ACE OF PACE. cos A sin A 2 cos A sin A cos A sin A. 4. What percent decrease in salaries would exactly cancel out the 20% increase?

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Augusta Harper
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1 AE OF PAE AE OF PAE (ADVANED) ODE The ages of two friends is in the ratio 6:5. The sum of their ages is 66.After how many years will the ages be in the ratio 8:7? (A) 1 Years 15 Years () 9 Years 18 Years (A) x1 6 x1 6k x 5 and x 5k Also, x1 x 66 k 6 current age 6 & 0 6 x 8 x 1 years 0 x 7. An athlete decides to run the same distance in 1/4th less time that she usually took. By how much percent will she have to increase her average speed? (A) 45 %. % (). % 4 % t 4 S t S ' S ' S 4. The expression (1- tan A + sec A) (1 cot A+ cosec A) has value (A) 1 0 () 1 1 tan A + sec A1 cot A cosec A cos A sin A 1 sin A cos A 1 1 cos A sin A cos A sin A cos A sin A 4. What percent decrease in salaries would exactly cancel out the 0% increase? 1 (A) () 0 (A) x x 1 x x x 40 then x (A) () ENTERS: MUMBAI / DELHI / AKOLA / KOLKATA / LUKNOW / NASHIK / GOA / PUNE # 1

2 Hence 4 x 6 6. Three numbers are in ratio ::4 and their LM is 40.Their H..F. is (A) 40 0 () 0 10 () Numbers are x, x, 4x Lcm 1x 40 x 40, 60, 80, HF = How many two-digit numbers are divisible? (A) 5 7 () 0 () 99 Required no If tan a cos sin then b cos sin is b a b a (A) () a b a b a b (A) cos sin 1 tan b a tan a / b cos sin 1 tan b a b a 0 0 cos 5 cos Find the value of 0 0 sin 59 sin 1 (A) 0 1 () o o o cos 5 cos 65 cos 65 sin 65 sin 59 sin 1 sin 59 sin 59 o o o o 10. Three quantities A, B, are such that AB 1 K, where K is a constant. When A is kept constant, B varies directly as ; when B is kept constant, A varies directly and when is kept constant, A varies inversely as B. Initially, A was at 5 and A: B; was 1: : 5. Find the value of A when B equals 9 at constant. (A) 8 8. () AB constant 515 A9 5 5 A 8. ENTERS: MUMBAI / DELHI / AKOLA / KOLKATA / LUKNOW / NASHIK / GOA / PUNE #

3 11. If a b c b c, then each fraction is equal to c a a b (A) a b c 1 ()1 4 0 a b c a b c 1 b c c a a b a b c AE OF PAE (ADVANED) ODE If 0 men working 7 hours a day can do a piece of work in 18 days, in how many days will 1 men working 8 hours a day do the same work? (A) 4 days.5 days () 0 days 45 days Total man-hours Let no. of days be x then total man-hours is x (as work is same) x x.5 days is the same as 69 (A) () () On Ashok Marg three consecutive traffic lights change after 6, 4 and 7 seconds respectively. If the lights are first switched on at 9.00 A.M. sharp, at what time will they change simultaneously? (A) 9:08:04 9:08:4 ()9:08:44 None of these They will charge again together after an integral multiple of LM of their individual tune period LM of (6, 4, 7) 504sec. 8 min and 4 sec. 15. Find the units digit of the expression (A) 4 () 7 0 Let U n denote units digit of n U U 11 U 1 U 1 U 14 U 15 U 16 U ENTERS: MUMBAI / DELHI / AKOLA / KOLKATA / LUKNOW / NASHIK / GOA / PUNE #

4 16. In the above figure, AD is the bisector of BA, AB 6 cm, A 5cm and BD cm. Find D. (A) 11.cm.5cm ().5cm 4cm A 6 5 B D AD is the angle bisector Hence AB BD A D 5 5 D In the given figure, AB and AD are right angle triangles with distinct integral sides and AB xcm, B ycm, D zcm and x. y z and x, y and z has minimum integral value. Find the area of ABD (A) (A) 6cm 64cm () 4cm 5cm A D x z B y As x, y, z are integers. Hence minimum value of x, y and z satisfying the given conditions are x ; y 4; z 1 A Hence Area ABD ENTERS: MUMBAI / DELHI / AKOLA / KOLKATA / LUKNOW / NASHIK / GOA / PUNE # 4

5 18. Three persons Amar, Akbar and Anthony inverted different amounts in a fixed deposit scheme for one year at the rate of 1% per annum and earned a total interest of Rs,40 at the end of the year. If the amount invested by Akbar is Rs more than the amount invested by Amar and the amount invested by Anthony is Rs. 000 more than the amount invested by Akbar, what is the amount invested by Akbar? (A) Rs. 1,000 Rs. 10,000 () Rs Rs Akbar Amar Anthony x 5000 x x 7000 Total principle x 1000 x S I x Divide a solid right circular cylinder in 8 parts identical to each other such that these parts are not cylinders. Find the surface area of each part. (Given that urved surface area of original cylinder is πrh and Non curved surface area of original cylinder is πr ) (A) (πr + πrh )/4 (πr + πrh )/4 + rh () (πr + πrh )/4 + rh None of these () S 1 S 4 S 5 S Surface of S 1 and S each r 8 Surface area of S & S 4 r h rh urved surface S5 8 Hence the total surface area S1 S S S4 S5 r rh r rh rh r rh rh 4 8 S ENTERS: MUMBAI / DELHI / AKOLA / KOLKATA / LUKNOW / NASHIK / GOA / PUNE # 5

6 0. I was born on x/y/198 z (i.e. on the x th day of the y th month of the year 198 z, where z is the unit s digit). It is known that y is a prime number & z = y. At a particular year in 1 st century, which is a perfect square, I will be exactly x y years old. Find my date of birth in DD/MM/YYYY format (A) 1/5/1987 1//1986 () /08/1984 0/0/1986 y can be, only as z y and z is a digit hence 0 z 9 either z 4 or 6 year 05 is a perfect square and age in that year = Hence x = 15 y z If sin and tan = 1, then lies in which quadrant (A) First Second () Third Fourth () sin 0 ; and tan 0. If sin 1 + sin + sin =, then cos 1 + cos + cos = (A) () 1 0 sin 1 sin sin sin 1 sin sin 1 1,, are odd multiples of 4. If tan then sin is (A) but not or () but not none of these 5 5 tan 0 lies in second or 4 th quadrant 4 4 sin or The coordinates of the points where the lines x y = 5, 6x y = 10 meet the y axis (A) (0, 5), (0, 10) ( 5, 0), ( 10, 0) () ( 5, 0), (0, 10) (0, 5), (0, 10) (A) Line x y 5 O meets y-axis at And line x meets y-axis at O 1 10 ENTERS: MUMBAI / DELHI / AKOLA / KOLKATA / LUKNOW / NASHIK / GOA / PUNE # 6

7 5. If the length and breadth of a room are increased by 1 m each, its area would increase by 1 m. If the length is increased by 1m and breadth is decreased by 1m, the area would decrease by 9 m. Find the area of the floor of the room, in m (A) () L = length of room, B = breath of room Then and ( L 1) B 1 LB 1 L B 0 L 1 B 1 LB 9 L B 8 B 11; L 19 Area LB Sridevi purchased cakes of two varieties of soap, Lux and Dove spending a total Rs. 60. If each Lux costs Rs 0 and each Dove costs Rs 40, then in how many different combinations could she have purchased the cakes? (A) 4 () 5 L no. of Lux soap cakes purchased D no of Dove soap cakes purchased 0L 40D 60 L, D 8, 4, 6 L 4D 6 7. Venu has as many sisters as he has brothers. If Karuna, Venu s sister has thrice as many brothers as she has sisters, then Venu has how many sisters? (A) 1 () 4 (A) m no. of male children f no. of female children Then, m 1 f... 1 f 1 m... f 1 f f 4 f, m 8 The area of a rectangle gets reduced by 80 square units, if its length is reduced by 5 units and breadth is increased by units. If we increase the length by 10 units and decrease the breadth by 5 units, the area is increased by 50 sq. units. Find the length and breadth of the rectangle (A) 0, 40 5, 5 () 40, 0 45, 5 () L = Length of rectangle B = Breadth of rectangle L 5 B LB 80 L 5B 70 L 10 B 5 LB 50 10B 5L 100 5B L 70 ENTERS: MUMBAI / DELHI / AKOLA / KOLKATA / LUKNOW / NASHIK / GOA / PUNE # 7

8 B L 0 B 0, L Find the greatest number that will divide 445, 57 and 699 leaving remainders 4, 5 and 6 respectively. (A) () 78 6 Let no. of x then 445 x k x k 5 k, k, k are integers 699 x k 6 x k x k 567 x k 69 Hence x is the H..F. of 441, 567, In the triangle AB, AB or B = 90. AB : BD : D = : 1 :. If A = 0 cm, then what is the length of AD (in cm)? A B D (A) 5 6 () A x 0 B x D x x x 4 0 x 4 Hence 5x 5 16 AD AD 4 10 ENTERS: MUMBAI / DELHI / AKOLA / KOLKATA / LUKNOW / NASHIK / GOA / PUNE # 8

9 1. In the following figure, ABD is a parallelogram, B is extended to F and the line joining D and F intersect AB at E. Then, F A E B D AD BF AD F BF F (A) () All of them are true AE BE AE D BE D F A E B D ADE and BFE are similar Hence AD = BF AE BE BEF and DE are similar Hence BF = F BE D. Dheeraj has twice as many sisters as he has Brothers. If Deepa, Dheeraj s sister, has the same number of brothers as she has sisters, then how many brothers does Deepa have? (A) () 4 annot be determined m no. of male child in the family f no. of female child in the family m 1 f and f 1 m m m 1 m ; f 4. A wheel makes 0 revolutions per hour. The radians it turns through 5 minutes is c (A) () 7 7 In the revolution when terms reduces 0 5 angle turned c ENTERS: MUMBAI / DELHI / AKOLA / KOLKATA / LUKNOW / NASHIK / GOA / PUNE # 9 c c 50

10 DIRETIONS (Q. NO. 4-6) : ODING DEODING. 4. If MADRAS can be written as ARSARS, how can ARKONAM be written in that code? (A) ROAAKNM ROAKANM () ROAKNNM ROAKNAM (A) 5. In a certain code, TELEPHONE is written as ENOHPELET. How is ALIGATOR written in that code? (A) ROTAGILA ROTAGAIL () ROTAGILE ROTEGILA (A) 6. If sky is star, star is cloud, cloud is earth, earth is tree and tree is book, then where do the birds fly? (A) loud Sky () Star Data inadequate () 7. Pointing to a man, a woman said, His mother is the only daughter of my mother. How is the woman related to the mother? (A) Mother Daughter () Sister Grandmother (A) 8. How many squares in the picture? (A) 9 () An examination consists of 100 questions. Two marks are awarded for every correct option. One mark is deducted for every wrong option and half mark is deducted for every question left, then a person scores 15. Instead, if half mark is deducted for every wrong option and one mark is deducted for every question left, then the person scores 1. Find the number of questions left unattempted by the person. (A) () 10 1 (A) ENTERS: MUMBAI / DELHI / AKOLA / KOLKATA / LUKNOW / NASHIK / GOA / PUNE # 10

11 40. A man bought 50 dozen fruits consisting of apples and bananas. A banana is cheaper than an apple. The number of dozens of apples he bought is equal to the cost per dozen of bananas in rupees and vice versa. If he has spent a total amount of Rs 1050, find the number of dozens of apples and bananas he bought respectively. (A) 1 and 8 14 and 6 () 15 and 5 8 and () 41. If starting from very first ball of the match, each batsman gets bowled out on the very first ball he faces. Which batsman will be left not out in the end? (A) Batsman number 11 Batsman number 8 () Batsman number 7 None of these 4. A boat takes 90 minutes less to travel 6 Kms downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 Km/h, the speed of the stream is (A) Km/h.5 Km/h () Km /h 4 Km/h (A) 4. After Yuvraj hit 6 sixes in an over, Geoffery Boycott commented that Yuvraj just made 10 runs in the over. HarshaBhogle was shocked and he asked Geoffery which base system was he using? What must have been Geoffery s answer? (A) 9 () A teacher throws a question in front of his class and says that he will give a chocolate as a prize to the student who solves it. He says, I have a two-digit number in my mind. If I square the number, then the last digit of both the numbers have the same last digit. None of the digits in the original number is zero. When the digits of the original is written in the reverse order, the square of the new number obtained has a last digit 6 and is less than 000. Now find the number of distinct possibilities for the number. Rajiv found the exact answer. What was his answer? (A) 6 () 8 9 (A) 45. Many years ago when Mr. Waugh was asked as to who among Steve and Mark was elder, he said, Two years from now Steve will be twice as old as he was two years ago and in three years from now Mark will be three times old as he was three years ago. How old is Mark today, if Mr. Waugh was asked the question 7 years back and who is older,mark or Steve? (A) 1 years,steve years, both are of the same age () 7 years,mark 4 years, can t say ENTERS: MUMBAI / DELHI / AKOLA / KOLKATA / LUKNOW / NASHIK / GOA / PUNE # 11

12 46. Mr. Srivastava has five children Dolly, Polly, Molly, Solly and Lolly named in the decreasing order of their ages. The age difference between any two consecutive children is the same (an integral number of years). If dolly is 14 years old, what are the possible ages of Molly? I. 1 years II. 1 years III 11 Years (A) only II () only I and II (A) only II and III All three of these 47. Sachin Tendulkar, The God of the cricket, scored 6000 runs in a certain number of innings. In the next five innings he was out of form and hence could make only a total of 90 runs, as a result of which his average fell by runs. How many innings did he play in all? (A) () (A) 48. If an ant can travel only in the North or in the East direction, in how many possible routs can an ant travel from cell P to cell Q? Q North East P (A) 4 8 () 6 5 () 49. What is the sum of all two digit numbers that give a remainder of when they are divided by 7? (A) () Evaluate x (A) 6 () 4 5 () ENTERS: MUMBAI / DELHI / AKOLA / KOLKATA / LUKNOW / NASHIK / GOA / PUNE # 1

Pair of Linear Equations in Two Variables

Pair of Linear Equations in Two Variables Exercise. Question. Aftab tells his daughter, Seven ears ago, I was seven times as old as ou were then. Also, three ears from now, I shall be three times as old as ou will be. (Isn t this interesting?)