IIT-JEE AIPMT AIEEE OLYMPIADS KVPY NTSE PCCP FACULTY SAMPLE TEST PAPER SUBJECT : MATHEMATICS OBJECTIVE-PAPER Time : 90 min. Maximum Marks : 50 GENERAL INSTRUCTIONS 1. Blank papers, clip boards, log tables, slide rule, calculators, mobile or any other electronic gadgets in any form is not allowed.. Write your Name in the space provided in the bottom of this booklet. 3. Each correct answer carries + 1 mark and each wrong answer 1/3 marks. 4. In case of any dispute, the answer filled in the OMR sheet available with the institute shall be final. 5. After completion submit the Question Paper back along with the Answer Sheet. 6. The Paper contains 50 quesitons. 7. All the questions are compulsory. Name : Roll No. : PCCP Head Office / Talwandi Campus : Address : C-8, Lakshya, Nursery Plots, Talwandi, Kota (Rajasthan)-34005 Contact. No. : +91-0744-3044, 3045, Fax : 0744-47146 Website : www.pccp.resonance.ac.in E-mail : pccp@resonance.ac.in
OBJECTIVE PAPER 1. In covering a distance of 30 km Amit takes hrs. more than suresh. f Amit doubles his speed, he would take one hour less than suresh. Amit s speed is : (A) 5 km/hr. (B) 7.5 km/hr. (C) 6 km/hr. (D) 6.5 km/hr. A square is drawn by joining the mid points of the sides of a square. A third square is drawn inside the second square in the same way and the process is continued indefinetly. If the side of the square is 10 cm, then the sum of areas of all the squares so formed is : (A) 100 (B) 00 (C) 50 (D) None of these 3. P and Q are the mid points of the sides AB and BC respectively of the triangle ABC, right-angled at B, then : (A) AQ + CP = AC (B) AQ + CP = 5 4 AC (C) AQ + CP = 4 5 AC (D) AQ + CP = 5 3 AC 4. Out of 800 boys in a school, 4 played cricket, 40 played hockey and 336 played basketball. Of the total, 64 played both basketball and hockey ; 80 played cricket and basketball and 40 played cricket and hockey 4 player all the three games. The number of boys who did not play any game is : (A) 18 (B) 16 (C) 40 (D) 160 5. Area of the shaded region if every circle is of unit radius is : (A) (C) 3 Sq. Units (B) 3 Sq. Units 4 4 3 Sq. Units (D) 3 Sq. Units 6. If a, b, c are real numbers such that a + b = 6, b + 4c = 7 and c + 6a = 13, then the value of a + b + c is equal to : (A) 14 (B) 1 (C) 8 (D) 35 PAGE # 1 1
7. Maximum value of 4x x is : (A) (B) 4 (C) 6 (D) 8 8. a, b, c are three positive integers s = a + b + c. If (s a) : (s b) : (s c) = 1 : 7 : 4, then the ratio a : b : c is equal to : (A) 8 : 10 : 6 (B) 11 : 5 : 8 (C) 9 : 4 : 1 (D) 7 : 8 : 9 9. In the Fig. AMN, APQ, QRM and PRN are all straight lines. The value of + is : (A) 70º (B) 55 (C) 90º (D) 75º 10. The ratio of the incomes of A and B is 5 : 4 and the ratio of their expenditures is 3 :. If at the end of the year, each saves Rs. 1600, then the income of A is : (A) Rs. 3400 (B) Rs. 3600 (C) Rs. 4000 (D) Rs. 4400 11. If m arithmetic means are inserted between 1 and 31 so that the ratio of the 7 th and (m 1) th means is 5 : 9, then the value of m is : (A) 9 (B) 11 (C) 13 (D) 14 1. log 10 (1 + 1/) + log 10 (1 + 1/3) + log 10 (1 + 1/4) +...log 10 (1+ 1/1999) when simplified has the value equal to : (A) 1 (B) 3 (C) 10 (D) 100 13. The last digit of the number (373) 33 is : (A) 1 (B) (C) 3 (D) 9 14. The graph of y = ax + bx + c is given in figure then identify the signs of a, b and c are : (A) a < 0, b > 0, c < 0 x' (B) a < 0, b < 0, c > 0 (C) a < 0, b > 0, c > 0 y A x (D) a < 0, b < 0, c < 0 y' PAGE #
15. A number when divided by 59 leaves a remainder 139. What will be the remainder when the same number is divided by 37? (A) 1 (B) 3 (C) 7 (D) 8 16. If the system of equations 3x + 4y = 1 and (a + b) x + (a b) y = 5a 1 has infinitely many solutions then a & b satisfy the equation : (A) a 5b = 0 (B) 5a b = 0 (C) a + 5b = 0 (D) 5a + b = 0 17. In the given figure, if C is the centre of the circle and PQC = 5 o and PRC = 15 o, then QCR is equal to : (A) 40 o (B) 60 o (C) 80 o (D) 10 o 18. What is the area of a right angle triangle with its hypotenuse and perimeter equal to x and y respectively? (A) 1 1 1 x (x y) (B) x (y x) (C) y (y x) (D) none of these 4 4 19. The area of a triangle is 1 sq. cm. Two sides are 6 cm and 1 cm. The included angle is : 1 (A) cos 1 3 1 (B) cos 1 6 1 (C) sin 1 6 1 (D) sin 1 3 0. One kilogram tea and 1 kg sugar together cost Rs. 95. If the price of tea falls by 10% and that of sugar rises by 0%, the price of 1kg each combined comes to Rs. 90. The original price of tea per kilogram is : (A) Rs. 80 (B) Rs. 7 (C) Rs. 55 (D) 90 1. Let A 0 A 1 A A 3 A 4 A 5 be a regular hexagon inscribed in a circle of unit radius. Then the product of the lengths of the line segments A 0 A 1, A 0 A & A 0 A 4 is : (A) 4 3 (B) 3 3 (C) 3 (D). The area of the triangle whose vertices are (a,a), (a + 1, a + 1) and (a +, a) is : (A) a 3 (B) 1 (C) a (D) 1/ 3 3 PAGE # 3 3
3. Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 1 hours. If all the three pipes are opened together, then the tank will be filled in : 13 8 9 1 (A) 1 hours (B) hours (C) 3 hours (D) 4 hours 17 11 17 4. A bucket is in the form of a frustum of a cone and holds 8.490 litres of water. The radii of the top and bottom are 8 cm and 1 cm respectively. Find the height of the bucket. [ Use = 7 ] (A) 10cm (B) 1 cm (C) 14 cm (D) None of these 5. Given 3 sin + 5 cos = 5, then the value of (3 cos 5 sin ) is equal to : (A) 9 (B) 5 9 (C) 3 1 (D) 9 1 6. Three parallel lines 1, and 3 are drawn through the vertices A, B and C of a square ABCD. If the distance between 1 and is 7 and between and 3 is 1, then the area of the square ABCD is : (A) 193 (B) 169 (C) 196 (D) 5 1 1 7. If x + = 4, then x + x =? x (A) 18 (B) 16 (C) 14 (D) 13 8. The sum of the series 1 + 4 + 9 + 5 +...100 is : (A) 95 (B) 385 (C) 45 (D) 65 9. If both the length and the width of a rectangle are increased by 10% and 0% each, then by what percentage does the area of the resulting rectangle exceeds the original size? (A) 3 % (B) 30 % (C) 10 % (D) 0 % 30. The sum of the series 11 + 1 + 31 + 41 +...+ 01 is (A) 1950 (B) 10 (C) 40 (D) 300 31. How many numbers greater than 4000 can be formed by using the digits,3,4 and 5? (repetitions is not allowed). (A) 1 (B) 14 (C) 0 (D) 4 PAGE # 4 4
3. D is a real number with non terminating digits a 1 and a after the decimal point. Let D = 0.a 1 a a 1 a... with a 1 & a both not zero which of the following when multiplied by D will necessarily give an integer? (A) 18 (B) 198 (C) 15 (D) 75 33. If 009 = p a.q b, where "p" and "q" are prime numbers, then find the value of p + q. (A) 3 (B) 48 (C) 51 (D) 009 34. In the adjoining figure, AD = BD = AC ; CAE = 75º and ACD = xº. Then the value of x is : E A 75º xº B D C (A) 45º (B) 50º (C) 60º (D) 37 1 º 35. If the diameter of the cross-section of a wire is decreased by 5%, how much percent will the length be increased so that the volume remains the same? (A) 8% (B) 11.8% (C) 10.8% (D) 9.8% Directions :(36 to 38) In the following questions numbers are written in a sequence. Find the missing number to replace the question mark from the alternatives. 36. 83, 8, 81,... 69, 60, 33 (A) 73 (B) 80 (C) 75 (D) 77 37. 77, 78, 77, 81, 73,... 55 (A) 69 (B) 71 (C) 8 (D) 89 38. 7 8 9 7 15 4 7? 46 (A) 33 (B) 3 (C) (D) 14 PAGE # 5 5
Direction : (39) In the following question, three sequences of letter/numerals are given which correspond to each other in some way. In question, you have to find out the letter/numerals that come in the vacant places marked by (?). These are given as one of the four alternatives under the question. 39. C B D B A B C C B 3 5 4???? p p q r q (A) 4 5 5 4 (B) 5 5 (C) 4 4 (D) 5 5 40. If RED is written as 4 and GREEN is written as 44 then WHITE will be written as: (A) 59 (B) 45 (C) 60 (D) 65 Direction: (41) Arrange the following group of letters such that when arranged in a specific order, meaningful word is formed. 41. R T A N U E 1 3 4 5 6 (A) 1,3,,6,4,5 (B) 3,,4,6,1,5 (C) 4,3,,5,1,6 (D) 4,6,5,,3,1 4. In a queue, A is eighteenth from the front while B is sixteenth from the back. If C is twenty-fifth from the front and is exactly in the middle of A and B, then how many persons are there in the queue? (A) 45 (B) 46 (C) 47 (D) 48 43. PQR is a three-digit number such that P 3 + Q 3 + R 3 = PQR. If PQR < 00, then Q is :- (A) 4 (B) (C) 1 (D) None of these Directions : (44 to 47) Study the given information carefully and answer the questions that follow. There are four people sitting in a row : one each from India, Japan, USA and Germany, but not in that order, (i) They are wearing caps of different colours - green, yellow, red and white, not necessarily in that order. (ii) One is wearing a kurta and one a T-shirt. (iii) The Indian is wearing a green cap and a jacket. (iv) The American is not seated at either end. (v) The persons with kurta and T-shirt are sitting next to each other. (vi) The persons with kurta wears a red cap and sits next to the Japanese. (vii) The Japanese wears a shirt and is not seated at either end. (viii) The man with white cap wears T-shirt and is seated at one end. PAGE # 6 6
44. Who wears the T-shirt? (A) Indian (B) Japanese (C) American (D) German 45. Who is wearing a kurta? (A) Indian (B) Japanese (C) American (D) German 46. What is the colour of the cap worn by the Japanese? (A) Red (B) Green (C) Yellow (D) White 47. Who precedes the man wearing T-shirt? (A) Indian (B) Japanese (C) American (D) German 48. How many triangles are there in the following figure? (A) 5 (B) 0 (C) 31 (D) 9 Directions : (49 to 50) A cube is coloured red on two opposite faces, blue on two adjacent faces and yellow on two remaining faces. It is then cut into two halves among the plane parallel to the red faces. One piece is then cut into four equal cubes and the other one into 3 equal cubes. 49. How many cubes do not have any coloured face? (A) 0 (B) 16 (C) 4 (D) 8 50. How many cubes do not have any red face? (A) 8 (B) 16 (C) 0 (D) 4 PAGE # 7 7