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fais 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 number 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 number 21 to 25 are Very Short Answer (VSA) type questions, carrying 2 marks each. (v) In Section-C, questions number 26 to 31 are Short Answer (SA) type questions, carrying 3 marks each. (vi) In Section-D, questions number 32 to 35 are Long Answer (LA) type questions, carrying 5 marks each. (vii) In Section-E, questions number 36 to 38 are Case Study based questions carrying 4 marks each. Internal choice is provided in 2 marks question 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 of 2 marks in Section-E. (ix) Draw neat diagrams wherever required. Take x= 2 wherever required, if not stated. (x) Use of calculator is NOT allowed. 30/412 {} Page 3 of 24 P.T.O. Oh SECTION -A Q. Number 1 to 20 are multiple choice questions of 1 mark each. 1. If PQ and PR are tangents to the circle with centre O and radius 4 cm such that “QPR = 90°, then the length OP is Q Yep [> R (A) 4cm (B) 4V2 em (C) 8cem @) 2V2 cm 2. An ice-cream cone of radius r and height h is completely filled by two spherical scoopes of ice-cream. If radius of each spherical scoop is a then h: 2r equals (A) 1:8 (B) 1:2 © 1:1 (@) 2:1 3. Are PQ subtends an angle 6 at the centre of the circle with radius 6.3 cm. If PQ = 11cm, then the value of 0 is (A) 10° (B) 60° (C) 45° (@) 100° 2 4, At kee 1l+cot“A (A) tan? A (B) -1 (C) -tan?A (D) cot? A 5. Three tennis balls are just packed in a cylindrical jar. If radius of each ball is r, volume of air inside the jar is ee PS PS NA (A) 2nr3 (B) 3nxr3 (C) 5nr8 (D) 4nr3 80/42 {} Page 5 of 24 P.T.O 11. If roots of the quadratic equation x2 — k/3x+2=0 are real and equal, then value of k is 8 (A) -2 (B) E (C) 1 @) 2 12. Observe the graph of polynomial PO. Number of zeroes of p(x) is /\ y=p(x) x l x f () y (A) 5 (B) 4 (C) 6 @) 3 13. Mean and Median of a frequency distribution are 43 and 40 respectively. The value of mode is (A) 34 (B) 43 (C) 38.5 @) 41.5 14. Area of sector of a circle with radius 18 em is 198 cm”. The measure of central angle is (A) 70° (B) 14° (C) 140° (@) 210° 15. If2tan A=8, then value of sec A equals 13 vi3 (A — B) — (A) 2 () a 2 v3 Cc) —_> wo (C) ir (D) 2 16. The value of k for which the system of linear equations Aa = 6 and 24+ky=7is inconsistent, is 3 4 A) = mi (A) a (B) 3 é 1 @ = @) 3 3 30/4/2 {a Page 9of24..~OS 17. InanA.P., a=-3 and Si7 = 357. The value of a7 is (A) 47 (B) 39 (C) 45 (D) 42 18. In the given figure, a circle is centred at (1, 2). The diameter of the circle is Y (A) 4 ®) 2/2 r © @) 2v5 (Assertion and Reason based Questions) Direction : Question Numbers 19 and 20 are Assertion (A) and Reason (R) ‘ based questions. Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the options (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 the Assertion (A). (B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A). i (C) Assertion (A) is true, but Reason (R) is false, (D) Assertion (A) is false, but Reason (R) is true. 19. Assertion (A) ; (V3 + V5 ) is an irrational number. Reason(R) : Sum of the any two irrational numbers is always irrational. 20. Assertion (A) : If probability of happening of an event is 0.2p, p > 0, then p can’t be more than 5. Reason (R) : P(E) = 1 - P(E) for an event E. a 27. (a) To protect plants from heat, a shed of iron rods covered with green cloth is made. The lower part of the shed is a cuboid mounted by semi-cylinder as shown in the figure. Find the area of the cloth required to make this shed, if-dimensions of the cuboid are 14mx 25mx 16m 16m 25m. OR (b) The internal and external radii of a hollow hemisphere are 5/2 cm and 10 cm respectively. A cone of height 57 cm and radius 5 v2 cm is surmounted on the hemisphere as shown in the figure. Find the § total surface area of the object in terms of m. (Use V2 = 1.4) 14m 28.7 (a) In a class test, Veer scored 6 more than twice as many marks as Kevin scored. If one of them had scored 4 more marks, their total score would have been 40. Find the marks obtained by Veer and Kevin. OR {by Solve the linear equations 3x + y = 14 and y = 2 graphically. 29. A bag contains 30 balls out of which ‘m’ number of balls are blue in colour. Gi) Find the probability that a ball drawn at random from the bag is not blue. (ii) If 6 more blue balls are added in the bag, then the probability of drawing a blue ball will be 2 times the probability of drawing a blue ball in the first case. Find the value of m. 30/4/2 {} Page 15 of 24 P.T.O. 30: Prove that : if a. u secx-tanx cosx cosx secx+tan x 31, The perimeter of sector OAB of a circle with centre O and radius 5.6 cm, is 15.6 cm. Find length of the arc AB. Also find the value of 0. A SECTION-D Q. Numbers 32 to 35 are long answer type questions of 5 marks each. 32. A kite is flying at a height of 60 m above the ground level. Ravi, standing at the roof of the house is holding the string straight and observes the angle of elevation of kite as 30°. From the bottom of the same building, the angle of elevation of kite is 45°. Find the length of the string and height of roof from the ground. (Use ¥3 = 1.78) 33. (a) Find mean and mode of the following frequency distribution : Class : 5-15 |15—25/25—35 35 —45/45-—55|55-65 Frequency : a 20 25 22 12 10 OR (b) The median of the following data is 32.5, find the missing frequencies x and ys [Class : 0-10| 10-—20|20-30]30—40]/40—50 50—60/| 60—70|Total] [Frequency : o 5 2 12 y 3 2 40 ] 34. (a) A person on tour has % 5,400 for his expenses. If he extends his tour by 5 days, he has to cut down his daily expenses by % 180. Find the original duration of the tour and daily expense. OR (b) The total cost of certain Piece of cloth was % 2,100. During special sale time, the shopkeeper offered 2 m extra cloth for free thus reducing the price of cloth per metre by ~ 120. What was the original Per metre price of cloth and its length ? 30/4/2 {} Page 17 of 24 P.T.O. ee (b) Is it possible to complete n number of squares using 100 dots ? If yes, then find the value of n. 37. Observe the map of Jaipur city placed on a Cartesian plane. Taking Rambagh Palace as origin, the location of some places are given below : Point A : (—4, 2) Rajasthan High Court Point B: (4, -4) Birla Mandir, Point C : (4, 3) Heera Bagh Point D : (-5, -2) Amar Jawan Jyoti Based on the above, answer the following questions : @) Advocate Rehana stays at Heera Bagh. How much distance she has to cover daily to go to the court and coming back home ? 1 (ii) There is a crossing on X-axis which divides AD in a certain ratio. Find the ratio. 1 (iii) (a) Is Birla Mandir equidistant from Heera Bagh and Amar Jawan Jyoti ? Justify your answer. 2 OR (b) Using section formula, show that points A, O and B are not collinear. 30/4/2 iF Page 21 of 24 P.T.O. Cc 65 cm 38. Carom board is a very popular game. The board is a square of side length 65 cm. It has circular pockets in each corner. Ansh strikes a disc, kept at position P with a striker. The disc, hits the boundary of the board at R and goes straight to pocket at corner C. It is given that PS = 9 cm, PQ = 35 cm, BR=x, ZPRQ = «a and CRB = 68, Based on the above information, answer the following questions : @ Using law of reflection i.e, PRT = ZCRT, prove that.6 = a. af (i) Prove that APQR ~ ACBR given that PQ is perpendicular to AB. (iii) (a) Find the value of x using similarity of triangles. 2 OR Area APQR_ PQ? (b) If ArsaOBR = Cp? , then find the value of x. 
