** Key facts:
**Generally there are four components in a clock

**(ii)** **hour dipping** , the dipping needle is slightly shorter than the minute dipping and it expresses the time as if the hour of needle is 4 ‘and the need for minute ’12 ‘, Then it will be indicative of the fact that the clock is ringing 4 times.

** (iii) minute dipping **minute dipping is slightly larger than the dipping needle and plays a supporting role in conveying the certainty of time together with the hourly needle, such as if the hours If the needle is on ‘6’ and the needle of minute is at ’12 “, then it will be indicative that ‘6’ is ringing in the clock. But if the hourly needle is slightly ahead of ‘6’ and the minute If the needle is on ‘3’, then it will be indicative that at the clock at just 6 Are happening.

**(iv) Second dipping ** Usually the needle of the second is slightly larger and thin than the minute dipping. It plays the role of assistants in the deviation of both the hours and minutes. The measurement of the entire circumference of the clock dial is 360 °, that is, we can say that if a dipping clockwise moves from ’12’ to ’12 ‘then it is indicative that the needle is 360 ° Has traveled the path.

The measurement of the angle between any two adjacent digits of the clock is ‘300’, for example, the angle between ‘2’ and ‘3’ is ‘300’.

Deviation of degrees (in degrees) per minute is as follows

Second dipping ⇒ 360° per minute

Minute dipping ⇒ 6° per minute

Hour dipping ⇒ 1/2° per minute

Generally three types of questions are asked from this chapter

**TYPE 1
**

**Questions about systemization of letters**

Normally, the letters of the English alphabet, or the opposite alphabet, in the corresponding direction of the letters of the alphabet, in the direction of clock move or in the opposite direction of the clock move, instead of a fixed number of letters The questions related to this matter will be asked, the questions will be asked.

Now, let’s take a closer look at the format of the questions and its interpretive solution under the arrangement of the letters.

** Example 1. **If the letters on the clock dial are arranged in place of the letters of the English alphabet in such a way that the letter “G” comes in place of the number “2” 3 “instead of the letter ‘H’, and the sequence of change continues in the same way, what will be replaced in place of the number 12?

** (a) **S** (b) **Q

** Solution: **(b) According to the question we see that the letter ‘G’ is used for the letter “2”, then for the number 3, the letter ‘H’ of the English alphabet It has been used, similarly, for the number ‘4’, the letters of the English alphabet ‘.’ Will be used.**
**Therefore

2 ⇒ + 5 ⇒ 7

3 ⇒ + 5 ⇒ 8

Similarly, 12 ⇒ +5 ⇒ 17

Here we see that the numeric value is equal to the number and alphabet, so the numeric value of the letters used in the English alphabet for ’12 ‘will be (12 + 5) = 17 and we know that in the English alphabet 17 is the letter ‘Q’ with the numeric value.

Hence the desired letter ‘Q’ will be. .

** Example 2.** If the letters of the English alphabet are arranged in place of the digits located on the clock dial in place of the letter ‘U’ instead of the number ‘6’, the number ‘5 Let’s get the letter ‘R’ in place of it, similarly the letter ‘O’ comes in place of number ‘4’ and if the sequence of changes continues in the same way, then what is the place of the letter ‘1’? Will come

** (a) **G** (b) **F

**Solution:** (b)

6 ⇒ × 3 + 3 ⇒21

5 ⇒ x 3 + 3 ⇒ 18

4 ⇒ × 3 + 3 ⇒15

Similarly, 1 ⇒ × 3 + 3 ⇒ 6 = F

Here we are seeing that the number obtained by adding 3 in its three times to each digit, the alphabet used for the same number in alphabetical order has come for that number. Similarly, on adding 3 to three times of the number ‘1’, the number is 6 and the letter ‘F’ is in the sixth place in alphabetical order. So the desired letter will be ‘F’.

**TYPE 2
**

**Degree Based Questions**

The degree related questions are given at a specific time and on the basis of that exact time, the candidate has to decide how many degree of angle between the hour and minute needle is formed during the given time.

To easily solve such questions, please take a closer look at the key sources below. The minute here implies the number used in the place of minute dipping, such as – 20 minutes, 4.30 minutes, 6.35 minutes, 7 etc. If the minute needle is behind the hourly dipping

Desired degree = difference in number between minutes and hour × 30 ± min/2

Minutes given in question

If minute needle is ahead of the hour dipping

⇒ Now, the questions asked in this chapter for clarification of the above facts Carefully observe the questions and their interpretive solution.

**Example 1.** If there are 7 to 30 minutes in a clock, then how many degrees will be the angle between the hour and minute swings?

** (a) **120°** (b) **95°

** Solution: **(c) Time = 7:30

In this situation the position of hour and minute needles will be on the needle of 6 and the dipping need will be between 7 and 8.

Hour dipping distracts ½° in one minute

Deviation of hourly dipping in 30 minutes = 1/2 × 30 = 15°

I.e. hour dipping will be 7 to 15°.

The difference in points from the position of the needles = 7-6 + 15° = 1 + 15°

The difference of 1 = 30°

1 + 15° = 30° + 15° = 45°

Therefore the desired angle = 45° formula as intended = (7-6) × 30° + 30°/2

= 1 × 30° + 15° = 30 + 15° = 45°

** Example 2. **If there are 5 to 45 minutes in a clock, how many degrees of angle between minute and hour swings will be made at that time?

** (a) **97½°** (b) **120°

** Solution: **(a) Time = 5: 45 In this situation the position of hour and minute needles will be on the needle 9-minute and the dipping need will be above 5. Also the minute needle is ahead of the hour dipping.

So now with the formula,

Expected angle = (9-5) × 30° – 45/2

= 120° – 22½° = 97½°

** Example 3. **If you are taking 12 to 20 minutes in a clock, how many degrees of angle between hours and minutes will be made at that time?

** (a) **110°** (b) **127°

** Solution: **(a) Time = 12: 20

The hour dipping will be only 12 o’clock at 20 minutes and the needle of minute will be 4. Also the minute needle will be ahead of the hourly dipping.

By formula, intended angle = (4-0) × 30 – 20/2

120 – 10 = 110 °

** ⇒ Note – **When the hour is 12 on the dipping, then counting it as ‘0’, we find the difference in the number between the minutes and the hours.

** Example 4. **If there are 4 hours and 47 minutes in a clock, how many degrees of angle between hours and minutes will be made at that time?

** (a) **97½°** (b) **83½°

** Solution: **(d) According to the formula, angle

** Example 5. **If you are getting 9 to 22 minutes in a clock, how many degrees of angle between hours and minutes will be made at that time?

** (a) **119°** (b) **145°

Solution: (C) Expected angle

**TYPE 3 **

** Questions about plane mirrors **

The plane mirror is divided into two sections based on its position.

** (i) vertical mirror – **A position of plane mirror placed in a vertical position at an angle of 90 ° relative to any horizontal plane, such a mirror Is called a vertical mirror. The reflection of the thing placed in front of such a mirror appears to be overturned, that is, the part of the object in the original pattern is on the left, in the image it is on the right side and the portion on the right is transferred to the left in the image. Carefully observe the diagrams below to understand it well.

In the diagram given here, we see that the hourly dipping in the original pattern is located at ‘8’ on the left side of the clock but the mirror ‘AB’, but it seems to be on the right side of the clock as a fictitious model, while the minute Since the needle is perpendicular, therefore, it seems to be stable in its own place even if it is reversed.

Actually, this certainly affirms that in the perpendicular mirror the left part of the object appears to be transferred to the right and the left part.

**(ii) Horizontal Mirror –** A horizontal mirror that is positioned in a parallel position of plane mirror such as a horizontal plane is called a horizontal mirror. The image of the object placed in front of such a mirror appears to be inverted, i.e. the shape of the top and bottom below the top, but the left part will remain left and the right part will remain right. Observe the diagram below to understand it well.

Here we are seeing that in the original pattern of the above diagram, the dipping needle is slightly lower than 9 on the left side of the clock and the dipping needle is located on the right side of the clock from 3 to one place above 2 but in the form of this hypothetical model in the mirror AB The lower the dipping of ‘9’ on the left side was as low as the ‘9’ and above the ‘dipping’ of the dual till 3 ‘above the right hand side, it appears to be as low as’ 3′ in the hypothetical pattern. .Thus, there is definitely a confirmation that in the horizontal mirror, the left part of the object is reversed in the right and right sides relative to 9 and 3.

**Major rules for resolving vertical mirror questions
**To solve the questions related to the mirror vertically, a specific time base 12:00 should be used as the following form.

If the time given is real time

Mirrored (hypothetical) time = 12:00 – real time

Like – if the real time = 5:30 then the hypothetical time = 12:00 – the actual time = 12:00 – 5:30 = 6:30

If the time given is a hypothetical time, then the real time = 12: 00 – the hypothetical time

As if hypothetical time = 4: 15

Real time = 12:00 – 4: 15 = 7:45

Now, let us carefully review some of the key examples related to this.

** Example 1. **In the triloki clock, marked marks have been marked in place of the digits. If it appears to be reflected in the reflected image of a mirror 12 to 35 minutes in the form of time, then tell how much time was actually happening at that time in his watch?

** (a) **1: 35** (b) **11:25

** Solution: **(b) Real-time = 24: 00 – 12: 35 = 11: 25

** ⇒ Note** – It is necessary to note that it is taken from hour if it is necessary to borrow at the time of the minute in relation to time. The time taken taken is always taken as 60 minutes ie one hour. Hours in this situation are less than 1 hour after its original condition. In addition to this, if the time limit is reduced from 12:00 pm to 00 00, or if you get a negative hour, then the time base will not be kept at 12: 00 p.m., but time base for this is 24: 00 Assuming the time will be reduced by giving reasonable time. Like -24: 00 – 12: 35 = 11: 25

** Example 2. **Dots are marked on the number of points on a clock. If this clock is taking 6 to 20 minutes, then when it will be placed in front of a mirror, how long will it be in the image of the mirror?

** (a) **5:40** (b) **4: 55

** Solution: **(a) Reflected time = 12:00 – 6: 20 = 5:40

** Major rules for solving horizontal mirrors / water-related reflections **

** I. **Usually the minute dipping 60 and hour dipping becomes distracted from its place ½ ° per minute. Like, if you are getting 7 to 30 minutes in a clock,

In this situation, the dipping points of the hour will be 7 to 15 ° above (i.e. between 7 and 8) and the minute dipping position will be ‘6’. But in the related questions of the horizontal mirror, there should not be consider the diversion of hourly dipping because in such a situation, real time can not be accurately determined by the reflected time or reflected time from the real time. Carefully study the frequency of the clock given below for clarification of the above facts.

Here we are seeing that in the actual or fictitious situation, the hourly sign of ‘7’ to 15 ° above i.e. in ‘OK’ and ‘8’ In place of ‘6’, however, the dipping needle in reflected time is reversed on the basis of the physical condition of real time, between 10 and 11, and the minute needle is described in place of 12. If considered, the horizontal mirror shape in the case of 7 to 30 minutes should definitely be in accordance with the reflected time pattern above but it is against the principle of time. That is because the minute needle is on ’12 ‘and the dipping needle between ’10’ and ’11 ‘is exactly the opposite of the principle of deviation of hour and minute screws which is not possible in any situation. Therefore, on the basis of the above facts we arrive at the conclusion that in the questions related to the horizontal mirror = 8:20, the need for hourly dipping should never be considered while distracting with the principle of time.

**II. **The image of the object in the horizontal mirror is always made upside down, that is, the mirror in the upper part of the object, ‘lower part’ and ‘lower part’, are reflected in the form of ‘upper part’.

Under the horizontal mirror, the original shape is reversed in the image, but its left and right parts do not change with each other, which confirms that the image in the horizontal mirror only appears inverted.To solve the horizontal issues, firstly consider ‘9’ and ‘3’ as the time base, on which we can easily change the reflected time or any reflection time in ‘real time’ You can determine the intended time.

In the above figure, we are seeing that the clock is taking 8 to 20 minutes and in this situation, the time of dipping of the time is based on the base ‘9’ one place below ‘8’ and the minute dipping time base 3 ‘one place At the bottom 4 is but the hour of dipping on the mirror is present at the base ‘9’ above one place above 10 and the dipping time of the minute time base 3 ‘one place above’ 2 ‘.

Therefore, on the basis of these facts, it is confirmed that time is as below the real time from the base 9, the higher the time in the mirror and the above time from the base ‘9’, the higher is in the mirror. It appears to be downconverted and precisely this factor also applies in the perspective of time base ‘3’ i.e. the same time as the needle of the time base ‘3’, the same as above / below the mirror Cover Under appears. –

Now let us carefully review the format of these related questions.

**Example 1. **If you look at Ghauri in a horizontal mirror, the time reflected in its clock reflects time of 10 to 20 minutes, then tell how real time is happening in its clock, Bindukinde marks in place of?

** (a) **10:20** (b) **8: 10

** Solution:** (b) Reflect time = 10:20

In the horizontal mirror, the position of the hour of dipping on the time-base = ‘9’ above one place above ’10 “and the position of minute dipping =” 3 “from one place down to 4 ‘

Therefore, in the real-time, the location of the hour of dipping needle = ‘9 “below the position of’ 8 ‘and the minute dipping position =” 3 “at one place above’ 2 ‘

Thus, real time = 8: 10

** Example 2. **In the clock of the moon, there is a marked sculpture in place of points. If his clock is just 12 o’clock in the clock, then seeing in a horizontal mirror, how much would he have seen in the clock?

** (a)** 6:30** (b) **12:00

** Solution: **(a) 12 in the actual clock and 12 hours dipping and minute dipping will be present on both ’12 ‘.

So when it is seen in a horizontal mirror, the clock and minute needle will be present on both ‘6’.

Hence the intended time in the horizontal mirror = 6: 30

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