SSC MAINS (MATHS) MOCK TEST-10 (SOLUTION)

Transcription

1 SS MINS (MTHS) MOK TEST-0 (SOLUTION). () x 8 y 8 Sum x and y together can finish the job. () 8 M minutes M W W (00 x) (50 50) (00 x) x 00 x 00 Extra workers needed 00. () x can copy 80 pages in 0 hrs x can copy 0 pages in hrs 80 x and y can copy 5 pages in 7 hrs x and y can copy 0 pages in hrs x y 0 5 x 5 sum y can copy 0 pages in 0 0 hrs.. () TQ, x can complete the job 6 days y can complete the job 6 days x 8 y 6 sum 5 time taken by x and y to complete the job days 5. () TQ, mount paid by Mr. x % mount paid by Mr. y % 6. () Percentage profit () Total reduction.5% % () Total marked price ` 0000 TQ, Total cost price ` 8500 cost of each window ` ` () : : : : 5 : : 5 : : 9 : 6 : 0 ( ) : ( ) (9 6) : (6 0) 5 : 6 0. () For first 8 months 00 8 : 00 8 For next months 00 : 50 For last months 50 : : 000 Ratio of profit of and : 0. () Let each bus has 00 seats fter leaving, seats needed to be occupied Required fraction () : : For first 6 months 00 6 : : 0 6 For last 6 months 00 6 : : : 6000 : 000 Ratio of profit of, and 600 : 6000 : : 0 : 5. () Initially, ratio of story books and other books 7 : Story books 5 other books 5 7 Finally, ratio of story books and other books 5 : 8

2 Other books total story books 5 60 The number of story books collected () Ratio of numbers 7 : 9 Product of numbers 575 greater number () TQ, The weight of th person kg 6. () Largest -digit number formed by 0, and 0 Smallest -digit number form by 0, and verage of numbers 7. () verage of six numbers.95 verage of first two numbers. verage of next two numbers.85 The average of remaining numbers () Let eight even numbers are a, a, a, a 6, a 8, a 0, a and a a ( a ) ( a ) ( a 6) ( a 8) ( a 0) ( a ) ( a ) 9 8 a 7 9 a 86 the largest number () a b > 50 a b > 00 (b) b > 00 0b > 00 b > 0 a b > 0 least value of a is 0. () Required average () Let. P. of watch ` 00.P. S.P 00 0% profit 0 0% less ` 0% profit actual cost price 00 0 ` () Let cost price `00 Loss 0% 50% of selling price ` 80 actual selling price ` (80 ) ` Percentage gain %. () Selling price of mixed tea ` 0/ kg ost price of mixed tea ` 800 Tea Tea Required ratio 0 : 60 :. () Selling price ` P Profit % ost price ` 00 P Selling price ` Q Loss % ost price ` 00 Q 96 TQ, ost price ost price Q 00 P Q : P 96 : 6 : 7 5. () Selling price of ost price of ` P Loss of 5% Selling price of ost price of 00 ` P 75 Profit of 0% ost price of ` P 75 0 ` 0 9 P 6. () ost price ` 5 Selling price ` Profit percent 00 0% 5 7. () Let population of country x Population of country after increase in population x x Percentage increase.78x x x %

3 8. () The number of days the same amount of juice would last is days 0 9. () Price of book after discount ` 70 If discount is between 0% and 5% then maximum possible original price ` () Ratio of cost price and selling price 0 : 0 Profit percent 00 0% 0. () Let time taken upstream x Then time taken downstream x Ratio of speed of downstream and upstream : ratio of speed of boat in still water and of current is : :. () P ( ) 6 P ( ) 6 Sum Time taken by both pipes to fill the tank 6 5 hours. () verage speed of farmer 6 9 S S km /hr Ratio of time with speed of km/hr and 9 km/hr 0 9 : 5 9 : 5 distance travelled on foot 6 kms. () TQ, Upstream speed kms/hr ownstream speed kms/hr The speed of current 8 6 km/hr 5. () Let principal P TQ, 0 P 00 P 00 0 P 00 0 P 00 ` () TQ, P P ` 700 principal ` 700 r 7. () mount S 00 S r () TQ, 9. () 0. () 0 P 00 0 P ` cm cm The whole surface area rea of base curved surface area of cylinder curved surface of cone r rh rl () () F E G 6 6 In and E E E E 6 F F FG Required volume () 9 5 0

4 . () rea of triangle inradius sum of length of sides External diameter internal diameter. () sq. cm m 5 sin 5 rea of cm 8. () Height of glass h sq. cm h Number of drops volume of drops ase area h 6 h cm. () TQ, Height circumference h c Volume of cylinder r h ( r ) h c c c 5. () 6. () TQ, rea of isosceles triangle b a b sq. units 7. () External diameter 78 m Internal diameter 700 m breadth of road m 8. () Radius of circle 8 cm Perimeter of square ircumference of circle r cms Length of the side of square 58 cm 9. () Increase in area () 0 cm 0 cm 0 cm S 5 cm rea of 5(5 0)(5 0)(5 0) cm rea of 75 5 rea of 50 5 cm 5. () Let side of square a cm rea of square a cm rea of new square 50 a 00 9 a Required ratio 9 a : a 9 : 5. () rea of circle sq cm Length of longest chord iameter 6 cm 5. () Let length of longer diagonal x TQ, x x 56 x 56 cm Length of larger diagonal cm 5. () m m %

5 55. () m 5 m m m 5...(i) n n n 5 n n n 5...(ii) m m n n m n m n 0 (m n)(m n) (m n) 0 (m n)(m n ) 0 m n 0 5x 5 y x y 5 z 0 z 5x 5 x 5 y y 5 5 z z () TQ, p m pm(p m) (p m) 7 pm(6) (6) 6 8 pm pm () TQ, x m m n x m n x 0 m n 0 m n 6. () (0, ) (, 0) rea of rea of O x 5x 5 y 5 y x y 5 z 5 z 5 z x y z 5 x y z () TQ, Related speed of nita and Romita 6 7 km/hr Speed of nita km/hr Speed of Romita (7 ) km/hr 57. () Side of square (x ) iagonal of square x x ( ) x x x x unit Side of square unit 58. () S a b c Let a, b and c s s(s c)(s a)(s b) ( ) ( )( ) () ab () ()abc 6 ( ) ()0 ( ) a b c () ( ) 6 sq. units p 6. () p p p p p p p 8 p p 0 6. () TQ, K K (K ) 0 K 6. () 5 E In E and E E E E E : 9

6 65. () P Q T 8 R S 7 O () rea of ab sin In TRO RT 6 8 cm 7. () 0 0 sin 5 5 sq. cm P 66. () OR 7 cm OT cm In TSO OT 5 cm OS 5 cm TS cm length of PS 0 0 cm () In equilateral triangle Inradius : outer radius : 68. () a O Q 8 In PQO O PO OQ 60 O OPQ PQ () In rectangle, m m length of diagonal 5 m TQ, a b b 0 ab 0 ab 0 (a b) a b ab (0) (0) () Perimeter of triangle cms ircumference of in-circle cms Inradius 7 7 cms rea of triangle radius perimeter of triangle 7. () Side of triangle : : : 5 : : 5 : () (5) 5 69 () So triangle is a right-angled triangle. 7. () sin cos ( cos ) cos cos cos cos cos 0 cos cos cos 0 cos(cos ) (cos ) 0 ( cos )(cos ) 0 Either cos 0 or cos 0 cos never be zero. So cos cm cos cos 60 60

7 75. () a, b and c are the sides of the triangle a b c ab bc ca (given) a b c ab bc ca a b ab b c bc c a ca 0 (a b) (b c) (c a) 0 a b c ll angles of the triangle are equal i.e sin sin sin sin () a sin b cos c squaring both sides, a sin b cos ab sin cos c...(i) a b a b...(ii) Subtracting equation (ii) from (i) a a sin b b cos ab sincos a b c a ( sin ) b ( cos ) ab sin cos a b c a cos b sin ab sincos a b c (a cos b sin) a b c a cos b sin ± a b c 77. () sin cos sin(90 ) sin cos cos sin cos cos cos sin cos sin cot cot cot 78. () (sec tan ) 5 (tan tan ) 5 6 tan 5 6 tan 5 tan 6 tan cos tan 79. () x cos 0 sin 60 x x 8 tan 5.sec 60 cosec 60 () () x () tan (given) cosec cosec sec sec sin cos sin cos sin sin cos sin sin cos tan tan 5 8. () sin( 0 ) 8. () sin( 0 ) cos cos 0 P Q QR PR QR 0 cm 0 cos 0 0 cm and PQ PR R 0 sin 0 sin 60

8 PQ 0 0 cm rea of PQR PQ QR cm 8. () cos cos 0 8. () ( cos) cos 0 cos 0 cos 0 cos cos cos cos 0 0 x y x y x y y x y y () 50% of x 0% of y 86. () x 0 00 y x y x y 5 x : y : 5 x y x y x y : () Let number x TQ, (x 5) x 5 x 50x 65 x 5 50x x 650 x 88. () Total armies 656 TQ, 656 (9) 8 remaining armies () 90. () x x x 7 x x x 7 0 x 9x 8x 7 0 x(x 9) 8(x 9) 0 (x 8)(x 9) 0 x 8 or () Total heads 80 Total legs 0 If all heads are of cows, then legs should be If all heads are of hens, then legs should be Hens ows : number of cows () n(n )(n ) is always divisible by () () 5 9. () Time exceed by only 8 hours Time exceed by only hours time required to finish the work together by and 6 hrs 6 hrs 8 hrs 5

9 95. () Person earns ` 000 for 50 hours Regular wages per hour ` ` 0 dditional wages per hour ` 0 ` 60 Total earning ` 00 dditional earning ` (00 000) ` 00 Extra hours worked hours 96. () Required ratio 00 : 70 0 : () verage mark in the second term () Number of students travelling by public bus () Students who use institute s bus Students do not use institute bus (800 80) 0 00.() Number of students who go to institute on foot ( ) SS MINS (MTHS) MOK TEST- 0 (NSWER KEY). (). (). (). () 5. () 6. () 7. () 8. () 9. () 0. (). (). (). (). () 5. () 6. () 7. () 8. () 9. () 0. (). (). (). (). () 5. () 6. () 7. () 8. () 9. () 0. (). (). (). (). () 5. () 6. () 7. () 8. () 9. () 0. (). (). (). (). () 5. () 6. () 7. () 8. () 9. () 50. () 5. () 5. () 5. () 5. () 55. () 56. () 57. () 58. () 59. () 60. () 6. () 6. () 6. () 6. () 65. () 66. () 67. () 68. () 69. () 70. () 7. () 7. () 7. () 7. () 75. () 76. () 77. () 78. () 79. () 80. () 8. () 8. () 8. () 8. () 85. () 86. () 87. () 88. () 89. () 90. () 9. () 9. () 9. () 9. () 95. () 96. () 97. () 98. () 99. () 00. () 6