2

CLOCK
(PRACTICE SHEET)
1. What angle is made by minute hand in 29 sec ? 9. If the time in clock is 12 : 23. What is the time in
mirror?
feuV dh lqbZ 29 lsdaM esa fdrus fMxzh dks.k cuk;sxh\

r
;fn ?kM+h esa le; 12%23 gS rks niZ.k esa le; D;k gS\

Si
(a) 1740º (b) 2.9º
(c) 29º (d) 260º (a) 12 : 33 (b) 11 : 37
(c) 12 : 37 (d) 1 : 23
2. What angle is made by hour hand in 36 sec ?
10. Time in a clock is 3 : 13, what time will be appear in
?kaVs dh lqbZ 36 lsdaM esa fdrus fMxzh dks.k cuk;sxh\

et
water?
(a) 120º (b) 3º ,d ?kM+h esa le; 3 % 13 gS] ikuh esa dkSu&lk le; fn•kbZ nsxk\

je
 3   10   (a) 3 : 17 (b) 2 : 17
(c)   (d)   (c) 3 : 23 (d) 2 : 13
 10   3 

am
3. What angle is made by minute hand in 59 sec ? 11. Time appears in water is 5 : 47, what time will be
correct in watch
feuV dh lqbZ 59 lsdaM esa fdrus fMxzh dks.k cuk;sxh\
ikuh esa le; 5 % 47 fn•kbZ nsrk gS] ?kM+h esa dkSu&lk le; lgh gksxk\
(a) 6º (b) 5º
(a) 12 : 47 (b) 12 : 43
kr
(c) 5.9º (d) 4.9º
(c) 1 : 47 (d) 1 : 43
4. What angle is made by second hand in 15 sec?
12. Water image of a clock is showing time 4 : 42 what is
lsdsaM gSaM }kjk 15 lsdaM esa dkSu&lk dks.k cuk;k tkrk gS\the real time?
Vi

(a) 15º (b) 1.5º ,d ?kM+h dh ty Nfo le; 4%42 fn•k jgh gS] okLrfod le; D;k
 1 
gS\
(c)   (d) 90º (a) 1 : 48 (b) 2 : 48
8
by

(c) 12 : 48 (d) 12 : 42
5. What time is shown by the mirror if the real time is 9
: 27. 13. If time in a clock is 7 : 35 then what time will be
appear in water?
;fn okLrfod le; 9 % 27 gS rks niZ.k }kjk dkSu&lk le; fn•k;k
;fn fdlh ?kM+h esa le; 7 % 35 gS rks ikuh esa dkSu&lk le; fn•kbZ
ng

x;k gS\
nsxk\
(a) 3 : 33 (b) 2 : 33
(a) 11 : 35 (b) 10 : 35
(c) 3 : 27 (d) 2 : 23
ni

(c) 10 : 05 (d) 10 : 55
6. Time appears in the mirror 11 : 09. Then what time
14. If time in a clock is 9 : 11, then what time will appear
will be appear in clock?
in water?
so

niZ.k esa le; fn•kbZ nsrk gS 11 % 09- rks ?kM+h esa dkSu&lk le;;fn
fn•kbZ
?kM+h esa le; 9 % 11 gS rks ikuh esa dkSu&lk le; fn•kbZ nsxk\
nsxk\ (a) 9 : 19 (b) 8 : 11
(a) 1 : 51 (b) 12 : 09
ea

(c) 8 : 19 (d) 9 : 30
(c) 12 : 51 (d) 1 : 09 15. If time in a clock is 8 : 52, then what time will appear
7. Time appears in the mirror 6 : 00. Then what correct in water
R

time in clock?
;fn fdlh ?kM+h esa le; 8 % 52 gS rks ikuh esa dkSu&lk le; fn•kbZ
niZ.k esa le; 6%00 fn•kbZ nsrk gSA rks ?kM+h esa dkSu&lk lgh le; gS\
nsxk\
(a) 5 : 58 (b) 6 : 60 (a) 8 : 38 (b) 9 : 52
(c) 6 : 00 (d) 6 : 01 (c) 8 : 22 (d) 9 : 38
8. If reflecting time is 3 : 43 then the real time of clock 16. What angle is made by minute and hour hand at 4 :
is? 12?
;fn ijkofrZr le; 3 % 43 gS rks ?kM+h dk okLrfod le; D;k gS\ feuV vkSj ?kaVs dh lqbZ 4 % 12 ij dkSu&lk dks.k cukrh gS\
(a) 3 : 17 (b) 7 : 17 (a) 66º (b) 44º
(c) 8 : 17 (d) 8 : 43 (c) 54º (d) 60.5º

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17. What is the angle between minute and hour hand at 9

8 3
: 53? (a) 2 : 32 (b) 2 : 27
11 11
9 % 53 ij feuV vkSj ?kaVs dh lqbZ ds chp dk dks.k D;k gS\
(a) 121.5º (b) 21.5º 10 4
(c) 2 : 10 (d) 2 : 16
(c) 130º (d) 68.5º 11 11
18. What is the angle between minute and hour hand at 26. At what time between 6 to 7 O’ clock minute and hour
12 : 46? hand will be at right angle or makes 90° angle
12 % 46 ij feuV vkSj ?kaVs dh lqbZ ds chp dk dks.k D;k gS\ 6 ls 7 cts ds chp fdl le; feuV vkSj ?kaVs dh lqbZ ledks.k ij
(a) 97º (b) 107º gksxh ;k 90 fMxzh dk dks.k cuk,xhA
(c) 153º (d) 7º
2 7 7 7
19. What is the angle between minute and hour hand at 7 (a) 6 : 38 , 6 : 43 (b) 6 : 43 , 6 : 49

r
: 09? 11 11 11 11

Si
7 % 09 ij feuV vkSj ?kaVs dh lqbZ ds chp dk dks.k D;k gS\ 1 4 4 6
(c) 6 : 49 , 6 : 16 (d) 6 : 16 , 6 : 54
(a) 120.5º (b) 160.5º 11 11 11 11
(c) 49.5º (d) 19.5º 27. At what time between 3 to 4 O’ clock minute and hour

et
20. What is the angle between minute and hour hand at hand are opposite to each other
11 : 10? 3 ls 4 cts ds chp fdl le; feuV vkSj ?kaVs dh lwb;ka ,d nwljs ds
11 % 10 ij feuV vkSj ?kaVs dh lqbZ ds chp dk dks.k D;k gS\ foijhr gksrh gSa\

je
(a) 265º (b) 175º
(c) 85º (d) 95º 7 2

am
(a) 3 : 43 (b) 3 : 38
21. What is the angle between minute and hour hand at 3 11 11
: 56? 1 6
3 % 56 ij feuV vkSj ?kaVs dh lqbZ ds chp dk dks.k D;k gS\ (c) 3 : 49
11
(d) 3 : 54
11
kr
(a) 152º (b) 228º 28. When did the minute and hour hand makes 180° angle
(c) 360º (d) 142º between 6 to 7 O’ clock?
22. What is the angle between minute and hour hand at 6 ls 7 cts ds chp feuV vkSj ?kaVs dh lqbZ dc 180 fMxzh dk dks.k
Vi

12 : 20
cukrh gS\
12 % 20 ij feuV vkSj ?kaVs dh lqbZ ds chp dk dks.k D;k gS\
(a) 260º (b) 110º 6
(a) 6 : 54 (b) 6 : 60
by

(c) 120º (d) 20º 11

23. At what time between 6 to 7 O’ clock minute and hour 5
hand will coincide? (c) 6 : 00 (d) 6 : 5
11
6 ls 7 cts ds chp fdl le; feuV vkSj ?kaVs dh lqbZ ,d lkFk
ng

29. At what time between 8 to 9 O’ clock the minute and

vk,¡xh\ hour will apart 7 minutes to each other?
2 7 8 ls 9 cts ds chp fdl le; feuV vkSj ?kaVs esa 7 feuV dk varj
(a) 6 : 38 (b) 6 : 43
gksxk\
ni

11 11

8 5 3 3
(c) 6 : 32 (d) 6 : 5 (a) 8 : 42, 8 : 51 (b) 8 : 36, 8 : 51
so

11 11 11 11
24. At what time between 10 to 11 O’ clock minute and
hour hand will coincide or makes 0° angle? 4 9
(c) 8 : 09, 8 : 47 (d) 8 : 17, 8 : 28
ea

11 11
10 ls 11 cts ds chp fdl le; feuV vkSj ?kaVs dh lqbZ laikrh gksaxh
;k 0 fMxzh dk dks.k cuk,axh\ 30. The minute hand of a clock overtakes the hour hand
at intervals of 64 minutes of correct time. How much
R

7 2 a day does the clock gain or lose?

(a) 10 : 43 (b) 10 : 38
11 11 ?kM+h dh feuV okyh lqbZ 64 feuV ds lgh le; ds varjky ij ?kaVs
6 10
okyh lqbZ ls vkxs fudy tkrh gSA ?kM+h ,d fnu esa fdruk ykHk ;k
(c) 10 : 54
11
(d) 10 : 10
11
gkfu djrh gS\
25. At what time between 2 to 3 O’ clock minute and hour 9 8
hand will be at right angle to each other or makes 90° (a) 43 minute loss (b) 32 minute gain
11 11
angle
2 ls 3 cts ds chp fdl le; feuV vkSj ?kaVs dh lwb;ka ,d nwljs ls (c) 33
9
minute gain (d) 32
8
minute loss
ledks.k ij gksaxh ;k 90 fMxzh dk dks.k cuk,axh 11 11

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31. The minute hand of a clock overtakes the hour hand ,d lVhd ?kM+h lqcg ds 9 cts dk le; fn[kkrh gSA tc ?kM+h mlh
at intervals of 66 minute of correct time. How much a fnu nksigj ds 3 cts dk le; fn[kkrh gS rks ?kaVs dh lwbZ fdrus fMxzh
day does the clock gain or lose?
rd ?kwesxh\
?kM+h dh feuV okyh lqbZ 66 feuV ds lgh le; ds varjky ij ?kaVs
UP Constable 17/02/2024 (Shift-2)
okyh lqbZ ls vkxs fudy tkrh gSA ?kM+h ,d fnu esa fdruk ykHk ;k
(a) 165º (b) 170º
gkfu djrh gS\ (c) 175º (d) 180º
109 109 38. A clock is started at noon. At 5:20 PM, the hour hand
(a) 11 minute gain (b) 11 minute loss has turned?
121 121
,d ?kM+h nksigj ds le; 5 ctdj 20 feuV ij 'kq: dh tkrh gSA rc
(c) 11
117
minute gain (d) 11
117
minute loss
?kaVs dh lqbZ fdrus fMxzh ?kwe pqdh gksxh gS\
121 121
UP Constable, 18/02/2024 (Shift-1)

r
32. A clock is set right at 8 a.m. on sunday. It gains 8 (a) 160º (b) 155º

Si
minutes in 24 houus. What is the correct time when (c) 150º (d) 145º
the clock indicates 9 p.m. on upcoming sunday? 39. An accurate clock shows the time as 2 PM. How many
,d ?kM+h jfookj dks çkr% 8 cts lgh lsV dh tkrh gSA 24 ?kVs esadegrees
;g will the hour hand rotate when the clock shows
8 feuV c<+ tkrk gSA tc ?kM+h jkr ds 9 cts vxys jfookj dks fn•krh6 PM on the same day?

et
gS rks lgh le; D;k gS\ ,d lVhd ?kM+h nksigj ds 2 cts dk le; fn[kkrh gSA tc ?kM+h mlh
(a) 9 P.M (b) 8 : 30 P.M fnu 'kke ds 6 cts dk le; fn[kkrh gS rks ?kaVs dh lqbZ fdrus fMxzh

je
(c) 8 P.M (d) 10 P.M rd ?kwesxh\
33. A clock is set right at 10 A.M on sunday. It loses 8 UP Constable, 18/02/2024 (Shift 2)

am
minutes in 24 hours. What is the correct time when (a) 120º (b) 125º
the clock indicates 9 P.M on next sunday? (c) 130º (d) 135º
,d ?kM+h jfookj dks çkr% 10 cts lgh lsV dh tkrh gSA ;g 2440.
?kaVs
What angle is made by minute and hour hand at 4 : 12?
feuV vkSj ?kaVs dh lqbZ 4 % 12 ij dkSu&lk dks.k cukrh gS\
esa 8 feuV •ks nsrk gSA tc ?kM+h vxys jfookj dks jkr 9 cts dk ladsr
kr
nsrh gS rks lgh le; D;k gS\ SSC JE, 06/11/2024
(a) 9 P.M (b) 9 A.M (a) 66º (b) 44º
Vi

(c) 10 A.M (d) 10 P.M (c) 54º (d) 60.5º

41. What is the angle between minute and hour hand at 9 : 53?
34. A watch which gains uniformaly is 4 minute slow at 9
A.M on Sunday, and is 4 minute 15 sec. fast at 9 P.M 9 % 53 ij feuV vkSj ?kaVs dh lqbZ ds chp dk dks.k D;k gS\
on upcoming Friday. When was it correct? DSSSB, 12/08/2024
by

34- jfookj dks çkr% 9 cts ,d ?kM+h tks ,dleku xfr çkIr djrh gS] (a) 121.5º (b) 21.5º
4 feuV èkheh gS rFkk 4 feuV 15 lsd.M gSA vkxkeh 'kqØokj dks (c)jkr130º (d) 68.5º
9 cts miokl djsaA ;g dc lgh Fkk\ 42. What is the angle between minute and hour hand at
12 : 46?
ng

(a) 2 A.M Thursday (b) 6 P.M Wednesday

12 % 46 ij feuV vkSj ?kaVs dh lqbZ ds chp dk dks.k D;k gS\
(c) 1 A.M Wednesday (d) 6 P.M
35. A watch which loses uniformaly is 3 minute fast at 6 DSSSB, 14/08/2024
ni

A.M on Thursday and is 3 minute 12 sec. slow at 5 (a) 97º (b) 107º
P.M on upcoming wednesday. When was it correct? (c) 153º (d) 7º
43. What is the angle between minute and hour hand at 7 : 09?
xq#okj dks lqcg 6 cts ,d ?kM+h tks ,d:irk •ks nsrh gS og 3 feuV
so

7 % 09 ij feuV vkSj ?kaVs dh lqbZ ds chp dk dks.k D;k gS\

rst gS vkSj 3 feuV 12 lsdaM gSA vkxkeh cqèkokj dks 'kke 5 cts èkheh
xfr lsA ;g dc lgh Fkk\ DSSSB JJA, 24/03/2024
(a) 120.5º (b) 160.5º
ea

(a) 9 P.M on Sunday (b) 9 A.M on Monday

(c) 49.5º (d) 19.5º
(c) 9 A.M on Sunday (d) 8 A.M on Sunday
44. What is the angle between minute and hour hand at
36. A clock is started at noon. At 4:10, the hour hand has 11 : 10?
R

turned? 11 % 10 ij feuV vkSj ?kaVs dh lqbZ ds chp dk dks.k D;k gS\

,d ?kM+h nksigj(noon) ds le; 'kq: dh tkrh gSA 4 ctdj 10
SSC GD, 20/02/2024
feuV ij] ?kaVs dh lwbZ ?kwe pqdh gksrh gSA
(a) 265º (b) 175º
UP Constable, 17/02/2024 (Shift 1) (c) 85º (d) 95º
(a) 135° (b) 130° 45. What is the angle between minute and hour hand at 3 : 56?
(c) 125° (d) 120° 3 % 56 ij feuV vkSj ?kaVs dh lqbZ ds chp dk dks.k D;k gksxk\
37. An accurate clock shows the time as 9 a.m. How many SSC GD, 24/02/2024
degrees will the hour hand rotate when the clock shows (a) 152º (b) 228º
the time as 3 p.m. on the same day? (c) 360º (d) 142º

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46. What is the angle between minute and hour hand at UPSI, (Mains Exam) 2001
12 : 20
(a) East/iwoZ (b) West/if'pe
12 % 20 ij feuV vkSj ?kaVs dh lqbZ ds chp dk dks.k D;k gS\
(c) North/mÙkj (d) South/nf{k.k
SSC GD, 26/02/2024 53. A clock is showing 4 o'clock. What will be the time
(a) 260º (b) 110º after the hour hand rotates 90 degrees?
(c) 120º (d) 20º
,d ?kM+h 4 cts dk le; fn[kk jgh gSA ?kaVs dh lqbZ ds 90 va'k ?kweus
47. At what time between 10 to 11 O’ clock minute and
hour hand will coincide or makes 0° angle? ds ckn D;k le; gksxk\
10 ls 11 cts ds chp fdl le; feuV vkSj ?kaVs dh lqbZ laikrh gksaxh UPSI, (Mains Exam) 2001
;k 0° dk dks.k cuk,axh\ (a) 8 o'clock (b) 7 o'clock
(c) 6 o'clock (d) None of the above
SSC GD, 07/03/2024 54. At 9 o'clock in the night the hour hand points towards

r
7 2 north. In which direction will the minute hand be at
(a) 10 : 43 (b) 10 : 38

Si
11 11 6:30 in the morning?
jkr ds 9 cts ?kaVs dk dkaVk mÙkj dh vksj gksrk gSA lqcg ds 6%30 cts
6 10
(c) 10 : 54 (d) 10 : 10 feuV dk dkaVk fdl fn'kk dh vksj gksxk\
11 11

et
48. At what time between 2 to 3 O’ clock minute and hour UP Constable 27/10/2019 (Shift-2)
hand will be at right angle to each other or makes 90° (a) North/mÙkj (b) East/iwoZ
angle (c) West/if'pe (d) South/nf{k.k

je
2 ls 3 cts ds chp fdl le; feuV vkSj ?kaVs dh lqb;ka ,d nwljs ls55. A clock is showing the time of 4:35. If the minute
ledks.k ij gksaxh ;k90° dk dks.k cuk,axh hand moves 270 degrees in a clockwise direction, in

am
which direction does the hour hand point?
SSC GD, 10/03/2024
,d ?kM+h 4%35 dk le; fn[kk jgh gSA ;fn feuV dh lqbZ 270 fMxzh
8 3
(a) 2 : 32 (b) 2 : 27 nf{k.kkorZ fn'kk esa pyrh gS] rks ?kaVs dh lqbZ fdl fn'kk esa bafxr djrk gS\
11 11
UP Constable 18/10/2018 (Shift-2)
kr
10 4 (a) South-East/nf{k.k&iwoZ (b) South-West/nf{k.k&if'pe
(c) 2 : 10 (d) 2 : 16
11 11 (c) East/mÙkj (d) North-East/mÙkj&iwoZ
49. The minute hand of a clock overtakes the hour hand 56. How many times are the hour and minute hands of a
Vi

at intervals of 64 minutes of correct time. How much clock at right angles in a period of two days?
a day does the clock gain or lose? nks fnuksa dh vofèk esa ?kM+h dh ?kaVs vkSj feuV dh lqbZ fdruh ckj ,d
?kM+h dh feuV okyh lqbZ 64 feuV ds lgh le; ds varjky ij ?kaVs
ledks.k ij gksrh gSa\
okyh lqbZ ls vkxs fudy tkrh gSA ?kM+h ,d fnu esa fdruk ykHk ;k
by

RRC Group D, 18/08/2022 (Shift-1)

gkfu djrh gS\ (a) 88 (b) 48
SSC GD, 01/03/2024 (Shift-1) (c) 92 (d) 77
9 8 57. How much angular distance will the minute hand of
ng

(a) 43 minute loss (b) 32 minute gain an accurate clock cover in a period of 3 hours 10
11 11
9 8 minutes?
(c) 33
11
minute gain (d) 32
11
minute loss ,d lgh le; crkus okyh ?kM+h dh feuV okyh lqbZ] 3 ?kaVs 10 feuV
ni

50. The angle between the hands of 3:40 o'clock is- dh vofèk esa fdruh dks.kh; nwjh r; djsxh\
3%40 cts dh lqb;ksa ds chp dk dks.k gS& RRC Group D, 22/08/2022 (Shift-3)
(a) 1000° (b) 1202°
so

UPSI, (Cancel Exam) 20/07/2017 (Shift-2)

(a) 100° (b) 110° (c) 978° (d) 1140°
(c) 130° (d) 150° 58. What will be the angular distance covered by the
51. At what time between 5 and 6 will both the hands of second hand of an accurate clock in 12 minutes?
ea

the clock be in line? ,d lgh le; crkus okyh ?kM+h dh lsdaM okyh lqbZ }kjk 12 feuV esa
5 vkSj 6 ds chp fdl le; ?kM+h dh nksuksa lqb;ka ,d lhèk esa gksaxh
r; dh\ xbZ dks.kh; nwjh fdruh gksxh\
R

UPSI, (Mains Exam) 20/07/2017 (2) RRC Group D, 23/08/2022 (Shift-1)

3 8 (a) 4762° (b) 5120°
(a) 5 ctdj 32 feUkV (b) 5 ctdj 23 feUkV
11 11 (c) 4320° (d) 5611°
3 3 59. If the mirror image of a 12-hour clock shows 3 : 55
(c) 5 ctdj 17 feUkV (d) 5 ctdj 27 feUkV pm, find the actual time.
11 11
52. A clock is showing 9 o'clock. If the small needle is in ;fn 12 ?kaVs okyh ?kM+h ds niZ.k çfrfcac esa 3 % 55 cts gS] rks
the east direction, then in which direction will the big okLrfod le; Kkr dhft,A
needle be?
RRC Group D, 25/08/2022 (Shift-1)
,d ?kM+h 9 cts dk le; fn[kk jgh gSA ;fn NksVh lqbZ iwoZ fn'kk(a)
esa 8:05
gS] (b) 8:25
rks cM+h lqbZ fdl fn'kk esa gksxh\ (c) 7:05 (d) 7:25

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60. What will be the approximate angle between the minute NTPC CBT-1, 13/01/2021 (Shift-3)
hand and the hour hand of a 12-hour clock when it is
(a) South/nf{k.k (b) West/if'pe
9 : 25?
(c) East/
tc 9 % 25 cts gks] rks 12 ?kaVs okyh ?kM+h dh feuV okyh lqbZ vkSj ?kaVsiwoZ (d) North/mÙkj
67. The time as per Nihal's watch is 1:30 and the hour
okyh lqbZ ds chp cuk dks.k yxHkx fdruk gksxk\ hand is pointing towards north-east. Assuming that
RRC Group D, 25/08/2022 (Shift-2) there is no change in Nihal's position, in which
(a) 150° (b) 190° direction will the minute hand point after 30 minutes?
(c) 100° (d) 130° fugky dh ?kM+h ls le; ds vuqlkj 1 ctdj 30 feuV gqbZ gS vkSj ?kaVs
61. At what time between 2 o'clock and 3 o'clock will the
hands of the clock be together? dh lqbZ mÙkj&iwoZ dh vksj b'kkjk dj jgh gSA ;g ekurs gq, fd fugky
2 cts ls 3 cts ds chp ?kM+h dh lqb;ka fdl le; ,d lkFk gksaxh\ dh fLFkfr esa dksbZ ifjorZu ugha gqvk gS] 30 feuV ds ckn feuV dh
RRC Group D, 26/08/2022 (Shift-3) lqbZ fdl fn'kk esa bafxr djsxh\

r
5 5 NTPC CBT-1, 21/01/2021 (Shift-3)

Si
(a) 2 ctdj 3 (b) 2 ctdj 6 (a) South/nf{k.k (b) East/iwoZ
11 11
12 10 (c) West/if'pe (d) North/mÙkj
(c) 2 ctdj 11 (d) 2 ctdj 10 68. According to Rajni's watch, the time is quarter past
11 11

et
62. How will quarter past eight be represented in 24 hour format? six. If the hour hand points towards south, then in
24 ?kaVs ds çk:i esa lok vkB dks dSls n'kkZ;k tk,xk\ which direction is the minute hand?
RRC Group D, 29/08/2022 (Shift-3) jtuh dh ?kM+h esa le; ds vuqlkj lok Ng cts gSaA ;fn ?kaVs dh lqbZ

je
(a) 20 % 15 ?kaVs (b) 19 % 45 ?kaVs nf{k.k dh vksj b'kkjk djrh gS] rks feuV dh lqbZ fdl fn'kk esa gS\
(c) 19 % 15 ?kaVs (d) 20 % 45 ?kaVs NTPC CBT-1, 22/01/2021 (Shift-3)

am
63. If the mirror image of a 12-hour clock is 5 : 40 o'clock, (a) East/iwoZ (b) West/if'pe
find the actual time. (c) South/nf{k.k (d) North/mÙkj
;fn 12 ?kaVs okyh ?kM+h ds niZ.k çfrfcac esa 5 % 40 cts 69.gks]
It isrks
7:30 am in a wristwatch. If the hour hand points
okLrfod le; Kkr dhft,A towards south-west, then in which direction will the
kr
RRC Group D, 30/08/2022 (Shift-1) minute hand point after 15 minutes?
(a) 2 : 10 (b) 2 : 50 ,d dykbZ ?kM+h esa lqcg 7%30 cts gSA ;fn ?kaVs dh lqbZ nf{k.k&if'pe
(c) 6 : 20 (d) 6 : 10 dh vksj bafxr djrh gS] rks 15 feuV ds ckn feuV dh lqbZ fdl fn'kk
Vi

64. If the hour hand of a wrist watch points towards North-

esa bafxr djsxh\
West at 6:00 AM, then which direction will the hour
hand point towards at 9:00 PM? NTPC CBT-1, 01/02/2021 (Shift-3)
;fn lqcg 6%00 cts ,d gkFk ?kM+h dh ?kaVs okyh lqbZ mÙkj&if'pe
by

fn'kk dks n'kkZrh gS] rks jkr 9%00 cts ?kaVs okyh lqbZ fdl fn'kk dks
(a) South/ nf{k.k (b) South-West/nf{k.k if'pe
n'kkZ,xh\ (c) West/if'pe (d) North/mÙkj
70. How will you write 1-11 hours into hours, minutes
RRC Group D, 13/09/2022 (Shift-1)
and seconds?
ng

(a) South/nf{k.k (b) North-East/mÙkj&iwoZ

vki 1-11 ?kaVs dks ?kaVs] feuV vkSj lsdaM esa dSls fy•saxs\
(c) North-West/mÙkj&if'pe(d) South-West/nf{k.k&if'pe
NTPC CBT-1, 07/04/2021 (Shift-3)
65. A working clock is placed on a table in such a way
(a) 1 ?kaVk] 6 feuV] 36 lsdaM
(b) 1 ?kaVk] 10 feuV] 1 lsdaM
ni

that at 9-00 pm its hour hand is pointing towards

north. If the position of this clock remains the same, (c) 1 ?kaVk] 10 feuV] 10 lsdaM
(d) 1 ?kaVk] 11 feuV
then in which direction will its minute hand point at 71. How will you write 9-11 hours in hours, minutes and
so

6.00 am? seconds?

,d est ij ,d dk;Z'khy ?kM+h bl çdkj j•h xbZ gS fd jkr 9-00 cts vki 9-11 ?kaVs dks ?kaVs] feuV vkSj lsdaM esa dSls fy•saxs\
bldh ?kaVs dh lqbZ mÙkj fn'kk dh vksj bafxr dj jgh gSA ;fn bl ?kM+h NTPC CBT-1, 08/04/2021 (Shift-1)
ea

dh fLFkfr leku cuh jgrh gS] rks lqcg 6-00 cts bldh feuV dh lqbZ (a) 9 ?kaVs] 11 feuV (b) 9 ?kaVs] 49 feuV
fdl fn'kk dh vksj bafxr djsxh\ (c) 9 ?kaVs] 10 feuV] 10 lsdaM
(d) 9 ?kaVs] 6 feuV] 36 lsdaM
R

72. At 8 a.m. on Sunday, a clock is found to be 5 minutes

NTPC CBT-2, 13/06/2022 (Shift-1)
behind. It then starts gaining and at 8 p.m. on Monday,
(a) North/mÙkj (b) East/iwoZ it is found to be 5 minutes ahead. At what time was it
(c) South/nf{k.k (d) West/if'pe perfect?
66. According to Rekha's watch, it is quarter past nine jfookj dks lqcg 8 cts] ,d ?kM+h 5 feuV ihNs ikbZ tkrh gSA blds
and the hour hand is pointing towards the west. In ckn ;g c<+us yxrh gS vkSj lkseokj dks 'kke 8 cts] 5 feuV rst ikbZ
which direction will the minute hand be after 75
minutes?
tkrh gSA fdl le; ;g ,dne lgh Fkh\
js•k dh ?kM+h ds vuqlkj lok ukS ct jgs gSa vkSj ?kaVs dh lqbZ if'pe RRB JE, 31/05/2019 (Shift-2)
fn'kk dh vksj bafxr dj jgh gSA feuV dh lqbZ 75 feuV ds ckn fdl (a) lqcg 2 cts] lkseokj (b) 'kke 8 cts] lkseokj
fn'kk esa gksxh\ (c) lqcg 8 cts] lkseokj (d) lqcg 6 cts] lkseokj

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 7

73. Find the angle between the clock hands at 3:30 pm. 78. A clock loses 5 minutes every hour and was set back
vijkÉ 3%30 cts ?kM+h dh lqb;ksa ds chp dk dks.k Kkr dhft,A to the correct time on Monday morning at 6 a.m. When
will it show the correct time again?
RRB JE, 28/06/2019 (Shift-3)
(a) 120° (b) 75°
,d ?kM+h çR;sd ?kaVs esa 5 feuV ihNs gks tkrh gS vkSj lkseokj çkr%
(c) 90° (d) 105° 6 cts ?kM+h lgh le; ij lsV dh x;h FkhA ;g nksckjk lgh le; dc
74. What will be the angle between the hour hand and the fn•k;sxh\
minute hand at half past two? ALP Tier-1, 30/08/2018 (Shift-1)
<kbZ cts ?kaVs dh lwbZ vkSj feuV dh lwbZ ds chp dks.k D;k (a)
gksxk\
vxys jfookj 'kke 6 cts (b) vxys lkseokj 'kke 6 cts
ALP Tier-2, 23/01/2019 (Shift-1) (c) vxys jfookj çkr% 3 cts (d) vxys lkseokj çkr% 3 cts
(a) 120° (b) 90° 79. A clock shows the time 1:40. If the minute hand points
(c) 105° (d) 75° towards south-west, then in which direction does the
75. What will be the value of the angle (in degrees) between

r
hour hand point?
the two hands of the clock at 8 o'clock?
,d ?kM+h 1%40 dk le; fn[kk jgh gSA ;fn feuV dh lqbZ nf{k.k&if'pe

Si
8 cts ?kM+h dh nksuksa ?kM+;ksa ds chp cus dks.k dk eku (fMxzh esa) D;k
dh vksj b'kkjk djrh gS] rks ?kaVs dh lqbZ fdl fn'kk dh vksj b'kkjk
gksxk\
djrh gS\
ALP Tier-1, 10/08/2018 (Shift-2)

et
(a) 60 (b) 120 UP Constable 19/06/2018 (Shift-2)
(c) 50 (d) 240
76. If the hour hand of a clock moves forward 18 degrees, (a) North-East/mÙkj&iwoZ (b) South/nf{k.k

je
then how many degrees will the minute hand move in (c) North/mÙkj (d) South-East/nf{k.k&iwoZ
the same time? 80. A clock shows 9 o'clock. If the small needle is in the
;fn ,d ?kM+h dh ?kaVs okyh lwbZ 18 fMxzh vkxs ?kwerh gS] rks mlhdirection,
nkSjku then in which direction will the big

am
east
feuV okyh lqbZ fdrus fMxzh ?kwesxh\ needle be?
ALP Tier-1, 14/08/2018 (Shift-3) ,d ?kM+h 9 cts dk le; fn[kk jgh gSA ;fn NksVh lqbZ iwoZ fn'kk esa gS]
(a) 168° (b) 276° rks cM+h lqbZ fdl fn'kk esa gksxh\
kr
(c) 196° (d) 216° (a) East/iwoZ (b) West/if'pe
77. In a clock, the hour hand points towards the east at 6 (c) North/mÙkj (d) South/nf{k.k
pm, then in which direction will the minute hand be
81. A clock shows 4 o'clock. What will be the time after
Vi

at 9:15 pm?
the hour hand rotates 90 degrees?
,d ?kM+h esa 'kke ds 6 cts ?kaVs dh lqbZ iwoZ fn'kk dh vksj ladsr djrh 4 cts dk le; fn[kk jgh gSA ?kaVs dh lqbZ ds 90 va'k ?kweus
,d ?kM+h
gS rks jkr ds 9%15 cts feuV dh lqbZ fdl fn'kk esa gksxh\ ds ckn D;k le; gksxk\
ALP Tier-1, 21/08/2018 (Shift-2) 8 cts 7 cts
by

(a) (b)
(a) East/iwoZ (b) South/nf{k.k
(c) 6 cts (d) mi;ZqÙkQ esa ls dksbZ ugha
(c) West/if'pe (d) North/mÙkj
ng

ANSWER KEY
ni

1. (b) 2. (c) 3. (c) 4. (d) 5. (b) 6. (c) 7. (c) 8. (c) 9. (b) 10. (a)
11. (b) 12. (a) 13. (d) 14. (a) 15. (d) 16. (c) 17. (b) 18. (b) 19. (b) 20. (c)
so

21. (d) 22. (b) 23. (c) 24. (c) 25. (b) 26. (c) 27. (c) 28. (c) 29. (b) 30. (b)
31. (b) 32. (c) 33. s(d) 34. (c) 35. (c) 36. (c) 37. (d) 38. (a) 39. (a) 40. (c)
ea

41. (b) 42. (b) 43. (b) 44. (c) 45. (d) 46. (b) 47. (c) 48. (b) 49. (b) 50. (c)
51. (d) 52. (d) 53. (b) 54. (c) 55. (a) 56. (a) 57. (d) 58. (c) 59. (a) 60. (d)
R

61. (d) 62. (a) 63. (c) 64. (b) 65. (b) 66. (a) 67. (d) 68. (a) 69. (c) 70. (a)
71. (d) 72. (a) 73. (b) 74. (c) 75. (d) 76. (d) 77. (b) 78. (a) 79. (a) 80. (d)
81. (b)



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Answer with Explanation

1. (b) 2.9° 9. (b) 11 : 37
feuVhand in 1 feuV= 6° Because the time 12 : 23 lies be-
tween 11 : 00 to 1 : 00, Hence we
feuVhand in 60 lsoaQM
= 6° H
substract that time from 23 : 60
M
6 23 : 60 – 12 : 23 = 11 : 37
Then, in 1 Sec =
60 10. (a) 3 : 17 14. (a) 9 : 19
In water Image the time 3 : 13 In this time 9 : 11, the hour hand
6
In 29 sec = × 29 = 2.9° has the both hands between 12 : of the clock is between 6 : 00 to
60

r
00 to 6 : 00 clockwise hence we 12 : 00 clockwise and feuVhand
subrtract that time from 6 : 30

Si
3  isbetween 12 : 00 to 6 : 00 clock-
2. (c)   6 : 30 – 3 : 13 = 3 : 17
 10  wise. Hence we substract that
time from 18 : 30.
?kaVs
hand in 1 hour = 30° 12
18 : 30 – 9 : 11 = 9 : 19

et
In 60 feuV= 30° 15. (d) 9 : 38
In 3600 sec = 30° M In this time 8 : 52, both the hands
3

je
H of clock are between 6 : 00 to 12
30 1
Then, In 1 sec. = = : 00 clockwise. Hence we
3600 120
6 substract that time from 17 : 90

am
1  3  17 : 90 – 8 : 52 = 9 : 38
In 36 Sec = × 36 =   11. (b) 12 : 43
120  10 
In the time 5 : 47 hour hands of
3. (c) 5.9 the clock is between 12 : 00 to 6 M
kr
feuVhand in 1 feuV= 6° : 00 and the minute hand of the
H
feuVhand in 60° lsoaQM
= 6° clock is between 6 : 00 to 12 : 00
clock wise hence we substract
Vi

1 that time from 5 : 90 16. (c) 54°

feuVhand in 1 sec. = 10
11
Angle = M – 30H
1 2
Then, in 59 sec. = × 59 = 5.9° M
by

10
H (Substract smaller from larger)
4. (d) 90° Hence H = 4, M = 12
lsoaQM
hand in 1 sec. = 6° 4 × 30 = 120°
Then in 15 sec = 15 × 6 = 90° 5 : 90 – 5 : 47 = 00 : 43
ng

11
5. (b) 2 : 33 0 : 43 means 12 : 43 12 × = 66°
2
Because the time 9 : 27 lies b/w 12. (a) 1 : 48
1 : 00 to 11 : 00, hence we 120° – 66° = 54°
In the time 4 : 42 hour hand of
ni

substrat this time from 11:60, the clock is between 12 : 00 to 6 17. (b) 21.5°
11 : 60 – 9 : 27 = 2 : 33 : 00 and the minute hand of the 11
6. (c) 12 : 51 clock is between 6 : 00 to 12 : Angle = M – 30H
so

2
Because the time 11 : 09 lies be- 00. Hence we sustruct that time
tween 11 : 00 to 1 : 00, Hence we from 5 : 90 H = 9, M = 53
substract that time from 23 : 60 5 : 90 – 4 : 42 = 1 : 48 9 × 30 = 270°
ea

23 : 60 – 11 : 09 = 12 : 51
11
7. (c) (6 : 00) 53 × = 291.5°
2
Because the time 6 : 00 lies be-
R

tween 1 : 00 to 11 : 00, hence M 291.5° – 270° = 21.5°

H
we substract that time from 11 : 18. (b) 107°
60 11
11 : 60 – 6 : 00 = 5 : 60 Angle = M – 30H
13. (d) 10 : 55 2
5 : 60 Means (6 : 00)
In this time 7 : 35 both hands H = 12, M = 46
8. (c) 8 : 17
are between 6 : 00 to 12 : 00 12 × 30 = 360°
Because the time 3 : 43 lies be- clockwise. Hence we substract
tween 1 : 00 to 11 : 00 Hence we 11
that time from 17 : 90 46 × = 253°
substract that time from 11 : 60 2
17 : 90 – 7 : 35 = 10 : 55
11 : 60 – 3 : 43 = 8 : 17 360° – 253° = 107°

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19. (b) 160.5°

11 1 4
M – 30× 6 = 0 26. (c) 6 : 49 , 6 : 16
11 2 11 11
Angle = M – 30H
2
360 8 6 ls 7 cts ds chp 90° dks.k
H = 7, M= 9 M= = 32 min
11 11
7 × 30 = 210° 11
Angle = M – 30H
8 2
11 6 : 32 min
9× = 49.5° 11
2 11
M – 30 × 6 = +90
210° – 49.5° = 160.5° 6 2
24. (c) 10 : 54
20. (c) 85° 11
11
11 10 ls 11 cts ds chp 0° dks.k 2
M = 270

r
Angle = M – 30H
2 11

Si
Angle = M – 30H 540 1
H = 11, M= 10 2 M= = 49
11 11
11 × 30 = 330°
11 AND
11 M – 30 ×10 = 0

et
10 × = 55° 2 11
2 M – 30 × 60 – 90
600 6 2
330° – 55° = 275°
M= = 54

je
But 275° is more than 180° 11 11 11
hence we substract this angle M = 90
2
from 360° 6

am
10 : 54
360° – 275° = 85° 11 180 4
M= = 16
21. (d) 142° 3 11 11
25. (b) 2 : 27
11 11 1 4
Angle = M – 30H 6 : 49 , 6 : 16
kr
2 2 ls 3 cts ds chp 90° dks.k 11 11
H = 3, M = 56
11 1
3 × 30° = 90° Angle = M – 30H
Vi

27. (c) 3 : 49
2 11
11
56 × = 308° 11 3 ls 4 cts ds chp lqb;ka ,d&nwljs ds
2 M – 30 × 2 = + 90 foijhr dc gksxh\
2
by

308° – 90° = 218°

But 218° is more than 180° 11 11
Angle = M – 30H
hence we substract this Angle M = 150 2
2
from 360°
360° – 218° = 142° 300 3 11
ng

M= = 27 M – 30× 3= 180
22. (b) 110° 11 11 2

11 AND 11
Angle = M – 30H M = 270
ni

2 11 2
Angle = M – 30H
H = 12, M = 20 2 540 1
12 × 30 = 360° M= = 49
so

11 11 11
11 M– 30 × 2 = –90
2
20 × = 110° 1
2 11 3 : 49
ea

11
360° – 110° = 250° M = 60 – 90 = –30
2 28. (c) 6:00
But 250° is more than 180°
hence substract this angle from 11 6 ls 7 cts ds chp 180° dks.k
R

M = 360–30
360° 2
11
360° – 250° = 110° Angle = M – 30H
11 2
8 M = 330
23. (c) 6 : 32 min 2
11 11
M – 30 × 6 = 180
2 2
11 M = 330 ×
Angle = M – 30H 11 11
2 M = 60 M = 360
2
11 3 vxj 180° ls vf/d gS rks360 esa ls
M –30H = 0 2 : 27
2 11 Minus ?kVkrs gSA

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 10

11 109 179 ?kaVs

of this clock
M = 360 – 360 31. (b) 11
2 121 24  15  179
=
11 Total loses in 66 feuVis = 66 – 358
M=0
2 5 720 = 180 hour of correct clock.
M=0 65 = 66 – The correct time would be = 9
11 11
6:00 p.m. + 1 hour = 10 p.m.
726 – 720 6
= = 34. (c) 1 A.M Wednesday
29. (b) 8 : 36, 8 : 51 3 11 11
11 Sunday 9 A.M Upcoming
6 Friday 9 P.M
11 In 1 feuV=
Angle =
2
M – 30H 11  66 –4 feuV4 feuV15 sec.

r
In 24 × 60 feuV Total gains = 8 min. 15 sec
feuV 6º

Si
1
7 feuV 42º 6  24  60 1440 15 1 33
= = =8+ =8+ = min.
11  66 121 60 4 4
11
M – 30 × 8 = 42 ?kaVs

et
2 109 Total = 5 days + 12 hr.
= 11
121
feuVloss.
11 = 120 + 12 = 132 hours
M = 282
2 32. (c) 8 p.m

je
33
564 3 Total hours form 8 a.m. Sunday feuVgains in = 132 hour
M=
11
= 51
11
feuV to 9 p.m. following sunday = 181
4

am
hours 132
AND
24 hours + 8 feuV 1 feuVgains in = 33 × 4
11
M – 30× 8 = -42º 8 2 360  2
2
24 + = 24 + = 132
4 feuVgain in =
kr
11 60 15 15 × 4 × 4 = 64
M =198 33
2 362
=
15
?kaVs hour
396
feuV ?kaVs
Vi

M= = 36 362 9 A.M Sunday + 64

11
15
?kaVs
of this clock 9 A.M Sunday + 2 dyas 16 hours
8 : 36, 8 : 51 3 = 1 A.M Wednesday
11  24 ?kaVs
of correct clock
35. (c) Sunday 9 A.M
by

8 15 6 A.M Thursday 5 P.M upcoming

30. (b) 32
11 1 ?kaVs
of this clock = 24 × ?kaVs
362 Wednesday +3 feu V –
Normal watch overtakes in of correct clock (3 minutes + 12 sec.)
181 ?kaVs
of this clock Total loses = 6 min. + 12 sec
ng

5
= 65 minute
11 24  15  181 12 1 31
= =6+ =6+ = min.
This watch overtakes in = 64 362 60 5 5
ni

minute
= 180 hours of correct clock Total ?kaVs
= 6 days + 11 ?kaVs
It means In 64 feuVthe clock The correct time would be = 24 × 6 + 11 = 144 + 11
gains
= 9 p.m – 1 ?kaVk = 155 ?kaVs
so

= 8 p.m
5 5 16 33. (d) 10 p.m. 31
= 65 – 64 = 1 = min. feuVlose in = 155 ?kaVs
11 11 11 Total hours of clock from 10 A.M 5
ea

“In one day = 24 × 60 feuV” Sunday to 9 P.M on

following Sunday = 179 ?kaVs 155
Then in 1 feuVclock gains 1 feuVlose in = 31 × 5
24 hour – 8 feuV= 23 ?kaVs
52 feuV
R

16
= 155
11  64 23+
52 345  13 358
= = hr. 3 feuVlose in = 31 × 5 × 3
60 15 15
In 24 × 60 feuVclock gains = 75 ?kaVs
358
=
16  24  60 ?kaVs
of this clock = 24 ?kaVs
of 75 ?kaVs
= 3 day + 3 ?kaVs
11  64 15
Thursday 6 A.M + (3 day + 3 ?kaVs
)
360 correct clock
= Sunday 9 A.M
=
11
feuV 15 36. (c) 125º
1 ?kaVk
of this clock = 24 × ?kaVs
8 358 Hour's hand 4 ctdj 10 feuV esa ?kaVs
= 32 feuVgain of correct clock dh lqbZ }kjk pyh xbZ nwjh
11

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 11

Hour' hand 44. (c) 85° 300 3

1 hour  30º and 60 m  30º 11 M= = 27
11 11
1 Angle = M – 30H
4 hour  120º 1 m  º 2 AND
2 H = 11, M= 10 11
1 Angle = M – 30H
vr%= 10 m  × 10 = 5º 11 × 30 = 330° 2
2 11
120 + 5 = 125º 10 × = 55° 11
37. (d) 180° 2 M– 30 × 2 = –90
330° – 55° = 275° 2
12 hour  360°, 1 hour  30°
But 275° is more than 180° 11
9 cts ls 3 cts rd ?kUVks dh la[;k hence we subtract this angle from M = 60 – 90 = –30
2
= 9 – 3 = 6 × 30° = 180° 360° 11
38. (a) 160º 360° – 275° = 85° M = 360–30

r
2
1 hour = 30º, 45. (d) 142°

Si
11
30 11 M = 330
1 minute = Angle = M – 30H 2
60 2
2
5 hour 20 minutes H = 3, M = 56 M = 330 ×
11

et
= 5 × 30º + 20 × 0.5º 3 × 30° = 90°
M = 60
 150 + 10 = 160º
11 5
39. (a) 120° 56 × = 308° 2:5

je
 1 hour = 30° 2 11
 2 cts ls 6 cts rd 308° – 90° = 218° 8
But 218° is more than 180° hence 49. (b) 32

am
 4 hour 11
we subtract this Angle from 360°
 4 × 30 = 120° Normal watch overtakes in
360° – 218° = 142°
40. (c) 54° 5
46. (b) 110° = 65 minute
11 11
11
kr
Angle = M – 30H Angle = M – 30H This watch overtakes in = 64
2 2 minute
(Subtract smaller from larger) H = 12, M = 20 It means In 64 feuVthe clock
Vi

Hence H = 4, M = 12 12 × 30 = 360° gains

4 × 30 = 120° 11
20 × = 110° 5 5 16
11 2 = 65 – 64 = 1 = min.
12 × = 66° 11 11 11
360° – 110° = 250°
2 “In one day = 24 × 60 feuV
by

”
120° – 66° = 54° But 250° is more than 180°
hence subtract this angle from Then in 1 feuVclock gains
41. (b) 21.5°
360° 16
11 =
Angle = M – 30H 360° – 250° = 110° 11  64
ng

2
6 In 24 × 60 feuVclock gains
H = 9, M = 53 47. (c) 10 : 54
9 × 30 = 270° 11 16  24  60
11
10 ls 11 cts ds chp 0° dks.k =
11  64
ni

53 × = 291.5° 11 360
2 Angle = M – 30H =
11
feuV
291.5° – 270° = 21.5° 2
42. (b) 107° 8
so

11
M – 30 ×10 = 0 = 32 feuVgain
11 2 11
Angle = M – 30H 50. (c) 130º
2 600 6
M= = 54
ea

H = 12, M = 46 11 11 11
12 × 30 = 360° 6 Formula:  Angle = 30H – M
10 : 54 2
11 11
46 × = 253°
R

2 3 11
360° – 253° = 107° 48. (b) 2 : 27 3 ctdj 40 feuV= 30  3 –  40
11 2
43. (b) 160.5°
2 ls 4 cts ds chp 90° dks.k = |90 – 220| = |–130| = 130º
11
Angle = M – 30H 11 3
2 Angle =
2
M – 30H 51. (d) 5 ctdj 27
11
feuV
H = 7, M= 9
7 × 30 = 210° 11
M – 30 × 2 = + 90 11
11 2 Formula:  Angle = 30H – M
2
9× = 49.5° 11
2
2
M = 150 5 ls 6 ds chp 0° dk dks.k
210° – 49.5° = 160.5°

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 12

;fn feuV dh lwbZ

270º clockwise esa 11
O = 30  5 –
11
M pyrh gSA lw=k% m  30H  90
2 2
12 11
11 m  30  2  90
O = 150 – M 6º 1min. 2
2 1
9 3 1º min. 11
6 m – 60 = 90
11 1 2
M = 150 270º ×270
2 6 6 11
= 45º m = 150
300 3 2
M= = 27 4 : 35 10
11 11
+ 45 11 m = 300 = 2 ctdj 10 11
62. (a) 20 : 15 ?k.Vs
3 4 : 80 = 5 : 20 min
vFkkZr % 5 ctdj 27 feuV ij nksuksa

r
11  ?kaVs dh lwbZ nf{k.k&iwoZ fn'kk esa gSaA
24 ?kaVs ds izk:i esa lok vkB

Si
lqb;ka ,d&nwljs ds lkFk jgsxhA = 5 : 20 feuV 20 : 15 dks lok vkB cksysxsA
52. (d) South 56. (a) 88 63. (c) 6 : 20
NksVh lwbZ iwoZ fn'kk n'kkZ jgh gS 9 cts nksdk
fnuksa ds vof/ esa ?kM+h dh ?kaVs vkSj feuV
niZ.k izfrfcac ¾ 11 %Formula
60 ( )

et
le;A ds lwbZ
90º dk dks.kA  5 % 40
According to question ?kaVs dh 90º
lwbZdk dks.k cukrh gSA 11 % 60 & 5 % 40 ¾ 6 % 20
S

je
1 ?kaVs ¾ 2 ckj 64. (b) mÙkj&iwoZ
E W 12 ?kaVs ¾ 22 ckj 6 % 00 ,d gkFk ?kM+h dh ?kaVs okyh lwbZ
mÙkj&if'pe fn'kkA

am
24 ?kaVs ¾ 44 ckj
N
48 ?kaVs ¾ 88 ckj N N
vFkkZr% cM+h lwbZ iwoZ fn'kk ds nkfgus ;kfu 12 12
uksV90º
% dk dks.k 2&3 vkSj 3&4 ds chpNW
nf{k.k fn'kk esa gksxhA NE E S

53. (b) 7 cts

esa 3 cts
common jgsxk] bldk eryc
kr
W9 3 E NE 9 3 W.S
30º ?kwerh gS ?kaVs= dh1 ?kaVk
lwbZ 2&4] nks ?kaVs90º esa
,d ckj gh cusxk]
blfy, 24 ?kaVs esa 44 ckj curh gS vkSj WS
48 SW N W
1
Vi

6 6
1º ?kwerh gS ?kaVs= dh lwbZ?kaVk ?kaVs esa 88 ckj cuk;sxhA S NW
30
57. (d) 1140º vr% 9 cts ?kaVs okyh lwbZ mÙkj&iwoZ fn'kk esa gksxhA
1
1º ?kwerh gS ?kaVs= dh lwbZ× 90 feuV dh lwbZ1 ?k.Vs esa
360º dk dks.k65. (b) iwoZ
30 cukrh gSA
by

E E
= 3 ?kaVk 1 feuV= 6º 12 12
4 cts ls 90º ?kweus ds ckn le; vr%3 ?k.Vs 10 feuV= 360° × 3 + 10
= 4 + 3 = 7 cts × 6° = 1140° N9 3S N 9 3S
ng

54. (c) West 58. (c) 4320º

jkr ds 9 cts ?kaVs dk dkaVk ¾
North 1 feuV ¾6º
9:00 PM 6 6
9 12 feuV ¾6 × 12 = 72° W W
ni

N
1 lsdaM ¾72° × 60 bl iz'u ds vuqlkj lqcg 6%00 feuV dh
6 12 W E
S
dks.kh; nwjh ¾
4320º lwbZ iwoZ fn'kk dks bafxr dj jgh gSA
so

3 59. (a) 8 : 05 66. (a) nf{k.k

lqcg 6 % 30 cts] niZ.k izfrfcac ¾ 11 %formula
60 ( ) N N
= 3 : 55 12 12
ea

9
N
= 11 : 60 – 3 : 55 = 8 : 05 10
6 12 W E 60. (d) 130º, 9 : 25 W9 3 E W9 3E
R

S
3 11
Formula dks.k 2  25  30  9
lqcg 6 % 30 cts feuV dk dkaVk if'pe 6
S
6
S
fn'kk esa gksxkA = |11 × 12.5 – 270|
¾ 9 % 15 (loka ukS cts)
55. (a) South-East = |137.5 – 270|
= |–132.5| rc] 75 feuV ckn
12 = 9 : 15 – 1 : 15 = 10 : 30
= 132.5 ~ 130º
10 bl iz'u ds vuqlkj 75 feuV ckn 10%30
9 3 4 : 35 61. (d) 2ctdj 10 11 feuV gksxk rks feuV okyh lwbZ
(South)
2 cts ls 3 cts ds chp 90º nf{k.k fn'kk dks bafxr djsxkA
6

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 13

67. (d) mÙkj 73. (b) 75º gj 24 ?kaVs2esa ?kaVs de gks jgh gSA
11 12 1
?kMh
3 : 30 dh lwb;ksa ds chp dk dks.k blfy,]
10 2 11 lkseokj= lqcg ds 6 cts]
dks.k
=
2
m  30H
eaxyokj= lqcg ds 4 cts]
9 3
8 4 11 cq/okj= lqcg ds 2 cts]
 30  30  3
7 6 5
=
2 xq#okj = 12 cts vk/h jkr]
1 % 30 ij mÙkj&iwoZ esa gS ysfdu fugky dh
= |11 × 15 – 90| 'kqØokj = 'kke ds 10 cts]
fLFkfr esa dksbZ ifjorZu ugha gqvk rks 30
= |165 – 90| = 75º 'kfuokj= 'kke ds8 cts]
feuV ckn 2 ctsxk vkSj feuV okyh74.lwbZ
(c) 105º jfookj= 'kke ds6 ctsA
mÙkj fn'kk esa gksxkA 2 % 30 cts ?kaVs dh lwbZ vkSj feuV 79.ds(a)
chpmÙkj&iwoZ
68. (a) iwoZ dk dks.k

r
Si
N 11 11
m  30H =  30  30  2 12
11 12 1 = 11 1
2 2
10 2 10 2
= |11 × 15 – 60|
W9 3E
= |165 – 60| = 105º 9 3

et
8 4
7 5 75. (d) 240 8 4
6
S 8:00 cts ?kMh ds nksuksa lqb;ksa ds chp dk 7 5
6 % 15 (lok 6 cts) ?kaVs okyh lwbZ nf{k.kdks.k= 8:00
6

je
fn'kk esa gS rks feuV okyh lwbZ iwoZ fn'kk esa gksxkA
69. (c) if'pe 11 11  vr%1:40 ij ?k.Vs dh lqbZ mÙkj&iwoZ
fn'kk
dks.k= 2 m  30H = 2  0  30  8

am
11 12
1 11 12
1
esa gSA
10 2 10 2 = |–240| = 240º 80. (d) nf{k.k
9 3 9 3 76. (d) 216º NksVh lwbZ iwoZ fn'kk n'kkZ jgh gS 9 cts dk
?kaVs okys lwbZ
kr
8 4 8 4 le;A
7 6 5 7 6 5 360º ?kwerh gS 12 ?kaVs 18º ?kwesxh
rks iz'ukuqlkj]
7%30 cts ;fn ?kaVs okyh lwbZ nf{k.k if'pe12H  360º
Vi

S
dh vksj bafxr djrk gS rks 15 feuV ckn 360
1H = = 30º
feuV dh lwbZ if'pe fn'kk dks bafxr djsxkA 12 E W

70. (a) 1 ?kaVs 6 feuV 36 lsd.M 30 1º N

by


1-11 ?kaVs dks ?kaVs] feuV vkSj lsd.M 1m = 60 2
1 ?kaVk] 10 feuV] 1 lsd.M vFkkZr% cM+h lwbZ iwoZ fn'kk ds nkfgus ;kfu
1º
Trick : vFkkZr~  1m nf{k.k fn'kk esa gksxhA
2
81. (b) 7 cts
ng

11 × 60, 60 × 60 rks18º pysxh ¾ 36 feuV esa

30º ?kwerh gS ?kaVs= dh1 ?kaVk
lwbZ
6.60 iz'ukuqlkj feuV okyh lwbZ pysxh
¾ 1 ?kaVs 6 feuV 36 lsd.M 360º  60 feuV 1
1º ?kwerh gS ?kaVs= dh lwbZ ?kaVk
ni

30
71. (d) 9 ?kaVs 6 feuV 36 lsd.M 360
1 feuV ¾ 60 ¾ 6º
9 ?kaVs]×-1160 ¾ 6-6 ¾ feuV] vkSj fiQj 1º ?kwerh gS ?kaVs
1
= dh lwbZ
so

× 90 =
-6 × 60 lsd.M 36 feuV esa pysxh = 36 × 6 = 216º 30
9 ?kaVs] 6 feuV] 36 lsd.M 77. (b) nf{k.k 3 ?kaVk
72. (a) lqcg 2 cts lkseokj W W 4 cts ls 90º ?kweus ds ckn le;
ea

=4+
12 12
?kM+h jfookj dks8lqcg cts 5 feuV /heh 3 = 7 cts
vkSj lkseokj dks8jkr cts rst ikbZ xbZA N 9 3S N 9 3S
R

jfookj lqcg 8 cts ls lkseokj jkr 8 cts


rd dk le; 36 ?kaVs 6 6 : 00 6 9 : 15
?kM+h 36 ?kaVs(5 + 5)esa
feuV rst gqbZA E E
bl iz'u ds vuqlkj 6 cts fn'kk dks bafxr
lgh le; fn[kkus ds fy, mls dsoy 5
djrk gS vkSj 9%15 cts feuV okyh lwbZ
feuV rst gksuk pkfg,A
nf{k.k fn'kk dks bafxr djsxkA
10 feuV = 36 ?kaVs esa rst gqbZA
78. (a) jfookj 'kke 6 cts
rks5 feuV rst gksxh
36
 5  18 ?kaVs esa 1 ?kaVs5esa feuV de gks tkrh gSA
10 12 ?kaVs60 esafeuV ;k 1 ?kaVk de gks
rks lkseokj dks lqcg
2 cts ,dne lgh FkhA tkrh gSA
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