SSC (PRE + MAINS) MATHS M O C K TEST PAPER HANSRAJ MATHS ACADEMY

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1 SSC (PRE + MINS) MTHS M O C K TEST PPER - 7 Quantitative ptitude (00 Questions) HNSRJ MTHS CDEMY

2 SSC MINS (MTHS) MOCK TEST PPER 7. In given figure = C = CD = DE = EF = FG = G, then the value of DE is (approximately) = C = CD = DE = EF = FG = G, DE G C E CD () 90º () 60º 0º cm of metal is used to cast a pipe of length 8 cm. If the internal radius of the pipe is 8 cm, the outer radius of the pipe is F D () º () 0º 0º º. How many three-digits number are there which are completely divisible by 6? () 0 () In a class with a certain number of students, if one new student weighing 0 kg is added, then the average weight of the class increased by kg. If one more student weighing 0 kg is added, then the average weight of the class increased by. kg over the original average. What is the original average weight (in kg) of the class? () 7 cm () 0 cm 9 cm cm 7. reservoir is in the shape of a frustum of a right circular cone. It is 8 m across at the top and 4 m across the bottom. It is 6 m deep. Find the area of its curved surface. () 8.4 m () 6.m 4 m 8.6 m 8. What is the total surface area of a triangular prism whose height is 0 m and the sides of whose base are m, 0 m and m respectively? () 46 () booster pump can be used for filling as well as for emptying a tank. The capacity of the tank is 400 m. The emptying capacity of the tank is 0 m per minute higher than its filling capacity and the pump needs 8 min lesser to empty the tank than it needs to fill it. What is the filling capacity of the pump? () 87 sq. m. () 7 sq. m. 6 sq. m. 4 sq. m. 9. In measuring the sides of a rectangular plot, one side is taken % in excess and the other 6% in deficit. The error percent in area calculated of the plot is () % ().%.% % 0. In an examination, it is required to get 96 of the total maximum aggregate marks to pass. student gets 9 marks and is declared failed. The difference of marks obtained by the student and that required to pass is %. What are the maximum aggregate marks a student can get? () 0 m /min () 60 m /min 7 m /min 6 m /min. In a quadrilateral CD, = 90º and D = + C + CD, then CD is equal to CD = 90º D = + C + CD, () 690 () Can't be determined

3 . One of a group of swans, 7 times the square root of the number are playing on the shore of the pond. The two remaining are inside the pond. What is the total number of swans? 7 () 0 () 4 6. If cosec sin= m and sec cos= n, then 4 m n + 4 mn =? cosec sin= m and sec cos= n, 4 m n + 4 mn =? () () /. If cos= a a, then cos will be equal to () cos= a a, cos a a a a () a 4. The least value of x + x is x + x () () 0 a a. If a + b + c = 0, then find the value of a b c a bc b ca c ab a + b + c = 0, () 4 () 0 a b c a bc b ca c ab 6. If x y = ; x, y0, then (x + y ) =? y x () 0 () 7. If a(a + ) = a + b + c; b(b + ) = a + b + c and c(c + ) = 8. If a + b + c, then the value of a is b c a(a + ) = a + b + c; b(b + ) = a + b + c c(c + ) = a + b + c, a b c () () 0 p q r b c, then p + q + r =? c a a b p q r b c c a a b p + q + r =? () 0 () 9. If the point (4, ) is the centroid of a triangle and (x, y), (, 7) and C(9, 7) are its verticles. Then find the area of the triangle? (4, ) (x, y), (, 7) C(9, 7) () 66 () Find the area of the triangle formed by the graph of ax+by = c (Where a, b are positive real number) and the co-ordinate axes ax+by = c ( a, b ) () c ab square units () a square units ab c ab square units a square units bc. If the graphs of the equations y = x and y = x + are drawn, then they will... to one another y = x y = x +... () parallel/ () coincident/ perpendicular/ /. Three different containers contain different quantities of a mixture of milk and water, whose measurements are 40 kg, 44 kg and 46 kg. What biggest measure be there to measure all the different quantities exactly? x y = ; x, y0, (x + y ) =? y x () 7 kg kg () kg 4 kg

4 . In a certain shop, 9 oranges cost as much as apples, apples cost as much as mangoes, 4 mangoes cost as much as 9 lemons. If lemons cost 48 paise, price of an orange is 7. nu is a working partner and imla is a sleeping partner in a business. nu puts in ` 000 and imla puts in ` nu receives.% of the profit for managing the business and the rest is divided in proportion to their capitals. What does each get out of a profit of ` 880? () paise paise () 4 paise paise 4. n express train travels 99 km between two cities. During the first km of the trip, the train travelled through mountainous terrain. The train travelled 0 km/hr slower through mountainous terrain than through level terrain. If the total time to travel between two cities was 7 hours, what is the speed of the train on level terrain? () 6 km/hr 47 km/hr () km/hr 88 km/hr. One type of liquid contains % of milk, the other contains 0% of milk. container is filled with 6 parts of the first liquid and 4 parts of the second liquid. The percentage of milk in the mixture is () 7% () % 9% % ` 6000 ` 880 () ` 400 and ` 480 () ` 460 and ` 40 ` 40 and ` 40 ` 470 and ` 40 ` alone would take 8 hr more to complete the job than if both and worked together. If worked alone, he took 4 hr more to complete the job than if and worked together. What time would they take if both and worked together? () 8 days days () days 6 days 4 9. Raju's factory kept increasing its output by the same percentage every year. Find the percentage increase every year if it is known that his output is doubled after two years. 6. The highest score in an innings was 9 of the total () 00 % () 00( )% score and the next highest was of the remainder. 9 These scores differ by 8 runs. What was the total scores in the innings? 9 00( )% 0( )% 0. Two pipes can fill a tank in 8 hr and hr respectively whereas an escape pipe can empty it in 6 hr. If the three pipes are opened at pm, pm and pm respectively, at what time will the tank be filled? 9 () () () 8 am am () 7 am 4

5 . The ratio of two liquids in a mixture is : and that in another mixture is 6 :. The ratio in which these two mixtures should be mixed so as to make the ratio of the liquids 7 : is : 6 : 7 : () 44 : 7 () 44 : 8 44 : 9 44 : 9. Three friends nita, indu and Champa divided ` 0 amongst them in such a way that if ` 0, ` 0 and ` are removed from the sums that nita, indu and Champa received respectively, then the share of the sums that they got will be in the ratio of : 8 : 4. How much did Champa receive? ` 0, ` 0 ` : 8 : 4 ` 0 () ` 49 () ` 0 ` 480 ` 7. The population of a colony was 600 three years back. It is 4800 right now. What will be the population three years down the line, if the rate of growth of population has been constant over the years and has been compounded annually? 7. triangle and a parallelogram are constructed on the same base such that their areas are equal. If the altitude of the parallelogram is 00 m, then the altitude of the triangle is () 00 m 00 m () 00 m 0 m 8. The perimeter of two similar triangle C and PQR are 6 cm and 4 cm respectively. If PQ = 0 cm, then the length of is C PQR PQ = 0 () 6 cm () cm 4 cm cm 9. Two small circular parks of diameters 6 m, m are to be replaced by a bigger circular park. What would be the radius of this new park, if the new park occupies the same space as the two small parks? () 0 m () 0 m m m 40. roller 0 cm long has diameter 70 cm. The level a playground, it takes 70 complete revolutions. The cost of travelling the pleyground at the rate of ` per m is ` () 6000 () truck covers a distance of 0 metres in minute whereas a bus covers a distance of km is 4 minute. The ratio of their speeds is () 4 : () : : 4 0 :. Walking /4 of his usual speed, a person is 0 min. late to his office. Find his usual time to cover the distance. () 0 min. 8 min. () min. min. /4 6. If x 7xy + y = 0, then the value of x : y is x 7xy + y = 0 x : y () : () : : and : : 6 () ` 000 () ` 90 ` 400 ` The reduced form of cos 6 x + sin 6 x + cos x sin x is equal to cos 6 x + sin 6 x + cos x sin x () () 0 sin x + cos 4. If asec + btan= and a sec b tan =, then a b + 4a is equal to a sec + b tan= a sec b tan = a b + 4a 9 () 9b () a b 9 4. If x = + / + /, then the value of x 6x + 6x is x = + / + /, x 6x + 6x () ()

6 44. In a cyclic quadrilateral CD, is double of its opposite angle and the difference between the other two angles is one-third of. The minimum difference between any two angles of this quadrilateral is CD () and. m () and 6 m and m and 4 m 49. well has to be dug out that is to be. m deep and of diameter 7 m. Find the cost of plastering the inner curved surface at ` per sq. m. () 0º () 0º 0º 40º 4. The area of four walls of a room is 0 m and the length is twice the breadth. If the height of the room is 4 m, then find the area of the floor. () 48 m () 49 m 0 m m 46. Rohit took a loan of ` 0000 to purchase one LCD set from a finance company. He promised to make the payment after three years. The company charges compound interest at the rate of 0% per annum for the same. ut, suddenly the company announces the rate of interest as % per annum for the last one year of the loan period. What extra amount does Rohit have to pay due to this announcement of the new rate of interest? LCD ` 0000 () ` 780 () ` 440 ` Water has been poured into an empty rectangular tank at the rate of 8 cu ft/min. for. min. The length of the tank is ft and the width is one half of the length. How deep is the water in the tank? () 4 ft ().86 ft. ft 4.44 ft 48. school room is to be built to accommodate 70 children, so as to allow. m of floor and m of space for each child. If the room be 4 m long, what must be its breadth and height? ` () ` 46 () ` 48 ` 47 ` person observes the angle of elevation of a building as 0º. The person proceeds towards the building with a speed of ( ) m/hr. fter hr, he observes the angle of elevation as 4º. The height of the building (in m) is ( ) 4º 0º () 00 () 0( ) 0 0( ). The LCM and HCF of two numbers are 84 and respectively. If the ratio of the two numbers is : 4, then the larger of the two number is : 4 () () printer numbers are pages of a book starting with and uses 89 digits in all. How many pages does the book have? () 074 () and can separately do a work in 0 and days respectively. They worked together for 6 days after which was replaced by C. If the work is finished in next four days, the number of days in which C alone can do the work will be C C () 4 days 40 days () days 6

7 4. Sita buys a fridge at 6 of its originals value and sells it for 0% more than its value. Then, gain percent is 6 ().% ().67% 6.67%. contractor employed labourers on a job. He was paid ` 7 for the work. fter retaining 0% of his sum, he distributed the remaining amount amongst the labourers. If the number of men to women labourers was in the ratio of : and their wages in the ratio of : 4, what wages did a woman labourerget? 7 : 4 : () ` 0 () ` 8 ` ` 6. Sumit lent some money to Mohit at % per annum simple interest. Mohit lent the entire money to irju on the same day at 8 % per annum. In this transaction after a year. Mohit earned a profit of ` 0, find the sum of money lent by Sumit to Mohit. ` 0 8 % () ` 0000 () ` 9000 ` computer is available for ` 9000 cash or ` 7000 as cash down payment followed by five monthly installments of ` 4800 each. What is the rate of interest per annum under the installment plan? ` 4800 ` 9000 ` 7000 ().7% () 7.7% 6.7% 8.7% 8. man sells a book at a profit of 0%. If he had bought it at 0% less and sold it for ` 8 less, he would have gained %. The cost price of the book is ` ` 8 () ` 80 () ` 70 ` 60 ` man buys apples at a certain price per dozen and sells them at eight times per hundred. What is his gain or loss percent? () 4% loss 4% gain () 8 4 % loss 6 4 % gain 60. The sum of money is to be divided amongst, and C in the respective ratio of : 4 : and another sum of money is to be divided between E and F equally. If F got ` 00 less than, how much amount did receive?, C : 4 : E F F ` 00 () ` 70 () ` 000 ` 00 can't be determined 6. If x 4, then x 8 + x will be x 8 x x 4 x 8, + x x 8 x () () 0 6. If a =, the value of 9a a () a = a 9a =? a =? a () 6. The sum of the reciprocals of the ages of two brothers is five times the difference of the reciprocals of their ages. If the ratio of the product of their ages to the sum of their ages is 4.4 :, find their ages. 4.4 : () 6 and 4 yr 8 and yr 9 9 () 4 and 0 yr and 9 yr 7

8 64. chemist has 0 L of a solution that has 0% nitric acid by volume. He wants to dilute the solution to 4% strength by adding water. How many litres of water must he added? 70. Two trains move from station and station towards each other at the speed of 0 km/hr and 60 km/hr. t the meeting point, the driver of the second train found that the train has covered 0 km more. What is the distance between and? () () If (a b) =, (b c) = and (c a) =, then the a b c abc will be a b c (a b) =, (b c) = (c a) =, a b c abc a b c () 7. () For what value of 'a' and 'b', (a > 0, b < 0) the expression 8x ax + x + b is a perfect cube? 'a' 'b' (a > 0, b < 0) 8x ax + x + b () a = 8, b = 7 () a = 6, b = 9 a =, b = 9 a = 6, b = D and E are two points on the sides and C of a triangle C in a such way that DEC. DE, divides triangle C into two parts of equal area, then what is the ratio between D and D? C D E C DEC DE, C D () : () : D : : 68. Out of the line segments of length cm, cm, cm and 6 cm. How many triangles can be formed by using any three of them?,, 6 () 4 () 69. CD is a rhombus. If is produced to F and is produced to E in a such manner that = E = F, then the result will be CD F F E = E = F () EDCF () ED > CF EDCF ED + CF = EF () 0 km () 00 km 0 km 960 km 7. train overtakes two persons walking along a railway track. The first one walks at 4. km/hr and the other one walks at.4 km/hr. The train needs 8.4 and 8. seconds respectively to overtake them. What is the speed of the train, if both the persons are walking in the same direction as the train? () 66 km/hr () 7 km/hr 78 km/hr 8 km/hr 7. rhombus OC is drawn inside a circle whose centre is at O in such a way that the vertices, and C of the rhombus are on the circle. If the area of the rhombus is m, then the radius of the circle is OC O, C () 64 m () 8 m m 46 m 7. If asin+ bcos= c, then the value of acos bsin will be asin+ bcos= c, acos bsin () a b c () a b c a b c a b c 74. If sec= x (0º < < 90º), then sec+ tanwill be 4x equal to sec= x (0º < < 90º), sec+ tan 4x () x x () x x & x 8

9 cos sin cos sin 7. If =, then is equal cos sin cos sin to 4 4 cos sin cos sin =, () 4 () If lcos + msin = < 90º, then tan=? lcos + msin = 90º; tan=? () l m l m 4 4 cos sin cos sin cos (cosec ), where 0º < cosec cos (cosec ) cosec () l m l m 0º < < 77. Two points X and Y are on the sides DC and D of the parallelogram CD. The area of X is CD DC D X Y X D X C Y () / of area YC/ YC () equal to area YC/ YC / of area YC/ YC twice the area YC/ YC 78. The area of the equilateral triangle made inside the square of side 'a' will be 'a' D 79. Two points are at a distance of x and y respectively on the same side of the base of a tower. If the angles of elevation of these points with the top of the tower are complementary. The height of the tower is x y () x y () x y xy x y 80. cylindrical tub of radius cm contains water up to a depth of 0 cm. spherical iron ball is dropped into the tub and thus the level of water is raised by 6.7 cm. The radius of the ball is () 7. cm 4. cm () 6 cm 9 cm 8. The value of is () () The LCM of 7, 7, 7, 7 8 is 7, 7, 7, 7 8 () 7 8 () The average salary per head of all the workers of an office is ` 9. The average salary of officers is ` and the average salary of the rest is ` 8. Find the total number of workers. ` 9 ` ` 8 () 64 () Men, Women and Children are employed to do a work in the proportion of : : and their wages are in the proportion of 6 : :. When 0 men are employed, total wages of all amount to ` 400. What is the weekly wages paid to a man, a woman and a child, in `? () C a a () a 6 : : : 6 : ` 400 a a 64 ` () 0, 0, 80 () 0, 0, 70 0, 0, 90 00, 0, 70 9

10 8. boatman goes km against the current of the stream in hr and goes km along the current in 0 min. How long will he take to go km in stationary water? D O 06º () hr 0 min hr () hr min 40 min 86. shopkeeper sold an article at a profit of 7.%. If he had bought it at 8% less and sold it at 0% profit, he would have earned `. more as profit. Cost price of the article is C () º () 4º 40º 7º Direction (9-9) : Study the graph carefully to answer the question that follow. (9-9) : Percent profit made by two companies over the years `. () ` 0 () ` 67 ` 70 ` Two roads of metre width cuts each other perpendicular by crossing a park of dimension 7m 48m in the middle. Each road is parallel to each side of the rectangle. What is the area of the remaining part of the field? Percent profit = Income Expenditure 00% Expenditure = 00% Company Company 7 48 () 6 sq. m. () 0 sq. m. 40 sq. m. 6 sq. m. 88. positive number is by mistake divided by 6 instead of being multiplied by 6. What is the percentage of the error committed on the basis of correct answer. Percent Profit Years () 0% () 0% pprox. 97% 89. Find the length of perpendicular drawn from the centre of circle with radius r to the chord of length r. r r () r () r r 90. In the following figure O is the centre and OD = 06º, so CD is CD r 4 O OD = 06º 9. If in the year 004 the expenditures incurred by Company and were the same, what was the ratio of the income of Company to that of Company in that year? () 7 : 8 () 4 : : 9 Can't be determined 9. If the amount of profit earned by Company in the year 007 was `. lakhs, what was its expenditure in that year? () `.96 lakhs `.7 lakhs `. () `.64 lakhs `.7 lakhs 0

11 9. What is the average percent profit earned by Company over all the years together? () 9 () If in the year 008, the incomes both the companies and were the same, what was the ratio of the expenditure of Company to the expenditure of Company in that year? () : () 7 : 9 : Can't be determined 9. What is the ratio of the amount of profit earned by Company to that by Company in the year 009? () : () 4 : 7 : Can't be determined Direction (96-00) : Study the chart table carefully to answer the question that follow. (96-00) : Ratio of man to woman Department Men Production HR IT Marketing 7 ccounts Women What is the number of men working in the marketing department? () () The number of men working in the production department of the organizsation is what percentage of the total number of employees working in that department? () () What is the ratio of the number of men working in the accounts departments to the total number of employees working in that department? Percent break-up of employees working in various departments of an organization Total number of employees = 800 ccounts Dept. 7% Production Dept. Marketing Dept. 8% IT Dept. % 8% HR Dept. 4% () 9 : () : : 9 6 : What is the ratio of the number of women working in the HR department of the organization to the total number of employees in that department? () : 4 () : : 9 : The number of women working in the IT department of the organization is approximately what percent of the total number of employees in the organization from all departments together? () 7 () 9 0