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Test Maths Paper-13
1. The test comprises of 30 questions.
There are 100 players numbered 1 to 100 and 100 baskets numbered 1 to 100. The first player puts one ball in every basket starting from the first basket (i.e. in baskets numbered 1, 2 , 3) . The second player puts 2 balls each in every second basket starting from the second ( i.e. in baskets numbered 2,4,6. . .) The third player puts three balls each in every third basket starting from the third , and so on till the hundredth player. a.96 b.98 c.100 d.none Ans: a 2. How many baskets will finally have exactly twice the number of balls as the number on the basket itself? a.8 b.6 c.4 d.2 Ans: d 3. In how many baskets will exactly two players put the balls? a.50 b.25 c.15 d.None Ans: b 4.The circle shown in the figure has an area of 154 sq. cm. DE + CF = AB - 4 cm. If AB is the diameter, what is the area of the quadrilateral ACBD a.35 b.121 c.70 d.140 Ans: c 5.After three successive increase , Vijay's slaray became equal to 378/125 of his intial salary. By what percentage was the salary raised the first time if the third rise was twice as high (in percentage) as the second rise and the second rise was twice as high(in percentage ) as the first rise? a. 10% b. 15% c. 20% d. 25% Ans: c 6. For sending one wagon of wheat, Food Corporation of India spends Rs. 300 for a distance of 20 kilometers and Rs. 500 for 200 kilometers. Find the cost of sending a wagon through 400 kilometres, assuming that cost = a + b x distance. a. Rs.7000/9 b. Rs.7500/9 c. Rs.6500/9 d. Rs.6000/9 Ans: c 7. A three digit number has an odd number as the digit in its hundred place. The difference between the hundreds digit and the units digit is 2. The sum of these two digits is equal to the middle digit but their product is less than the middle digit. The number can be a. 583 b. 143 c. 385 d. either 1 or 3 Ans: b 8. At SM Institute, 40% of the students drink tea, 30% drink coffee, and 20% drink both. 5% of those who drink at least one of the two drinks and 25% of those who drink neither of the two, smoke. 18% of the smokers smoke Charminar. If SMI has 300 students, how many smoke brands other than Charminar? a.54 b.46 c.123 d.75 Ans: c 9. Find the are of the triangles formed by the intersections of lines x + y - 5 = 0 and x - y + 1= 0 and x axis. (in sq. units) a.4.5 b.5 c.8.75 d.9 Ans: d 10. Find the probability that the number chosen randomly from the first 1000 natural numbers is a multiple of 4 or a perfect square. a.53/200 b.133/500 c.281/1000 d.1093/4000 Ans: b 11. Four friends bought a car. The first friend paid half of the sum paid by the others, the second paid one third of the sum paid by the others; the third one-quarter of what was paid by the others. If the fourth paid Rs. 13,000, then find the cost of the car. a.Rs.39,000 b.Rs.52,000 c.Rs.60,000 d.None Ans: c 12. f(x)= 2x3 + px2+ qx - 4 and f(2)=0 , find the value of p+q , where p and q are non zero. If f(x)=0 has three real roots, all of them being integers and further two of three roots are equal. a.-6 b.2 c.either (b) or (c) d.none Ans: b 13. In a triangle PQR, PQ = 6 cms QR = 8 cms and PR = 10 cms. The length of the median bisecting the shortest side is: a.10 cms b.8.5 cms c.9 cms d.None Ans: b 14. How many 2-digit code numbers can be formed using the digits 1,2,3,4,0; if no number can start with a 0? a. 20 b. 25 c. 16 d. None Ans: a 15.How many 3 digit numbers can be made using at least one 2 and at least one 3 in each of them? a. 60 b. 58 c. 52 d. 50 Ans: d 16. Anusha and Bipasha pick up a ball at random froma bag containing M red and N yellow coloured balls, one after the other , replacing the ball every time till one of them gets a red ball. The first one to get a red ball is declared the winner . If Anusha begins the game and the odds in favour of her winning the games are 3 to 2 , then find the ratio M : N.a. 3:1 b. 1:2 c. 2:3 d. 3:2 Ans: b 17. Find the number of whole number less than 100 such that the sum of the factorials of its digit(s) is less than or equal to the numbera.16 b.17 c.20 d.19 Ans: d 18. if f(x) = kx +1 ; g(x) = 3x + 2 if fog = gof , find ka.1 b.3 c.8 d.Indetermine Ans: c 19. [log x + log ( x - 15 )] / [ log 1000 - log 10] = 1. The positive root of x isa.Not solvable b.5 c.20 d.15 Ans: c 20. If a year has 360 days and all months with 30 days . what is the probability that your birthday falls on a Monday and that is an even day of an even month, if January 1 is a Monday?a. 1/30 b. 13/360 c. 1/28 d. 11/360 Ans: b 21. If the roots of the quadratic equation ax2+ bx + c= 0 are 2 + √ 3 and 2 - √3 then {a( c - b)}/ bc ?a. 5/4 b. -5/4 c. 4/5 d. -4/5 Ans: b 22.Find three numbers in GP whose sum is 52 and the sum of whose products in pair is 624.a. 7, 15, 30 b. 4, 8 , 40 c. 4, 12 , 36 d. 6, 12, 34 Ans: c 23. A quadratic expression f(x) = ax2 + bx + c is such that f(-2) < 4 ; f( 2) > -4 and f(3) < -11. Which of the following is always true?a. a < -2 b. a < -1 c. a > 1 d. a > 2 Ans: b 24. IF a = bc and (a + b)2 = c2 where a, b and c are positive , which of the following is true ?a. b > 1 b. b = 1 c. b < 1 d. can not be determined Ans: c 25. AB is diameter of the circle and the points C and D are on the circumference such that triangle CAD = 30 degree. What is the measure of triangle ACD ?a. 40 degree b. 50 degree c. 30 degree d. 90 degree Ans: a 26. If AB is a two digit number to the base n and (AB)n = 4(BA)n , then what is the decimal equivalent of (AB)n when n takes the minimum possible value ?a. 1:3:2 b. 2:1:3 c. 3:2:1 d. 1:2:3 Ans: d 27. A and B start from two points P & Q (2000 km apart) respectively with uniform speeds. A is headed towards Q and B towards P. A rests whenever B is on the move and B rests whenever A is on the move. A’s speed is 40 kmph , while B's speed is 50kmph . A starts first and reaches the destination in 60 hrs. Find the least time that B would take to reach his destination after A startsa. 100hrs b. 90hrs c. 80hrs 1:4 d. 75hrs Ans: b 28. The sum of the smallest angle in a triangle and 7 times the second smallest angle equals 120 degree. The largest angle in the triangle cannot be less than (in degrees)a. 158 b. 156 c. 154 d. 150 Ans: d 29. The area of the triangle with vertices at the point (a, b+c), (b, c+a) , (c, a+b ) is ( a , b and c are all different)a. 0 b. a+b+c c. ab + bc + ca d. a2+b2+c2 Ans: a 30. Number of triangles formed in a decagon by joining its vertices isa.10 b.270 c.120 d.30 Ans: c
1. The test comprises of 30 questions.
1. What is the value of n for which (n17 - n)(42n - 1) is divisible by 289?a.7 b.51 c.17 d.34 Ans: d 2. A number is picked from the odd numbers formed by the products of numbers shown up when 5 dice are rolled. What is the probability that it ends with 5?a.1- (2/3)5 b.1 - (1/3)5 c. 1- (1/6)5 d. 0 Ans: a 3. if f(x)= (x2 + 12x + 12)/(x2 + 3x + 3) , then find max f(x)a.2 b.4 c.8 d.cannot be determined Ans: b 4.The sides of a right-angle triangle have lengths which are integers in AP. In which of the following smallest side of a triangle does there exist such a triangle ?a.2000cm b.2001cm c.2002cm d.none Ans: b Directions for Questions 5 & 6.A , B , C , D are four item who are being weighed one after the other in the same order . Each time whena item is weighed the average weights till then is recalculated . It is found that the average weights so calculated were in A.P. with common difference of 2 kg. 5.The minimum weight of D if the weights of A, B , C and D are natural numbers isa. 7kg b. 9kg c. 13kg d. 28kg Ans: c 6. What is the average weight of A , B , C, D if the weight of A is 4 kg?a. 7kg b. 10kg c. 28kg d. none Ans: b 7. A man enters a shop which sells bottled water . There are full one liter bottles which cost Rs.22 half liter bottles which cost Rs. 11 and empty bottles which cost Rs.1 . He wants to buy at least 2 liters water and 3 bottles . How many of each will he have to buy to ensure that he spends the least amount of money ?a.2 full , 0 half , 1 empty b.1 full , 2 half , o empty c.1 full 1 half 1 empty d.there can be more than one way Ans: d 8.There is an alloy (A) of silver and copper . A certain weight of this alloy is mixed with 15kg of pure silver and melted . The new alloy (B) contains 90% of silver . If the alloy ( A) is mixed with 10kg of a 90% silver alloy, the new alloy (C) is found to contain 84% silver . Find the percentage of silver in (A)a.80% b.90% c.75% d.84% Ans: a 9. A big cube is cut into 64 equal cubes . If 6 liters of paint was used to paint the big cube , how many more litres will you need for the smaller cubes to be painted on all sides?a.24 liters b.23 liters c.30 liters d.18liters Ans: d 10. If n> 1 and x ≠ 0 , then (1+x)n - nx - 1 is divisible by :a.x3 b.x2 c.x4 d. All of these Ans: b 11. How many factors of 1296 will have total number of factors exactly equal to 3?a.1 b.2 c.3 d.4 Ans: b 12. If (52a)b = (169)11 and a and b differ by two , find (a + b).a.6 b. 8 c.10 d.14 Ans: c 13. Find the number of integral solution to |x| + |y| + |z| = 15.a.902 b.728 c.734 d.904 Ans: a 14. A circle is inscribed in a right angled triangle . The point of tangency with the circle divides one of the sides into two segments 6 cm and 10cm in length . The area of the triangle is ?(in cm2)a. 192 b. 320 c. 200 d. 240 Ans: d 15.Two friends A and B leave at 8 A.M everyday to meet each other at point P after two hours. On one day A walks at 5/6 th of the usual speed while B starts one hour late , so he increases his speed by 25% . Now A takes 1/2 hour more than usual to meet B and they meet half kilometer away from point P. Find out the speeds of A and B and total distance traveled by them. ?a.5 kmph 5 kmph 20km b.6kmph 4kmph 22km c.6kmph 4kmph 20km d.4kmph 6kmph 20km Ans: c 16. 11 22 36 412 520 . . . . . . 25 terms . Find the highest power of 75 that can divide the given series?a.66% b.42% c.74% d.cant be determined Ans: d 17. A man had three daughters , who celebrated their birthday on the same day , but were born in 1955 , 1978 and 1979 respectively . On one such birthday , if the product of their ages was divided by their respective ages in turn , the sum of quotients , would have been 74 . The age of the oldest daughter isa.6 yrs b.8 yrs c.7yrs d.None Ans: d 18. Find the remainder when (((1112)13)14) is divided by 9 ?a.8 b.1 c.2 d.0 Ans: b 19. There are 3 clubs X , Y and Z in a town with 40 , 50 and 60 members respectively . While 10 people are members of all the 3 clubs , 70 are members in only one club. How many belong to exactly two clubs?a.20 b.25 c.50 d.70 Ans: b 20.In a six node network , two nodes are connected to all the other nodes. Of the remaining four , each is connected to four other nodes . What is the total number of links in the network ?a. 13 b. 15 c. 18 d. none of the above Ans: a 21. If s(n) is the set of all factors of n , then what is the probability that a randomly chosen element of s(1050) is a multiple of 5 ?a. 1/5 b. 1/4 c. 1/3 d. 2/5 Ans: c 22.In a circular pond, a fish starts from a point on the edge , swims 600 feet due east to reach another point on the edge , turns south and swims 800 feet to reaxh yet another point on the edge. The diameter of the pond isa. 600ft b. 700ft c. 800ft d. 1000ft Ans: d 23. Let A , B and C be distinct positive integers satisfying A < B < C and A+B+C=k . What is the smallest value of k that does not determine A , B , C uniquely ?a. 9 b. 6 c. 7 d. 8 Ans: d 24. A box contains 6 black and 5 white balls. Each ball is of a different size. The probability that the black ball selected is the smallest black ball , isa. 1/8 b. 1/3 c. 1/6 d. 2/3 Ans: c 25.If log 7 log5 √(x + 5) + √x ) = 0 , find the value of x .a.1 b.0 c.2 d.none Ans: b Directions for Questions 26 to 28.Two people P and Q moved between two points A and B. Q started to move from point B towards point A exactly an hour after P started from A in the opposite direction. Q's speed was twice that of P. when P had covered oneâ€“sixth of the distance between the points A and B. Q had also covered the same distance. 26. The point where P and Q would meet isa. closer to A b. Exactly between A and B c. Close to B d. P and Q will not meet at all Ans: a 27. How many hours would P take to reach B?a. 2 b. 5 c. 6 d. 12 Ans: d 28.How many more hours would P (compared to Q) take to complete his journey?a. 4 b. 5 c. 6 d. 7 Ans: c 29. If the HM between two positive numbers is to their GM as 12:13 , then the numbers could be in the ratioa. 12:13 b. 1/12:1/13 c. 4:9 d. 2:3 Ans: c 30. Let Un+1 =2Un + 1 ; (n =0 ,1 ,2 . . . .) and U0 = 0 . Then U10 is nearest toa.1023 b.2047 c.4095 d.8195 Ans: a |

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