## Exercise 17 B

Question 1

**In the given fig. Q1 , which setting will the pointer face after it turns **

**(i) 45º clockwise from normal ?**

Sol :

A circle consist of total angle of 360º . Now lets find the angle between two options .

And to do so , we take

= 45º

According to question as we move from normal in clockwise direction 45º , then pointer face normal .

**(ii) 135º anti-clockwise from off ?**

Sol :

As we already know angle between two options is .

So , if we divide 135º by 45º

Which means from off position pointer have to move 3 steps in anti-clockwise direction .

First step = off→very hot

Second step = very hot→hot

Third step = hot→warm

So , at last pointer stop at warm position .

**(iii) 360º anti-clockwise from hot ?**

Sol :

We know angle between two options is

So , if we divide 360º by 45º

Which means from hot position pointer have to move 8 steps in anti-clockwise direction .

First step = hot→warm

Second step = warm→normal

Third step = normal→cool

Fourth step = cool→cold

Fifth step = cold →very cold

Sixth step = very cold →off

Seventh step = off →very hot

Eighth step = very hot →hot

So , at last pointer stop at hot position .

**(iv) 270º clockwise from cold ?**

Sol :

We know angle between two options is

So , if we divide 270º by 45º

Which means from cold position pointer have to move 8 steps in anti-clockwise direction .

First step = cold→cool

Second step = cool→normal

Third step = normal→warm

Fourth step = warm→hot

Fifth step = hot →very hot

Sixth step = very hot → off

So , at last pointer stop at off position .

Question 2

**There are markings as shown on a domestic appliance . Through how many degrees does the pointer turn when it move in the fig.Q1**

**(i) clockwise from off to cold**

Sol :

Between two options , angle is

And moving from off to cold option in clockwise direction there are total 2 steps i.e.

First step = off→very cold

Second step = very cold→cold

And single step covers 45º , then 2 steps cover 2×45º = 90º

**(ii) anti-clockwise from hot to warm**

Sol :

Between two options , angle is

And moving from hot to warm option in anti-clockwise direction there are total 1 steps i.e.

hot→warm

And single step covers 45º

**(iii) anti-clockwise from very cold to very hot**

Sol :

Between two options , angle is

And moving from very cold to very hot option in anti-clockwise direction there are total 2 steps i.e.

First step = very cold →off

Second step = off→ very hot

And single step covers 45º , then 2 steps cover 2×45º = 90º

**(iv) clockwise from warm to cool**

Sol :

Between two options , angle is

And moving from warm to cool option in clockwise direction there are total 6 steps i.e.

First step = warm→hot

Second step = hot→very hot

Third step = very hot→off

Fourth step = off→very cold

Fifth step = very cold →cold

Sixth step = cold → cool

And single step covers 45º , then 2 steps cover 6×45º = 270º

Question 3

**Answer the following questions related to a clock in the fig. Q3.**

**(i) When the seconds hand has moved from 12 to 6 , how many degrees has it turned through ?**

Sol :

As we know which means 30º per hours .

And from 12 to 6 we have 6 hours ,= 30º×6

= 180º

**(ii) When the seconds hand has moved from 6 to 8 , how many degrees has it turned through ?**

Sol :

As we know which means 30º per hours .

And from 6 to 8 we have 2 hours ,= 30º×2

= 60º

**(iii) What is the time on the clock when hour hand moves clockwise ?**

**(a) 60º from 6 O’ clock ?**

Sol :

As we know hour hand moves 30º per hour . So , on dividing 60º by 30º we get which means 2 hours

Which means 6 + 2 = 8 O’ clock is the answer

**(b) 180º from 10 O’ clock ?**

Sol :

As we know hour hand moves 30º per hour . So , on dividing 180º by 30º we get which means 6 hours

Which means 10 + 6 = 16 = 12 + 4 i.e at first hour hand moves from 10→12 then 12→4

4 O’ clock is the answer

**(c) 270º from 12 O’ clock ?**

Sol :

As we know hour hand moves 30º per hour . So , on dividing 270º by 30º we get which means 9 hours

Which means hour hand moves from 12 → 9

9 O’ clock is the answer

**(iv) Through how many degrees does the minute hand of a clock turn in **

**(a) 1 minute**

Sol :

As we know which means minute hand moves 6º per minutes .

So , in 1 minute it covers 6º

**(b) 8 minutes **

Sol :

As we know minute hand moves 6º per minutes . Then , in 8 minutes it covers 6×8 = 48º

**(c) **

Sol :

Firstly , lets convert hours to minutes . We know 1 hour = 60 minutes

on multiplying both sides by 3/4 we get

and as we know minute hand moves 6º per minutes . Then , in 45 minutes it covers 6×45 = 270º

**(d) **

Sol :

Firstly , we convert mixed fraction to improper fraction

Lets convert hours to minutes . We know 1 hour = 60 minutes

On multiplying both sides by 3/2 we get

and as we know minute hand moves 6º per minutes . Then , in 90 minutes it covers 6×90 = 540º

**(v) Through how many degrees does the hour hand of a clock turn in **

**(a) 1 minutes**

Sol :

which means hour hand moves 0.5º per minutes

So , in 1 minute it turns only 0.5º or

**(b) 10 minutes**

Sol :

which means hour hand moves 0.5º per minutes

So , in 10 minute it turns 10×0.5º = 5º

**(c) 30 minutes**

Sol :

which means hour hand moves 0.5º per minutes

So , in 30 minute it turns 30×0.5º = 15º

**(d) 2 hours **

Sol :

which means hour hand moves 30º per hour

So in 2 hour , the hour hand moves 2×30 = 60º

Question 4

**In the given Fig. Q.4 , find the number of degrees , when we turn in a clockwise directions**

(i) From NW to SW

Sol :

(ii) From N to S

Sol :

(iii) From N to E

Sol :

(iv) From NE to W

Sol :

Question 5

Look at Fig. Q.5 . The circle is divided into 16 equal parts . Find

(i) ∠A_{1}OA_{2}

(ii) ∠A_{1}OA3

(iii) ∠A_{1}OA5

(iv) How many times is the angle ∠A_{1}OA12 of the angle ∠A_{1}OA_{2 }?

(v) How many times is the angle ∠A_{1}OA4 of the angle ∠A_{1}OA2 ?

(vi) What fraction of the whole revolution is the angle ∠A_{5}OA_{7} ?

Sol :

Question 6

**Add the following .**

**(i) 36º 45′ and 56º 87′**

**(ii) 47º 28′ 55” and 27º 35′ 49”**

Question 7

**Subtracting the following**

**(i) 39º 39′ from 50º 15′**

**(ii) 26º 31′ from 50º 8′**