SSC MAINS (MATHS) MOCK TEST-1 (SOLUTION)

Transcription

1 007, OUTRM LINES, ST FLOOR, OPPOSITE MUKHERJEE NGR POLICE STTION, DELHI-09 SSC MINS (MTHS) MOCK TEST- (SOLUTION). (B) Order of surds re,,. LCM of, nd is. So, convert ec surd into surd of order > 0 >. (C) ( 9) ( 8) 0 8, 9 y y y 0 y y y 0 0 (y ) (y ) 0 y, Now y 8.() Difference ( ) Sum Te required nswer (D) Let two digit numer e 0 y y () 0y 0 y or, y 9 () From eq n () & () 9 nd y Te required numer (B) Te required reminder d r r were, d te first divisor r te first reminder r te second reminder 6 Te required reminder (B) LCM of nd 7 Now, divide 00 y nd te quotient otined is te required numer of numers Tus, tere re 8 numers. 7.() Let te middle numer e. ccording to question, (D) Te required nswer 9.(C) Let frction e /y Now y y 9 7y () nd y y y () Now, eqution () eqution () 7 nd y 6 8 Sort cut Te required nswer smller vlue 66 8 y 6 0.(C) Let numer e. < < 96 < < 0 Numer will e etween 96 nd 0. Since one prt of te numer is te squre of 6 it mens one fctor is 6 LCM of 6 nd 80 P ,

2 007, OUTRM LINES, ST FLOOR, OPPOSITE MUKHERJEE NGR POLICE STTION, DELHI-09 Numer will e multiple of 80 i.e Te only vlue wic stisfies te condition is 980..(C) Let te tree consecutive numers e, nd respectively. Difference etween first nd tird numer.() Let numers e, y, z. Ten y nd y z y z y z 9 0 y z So, second numer 0 0.(C) Numer of one digit pges from to 9 9 Numer two digit pges from 0 to Numer of tree digit pges from to 00 0 Totl numer of required figures (9 ) (90 ) (0 ) 9.() Required numer LCM of, 0 nd LCMof,, nd HCF of, 0nd.(B) LCM of 6, 7, 8, 9 nd 0 0 Te gretest numer of si digits is Dividing y 0, we get 079 s reminder. Hence te numer divisile y 0 is Since 6, 7, 8 6, 9 7, 0 8 te reminder in ec cse is less tn te divisor y. Te required numer (D) LCM of,,6,8, 0,, 0 Required numer 0 K ; K is positive integer. ) 0 ( K ( 9 ) K ( 9 K) (K ) For every vlue of K, ( 7 K) is lwys divisile y. Pulting vlue of K equl to,,,, --- etc. in succession, we find tt numer8. Lest vlue of K wic will mke (K )divisile y is 8. Te required numer (B) `dsfsd0-p -P Numer of coins Vlue 7.7 P , (B) Silver Copper st nd Mi (C) leps of ound 6 leps of re. 0.(B) 7 leps of ound 6 7 leps of re rte of ound rte of re 8 I E S B (7 8) (000 0) 000 's income B's income B 8 000

3 .(B) 007, OUTRM LINES, ST FLOOR, OPPOSITE MUKHERJEE NGR POLICE STTION, DELHI-09 7 (lengt) unit/r St nd 7 r r Let fter t time t 7t t 6 t t 6 t 8t t 8 rs t r 0 min.() Lmn Gopl Lst yer Lst yer Present Yer Lmn / Gopl 6 Present yer Lmn Gopl 6 8 Lmn's Slry 60 8 `600. () B's profit ` ` 9 's profit ` 9 ` 0 's profit per mont ` 0 B's profit per mont ` 9 Teir cpitls re proportionl to teir profit, 's cpitl B cptitl Difference etween teir cpitls 7, ut te ctul difference is 00. 's cpitl 0 ` 0.() Houses contining only one person 0 60% Houses contining only mle 60 0 % Houses contining only one femle 60 8%. (D) Present ge of usnd nd wife 6 yers Present ge of usnd, wife nd cild 0 60 yers Present ge of cild (60 6) yers 6. (B) Let son's ge e, ten Kml's ge 0 yers Kml's ge t te time of mrrige (0 6) yers. 0 (0 6) or or yers. 7.(D) Let Mrked price nd cost price y 6 96 y y Required % 8.(C) 0% % % st I mont nd mont On tis e gets ( ) 0 00 In I st mont (B) Rtio of prts 0% % P , Difference etween gretest nd smllest 76 ( 0) ` 0 0. () Let mount lent t % (000 ) `.(B) SI for yers ` 00 SI for yer ` CI for yers SI for yers Interest on st yer's SI

4 007, OUTRM LINES, ST FLOOR, OPPOSITE MUKHERJEE NGR POLICE STTION, DELHI (C) 900 P P ` 000 ` 0 6 CI Difference `.08.(D) Pyment is qurterly, so r %, t 8 yers Required nswer.() 0% P.() 6.(B) 7.(B) ` Totl interest 60 0 ` 90 I 6% 6% II 8% fter tking out 0 litres of miture B B 0 0 Mke equl ecuse it is not cnging. Miture s initil quntity () 0 0 's quntity C B 0 8 Litre 8 B C 9 B, C, ( B C)'s dy work unit dy's work unit will tke 8 dys B will tke 6 dys C will tke 8 dys 8.() is times s fst s B. It mens if does work in dy ten B will do in dys. 60 Totl 60 dys B 9.(B) Required time 9 6 minutes 0.(B) Totl time 8.(C).(B) 8 60 ours ours min 8 ours min P Q R - Time tken y to rec R from P Time tken y B to rec Q nd return from Q to R km P , of totl time in trin ours Totl time in trin ours Totl time spent in ir 8 ours By ir, in rs distnce trvelled 00 Km in ours, distnce trvelled Km Distnce covered y trin km So, te required rtio 00

5 .(B) 007, OUTRM LINES, ST FLOOR, OPPOSITE MUKHERJEE NGR POLICE STTION, DELHI-09 Let originl speed e km/our. ( ) ( ) 7 Km/our. () Let distnce etween Deli nd Knpur is. Let trin leving from Deli is nd from Knpur is B. 's speed 0m m B's speed pm 7m Km/our 7 Km/our Distnce covered y till 7 m Km / () / 7.(D) z z sin sin sin sin sin sin sin sin sin sin sin sin sin sin sin sin z sin sin z sin sin sin Remining Distnce Km Reltive speed Km/our 7 Time tken y ot trins to cover te distnce 7 ours ours min Te two trins will meet t 7 m our min 8 m.(c) tn tn ( B B) tn ( B) tn ( B) tn ( B) tn ( B). sin 90º 6.(D) Tke º y 8.() sin z sin cos z sin z cos sin z cosec cot sin y sin y y sin y sin y sin y sin sin cosy cos sin y sin cosy cos sin y sin cosy cos sin y sin cosy cos sin y sin cosy cos sin y tn tn y 9. (D) cosec y y ( y) / ( y ) / cot cosec / /. cot y y P ,

6 007, OUTRM LINES, ST FLOOR, OPPOSITE MUKHERJEE NGR POLICE STTION, DELHI-09 cot cot y y y y cot y y 0.(C) ( cot cosec ) ( tn Sec ) Put º, (cot º cosec º) ( tnº sec º) ( ) ( ) ( ) ( ).(C) sin sin.. sin. cos ( sin sin ) cos sin cos cos cos cos 0 cos cos cos 0 cos (cos ) (cos ) 0 ( cos ) (cos ) 0 cos or.(d) sin º sin 0º sin º --- sin 8º sin 90º sin º sin 8º sin 0º sin 80º. () sin º sin 90º So, 8 9 tn 60 tn 60 θ θ 60 60m tn tn tn.(b) P , m Let speeds re nd 9 m/s lengt of I st trin m lengt of II nd trin 9 m Time to cross ec oter Sumof lengts Sumof speeds 9 70 sec.() P Q R I cn row from P to R in ours. I cn row from P to Q in ours. I cn row from P to Q nd ck in 0 ours. I cn row from Q to P in (0 ) 8 ours Hence in rowing wit te current, I tkes ours nd in rowing ginst te current, I tkes 8 ours. Te distnce is sme, terefore, down rte nd te up rte re inversely proportionl to te times. down rte up rte 8 speed of ot in still wter speed of river 6.(C) B C (mke B equl) In 0 m rce, cn et C y m. In m rce, cn et C y 9 m

7 007, OUTRM LINES, ST FLOOR, OPPOSITE MUKHERJEE NGR POLICE STTION, DELHI-09 7.(C) Now, 8.(C) ( ) 9.(B) / / By compring 9 60.(C).. 8 Now, (B) If y z, y z, z y y z y y y y z y y z z z z (from given condition) 6.(B) c c c c c c c c c c c z y z c c c c c c c c c P ,

8 007, OUTRM LINES, ST FLOOR, OPPOSITE MUKHERJEE NGR POLICE STTION, DELHI-09 c 68. (B) Boys Girls c 6.() Ceck troug options. Wen ( c) c c c c c c c c c c c c c c c c c c c (c) 6.(C) Let numers e 7 nd 7y, were nd y re co-primes. LCM of 7 nd 7y 7y ccording to te question, 7y 7 y nd y 7 or 7 nd y 6 First numer Second numer Sum of numers (C) ( 6) ( ) 0 6, ecuse cn't e considered 66.() ( ) 6 ( 6 6) 6 8 wic is divisile y () y y 7 y K y K y 7K ( y) ( y) 9 K K y 8 K 6 K 8 K K 68 8 % of oys in clss 60% 69.(B) Percentge of fmilies ving eiter cow or ufflo or ot % It mens % of fmilies do not ve eiter cow or ufflo Required numer of fmilies % of (D) Let totl votes 96 Vlid votes % % % % 0% of votes 7.(B) Rtio of cpitl investment B C,000 0,000,000 6 Let totl profit e. get 0% for mngement Remining profit 70% 7.() 000 s sre 0 70 % (BC) s sre % Wen, difference 0, ten totl profit Wen difference ` 00, ten totl profit 0 ` 000 0% % 0 o r 0,800 0% or 000 ` y K 7.(B) Present wort P P , T R

9 007, OUTRM LINES, ST FLOOR, OPPOSITE MUKHERJEE NGR POLICE STTION, DELHI ` () ccording to question, M W B M D M D (M W B) 7 B D (B B B) 7 B D D 9 dy 7.(D) 76.(C) r O r C r r r D B OCD is equilterl tringle. COD 60º CBD 0º (Property) CB 90º BCP 80º 90º In CBP BCP CBP CPB 80º 90º 0º CPB 80º CPB 60º nd PB 60º N B T P 78. (*) 79.(B) VT DM V D T M 6 M M TM 6 CDM CBT CD BD CM TM CM 6 CM 6 TC CM TM 6 6 B P D C B C D is mid point of C P B D (Property) P B P B B M P PB B PB P 77.(C) D C If re TM, ten re MN re BPM 8 re MNP 8 re MTP TM TMP V T M B B 80.(C) sin cos 7 sin sin 7 sin sin 8 0 sin sin 0 sin 8 0 sin (sin ) (sin ) 0 ( sin ) ( sin ) 0 sin cot B D C T 6 (Given) P ,

10 007, OUTRM LINES, ST FLOOR, OPPOSITE MUKHERJEE NGR POLICE STTION, DELHI (B) Let sides e,, (D) inrdius S 7 tn 60º S 6 0 Smllest ltitude will e on te longest side re of 6 re of regulr egon 6 8. (B) 6 D 0º 0 In DEC E 6 C sin 0º EC CD EC 0 EC cos 0º ED CD ED 0 ED In ECB EB BC EC EB 6 EB 6 EB EB BD ED EB BD 6 6. B ( ) m cm. Red; "Heigt nd se rdius of te cone re sme" of te question s "Heigt nd se rdius of te cone re respectively equl to te eigt nd se rdius of te cylinder" 8.(B) l 8 l 6 l r 8 cm cm l 89 l 7 cm Totl surfce re r r rl [ ] 0 cm 8.(D) R cm H cm BC DE D r B C R r r E P ,

11 86.() 007, OUTRM LINES, ST FLOOR, OPPOSITE MUKHERJEE NGR POLICE STTION, DELHI-09 r Volume of frustrum (R r Rr) 0 7 ( r)( r r) ( r) ( r r) ( r) ( r r) r r r 0 r 0 cm 88. (B) Let Mn cn do unit work in dy, ten 0 men will do in 0 dys unit work. Dys Men Work Totl dys 0 89.() Rtio of efficiency B C Working togeter tey will empty in ours 9 units 9 E In 6 ours 0 min 0 ours, tey will. empty units B 6 BC D EDC BC m C l C B BC 8 m Lterl surfce re rl m 87.(B) re covered y roller in one revolution r cm Let totl re e 88% of 88 60,000 cm Totl cost of levelling.. 60,000 ` 0000 will empty te pool in (C) If (sin cos ), y (sin cos ) Now, y ours. (sin cos ) (sin cos ) sin cos sin cos sin cos sin cos 9.(C) Required nswer 0 (0 ) 60 lks 9.(D) Percentge vrition Model Model B Model C () Required difference % % % P ,

12 007, OUTRM LINES, ST FLOOR, OPPOSITE MUKHERJEE NGR POLICE STTION, DELHI lks (B) Required production 0 lks (C) Required nswer lks (D) % 60º % 60 º 60º 0 0% 6º 97.(B) % Totl cost ` 700 % of totl cost ` 700 ` (C) Difference in percent cost of inding nd cutting crges nd roylty (8 )% % % of totl cost ` 6000 % of totl cost ` 6000 ` (B) Difference in percent epenses on printing cost nd dvertisement crges ( 8)% 7% Now, %.6º 7%.6º 7 6.º.(B) Te required percentge 0 8.6% (ppro.) SSC MINS(MTHS) MOCK TEST- (NSWER KEY). (B). (C). (). (D). (B) 6. (B) 7. () 8. (B) 9. (C) 0. (C). (C). (). (C). (). (B) 6. (D) 7. (B) 8. (B) 9. (C) 0. (B). (B). (). (). (). (D) 6. (B) 7. (D) 8. (C) 9. (B) 0. (). (B). (C). (D). (). () 6. (C) 7. (B) 8. () 9. (B) 0. (B). (C). (B). (B). (). (C) 6. (D) 7. (D) 8. () 9. (D) 0. (C). (C). (D). (). (B). () 6. (C) 7. (C) 8. (C) 9. (B) 60. (C) 6. (B) 6. (B) 6. () 6. (C) 6. (C) 66. () 67. () 68. (B) 69. (B) 70. (D) 7. (B) 7. () 7. (B) 7. () 7. (D) 76. (C) 77. (C) 78. (*) 79. (B) 80. (C) 8. (D) 8. (B) 8. (B) 8. (B) 8. (D) 86. () 87. (B) 88. (B) 89. () 90. (C) 9. (C) 9. (D) 9. () 9. (B) 9. (C) 96. (D) 97. (B) 98. (C) 99. (B). (B) P ,