SSC MAINS (MATHS) MOCK TEST-14 (SOLUTION)

Transcription

1 SSC MINS (MTHS) MOCK TEST- (SOLUTION). () b c a a c b b c a a c b 0 a b c a b c. (C) y hours 8 min hrs. b c a a a c b b a b c 0 c hours 0 min hrs. (a b c) a b c 0 V V T T /5 0 / a b c. () y ² y² ( y) ( y) ( y) 85 y 5. (C) Shaded area a² a a a² sq. unit Required result a² a ² sq. unit. () Pant cloth 5 m shirt cloth m for one pant 5 m cloth needed so, total pant 5 5 / (nearly) total no, of shirt / 80 nearly 5. () Difference in rate of interest (0 8) % % P ()% 0 P 00 0 P ` (C) ( )² (y 5)² (z )² 0 If a² b² c² 0 then a 0, b 0, c 0, y 5, z V km/hr 5 8. () Sum of pocket money of ( C) money spend by ( C) (given) C (given) C 60 (spend pocket money) 6 60 `0 9. () milk left total quantity 8 6 this process is repeated two more time Left milk 6 total quantity of water 6 litres 0. () rown lack Cost 5 total number 6 of item ctual cost 0 changed cost 5 5% () r² 500 (cm/sec) T T Ph: ,

2 sec 6 min. (D) 5 (5)³ n 6 n n 60. (D) 60. () 5 5/ 6 cm cm Required time 5 5 hr. 0 min after.m : 0 P.M y y a a y y 6 y : : C () 6 5% 0% 0 % () : Income 8 Ependiture y y Saving 0,000 5,000 8 y 0,000] y 5,000] y 0,000 y 5, Income of `0,000 Income of `55, () I II III 9 % (loss) 5% (Profit) 9 % (Profit) ( l) (C.P) 0 S.P (selling price) ` similarly, b y and c z z 9. () % (Loss) so a b c y z y z y z 0 % 0. () 8 0% a b c b 8 a b c b bc ac ab abc 6 abc ab bc ac 5. () C ( ) (6 ) (²)² ² ² Ph: ,

3 ² ² 6 ² ² (C) P 5% (Interest) 0(Principal) (Instalment) P 0 square 00 Sum borrowed `60 Short: () 6 00 R R 00 6R ³. () ² R % 9 ³ ² ³ ² ³ ³ (Instalment) [y C & D]. () ² 5 5 Let y y 5 y 5 6 y () Required verage speed 6. (D) km/hr. In C 5 ( )² ² ( 5 )² ² ² 0 ² 6 0 ² 8 0 ( ) ( ) 0, C cos² cos²c. () 5 5 c 5 sin ³ cos ³ cos² cos ³ sin ³ sin² sin ² cos ² sin cos sin ³ cos cos ³ sin ² cos ² sin sin cos Ph: ,

4 sin cos sin ² cos ² sin cos sin cos sin ² cos ² ² sin ² cos ² 0 8. () sin cos sin cos sin ² cos ² sin cos a sin b cos sin cos min a² b² sin cos () 5 a 5 b 5 c n n ² n n a 0 b c so, a b c 0 0. () tan sec m sec m tan On squaring both sides, we get (sec)² (m tan)² sec² m² tan² m tan sec² tan² m² m tan m² m tan ( sec² tan² ). () m² tan m On putting the value of tan in Initial equation, we get m² m sec m sec m m² m sec m ² m ² m sec tan cos sec tan sin m² m cos sin cos cos cos sin sin. () cos cos sin cos sin sin cos sin sin ² cos cos sin cos sin² sin cos cos cos sin cos cos ² sin cos cos ( sin² cos²) cos sin cos cos sin cos 9 9. () Let 0º and 5º then P and q and tan Now p q. (C) cos sin² cos cos² (cos² cos ) q² p ² / / tan cos cos sin cos cos cos sin sin cos cos maimum value occurs at cos and it is and minimum value occurs at cos and it is Ph: ,

5 5. () the required ratio is Present age 0 yr. 0 yr. ago 0 yr. 0 yr. 50 yr. total yrs. 6. (D) Let the total number of swans be. The number of swans playing on the 0. (C) Interior eterior 6 80 n So, n n 0 D C shore of the pond Number of swan inside the pond ( ) (² ) 9 ² ² on solving 6 Number of swans 6. (D) y 9, y 5, 6 (, y) (6, 5) y y y y y y y rea unit² 8. () Let rate of population increase R% per annum R So, R 00 Now, the population after years R () Interior eterior 08 Interior eterior 80. () DC DC DC DC CD D C D º F N E M Let EM, MNC (corresponding angles) 80 (Linear angle) º. () Chair left 99. () C Tables left So, number of people who can work 90 C 5º sin 5º sin 5º C cos 5º C cos 5º rea C Ph: ,

6 sin5º cos5º sin5º cos5º (multiply /) 8. (C) tan tan (given) 90º 5 90º cos² 5 sin 0º 8 m² cm². () 0% yearly 0% half yearly. 5. () 0 0, n half years Diff 6. () years n n L Perimeter (Length readth) 0 ( ) 0 0 length 6 cm readth cm rea 6 cm² cos² 90 cos² 5º 0 9. () Number of stoppage for epress train Duration of stoppage 60 0 hrs. total time hrs. Distance travelled by local train without stoppage km Number stoppage for local train.5 5 (In whole number) Duration 60 5 So distance travelled in km Required distance km 50. () Let be the total score in an innings. so, the highest score 9 and the net highest score 9 of the. (D) a b squaring both side ² a b cubing both side 6 a³b 5 a³b 5 a³ b remaining runs 9 9 So, according the question Ph: ,

7 (C) (² ) ( ) () Divisible by 5. () Total Income (00%) 5,000 food 5% (total) 00% 5000 Rent % total `50 5. () Spending on education : Spending on food 5% : 5% : 5. () % of ependiture on rent than on the fuel % 55. () fuel education others 0% 00% 60º % % º 56. (D) Work remaining 60% work done 0% ( ) ( ) , 0 so, work done by alone in 0 days 0 and work done by alone in 0 days. 5. (C) 0º 5º C D 50( )m 6. (D) 8 days Ph: , h CD 50 ( ) m Let be the building and its height be h and D be h tan 5º h h 50 tan 0º h 50 from equation (i) and (ii) h h 50 h ( ) 50( ) h 50 m 58. () Total circumference r...(ii) 8 circuference of circle perimeter of square a a 6 cm 59. (C) Let number be a, b ( HCf, a, b are co-prime number) LCM ab a b ab a b ab a, b numbers are 6, Smaller number 60. () Required verage y y y y y² y² y...(i)

8 (whole work) days 5 0 days 6 (whole work) 96(unit) oth will work by ( ) 96 5 days 66. () Let the number be a 6. () a a 00 a a 00 a 00 a 5 a () a : b 9 : : b : c : 5 : 5 d : c 0 : 5 : 6 a : b : c : d : : 90 : 05 6 : : 0 : 5 6. () speed of Suraj 550 speed of Rohit m/min m/min 550 Required ratio 00 : 6. () Required Price 9000 (8.5)% ` (C) Passed boys 60% Failed boys (00 60)% 0% Failed girls (00 50)% 50% Failed boys Failed girls Required % failed condidates % 5 5 5² 5² () rea of two circles (5² ²) 69cm² r² 69 r² 69 r c.m radius of third circle cm 69. (C) l b h cm length of diagonal 5 cm. l² b² h² 5 l² b² h² 5 (l b h)² (lb bh lh) 5 ()² (lb bh lh) (lb bh lh) 5 (lb bh lh) total surface area 5 cm² 0. (D) Volume of cone Lateral surface rea r²h rl (l h² r ² ) rh h² r ² squaring both sides. 9 h² r ² r ² h² 9 h² r ² h ² r ² r ² h² 9 r ² h². () a b b c (a b) c b b c bc...(i) Ph: ,

9 similarly, b c c a ca...(ii) a b c a...(iii) ab multiplying by equation (i), (ii) and (iii) a b b c c a (a b) (b c) (c a) abc ². (C) cos a a abc ± squaring both sides,. (C) efficiency If both pipe open together (C) Z 5 min. (D) cos² a a cos² a a subtracting from both sides, cos² LH.S 5 cm G D cm a² a² a² a² a² a² 5 cm C y appollonius theorem, ² C² (D² D²) 5 65 (² 8) 850 ² 8 ² 5 8 ² GD cm X oys Z X girls z girls part X z Z 6. () ccording to the question verage age of eleven cricket players is 0 years. total age 0 0 If the age of coach is included then the average age increases by 0% years 00 total age of eleven player and coach 6 yr. ge of coach 6 0 years.. (C) ccording to the question verage of Put m m ² ² ² ² m Now check from the option option (C), m², put m (satisfied) 8. () M.P of pen ` fter I st Discount II nd Discount % Ph: ,

10 % () Let C.P 00 % Profit 00 % Loss y 96 y : 80. () Let the first part ` Hence second part `(000 ) ccording to the question (000 ) `8000 I st part `8000 II nd part `(, ) `000 Hence maimum part ` () us fare : Train fare : (given) Now as given in question, bus fare is increased by 0% & train fare is decreased by 5% 0 00 : : 5 5³ 8. (D) ottles Required () Upstream speed, U 6 km/hr. Downstream speed D 0 5 km/hr. speed of boat in still water, D U 9.5 km/hr. speed of current D U 0.5 km/hr.5 km/h and 0.5 km/hr. 8. (D) Father (f) son (s) 00 F s 00 F 5 s 5 Ph: , (F 5) (S 5) F 5 S 0 F S 5 y (i) & (ii) F S 00 F S 5 S 05 S 5 f ratio of age after 0 years father : son 65 0 : : 5 5 : 85. (D) Total area of play ground. 50 rh cm² 5 m² total cost of travelling 5 ` () sum of P and Q sum of Q R sum of P R (P Q R) Monthly income of P ` () Let the price be 00 So, new price of the article r r 00 r 00 given r ² ,000 r ² r ² r...(i)...(ii)

11 88. (D) 0% lcohol 5 Miture Water : lcohol Required % () ccording to question 6 00 D C 00 0º % 89. () ccording to the question 0% ank % 500 8% Remaining % Post Office Hence, required number of share holders is (D) ccording to the question milk water Vessel 8 : 5 Vessel 5 : Now miture containing 69 % 900 milk i.e 9 00 milk Now using ligation new ratio : 9. () : 5 9 given is a diameter C 0º s we know that C 90º C C C 80º C 80º 90º 0º C 60º Note : In a cyclic trapezium sum of opposite angle is 80º D 80º D 80º 60º D 0º 9. (C) rea of four walls h (l b) l b and h m 0 8 b b 0 5 and l 0 8 rea of floor l b m² 9. () Height : Shadow 95. () stick : 8 : 0 0 tower 60 m : 0 m Ph: , R R 00 (5R)² R 5 R³ 00

12 R³ 00 5 R so radius 5 cm height cm slant height cm 96. (D) a b 6 a b a b (C) a b Corporation ta Ecise duty 98. (D) 00% 60º : Customs duty.% (C) 0.% of 00 8º (ppro) crores (ppro) 00. (C) (.5. 0.) (.5.5) 60 9 % SSC MINS (MTHS) MOCK TEST- (NSWER KEY). (). (). (C). () 5. () 6. (C). (C) 8. () 9. () 0. (). (). (D). (D). () 5. () 6. (). () 8. () 9. () 0. (). (C). (). (). () 5. () 6. (D). () 8. () 9. () 0. (). (). (). (). (C) 5. () 6. (D). (D) 8. () 9. () 0. (C). (). (). (). () 5. () 6. (). (D) 8. (C) 9. () 50. () 5. (C) 5. () 5. () 5. () 55. () 56. (D) 5. (C) 58. () 59. (C) 60. () 6. (D) 6. () 6. () 6. () 65. (C) 66. () 6. () 68. () 69. (C) 0. (D). (). (C). (D). (C) 5. (C) 6. (). (C) 8. () 9. () 80. () 8. () 8. (D) 8. () 8. (D) 85. (D) 86. () 8. () 88. (D) 89. () 90. (D) 9. () 9. () 9. (C) 9. () 95. () 96. (D) 9. (C) 98. (D) 99. (C) 00. (C) Ph: ,