Page 1 :
Clock and calendar are the basic instruments, that are being used to measure time in, , different units., , Clock, , A Clock is an instrument that indicates time. It, has three hands i.e. a short hand that indicates, hour (hour hand), a long hand that indicates, minutes (minute hand) and a thin long hand, that indicates seconds (second hana)., , The face or dial of a clock is divided along the, circumference into 12 equal parts called hour, spaces and 60 equal parts called minute, , | spaces., , The basic structure of clock is as follows., , , , Minute hand, , Hour hand, , te, 60 minute spaces = 360°, 1 minute space = 6°, , Similarly,12 hour space = 360°, i 1 hour space = 30°, 60 min = 1 hour, 30 min = Half an hour, , 15 min = Quarter of an hour, 1 min = 60s, , ., , , , Clock and Calendar, , Fast and Slow Clock, , If a watch or a clock indicates 6:15, when the, correct time is 6, it is said to be 15 min fast., , On the other hand, if it indicates 5:45, when the, correct time is 6, it is said to be 15 min slow., , i a, , * In 60 min, the minute hand gains 55 min space over, hour hand., , * In every hour, both the hands coincide once., , * The hands are in the same straight line, when they, are coincident or opposite to each other., , * When the two hands are at right angles (90°), they, are 15 min space apart., , * When the hands are in opposite directions, they are, 30 min space apart., , » Angle traced by hour hand in 12 h =360°, , 360°, , .. Angle traced by hour hand in 1 h= ae 30°, , , , .. Angle traced by hour hand in 1 min = a, , , , , , Angle traced by minute hand in 60 min = 360°, , -. Angle traced by minute hand in 1 min = 300" = 6°, 60, , * The angle between the minute hand and hour hand, , of a clock is,, , 1, , 6= Ui m~ 30h), 2, , , , where, h = hours andm= minutes, , Both hands of a clock occurs at right angle twice in, one hour, 22 times in 12 h and 44 times in 24 h., Both hands of a clock occurs in a straight line or are, opposite once in one hour, 11 times in 12 h and, 22 times in 24h.

Page 2 :
How to crack Test of Ri, , time when, following da, 11:40pm, (b) 12:48pm, (9 2pm, (a) 10pm, Solution (b) Time from 8am of aj, the f ing day = 29h, Now, the clock gains 10 4, in of this clock is equal to 24 hy, , year which has, not divisible by 4. @, tc. Ordinary ye, , has 366 days. Su, divisible by 4., , Tlustration 5. At what time bet, 8 O'clock will the hands of % a 1, straight line but not tog, , , , (@)52 min past7, pty, , (b) 5 min past 7, (0) 15 min past 7, , (4)7 3 min pas, ip min past 7, , Solution (a) At 7 O'clock the hour f, minute hand is at 12. Thus, tl, apart, To be in a straight line but, be 30 min spaces apan,, , So, the minute hand have to, , Now, 55 min spaces are g, , "of ode days, , Ox, , = 2041 97d, ‘min past 7, = weal, , “The hands will be in a, ase, VW

Page 3 :
———_—_ |, , How to Crack Test «, , , , Mlustration 9. What was th atl, en first Rept what ine, , , , (@) Friday, , , , , , Solution (c) Number of odd day, = Sunday +1 Number of odd days ii, + at Now, in 49 yr, there are: ‘st ovhat time between 4 1 h. Wha, 2 = Monday +2= years. the hands of a watch Reeser ric eat, oN 4, , (b) 11:00 pm, an ordinary : a @ 12:30pm, =24+37=61 ae min d of a clock overtakes the, 8 i srvals of 63 min of the, = 8 weeks +5 vals : a, Number of odd days in does a clock gain, Now, for 26 January, = Number of odd days, , , , , , jendar of year 1997., , , , , (@) Tuesday, Thursday, 5. Athalf past 5 in the, angle between the hot, a clockis id, (10° py 128, 6. The angle between, minute hand of a, will be, , art, , The last day of a cer, 1 Tuesday, TI. Saturday, (a) Land 1, , , , , , , , , a, Q—, (b) zi, , , , , , , , (9 29 5, ; Z, € the angle betw. - A clock was set co, nd if lock shores ut hand 10 minutes per, Shows 8:30 pm? between the hour, OF 07 yay *SPOvB00 lock after one ho, , (d) 85°

Page 4 :
y, , How to Crack Test of F, , 30. Mrs. Susheela_, anniversary on Tt, 1997, When will, wedding anniver, (a) 30th September, 200, (b) 30th September,, , 30th September,, , ath October, 2003, , 31, If the Republic Day o}, l saturday, X was, 3 Monday, then what SY ee, , s INovember, 1994? if, maT 2013, , , , , , , , (c) Wednesday, (a) None of these,, , 32. Nasir’s birthday is on., 3 hat day of the w, ved that January 1, 2023 is a ws i ‘, ‘ Birthday in the same, hich year again the January 1st pai vin, , , , will eo) x00 MPPSC 2018 () Wednesday, 264 (4) 2037 () Saturday ‘, (©) Friday oh, , r 1990 will have the same (a) Thursday }, , 33. The birthday of ¥ was ¢, bet, , m on August 11. Mohan is older Peg day, days, This year’s Sunday. On which day, , day falls on Monday. The day birthday ifibiyas, , Mohan’ birthday will fall this year (@) Weddesday, , (©) 1996 (4) 1992, , , , if, (0) Tuesday, (d) Thursday, , , , , , , , , , , , , , , , , , o | 3 | &, (a) | 18, © | 2, , 4, , , , , , , , , , , , , , , , , , », , , , go o.dock there iS: @, , gociock., {a), __ angie raged by hour}, , me period between 8, Hence, angle traced by ho, =6x., , , , , {b) We know that, @, , , , Here, h=S8andm=, e- ox 30-901, , = 0=75° ", , q, , ) Angie traced by hour he n, , ue, , (o) We know that, 6=|——, 2mm, , Here, m= 30andh=5, , , , > 6=15°, (@) We know that, =| z, a, , Here,m=25, andh=3, 18 25-2039), , , , (b) The clock loses 10, So, in one hour the, , 1, we can say that a, time as 12:50,, , , , , , o=|"xs0-%, 18) A3.0 :, fom the nea hae, AS. 55 min are, , 4, jin = 16— min, 15) in Ler, , coincide ates min past 3.

Page 5 :
How to Crack Test of Rec, , «min apart and to be at, , ir tee 15 min apart, ‘Since, we have to, , 5 a, iock between 5:30 aN, of hands of clock, the postions 45. (@) Three days after S ie of days in da, ans :, , Hence, today is Frid Jotal = 146 = 20 W, , , , , , 16. (¢) The last day of ce, ‘Tuesday, Thursday ou. on November 1,, 363, 83 ey, ae ig dumber of edd days, , is ye, , Lin Therefore the hands are at right ang! «Thursday + 6days=V sjumber of odd days in 400, , 48, (b) Each day of the ., Number of odd days in, , rrin past S So, after 63 days, it wil Now, in 83 yt, there are 20, , - F Therefore, after 61 days, Dodinary years. i, , cook gas = 3minyh 19. (a); Saturday is on J Number of odd days it, cecond dock gains = Sminvh =. Day on January 1,2001 = 14 weeks + 50dd, , Number of odd days ir, , ‘g.amto 6 pm on Monday = 9h, Number of odd days fro, , jock gains in 9h = (9x 3) min = 27 min 20. (a) Total number of days in ¢, ime as 6 : 27 pm. Also, the second 4 to March 1 = 30+ 29+ 1, = 184 = 26), . Total number of odd, , , , , , gh=(9x5)min = 45min and shows 60 +7 = Bweeks, =o So, the fourth day from, 5 am of a particular day to 10 pm., , , , , , 89h, Now, the clock loses it will be Sth Friday, other wor we can say that f, of this clock is equal to 24h of the 22. (a) Day on 26th Januely 18, iv Number of days from., coneet ck or (23+ = inaleap year, @ = 54294 314 3043, , =28 weeks + 6 odd <, , 3%, , = = hot this lack = 24 h of the correct clock, s :. Day on 15th August 2032 will have 2 odd de, ES of this clock Now, number of odd “The sum of odd days,, , to 15th August 2000 =1 2028-2033 =, , :.Day on 15th August W244 14 1424, the correct clock a =14day, “Onthis clock loses 1h 23. (¢) 18th February, 19, , , , -( — x 22)hotconect clock, , , , , , , , , Cock shows 10 pm., 14) hee es Again 18th February, (9 Th, oe ioe i in a conect clock, the minute Hence, 18th Fabra 19 i 1801 5 Be, fe spaces over the hour hand in 24. (We know that, the bith hes 366 days aa, iF 4 ; .€. 20, het again, the minute hand must gain celebrated Ona 14,1995 have 1 0, e hour hand Number of odd days, £60 min are gained in ( 60 if, in 3700) = 655 min, , But they are together ater 63 min, , Gai insomine( 5, in=| 652 ~g3\-9 5, rr 63-25-21 min