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Series C5ABD/5 SET~2 amob Z§. àíZ-nÌ H$moS> Q.P. Code 430/5/2...

Series C5ABD/5 SET~2 amob Z§. àíZ-nÌ H$moS> Q.P. Code 430/5/2 Roll No. narjmWu àíZ-nÌ H$moS> >H$mo CÎma-nwpñVH$m Ho$ _wI-n¥ð >na Adí` {bIo§ & Candidates must write the Q.P. Code on the title page of the answer-book. ZmoQ> / NOTE : (i) H¥$n`m Om±M H$a b| {H$ Bg àíZ-nÌ _o§ _w{ÐV n¥ð> 23 h¢ & Please check that this question paper contains 23 printed pages. (ii) H¥$n`m Om±M H$a b| {H$ Bg àíZ-nÌ _| >38 àíZ h¢ & Please check that this question paper contains 38 questions. (iii) àíZ-nÌ _| Xm{hZo hmW H$s Amoa {XE JE àíZ-nÌ H$moS H$mo narjmWu CÎma-nwpñVH$m Ho$ _wI-n¥ð> na {bI| & Q.P. Code given on the right hand side of the question paper should be written on the title page of the answer-book by the candidate. (iv) H¥$n`m àíZ H$m CÎma {bIZm ewê$ H$aZo go nhbo, CÎma-nwpñVH$m _| àíZ H$m H«$_m§H$ Adí` {bI| & Please write down the serial number of the question in the answer-book before attempting it. (v) Bg àíZ-nÌ H$mo n‹T>Zo Ho$ {bE 15 {_ZQ >H$m g_` {X`m J`m h¡ & àíZ-nÌ H$m {dVaU nydm© _| 10.15 ~Oo {H$`m OmEJm & 10.15 ~Oo go 10.30 ~Oo VH$ N> mÌ Ho$db àíZ-nÌ H$mo n‹T>|Jo Am¡a Bg Ad{Y Ho$ Xm¡amZ do CÎma-nwpñVH$m na H$moB© CÎma Zht {bI|Jo & 15 minute time has been allotted to read this question paper. The question paper will be distributed at 10.15 a.m. From 10.15 a.m. to 10.30 a.m., the students will read the question paper only and will not write any answer on the answer-book during this period. J{UV (~w{Z`mXr) MATHEMATICS (BASIC) {ZYm©[aV g_` : 3 KÊQ>o A{YH$V_ A§H$ : 80 Time allowed : 3 hours Maximum Marks : 80 15-430/5/2 Page 1 P.T.O. General Instructions : Read the following instructions very carefully and strictly follow them : (i) This question paper contains 38 questions. All questions are compulsory. (ii) This question paper is divided into five Sections – A, B, C, D and E. (iii) In Section A, Questions no. 1 to 18 are Multiple Choice Questions (MCQs) and questions number 19 and 20 are Assertion-Reason based questions of 1 mark each. (iv) In Section B, Questions no. 21 to 25 are Very Short Answer (VSA) type questions, carrying 2 marks each. (v) In Section C, Questions no. 26 to 31 are Short Answer (SA) type questions, carrying 3 marks each. (vi) In Section D, Questions no. 32 to 35 are Long Answer (LA) type questions carrying 5 marks each. (vii) In Section E, Questions no. 36 to 38 are case study based questions carrying 4 marks each. Internal choice is provided in 2 marks questions in each case study. (viii) There is no overall choice. However, an internal choice has been provided in 2 questions in Section B, 2 questions in Section C, 2 questions in Section D and 3 questions in Section E. 22 (ix) Draw neat diagrams wherever required. Take p = wherever required, if not 7 stated. (x) Use of calculator is not allowed. SECTION A This section comprises multiple choice questions (MCQs) of 1 mark each. 20´1=20 1. A tree casts a shadow 7 m long on the ground, when the angle of elevation of the Sun is 45°. The height of the tree is : 7 (A) 7 3 m (B) 3 m 3 (C) 7m (D) 3·5 m 15-430/5/2 Page 3 P.T.O. 2. The length of an arc of a circle with radius 12 cm is 10p cm. The central angle subtended by this arc at the centre, is : (A) 120° (B) 6° (C) 75° (D) 150° 3. In the given figure, in D ABC, DE || BC. If AD = 2x cm, AE = (x + 2) cm, DB = 4 cm, EC = 3 cm, then the value of x is : (A) 3 (B) 2 (C) 6 (D) 4 4. HCF ´ LCM for the numbers 40 and 30 is : (A) 12 (B) 120 (C) 1200 (D) 40 5. It is given that D ABC ~ D DEF. If Ð A = 55°, Ð E = 45°, then Ð C is : (A) 80° (B) 90° (C) 55° (D) 45° 6. If the angle between the two radii of a circle is 130°, then the angle between the tangents at the ends of these radii, is : (A) 50° (B) 60° (C) 90° (D) 130° 15-430/5/2 Page 5 P.T.O.  1 7. If sin2 q = , then the value of tan 2 q is : 2 1 (A) (B) 3 3 (C) 0 (D) 1 8. If the difference of mode and median of a data is 24, then the difference of median and mean of the same data is : (A) 8 (B) 12 (C) 24 (D) 34 9. The area of a quadrant of a circle whose circumference is 22 cm, is : 11 11 (A) cm2 (B) cm2 4 2 33 77 (C) cm2 (D) cm2 4 8 10. The mid-point of the line segment AB joining A(– 2, 8) and B(– 6, 4) is : (A) (2, 6) (B) (– 4, 12) (C) (– 4, 6) (D) (4, – 6) 11. AP and AQ are tangents drawn from an external point A to a circle with centre O and inclined to each other at an angle of 90°. If the length of each tangent is 2 cm, then the radius of the circle is : (A) 4 cm (B) 2 cm (C) 2 2 cm (D) 1 cm 15-430/5/2 Page 7 P.T.O. 12. The pair of linear equations 2kx + 5y = 7, 6x + 5y = 11 have a unique solution, if (A) k¹3 (B) k¹–3 1 1 (C) k¹ (D) k¹– 3 3 13. If x is a whole number, then 8x ends with an even digit, except for which value of x ? (A) 6 (B) 4 (C) 2 (D) 0 æ 5 5 ö÷ 14. ç – is equal to : ç cot 2 q cos 2 q ÷ è ø (A) 1 (B) 5 (C) –5 (D) 0 15. The discriminant of the quadratic equation x2 – 4x + 3 = 0 is : (A) 28 (B) –8 (C) 4 (D) 2 16. A bag has 4 red balls and 2 yellow balls. A ball is drawn at random from the bag without looking into the bag. What is the probability of getting a yellow ball ? 1 2 (A) (B) 6 3 1 (C) (D) 1 3 17. The roots of the quadratic equation x2 + 3x + 2 = 0, are : (A) – 1, – 2 (B) 1, 2 (C) 1, – 2 (D) – 1, 2 15-430/5/2 Page 9 P.T.O. 18. Prime factorisation of 882 is : (A) 22 ´ 3 2 ´ 7 (B) 2 3 ´ 3 ´ 72 (C) 2 ´ 32 ´ 7 2 (D) 2 2 ´ 33 ´ 7 Questions number 19 and 20 are Assertion and Reason based questions. Two statements are given, one labelled as Assertion (A) and the other is labelled as Reason (R). Select the correct answer to these questions from the codes (A), (B), (C) and (D) as given below. (A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A). (B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A). (C) Assertion (A) is true, but Reason (R) is false. (D) Assertion (A) is false, but Reason (R) is true. 19. Assertion (A) : Common difference of the A.P. 5, 1, – 3, – 7.... is 4. Reason (R) : Common difference of the A.P. a1, a2, a3...., an is obtained by d = an – an – 1. 20. Assertion (A) : The probability of getting number 8 on rolling a die is zero (0). Reason (R) : The probability of an impossible event is zero (0). 15-430/5/2 Page 11 P.T.O.  SECTION B This section comprises Very Short Answer (VSA) type questions of 2 marks each. 5´2=10 1 5 21. If is a root of the quadratic equation x2 + kx – = 0, then find the 2 4 value of k. 22. Evaluate : tan2 30° – tan2 60° + cosec2 45° 23. The length of a tangent drawn to a circle from a point A, at a distance of 10 cm from the centre of the circle, is 6 cm. Find the radius of the circle. 24. (a) If a, b are zeroes of the quadratic polynomial 2x2 + 7x + 5, then find the value of a2 + b2 + ab. OR (b) If one zero of the quadratic polynomial 6x2 + 37x – (p – 2) is reciprocal of the other, then find the value of p. 25. (a) Find the ratio in which the point (3, y), divides the line segment joining the points (– 2, – 5) and (6, 3). Also, find the value of y. OR (b) Find a point on y-axis which is equidistant from the points A(6, 5) and B(– 4, 3). 15-430/5/2 Page 13 P.T.O.  SECTION C This section comprises Short Answer (SA) type questions of 3 marks each. 6´3=18 26. (a) Prove that the parallelogram circumscribing a circle is a rhombus. OR (b) Prove that the lengths of the tangents drawn from an external point to a circle are equal. 27. (a) A horse is tied with a 14 m long rope at one corner of an equilateral triangular field having side 20 m. Find the area of the field where the horse cannot graze. OR (b) The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand between 8:00 am and 8:05 am. 28. Find the coordinates of the points of trisection of the line segment joining the points A(5, – 3) and B(– 4, 3). 29. Prove that 3 – 2 5 is an irrational number, given that 5 is an irrational number. 1 30. Prove that : (cosec q – sin q) (sec q – cos q) =. tan q + cot q 31. Find the zeroes of the quadratic polynomial 6x2 – 7x – 3 and verify the relationship between the zeroes and the coefficients of the polynomial. 15-430/5/2 Page 15 P.T.O.  SECTION D This section comprises Long Answer (LA) type questions of 5 marks each. 4´5=20 3 32. A fraction becomes , if 2 is added to the numerator and 1 is added to 4 the denominator. If 2 is subtracted from the numerator and 1 is 1 subtracted from the denominator, it becomes. Find the fraction. 2 33. The following table shows the ages of the patients admitted in a hospital during a year : Age (in years) 5 – 15 15 – 25 25 – 35 35 – 45 45 – 55 55 – 65 Number of 6 11 21 23 14 5 patients Find the median of the above given data. 34. (a) A toy is in the form of a cone of radius 7 cm mounted on a hemisphere of same radius. The total height of the toy is 31 cm. Find the surface area of the toy. OR (b) A wooden article was made by scooping out a hemisphere from each end of a solid cylinder. If the height of the cylinder is 15 cm and its base is of radius 4·2 cm, then find the total surface area of the article. 15-430/5/2 Page 17 P.T.O. 35. (a) Sides AB, BC and median AD of D ABC are respectively proportional to sides PQ, QR and median PM of D PQR. Show that D ABC ~ D PQR. OR (b) Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides at distinct points, then the other two sides are divided in the same ratio. SECTION E This section comprises 3 case study based questions of 4 marks each. 3´4=12 Case Study – 1 36. Sumant’s mother started a new shoe shop. To display the shoes, she put 3 pairs of shoes in the 1st row, 5 pairs in the 2nd row, 7 pairs in the 3rd row and so on. Based on the above information, answer the following questions : (i) How many pairs of shoes are displayed in the 6th row ? 1 (ii) What is the difference of pairs of shoes in the 1 st row and the 6th row ? 1 (iii) (a) Find the total number of pairs of shoes displayed in the first 15 rows. 2 OR (b) If the pairs of shoes displayed in the 4th row are ‘on sale’ at price of < 500 for each pair, then find the total amount (money) earned by Sumant’s mother if all shoes displayed in the 4th row are sold out. 2 15-430/5/2 Page 19 P.T.O.  Case Study – 2 37. Two poles of different heights stand on level ground and at a distance of 40 m. Both poles are supported by wires attached from the top of each pole to the bottom of the other. A coupling is placed at point C, where the two wires cross (as shown in the figure). Based on the above information, answer the following questions : (i) Find the height of pole AB. 1 (ii) Find the height of pole PQ. 1 (iii) (a) If the angle of elevation of the top of the pole PQ from the top of the pole AB is 30°, find the distance BQ. 2 OR (b) If the coupling is at a height of 20 m from the ground, how far down the wire from the smaller pole AB is the coupling ? 2 15-430/5/2 Page 21 P.T.O.  Case Study – 3 38. Family structure : In a recent survey of this year, 51% of the families in the United States of America had no children, 20% had one child, 19% had two children, 7% had three children and 3% had four or more children. A family is selected at random. Based on the above information, answer the following questions : (i) Find the probability that the selected family has two or three children. 1 (ii) Find the probability that the selected family has more than one child. 1 (iii) (a) Find the probability that the selected family has less than three children. 2 OR (b) Find the probability that the selected family has more than two children. 2 15-430/5/2 Page 23 P.T.O.