# CCE PR. Œ æ fl : V {}

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1 SL. No. : J Jlflo Æ ÀÊ-V MSÊ : 50 ] [ Jlflo» flfl } Æ lv MSÊ : 1 CCE PR Total No. of Questions : 50 ] [ Total No. of Printed Pages : 1 MOÊfi} MSÊ : 81-E Code No. : 81-E Œ æ fl : V {} Subject : MATHEMATICS ( BMW«ŒÈ Œ M} / English Version ) ( Ê Æ p O» fl / New Syllabus ) ( Æ» ~%} S % / Private Repeater ) MO : ] [ Date : » flæ fl : ÊÿVÊX 9-30 M» fl -1-45» ÊVÊ ] [ Time : 9-30 A.M. to 1-45 P.M. V Œ V fl : 100 ] [ Max. Marks : 100 General Instructions to the Candidate : 1. This Question Paper consists of 50 objective and subjective types of questions.. This question paper has been sealed by reverse jacket. You have to cut on the right side to open the paper at the time of commencement of the examination. Check whether all the pages of the question paper are intact. 3. Follow the instructions given against both the objective and subjective types of questions. 4. Figures in the right hand margin indicate maximum marks for the questions. 5. The maximum time to answer the paper is given at the top of the question paper. It includes 15 minutes for reading the question paper. TEAR HERE TO OPEN THE QUESTION PAPER Æ ÀÊ-Æ ~ OÊæ fl fl-}ê Êæ flƒfl BΔ«O } BΔ«M O } PR-N-1010 Tear here [ Turn over

2 81-E CCE PR I. Four alternatives are given for each of the following questions / incomplete statements. Only one of them is correct or most appropriate. Choose the correct alternative and write the complete answer along with its letter of alphabet. 8 1 = 8 1. If U = { 1,, 3, 4, 5, 6, 7, 8 }, A = { 1,, 3 } and B = {, 3, 4, 5 } then ( A U B ) l is (A) { 5, 6, 7 } (B) { 6, 7, 8 } (C) { 3, 4, 5 } (D) { 1,, 3 }. LCM of 18 and 45 is (A) 9 (B) 45 (C) 90 (D) The mean ( X ) and the standard deviation ( σ ) of certain scores are 60 and 3 respectively. Then the co-efficient of variation is (A) 5 (B) 6 (C) 7 (D) 8 PR-N-1010

3 CCE PR 3 81-E 4. Rationalising factor of x y is (A) x y (B) x (C) x + y (D) x y 5. If f ( x ) = x x + 15 then f ( 1 ) is (A) 14 (B) 18 (C) 15 (D) In a circle, the angle subtended by a chord in the major segment is (A) a straight angle (B) a right angle (C) an acute angle (D) an obtuse angle. PR-N-1010 [ Turn over

4 81-E 4 CCE PR 7. The length of the diagonal of a square of side 1 cm is (A) 5 cm (B) 144 cm (C) 4 cm (D) 1 cm. 8. The distance between the origin and the point ( 1, 5 ) is (A) 13 units (B) 1 units (C) 10 units (D) 5 units. II. Answer the following : 6 1 = 6 9. Write the value of 100 P What is the probability of a certain event? 11. Find the mid-point of the class-interval Find the value of cos 48 sin Write the slope and y-intercept of the line y = 3x. 14. Write the formula used to find the total surface area of a solid hemisphere. PR-N-1010

5 CCE PR 5 81-E III. 15. If A and B are the sets such that n ( A ) = 37, n ( B ) = 6 and n ( A U B ) = 51, find n ( A I B ). 16. Write the formula used to find a) arithmetic mean between a and b ( a > b ) b) harmonic mean between a and b ( a > b ). 17. Find the sum to infinity of the geometric series Prove that is an irrational number. 19. Find how many triangles can be drawn through 8 points on a circle. 0. If 1 1 x + = then find the value of x. 8! 9! 10! 1. A box has 4 red and 3 black marbles. Four marbles are picked up randomly. Find the probability that two marbles are red.. Calculate standard deviation for the following scores : 5, 6, 7, 8, Solve x x 4 = 0 by using formula. Determine the nature of the roots of the equation x x 3 = 0. PR-N-1010 [ Turn over

6 81-E 6 CCE PR 4. In a circle of radius 3 5 cm draw two radii such that the angle between them is 80. Construct tangents to the circle at the non-centre ends of the radii. 5. In Δ ABC, D is a point on BC such that B A C = A D C. Prove that AC = BC DC. In ABC, A B C = 90 and BD AC. Prove that AB BC = AD CD 6. Find the value of sin 30. cos 60 tan Find the radius of a circle whose centre is ( 5, 4 ) and which passes through the point ( 7, 1 ). 8. The radii of two right circular cylinders are in the ratio : 3 and the ratio of their curved surface areas is 5 : 6. Find the ratio of their heights. PR-N-1010

7 CCE PR 7 81-E 9. The radius of a solid metallic sphere is 10 cm. It is melted and recast into small cones of height 10 cm and base radii 5 cm. Find the number of small cones formed. 30. Draw a plan by using the information given below : [ Scale : 5 metres = 1 cm ] Metre to D to C 100 to E to B From A 31. If A and B are non-disjoint sets, draw Venn diagram to illustrate A U B. 3. In a geometric progression if the first term is 1 and the common ratio is, find the 5th term by using formula. 33. Simplify ( 3 3 ) ( 3 4 ) Draw pie chart for the survey carried out in the class regarding places of visit for excursion and the number of students who opted each place : Places Mysuru Vijayapura Gokarna Chitradurga Number of students PR-N-1010 [ Turn over

8 81-E 8 CCE PR 35. Write sum of the roots and product of the roots of the equation ax + bx + c = In the figure PQ, PR and BC are the tangents to the circle. BC touches the circle at X. If PQ = 7 cm, find the perimeter of Δ PBC. 37. In the figure, DE AB, AD = 7 cm, CD = 5 cm and BC = 18 cm. Find CE. 38. Verify whether the following measures represent the sides of a right angle triangle : 1,, Given tan A = 4 3, find the value of sin A and cos A. 40. Find the curved surface area of a right circular cylinder whose height is 30 cm and radius of its circular base is 3 5 cm. PR-N-1010

9 CCE PR 9 81-E IV. 41. Rationalise the denominator and simplify : Find the quotient q ( x ) and remainder r ( x ) on dividing p ( x ) = x 3 + 4x 5x + 6 by g ( x ) = x + 1 and hence verify p ( x ) = [ g ( x ) q ( x ) ] + r ( x ). 3 Find the quotient and remainder by using synthetic division : ( 4x 3 16x 9x 36 ) ( x + ). 43. Find three consecutive positive integers such that the sum of the square of the first integer and the product of the other two is 9. 3 Sum of the squares of any two numbers is 180. If square of the smaller number is equal to 8 times the bigger number, find the two numbers. 44. Prove that If two circles touch each other externally, the centres and the point of contact are collinear. 3 PR-N-1010 [ Turn over

10 81-E 10 CCE PR 45. In an equilateral triangle ABC, AN BC, prove that 4 AN = 3AB. 3 In Δ ABC, AD BC, prove that AB + CD = AC + BD. 46. Prove that tan A sin A = tan A. sin A. 3 From the top of a building 50 3 m high the angle of depression of an object on the ground is observed to be 30. Find the distance of the object from the foot of the building. V. 47. The sum of 3rd and 5th terms of an arithmetic progression is 30 and the sum of 4th and 8th terms of it is 46. Find the arithmetic progression. 4 If the fourth term of a geometric progression is 8 and its eighth term is 18, find the sum of first ten terms of the progression. PR-N-1010

11 CCE PR E 48. Solve x x 3 = 0 graphically Construct a pair of direct common tangents to two circles of radii 4 cm and cm whose centres are 8 cm apart. Measure and write the length of the direct common tangent Prove that If two triangles are equiangular, then their corresponding sides are in proportion. 4 PR-N-1010 [ Turn over

12 81-E 1 CCE PR PR-N-1010

### CCE RR. Œ æ fl : V {}

SL. No. : J Jlflo Æ ÀÊ-V MSÊ : 40 ] [ Jlflo» flfl } Æ lv MSÊ : 1 CCE RR Total No. of Questions : 40 ] [ Total No. of Printed Pages : 1 MOÊfi} MSÊ : 81-E Code No. : 81-E Œ æ fl : V {} Subject : MATHEMATICS

### CCE PF CCE PR. Œ æ fl : V {}

SL. No. : G Jlflo Æ ÀÊ-V MSÊ : 50 ] [ Jlflo» flfl } Æ lv MSÊ : 1 CCE PF CCE PR MOÊfi} MSÊ : 81-E Code No. : 81-E Œ æ fl : V {} Total No. of Questions : 50 ] [ Total No. of Printed Pages : 1 Subject : MATHEMATICS

### CCE RF CCE RR. Œ æ fl : V {}

SL. No. : AA Jlflo Æ ÀÊ-V MSÊ : 40 ] [ Jlflo» flfl } Æ lv MSÊ : 1 CCE RF MOÊfi} MSÊ : 81-E CCE RR Code No. : 81-E Œ æ fl : V {} Total No. of Questions : 40 ] [ Total No. of Printed Pages : 1 Subject :

### RR+PR. Œ æ fl : V {}

RR+PR 1 81-E MOÊfi} MSÊ : 81-E Code No. : 81-E RR+PR Œ æ fl : V {} Subject : MATHEMATICS (BMW«ŒÈ Œ M} / English Version ) ( Ê Æ p O» fl / Old Syllabus ) ( Æ» ~%} @ % + Æ» ~%} S W @ % / Regular Repeater

### KARNATAKA SECONDARY EDUCATION EXAMINATION BOARD, MALLESWARAM, BANGALORE G È.G È.G È.. Æ fioê, d È 2018 S. S. L. C. EXAMINATION, JUNE, 2018

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### CCE RR. ( / English Version ) ( / New Syllabus ) ( / Regular Repeater )

CCE RR 1 81-E : 81-E Code No. : 81-E CCE RR Subject : MATHEMATICS ( / English Version ) ( / New Syllabus ) ( / Regular Repeater ) General Instructions : i) The Question-cum-Answer Booklet consists of objective

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CCE RR O %lo ÆË v ÃO y Æ fio» flms ÿ,» fl Ê«fiÀ M, ÊMV fl 560 00 KRNTK SECONDRY EDUCTION EXMINTION BORD, MLLESWRM, BNGLORE 560 00 G È.G È.G È.. Æ fioê, d È 07 S. S. L. C. EXMINTION, JUNE, 07» D} V fl MODEL

### KARNATAKA SECONDARY EDUCATION EXAMINATION BOARD, MALLESWARAM, BANGALORE S. S. L. C. EXAMINATION, MARCH/APRIL, » D} V fl MODEL ANSWERS

CCE RF CCE RR O %lo ÆË v ÃO y Æ fio» flms ÿ,» fl Ê«fiÀ M, ÊMV fl 560 00 KARNATAKA SECONDARY EDUCATION EXAMINATION BOARD, MALLESWARAM, BANGALE 560 00 G È.G È.G È.. Æ fioê,» ^È% / HØ È 08 S. S. L. C. EXAMINATION,

### KARNATAKA SECONDARY EDUCATION EXAMINATION BOARD, MALLESWARAM, BANGALORE G È.G È.G È.. Æ fioê, d È 2018 S. S. L. C. EXAMINATION, JUNE, 2018

CCE RR REVISED & UN-REVISED O %lo ÆË v ÃO y Æ fio» flms ÿ,» fl Ê«fiÀ M, ÊMV fl 560 00 KARNATAKA SECONDARY EDUCATION EXAMINATION BOARD, MALLESWARAM, BANGALORE 560 00 G È.G È.G È.. Æ fioê, d È 08 S. S. L.

### Total No. of Questions : 58 ] [ Total No. of Printed Pages : 40. ê ÂŒÈ : πâä Â FOR OFFICE USE ONLY

Roll No. Serial No. of Q. C. A. B. ÈJ ÂX applerπâ Â Â zapplew : 58 ] [ ÈJ ÆÂÈÈåX Â ÂÏ πâ Â Â zapplew : 40 Total No. of Questions : 58 ] [ Total No. of Printed Pages : 40 ê ÂŒÈ : πâä Â Â xë Â Â zapplew

### 81-E If set A = { 2, 3, 4, 5 } and set B = { 4, 5 }, then which of the following is a null set? (A) A B (B) B A (C) A U B (D) A I B.

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### O %lo ÆË v ÃO y Æ fio» flms ÿ,» fl Ê«fiÀ M, ÊMV fl KARNATAKA SECONDARY EDUCATION EXAMINATION BOARD, MALLESWARAM, BANGALORE

CCE PF CCE PR O %lo ÆË v ÃO y Æ fio» flms ÿ,» fl Ê«fiÀ M, ÊMV fl 50 00 KARNATAKA SECONDARY EDUCATION EXAMINATION BOARD, MALLESWARAM, BANGALORE 50 00 G È.G È.G È.. Æ fioê,» ^È% / HØ È 0 S. S. L. C. EXAMINATION,

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CCE RF CCE RR O %lo ÆË v ÃO y Æ fio» flms ÿ,» fl Ê«fiÀ M, ÊMV fl 50 00 KARNATAKA SECONDARY EDUCATION EXAMINATION BOARD, MALLESWARAM, BANGALE 50 00 G È.G È.G È.. Æ fioê,» ^È% / HØ È 0 S. S. L. C. EXAMINATION,

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### Total No. of Questions : 58 ] [ Total No. of Printed Pages : 32. ê ÂŒÈ : πâä Â FOR OFFICE USE ONLY

Roll No. Serial No. of Q. C. A. B. ÈJ ÂX applerπâ Â Â zapplew : 58 ] [ ÈJ ÆÂÈÈåX Â ÂÏ πâ Â Â zapplew : 32 Total No. of Questions : 58 ] [ Total No. of Printed Pages : 32 ê ÂŒÈ : πâä Â Â xë Â Â zapplew

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