SSC Mains Mock Test 227 [Answer with Solution]

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1 SS Mins Mock Test 7 [nswer with Solution]. (D) E ccording to question, G G GF, F D Let, GF GF Now, eterior ngle FGE FGE FEG Now, eterior ngle D In DE, º 80º 7 5º (ppro.). () I st digit no. divided b 6 0 Lst digit no. divided b 6 6 P 0,..., 6, (cd 6) (n ) 6 n 50. (D) Let '' be the number of students nd 'w' be their verge weight. ccording to question, w 50 w + + w w gin, w (i) 0 00 ( 0) 8 ( + 0) m /min (use option) 5. () Given, D + + D 0º? In, + D + D 0º 6. () Let the outer rdius of pipe be 'r'. Then, volume of the metl 8 (r 8 ) 6 8 (r 8 ) r r r cm 7. () urved surfce re of frustrum (r + R)L D Here, R 8 m, r m.5 + w 7 From equtions (i) nd (ii) We get, w 7. () Let the rte of filling tnk be '' m /min. Then, the rte of empting the tnk ( + 0) m /min. nd L h (R r) L 6 0 urved surfce re, 7 ( + ) m (ppro.)

2 8. () Totl surfce re of prism lterl surfce re + (re of bse) Here, s b c 0 7 Required re ( ) 0 + 7(7 )(7 0)(7 ) sq. m.. () The error percent in re % () Let the mimum mrks be. Then, 6 5 5% of (D) Let the totl number of swns be. The number swns pling on the shore of the pond 7 Number of swns inside the pond 7 +. () cos squring both sides, cos cos Subtrcting from both sides, cos LHS :. () Using M GM + 5. () + b + c 0 +. Put, b, c Given epression, ( ) 7 ( + ) On solving 6 Number of swns 6 OR use option to solve the eqution ( ) 7. (D) Put, m n bc + b b c + 6. () + 0 c c b Multipling both sides ( + ) ( + ) ( + ) 0 So, ( + ) 0 7. () Put b c ( + ) + + 0

3 8. () using the vlues we get p b c q c r b P k(b c), q k(c ), r( b) Then, p + q + r k(b c + c + b) (D), 5, 6 (, ) (6, 5) re [ ( ) ( ) ( )] 0. () [6( 7 7) (7 5) ( 5 7)] 7 unit. () 0 c/ c/ 0 re b h 0 & + c b c c b + 0 b b c c (0, c/) + & re prllel. () Required mesurement (c/, 0) HF of 0 kg, kg nd 65 kg kg.. () ost of lemons 8 pise pise So, cost of mngoes cost of mngoes cost of 5 pples ost of ornges 08 pise ost of ornge 08 pise 08 pise. () Let the speed of trin on level terrin km/hr So, speed of trin through mountinous terrin ( 0)km/hr km Mountinous Level km 88 km ccording to question, ( 0) km/hr 5. () Milk in miture Required percentge 70 (6 ) 7% () Let be the totl score in the innings. So, the highest score nd, the net highest score of the remining runs

4 So ccording to question, 8 Remining prt Now, let be the time tken b ll three pipes work to fill the remining prt of tnk (6 8) ().5% of profit (D) 880 ` 0 Remining ` 770 is divided in the rtio 5000 : : 6 Profit to nu ` 60 Profit to iml ` 0 Required profits re ` 60 nd ` ds. () Let the output be '' nd percentge b ''. Then, ( ) 00% 00( )% 0. () Till pm, prt of tnk filled prt 8 6 hrs. Durtion of time 6 hours nd, tnk will be filled t pm + 6 hrs. 7 m. (D) : : : : 5 6 : 7 : : : Required rtio 70. () Let the shres of nit, indu nd hmp re, 8 nd respectivel. So, mount received b hmp ` 5. () Let rte of popultion increse R% per nnum R So,

5 R 00 Now, the popultion fter ers R () Speed of the truck 550 m/min. Speed of the bus, m/min. m/min....(i) 7 7 5, nd 7. () Let the common bse meter. Then, re of tringle re of prllelogrm ltitude 00 ltitude 00m 8. (D) For two similr tringles nd PQR. 0 cm P Required rtio : () Let his ctul speed nd time tken t Distnce t...(i) gin, from question New speed & New time t + 0 min. Distnce (t + 0) From (i) & (ii) t (t + 0) t 0 min. 6. () PQ cm. () Totl re of two prks (8 + 6 ) 00 re of bigger prk 00 r 00 r 00 r 0 m. 0. (D) Totl re of plground 750 rh Q cm 75 m R b b c Totl cost of trvelling 75 ` 50. (D) cos 6 + sin 6 + sin cos (cos ) + (sin ) + sin cos (sin + cos ) 5

6 (cos + sin ). () Given, sec+ b tn...(i) nd, sec b tn 5 From equtions, (i) nd (ii), sec b tn 5...(iii) From equtions, (i) nd (iii), sec...(iv) b tn...(v) From equtions, (iv), nd, 0º Now, D 0º 0º 70º Minimum difference between n two ngles is 0º. 5. () re of four wlls h(l + b) l b nd h m 0 8 b sec ( + tn ) b 0 5 nd l 0 b b + b. () + / + / ( ) / + /...(i) ubing both sides, ( ) [ / + / ] ()() ( ) ( / ) + ( / ) + ( / ) ( / ) [ / + / ] ( ) From (i), () D Given, lso, + 80º [ D is cclic] 60º re of floor l b m 6. (D) ctul mount to be pid ` 780 So, required etr mount ` (D) Let wter in the tnk is h deep. h 8.5 h 8.5. ft. 8. () Let the bredth nd height of 'b' nd 'h' respectivel. Then, 70. b b m lso, b h h 5 m.. () Totl cost of plstering inner surfce ` 85 6

7 50. () 5. () Here, 0 ds nd 5 ds Work done b & in 6 ds h 0º 5º D 50( ) m Distnce trvelled in h, D 50( ) m Let be the building nd its height be 'h' nd D be ''. h h h tn5º h...(i) h 50( ) tn0º 50( ) + From eqution (i) nd (ii) h 50( ) h ( ) 50( ) h 50 m 5. () Let the number b nd. Then, 8 76 Hence, the lrgest number is 8 5. () Totl one-digit number No. of digits Totl two-digit number 0 No. of digits 80 Totl three-digit number 00 No. of digits 700 Let there re digits number. ccording to question, Number of pges Remining work From question, Work done b & in ds 0 or, c c c 0 ds 5. (D) Let the originl vlue of fridge be `. Then, cost price 5 6 selling price Gin percent % 55. () Number of men Number of women mount distributed mong men nd women 75 80% ` 0 Let the wges pid to mn be ` 5 nd to womn be `, then Wges received b womn ` 8 7

8 56. () ccording to question, 8 % 5% of sum (D) sh price, P ` 000 sum ` 0000 sh down pment, DP ` 7000 lnce due, fter I st instllment, D ` 000 P vlue of instllment ` 800 n no. of instllments 5 R rte of interest ccording to question, nr 00 D (n )R 00 np Loss percent Loss.P % (D) s the sum of mone tht re to be divided mong, nd nd between E nd F re not given. So, the mount tht receive cnnot be determined. 6. () 8 On ppling componendo nd dividendo : (i) 5R R gin, 5R 00 R R R R 00 R 00 R 00 R % 58. (D) Let the cost price of book be `. Then, (. 8) ` () Let the cost price of pples be ` 00. Then, selling price of 00 pples will be ` 800.P. of pple 00 ` 5 nd S.P. of pple ` 8 5 Loss 8 ` From equtions (i) + (ii) (D) ( ) Multipling both sides b Squring both sides,

9 6. () Let their ges be nd ( ) 6 Now,.. ( + ) From equtions (i) nd (ii) ers nd 6 ers....(i) 6. () Quntit of nitric cid 0 0 litre wter 0 litre Suppose '' litre wter is dded in the solution. Then, (0 + ) 5 litre 65. () + b + c bc 00 ( + b + c) [( b) + (b c) + (c ) ] b c bc b c ( b c)[( b) (b c) (c ) ] ( ) (D) b b c ( ) 8 ( ) On compring with the given epression 6, b (D) DE (Given) D E DE nd re similr. re( DE) D re( ) D D D 68. () The sum of n two sides of tringle is greter thn the rd side. + > 5, which is wrong. + > 6, which is wrong. (,, 5) or (,, 6) will not form tringle. Triplets (, 5, 6) & (, 5, 6) re true for the sides of tringle. tringles 6. () E F In DE, D O E E D E D (s) + Similrl, In F, F F F (s) In OEF, + 80º + 80º + 0º EOF 0º EDF

10 70. () Let the distnce covered b the first trin be '' km/hr. s both trins hve trvelled for sme time Totl distnce + ( + 0) 0 km 7. (D) Let the speed of trin be km/hr. s both the persons re wlking in the sme direction of trin. So, (.5) 8. ( 5.) km/hr 7. () O is rhombus with centre O. Let digonl of the rhombus be P O O nd Rdius of the circle O O O In PO, O OP + P () + + lso, re of rhombus () () Rdius of circle 8 m. 7. () sin+ b cos c On squring, sin + b cos + b sincos c Let cos b sin k cos + b sin b sincos k From eqution (i) & (ii),...(i) (sin + cos ) + b (sin + cos ) c + k k + b c k 7. (D) sec 75. (D) b c b, h + Then, + P ( ) () cos cos + sin sin tking,, it stisfies the bove eqution cos cos + sin sin 76. () l cos + m sin or, cos sin cot sin l cos + m m cos + cos l cos + cos m cos m cos sec or, tn + or, or, tn tn tn m l m l m m l m m l m m m l m l m 0

11 77. () re(x) (re of prllelogrm)...(i) 78. () Similrl, [Hving sme bse] re(f) (re of prllelogrm) From (i) nd (ii), re(x) re(f). E F D, EF re of equilterl (EGF) 7. () D [EF D nd EF D] 6 cot tn From eqution (i) nd (ii) () 80. (D) Volume of the bll Volume of rised wter 8. () r () (6.75) r 7 r cm () LM of 7, 7, 7, D 8. () Let totl no. of workers Totl slr 5...(i) In, tn D tn...(i) gin, Totl slr ( 5) 85 From (i) & (ii) ( 5) 85 In, tn tn(0 )

12 8. () The totl number of men emploed 50 So, totl number of women emploed 00 & totl number of children emploed 50 Now, let the men, women nd children wges re 6, nd respectivel or, Per d wges pid to mn, womn nd child re ` 0, ` 5 nd ` 0. Weekl wges pid to mn, womn nd child re ` 0, ` 05 nd ` () Upstrem speed km/hr Downstrem speed km/hr 8. () % (ppro.) O M OM r M M r Speed in sttionr wter 6 Required time 5 hr. 5 min. 86. () Let cost price of the rticle ` km/hr OM O M r r OM r r So, ( ) 00 ` () Required re re of rectngle re of the rod long length re of the rod long bredth + re of the centrl squre m 88. () Let number True nswer number 6 6 & Wrong nswer number 6 6 % of the error committed on the bsis of correct nswer (6 ) (D) OD 80º OD 80º 06º 7º OD D [centrl ngle is lws twice the inscribed ngle] 7º D D 7º nswer Ke. (D). (). (D). () 5. () 6. () 7. () 8. (). () 0. (). (D). (D). (). () 5. () 6. () 7. () 8. (). (D) 0. (). (). (). (). () 5. () 6. () 7. () 8. (D). () 0. (). (D). (). (). () 5. () 6. () 7. () 8. (D). () 0. (D). (D). (). (). () 5. () 6. (D) 7. (D) 8. (). () 50. () 5. () 5. () 5. () 5. (D) 55. () 56. () 57. (D) 58. (D) 5. () 60. (D) 6. () 6. (D) 6. () 6. () 65. () 66. (D) 67. (D) 68. () 6. () 70. () 7. (D) 7. () 7. () 7. (D) 75. (D) 76. () 77. () 78. () 7. () 80. (D) 8. () 8. () 8. () 8. () 85. () 86. () 87. () 88. () 8. () 0. (D). (). (D). (D). (D) 5. (D) 6. (D) 7. () 8. (). () 00. (D)

Form 5 HKCEE 1990 Mathematics II (a 2n ) 3 = A. f(1) B. f(n) A. a 6n B. a 8n C. D. E. 2 D. 1 E. n. 1 in. If 2 = 10 p, 3 = 10 q, express log 6

Form 5 HKCEE 1990 Mathematics II (a 2n ) 3 = A. f(1) B. f(n) A. a 6n B. a 8n C. D. E. 2 D. 1 E. n. 1 in. If 2 = 10 p, 3 = 10 q, express log 6 Form HK 9 Mthemtics II.. ( n ) =. 6n. 8n. n 6n 8n... +. 6.. f(). f(n). n n If = 0 p, = 0 q, epress log 6 in terms of p nd q.. p q. pq. p q pq p + q Let > b > 0. If nd b re respectivel the st nd nd terms