SSC (Tier-II) (Mock Test Paper - 2) [SOLUTION]

Transcription

1 SS (Tier-II) - 0 (Mock Test Paper - ) [SOLUTION]. () R R (D) Let the first odd integer the second odd integer + Difference between the squares of these two consecutive odd integers ( + ) + + ( + ) will be divisible by as ( + ) will be even ( + ) will be divisible by i.e. by 8. (D) Let the larger number and y the smaller number TQ, y 9... (i) and y ; Quotient 7 and Remainder 7y +... (ii) Now on putting value of y from (i) in (ii) We get, 7( 9) + or, or, () Let,, and D are four consecutive prime numbers in descending order ( > > > D) TQ,... (i) and D (ii) both and 00 are divisible by. i.e. is a common factor of both and 00. and & are the common factors of and 00. Out of &, one must be. from (i), Product of other two prime nos. and 7 Out of, and, one is 7, one is and one is. and > > 7, and the largest given prime no. 7. () 8 ( ) ( ) ( ) ( ) ( ) () ( ) square root of ( ). () i.e ( ) LM of 0.,. &.8 LM of, 0 & Ph: , (M) LMof,& HF of,0 & 7. () Required multiplication Here, nos. (o) no. of complete pairs of &. no. of [ here n() < n()] () (0.7) (0.) (0.7 0.) (0.7) (0.) (0.7 0.) (0.7 0.) 9. (D) each three distance is same. Let, S, S and S respectively are the speeds with which three distances have been covered.

2 S S S When train from station starts to verage Speed move; the another train will be ' and SS SS SS distance between & ' 0 0 (00 0) km 70 km Relative speeds of trains 0 0 ( ) km/hr km /hr 000 Time taken by each train to reach km/hr 0 70 each other hr. hrs () + part 7 nd in hours, distance travelled by and, part part part 7 or, Wage of 90 Rs () Let,. (*) ( + ) days alone ( + 8) days and, alone ( + 8) days part In such type of questions The no. of days taken by and working together to do the work 8 8 days Ratio of speed Ratio of duration Ratio of distance covered during any same duration of time. () 00 km days days : : ( Distance Speed time ) ' 70 km 0 km Distance covered by before movement of. i.e. Distance covered by in 0 minutes 0 90 km 0 0 km (00 ) km 00 kms oth train will cross each other at a distance 00 km & from i.e. at the eact middle point of and.. () Let the required speed Home km/hr 0 hr. + km/hr 0 hr. Office km/hr. () Ratio of speeds Time taken ( + 8)hr : hr. (where time taken by to cover the distance) s the distance is same. ( + 8) + hr. ctual time taken by to cover the distance i.e. ( + 8) hr. ( + 8) hrs 0 hrs.. () Sum of wrongly entered marks and Sum of correct marks i.e. Sum of corrected marks <sum of wrongly marks (by marks) ctual average (after rectification) marks 7. () n n + n + n + n + Ph: , (M) 880--

3 The average of above consecutive integers 0% of nd no. 0% of 9 & % of st no. % of 0 nd, 9 is times of. n n m m n + n + n + n + n + n + n + 7 The average of above consecutive integers n n 7 n n 9 ( n ) m 8. (D) Total money spent by all of them (8 ) + { ( + )} () Let no. of girls 00 yr 9 months yrs + (00 ) yrs 700 yr. ( )yr () Vessel '' Vessel '' Water Milk Water Milk : : Ratio of contents of vessel '' to vessel '' to mi with each other : Ratio of water and milk in the resulting miture () Initial Ratio : : 9 Initial nos.,, 9 Final Ratio 7 : 9 : (on increasing students in each class) 7 9 or, Total no. of students in the three classes before the increase () TQ 0% of st no. or, of st no. 0 st no. 0 and, Ratio of st no. to nd no. : Nos. are 0 & 0% of nd no. is times of % of the first no.. (D) st no. : nd no. & nd no. : rd no. : : st no. : nd no. : rd no. 9 : : Let the nos. are 9, & TQ, (9) + () + () + the nd no. i.e.. (?) Table hair 0% profit % profit : : profit 0 : : : Rs.. ost price of table Rs.. lternative method:- Let,.P. of table (00 ).P. of chair TQ, Profit on table + profit on chair Total profit or, 0% of + % of (00 ) % of or, (00 ) or, or, 90 or, or, Rs.. Ph: , (M) 880--

4 . () 's share Rs (D) 0% profit on one and 0% loss on other net loss of (00% 0%) of total 8 (0) profit and loss % % 00 8 of 80% of total profit 80% of total profit Rs Total profit (i.e. 00% ) Rs Rs () Let the third no. be 00. and will be 80 and 7 respectively. required % difference of & 00% value of 8 00% 0% () Total no. of illiterate persons in the town no. of literate men + no. of illiterate women 0 ( 00% %)of (00% 8%)of () Let maimum marks TQ, 0% of or, marks 0 9. (D) Let man's initial income Man's increased income ( + 00) TQ, % of 0% of ( + 00) 0( + 00) or, increased income; i.e Rs Rs. 00 Rs. 700 Total SP (00 )% of total P. lakh 9% of total P loss i.e. % of total P. lakh 9 Rs. 700 loss of Rs () Required single discount ( ) 00% ( 0.) 00% 0.% 00% %. (D) SP per mango Re. 0 0% of P per mango P per mango (i.e. 00% ) 00 Re. Re. 0 0 mangoes for Re... () Let P of nd watch (0 ) P of st watch TQ, Profit Loss % of (0 ) 0% of (0 ) Rs. 7. (D) 0% ( +.)% 7 % gap % : gap %.% % Ph: , (M) : 0 pens (0 0) pens 00 pens. (D).P. of 0 article SP of articles In such type of questions, 0 Gain percent 00% 00% 0%

5 . () Rs. 00.P. S.P. % value of L.P. Rs. 00 Rs. Rs. + Rs L.P. (i.e. 00% ) Rs. Rs Rs. Rs. Rs. Tarun bought the TV at 80% of L.P Rs Rs. 00 Rs Rs. Rs. 0. () % p.a. for yrs. % of sum % p.a. for yrs. 0% of sum TQ, Rs. Rs. (% 0% ) of sum Rs. 0 % of sum Rs (*) M.P. Rs. Rs. 00 P of i.e. Rs. 00 Rs. Rs. 00 0% discount Price after 0% discount 9 Rs. Rs. 0 gain, 9 % discount 9 9 Rs. Rs. Rs. 8 0 (additional) 00 0 The original marked price i.e Rs. 9 9 Rs () Single equivalent discount of 0% & then %. 0 0% % % 00 % discount.p. 0% gain % discount S.P. Rs. 00 (let) Rs. 0 7% of M.P. 0 00% of MP 00 7 Rs. 0 MP should be above P by M.P % 00 0% 9. () 0% discount on L.P. % discount on L.P. Rs % value of L.P. 7% value of L.P.. (). () sum Rs. For st year For nd year S.I. Rs. Rs..I. Rs Rs. 700 if r rate of interest per annum r% of 7 r 7 00 Ph: , (M) lso, 0% of the sum sum For years For years 00 Rs. 7 0.I. Rs. 80 Rs. 9 Rs Rs. 9 if r rate of interest per annum r% of 80 9 r. () TQ, P + 0 t > P 00 or, 0 t 9 00.% 80 where P Principal & t required no. of years or,, but Required least no. of complete yrs. yrs. t

6 . (D) M + 0 days... (i) Rate of filling of tank by pipe 8M + 0 days 9M + 0 days... (ii) litre per hour From (i) & (ii) We have litre per hour M + 9M + and rate of filling of tank by pipe M 9 M litre per hour litre per hour Efficiency of a man to that of a boy : Rate of filling of tank by pipe & together. () 8 litre per hour Prem 0 days Prem lso, Raj Raj in day in day part of work 0 days part of work Work done by Prem in initial days 0 part of work Remaining part of the work part of the work mount of work done by Prem & Raj together in day 0 part of the work 0 No. of days taken by Prem & Raj together to do the remaining part of the work 0 0 days Raj actually did the work for days.. (*) hours hours Let the capacity of tank litres Pipe was opened hour earlier than pipe. Volume of tank filled by pipe in hour litre Remaining part of the tank which is still empty ( ) litre 9 litre Time required to fill 9 litre of tank by pipe & together 8 9 hours hours 8 hours 7. minutes Required point of time : 0 pm + hour 7. mins Ph: , (M) : 7. pm or : 7 pm lternative method Part of tank filled by pipe alone in hour part Time taken by pipe & together to fill the remaining part 9 8 hours Required point of time : 0 pm + hour 7. min : 7 pm 7. () Let hour time taken by pipe alone to empty the pool hr. time taken by pipe

7 alone to empty the pool n Time taken by pipe & together to i.e. 80 { ( ) + (n )} empty the pool hours hours hours Time taken by pipe alone to empty the pool hours hours Part of the pool which will be empty when, & work together part part 9 part Total time taken by, & working together to empty the pool 00 minutes 9 [ hour 0 minutes 00 min] 00 9 minutes 900 minutes hours 8. () km up + 8 km down in hrs. km up + km down in 9 hrs.... (i) lso, km up + km down From (i) & (ii), we get, in hrs.... (ii) 0 km down in hours S down (i.e. S + S ) km/hour lso, S up (i.e. S + S ) 8 km/hour Speed of current i.e. S S down 8 km/hour km/hour 9. (), 0,,... Let, n required no. of terms S n n {a + (n )d} S up or, 80 n ( 8 + n ) or, 0 n n or, n n 0 0 n 8 0. (D) 8 7 9? The missing no () Ph: , (M) On cubing both the sides we get, or, or, 0 or, ( ) + ( ) + ( ) 9 + ( ) + ( ) + + ( ) + ( ) + ( ) 9 + ( ) + ( ) + ( ) / /. () Let ( 7 7) (7 7) / / (7 7) (7 7) {( 7 7) (7 7)} + (79 7) / + ( 7) ( )( + + 8). (D) a d + b c abcd + a c + b d + abcd a (c + d ) + b (c + d ) (a + b )(c + d ). () 8 7

8 8 ( ) a + b + c abc (a + b + c) {a + b + c (ab + bc + ca)} i.e. abc ( ) 8 ( ) abc 8 abc ( 8 ) 9. (D) ( + + 0) - ( 0) ( ) will be maimum when ( 0) is minimum and maimum. () value of () n 7 7. () n () ( ) ( n ) ( K ) ( K ) or, (K ) K or, K + K or, K + K K K 7 ( ( ) ) 8. () a + b + c On squaring both sides, we get (a + b + c) or, a + b + c + (ab + bc + ca) or, + (ab + bc + ca) ab + bc + ca i.e. ab + bc + ca Required maimum value Ph: , (M) (D) sin cos sec cosec. (D). (*) tan cot (sin cos ) (sec tan ) tan tan (cosec cot cot (tan cot ) ) cot {(tan cot ) tancot } {(tan cot ) } (tan cot ) 7 (tan cot ) 7 (tan cot ) 0 sin P P sin sin and Q cos cos sin R sin sin cos ( sin) cos R sin P Q R sin cos tan7º cot 7º cot º tanº tanº cotº tanº cotº

9 ( tanº tanº ) º tanº tanº (tanº tanº ) tanº tanº tanº tanº tanº tanº cotº cot7º tan7º. (D) sin sin sin sin sin cos sin ( sin ) cos sin( cos cos ( cos cos cos ) cos ( cos )[ cos cos cos cos cos cos ] cos cos cos cos 8cos 0 cos cos 8cos. () Let sin cos. () sin cos sin cos sin and cos sin cos 0sin cos sincos 0 sin cos sin cos sin cos sin0 sin0 sin0 sin70 sin(90 80 )sin(90 0 )sin(90 0 )sin cos0 cos 0 cos 80 We know, cos cos cos cos cos 0cos 0cos 80 0 cos( 0 ) cos 0º 8 8. () 7. () 8. (D) sec tan 0 tan tan tan 0 tan tan tan 0 tan tan tan 0 tan tan 0 tan 0 tan 000 mtr. Ph: , (M) mtr. 0 0 D 0 D 000 mtr. Let, D mtr. From, 0 tan0 º 000 mtr. 000 mtr. From D, h 0º 0 D 000 tan D D - D mtr. 90 h

10 tan h h...(i) h tan90 D D 7. () Let side of D ( ) 9. (D) 70. (D) 7. () h cos tan h From (i) & (ii) h h 8h h h 8 h sin or, sin [ a b ( a b ) ab ] sin...(ii) 0 sin 0 lso, sin Per( ) Per ( DEF ) DE Per( ) 9.. Per () 7. () & + 8 In, + cm + cm + 8cm ( + + ) cm + + cm TQ r π r cm cm 7 7 r cm 7. (D) Sum of all interior angles sum of all eterior angles 7. () n 80º 0º or, n 80º 70º (n ) n Required no. of sides of the polygon D D In an equilateral triangle, side inradius Ph: , (M)

11 7. (D) i. e. a r cm cm cm 7 cm D Here, D angle bisector of D D In such case, D : 7 D (*) No. of diagonals of a polygon of n sides n n TQ, n n n n + n( n ) n () n + n n n 08 + n n n 08 0 n, 9 n [ n cannot be negative.] 78. () º Here, in OP, O OP P PO PO OP 80 ( ) 0º PO80º 0º 70º lso, In PO, O OP 80º 70º PO OP º P º 79. () Ph: , (M) º I.º lso, º I 7.º I 80º ( I I) I 80º 0º 0º 80. () Ratio of no. of sides : Then, Let the nos. of sides are n and n Ratio of their interior angles : n 90º n n 90º n n n n n n 8 n Respective nos. of sides of these polygons are and 8. a a 8. () : a a 8 8. (?) r (r + h ) r(l + r) or, r (r + h ) l + r r (r + h ) or, r r + h or, r h r : h : gain, r l + r or, r r h + r or, r r h 9r r h 8r h r h r : h : r(h ) : h : h : :

12 8. () 8. () 0 cm cm r 0 cm Let the sides are, and. TQ, or, 0 0 Sides are of length 9m, 80m and 7m. Ratio of sides are : : (Pythagorian triplet) Triangle is a right angled triangle. rea of triangle base height 80 7 m 70 sq. meter Volume of the cylinder r h r cm 7 0 r 7 cm r 7 cm 0 m. 8. () Volume of cube a (where a length of a edge) When each edge is increased by 0%. length of the new edge.a Volume of new cube (.a).7 a Required % increase 87. ().7a a 00% a (.7 00)% 7.% 8. () h cm h cm r l r 0 cm Let radius is increased by cm. New volume of cylinder (0 ) gain, Let the height is increased by cm. New volume of cylinder 0 ( ) (0 ) 0 ( ) (0 + ) 00( + ) (0 + ) ( + ) ( ) 0 cm l h + r + 7 cm Volume of cone cm r h cm r cm 7 r 7 r 9 cm r 7 cm urved surface area of cone rl 7 cm 7 0 cm Ph: , (M) 880--

13 88. (D) cm 8 cm Perimeter of the rectangle ( + 8) cm 88 cm r r rea of the circle i.e. r 89. () 90. () 7 cm a a cm cm O 8 cm a rea of 88 7 cm rea of ( O O O) a a( 8 ) a 9 cm a cm rea of empty space ( ) 87 cm Volume of water needed to fill the empty space Volume of cylinder Volume of cone r h r h r h h r 9. () r h 7 cm cm 7 cm 7cm 7cm In right angled isosceles, lso, D D D 7cm circum radius (where D ) Required area rea of semicircle rea of cm 7 (77 9) cm 8 cm 9. () Ph: , (M) F 8 G D 0 In the given, D, E and F are medians and they cut one another at G. G G G GD GE GF Here, D 9 cm, E cm and F cm G + GD D 9 cm G cm and GD cm lso, G + GE E cm G 8 cm and GE cm lso, G + GF F cm G 0 cm and GF cm rea of G 8 cm rea of E G cm 7 cm

14 9. () T.S.. of prism.s.. + rea of base 08 Perimeter of base height + rea of base 08 + (where side of square) ( 8) ( + 8) 0 8 Volume of prism rea of base height cm 9. () ( r ) r ( r r r ) r 7 (r + ) r + 7 r r cm 9. () Volume of water due to cm rain on a square km land km km cm 000m 000m m m 0% of volume of rain drops 0000m Required level by which the water level in the pool will be increased 0000 m 00m 0m 0m 9. () Total income Rs Required difference (% % ) of Rs Rs () Maimum ependiture of the family other than on food, was on others. 98. () Saving % Housing 99. (D) Required % 0% + % + % 7% 00. (D) Money spent on food % of Rs Rs. 00 Ph: , (M) 880--

15 SS (Tier-II) - 0 (Mock Test Paper - ) (NSWER SHEET). (). (D). (D). (). (). () 7. () 8. () 9. (D) 0. (). (). (*). (). (). (). () 7. () 8. (D) 9. () 0. (). (). (). (D). (*). (). () 7. () 8. () 9. (D) 0. (D). (). (). (). (D). (D). () 7. (*) 8. () 9. () 0. (). (). (). (). (D). (). (*) 7. () 8. () 9. () 0. (D). (). (). (D). (). (). () 7. () 8. () 9. (D) 0. (D). (D). (*). (D). (). (). () 7. () 8. (D) 9. (D) 70. (D) 7. () 7. () 7. () 7. (D) 7. () 7. (D) 77. (*) 78. () 79. () 80. () 8. () 8. (*) 8. () 8. () 8. () 8. () 87. () 88. (D) 89. () 90. () 9. () 9. () 9. () 9. () 9. () 9. () 97. () 98. () 99. (D) 00. (D) Ph: , (M) 880--