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Questions Related to maths

Multiple choice maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

Let $A$ be the angle between the minute and the hour hand at $6$ p.m. and $B$ be the angle between them at $12$ a.m. Then which of the following statements is true?

  1. $A < B$
  2. $A > B$
  3. $A=B$

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

At 6 p.m., the minute hand points at 12 and the hour hand points at 6, forming a straight line, which is an angle of 180 degrees (A = 180). At 12 a.m., both the minute and hour hands coincide at 12, forming an angle of 0 degrees (B = 0). Therefore, A is greater than B.

Multiple choice maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

What friction of a clockwise revolution does the hour hand of a clock turn through, when it goes from

  1. $3$ to $9$
  2. $4$ to $7$
  3. $7$ to $10$
  4. $12$ to $9$
  5. $1$ to $10$
  6. $6$ to $3$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let us consider that for one hour the fraction of revolution is $\dfrac{1}{12}$

then :

(i)  $3$ to $9$ means $6$ hours

therefore; fraction of revolution $\dfrac{6}{12}=\dfrac{1}{2}$

(ii)  $4$ to $7$ means $3$ hours

therefore; fraction of revolution $\dfrac{3}{12}=\dfrac{1}{4}$  

(iii)  $7$ to $10$ means $3$ hours

therefore; fraction of revolution $\dfrac{3}{12}=\dfrac{1}{4}$

(iv)  $12$ to $9$ means $9$ hours

therefore; fraction of revolution $\dfrac{9}{12}=\dfrac{3}{4}$

(v)  $1$ to $10$ means $9$ hours

therefore; fraction of revolution $\dfrac{9}{12}=\dfrac{3}{4}$

(vi)  $6$ to $3$ means $9$ hours

therefore; fraction of revolution $\dfrac{9}{12}=\dfrac{3}{4}$

Multiple choice maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

At what time between $2$ and $3$ the acute angle between the hour hand and the minute hand will be $50^{o}$

  1. $2:20$
  2. $2:25$
  3. $2:35$
  4. $2:40$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The formula for the angle between clock hands is |30H - 5.5M|. For 2:20, |30(2) - 5.5(20)| = |60 - 110| = 50 degrees. This matches the requirement.

Multiple choice maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

The angle between the minute hand and the hour hand of a clock when the time is 3:30 in degree is

  1. 90

  2. 09

  3. 88

  4. 75
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Angular speed of hour hand $= 30degree \,per\, hour. =0.5$ degree/minute.

In $30$ minutes , the angle swept by hour hand is $30\times 0.5 = 15$ degree.

At $3:30$ , the minute hand is at number $6$.

At $3:00$ the hour hand was at number $3$.

Now it has moved $15$ degree.

Hence the angle between the two is $\left(90 -15\right) = 75$ degree.
Multiple choice maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

The angle between the minute hand and the hour hand of a clock when the time is 4:20 in degree is:

  1. 20

  2. 30

  3. 10

  4. 80
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
The speed of hour hand is ( $30$ degree per hour) ${0.5}^{\circ}$ per minute.

The speed of minute hand is ($360$ degree per hour) ${6}^{\circ}$ per minute.

Relative to hour hand the speed of minute hand is $6-0.5 = {5.5}^{\circ}$per minute.

At $4$ O clock , hour hand is at $4$ and minute hand is at $12$.

Angle between them is ${120}^{\circ}$.

Keeping hour hand at $4$ , minute hand moves $20\times 5.5 = {110}^{\circ}$, in $20$ minutes.

Angle between them is ${120}^{\circ}-{110}^{\circ}={10}^{\circ}$.

Multiple choice maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

At what time between 4 and 5, will the hands of a clock coincide?

  1. 15.81 min

  2. 21.81min

  3. 23.81 min

  4. 33.48 min
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
We know minute hand of a clock covers ${360}^{\circ}$ in $60\ min$ or ${6}^{\circ}$ in $1$ minute and hour hand of a clock covers ${360}^{\circ}$ in $12\ hrs$ or ${30}^{\circ}$ in $1$ hour or $.5$ degree in $1$ min.

So at $4:00$ the minute hand has covered $0$ degrees and hour hand has covered $120$ degrees

Now let time after which these two coincide be $x$ min.

So hour hand covers $120+\dfrac{x}{2}$ upto that time and minute hand covers $6x$ degrees upto that time when they coincide the angles should be same

So, $120+\dfrac{x}{2}= 6x$

Solving we get $6x-\dfrac{x}{2}=120$

$\Rightarrow\,\dfrac{12x-x}{2}=120$

$\Rightarrow\,11x=240$

$\Rightarrow\,x=\dfrac{240}{11}$minutes

$\therefore\,x=21.81\ mins$
Multiple choice maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

Angle between the minutes hand of a clock and hour hand when the time is 7 : 20 am is 

  1. $\displaystyle 80^{\circ}$
  2. $\displaystyle 100^{\circ}$
  3. $\displaystyle 120^{\circ}$
  4. $\displaystyle 140^{\circ}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

At 7:20, the minute hand is at 4 (20 minutes). The hour hand has moved past 7 by 20/60 of the way to 8. Hour hand position = 7 + 20/60 = 7.33. Angle = |(30 * 7.33) - (6 * 20)| = |220 - 120| = 100 degrees.