fixed point:

$O$ is the origin and $A$ is the point $(3,4)$. If a point $P(x,y)$ moves such that the line segment $OP$ is always parallel to the line segment $OA$,then the equation of the locus of $P$ is:

Suppose we have to cover the $XY$-plane with identical tiles such that no two tiles overlap and no gap is left between the tiles. Suppose that we can choose tiles of the following shapes: equilateral triangle,square,regular pentagon,regular hexagon. Then,the tiling can be done with tiles of

Ten ants are on the real line. At time $t=0$,the $k$-th ant starts at the point $k^2$ and,travelling at a uniform speed,reaches the point $(11-k)^2$ at time $t=1$. The number of distinct times at which at least two ants are at the same location is

If a point $(x, y) = (\tan \theta + \sin \theta, \tan \theta - \sin \theta)$,then the locus of $(x, y)$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module