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Class 9 Cbse Maths Question Paper

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Class 9 Cbse Maths Question Paper

1. 1. w w w .edurite.com 041/IX/SA2/30/A1 1 Class - IX MATHEMATICS Time : 3 to 3½ hours Maximum Marks : 80 â×Ø : 3 âð 3½ æÅUð ¥çÏ·¤Ì× ¥´·¤ : 80 Total No. of Pages : 11 ·é¤Ü ÂëcÆUæð´ ·¤è â´Øæ : 11 General Instructions : 1. All questions are compulsory. 2. The question paper consists of 34 questions divided into four sections A, B, C and D. Section - A comprises of 10 questions of 1 mark each, Section - B comprises of 8 questions of 2 marks each, Section - C comprises of 10 questions of 3 marks each and Section - D comprises of 6 questions of 4 marks each. 3. Question numbers 1 to 10 in Section - A are multiple choice questions where you are to select one correct option out of the given four. 4. There is no overall choice. However, internal choice has been provided in 1 question of two marks, 4 questions of three marks each and 2 questions of four marks each. You have to attempt only one of the alternatives in all such questions. 5. Use of calculators is not permitted. 6. An additional 15 minutes time has been allotted to read this question paper only. âæ×æØ çÙÎðüàæ Ñ 1. âÖè ÂýàÙ ¥çÙßæØü ãñ´Ð 2. §â ÂýàÙ-Âæ ×ð´ 34 ÂýàÙ ãñ´, Áæð ¿æÚU ¹ÇUæð´ ×ð´ ¥, Õ, â ß Î ×ð´ çßÖæçÁÌ ãñÐ ¹ÇU - ¥ ×ð´ 10 ÂýàÙ ãñ´ ¥æñÚU ÂýØð·¤ ÂýàÙ 1 ¥´·¤ ·¤æ ãñ, ¹ÇU - Õ×ð´ 8 ÂýàÙ ãñ´ ¥æñÚU ÂýØð·¤ ÂýàÙ 2 ¥´·¤æð´ ·ð¤ ãñ´, ¹ÇU - â×ð´ 10 ÂýàÙ ãñ´ ¥æñÚU ÂýØð·¤ ÂýàÙ 3 ¥´·¤æð´ ·¤æ ãñ, ¹ÇU - Î×ð´ 6 ÂýàÙ ãñ´ ¥æñÚU ÂýØð·¤ ÂýàÙ 4 ¥´·¤æð´ ·¤æ ãñÐ 3. ÂýàÙ â´Øæ 1 âð 10 Õãéçß·¤ËÂèØ ÂýàÙ ãñ´Ð çÎ° »° ¿æÚU çß·¤ËÂæð´ ×ð´ âð °·¤ âãè çß·¤ËÂ ¿éÙð´Ð 4. §â×ð´ ·¤æð§ü Öè âßæðüÂçÚU çß·¤ËÂ Ùãè´ ãñ, Üðç·¤Ù ¥æ´ÌçÚU·¤ çß·¤ËÂ 1 ÂýàÙ 2 ¥´·¤æð´ ×ð´, 4 ÂýàÙ 3 ¥´·¤æð´ ×ð´ ¥æñÚU 2 ÂýàÙ 4 ¥´·¤æð´ ×ð´ çÎ° »° ãñ´Ð ¥æÂ çÎ° »° çß·¤ËÂæð´ ×ð´ âð °·¤ çß·¤ËÂ ·¤æ ¿ØÙ ·¤Úð´UÐ 5. ·ñ¤Ü·é¤ÜðÅUÚU ·¤æ ÂýØæð» ßçÁüÌ ãñÐ 6. §â ÂýàÙ-Âæ ·¤æð ÂÉ¸Ùð ·ð¤ çÜ° 15 ç×ÙÅU ·¤æ â×Ø çÎØæ »Øæ ãñÐ §â ¥ßçÏ ·ð¤ ÎæñÚUæÙ ÀUææ ·ð¤ßÜ ÂýàÙ-Âæ ·¤æð ÂÉ¸ð´»ð ¥æñÚU ßð ©æÚU-ÂéçSÌ·¤æ ÂÚU ·¤æð§ü ©æÚU Ùãè´ çÜ¹ð´»ðÐ
2. 2. w w w .edurite.com 2041/IX/SA2/30/A1 SECTION - A Question numbers 1 to 10 carry 1 mark each. For each of the questions 1 to 10, four alternative choices have been provided of which only one is correct. You have to select the correct choice. 1. Which of the following is not a linear equation ? (A) ax1by1c50 (B) 0x10y1c50 (C) 0x1by1c50 (D) ax10y1c50 2. Which of the following is a solution of the equation 4x13y516 ? (A) (2, 3) (B) (1, 4) (C) (2, 4) (D) (1, 3) 3. In figure, PQRS is a rectangle. If RPQ 30∠ 5 8 then the value of (x 1 y) is (A) 908 (B) 1208 (C) 1508 (D) 1808 4. Two polygons have the same area in figure : (A) (a) (B) (b) (C) (c) (D) (d) 5. Two consecutive angles of a parallelogram are in the ratio 1 : 3, then the smaller angle is : (A) 508 (B) 908 (C) 608 (D) 458 6. In figure, PQRS is a parallelogram in which ∠PSR 1255 8 , RQT∠ is equal to (A) 758 (B) 658 (C) 558 (D) 1258
3. 3. w w w .edurite.com 3041/IX/SA2/30/A1 7. The diagonals of rhombus are 12 cm and 16 cm. The length of the side of rhombus is (A) 10 cm (B) 12 cm (C) 16 cm (D) 8 cm 8. The length of the diagonal of the square is 10 cm. The area of the square is (A) 20 cm2 (B) 100 cm2 (C) 50 cm2 (D) 70 cm2 9. The length of the longest pole that can be put in a room of dimensions 10 m 3 10 m 3 5 m. (A) 15 m (B) 16 m (C) 10 m (D) 12 m 10. The range of the data 25.7, 16.3, 2.8, 21.7, 24.3, 22.7, 24.9 is (A) 22 (B) 22.9 (C) 21.7 (D) 20.5 SECTION - B Question numbers 11 to 18 carry 2 marks each 11. Find the mean of factors of 24. 12. The length, breadth and height of a room are 5 m, 4 m and 3 m respectively. Find the cost of painting the walls of the room and ceiling at the rate of Rs. 50 per m2. 13. How many litres of water flow out through a pipe having an area of cross-section of 5 cm2 in one minute, if the speed of water in pipe is 30 cm/sec. 14. Two parallel chords of a circle whose diameter is 13 cm are respectively 5 cm and 12 cm. Find the distance between them if they lie on opposite sides of centre. 15. In a paralleloram, show that the angle bisectors of two adjacent angles intersect at right angle. 16. The angle between the two attitudes of parallelogram through the vertex of an obtuse angle is 508. Find the angles of parallelogram. OR D is the mid point of side BC of DABC and E is the mid point of AD, then show that ar (BED) 5 1 4 ar (ABC) 17. Two congruent circles intersect each other at points A and B. Through A a line segment PAQ is drawn so that P and Q lie on the two circles. Prove that BP 5 BQ. 18. Express y in terms x in equation 2x23y512. Find the points where the line represented by this equation cuts x-axis and y-axis.
4. 4. w w w .edurite.com 4041/IX/SA2/30/A1 SECTION - C Question numbers 19 to 28 carry 3 marks each 19. Draw the graph of two lines whose equations are 3x22y1650 and x12y2650 on the same graph paper. Find the area of the triangle formed by two lines and x-axis. 20. The taxi fare in a city is as follows. For the first kilometre, the fare is Rs. 8 and for the subsequent distance it is Rs. 5 per km. Taking the distance covered as x km and total fare as Rs. y. Write a linear equation for this information and calculate from the equation total fare of 15 km distance. 21. Construct a DABC in which AB55.8 cm, BC1CA58.4 cm and B 60∠ 5 8 . 22. In figure, ABCD is a parallelogram. The circle through A, B and C intersects CD produced at E. Prove that AE 5 AD. 23. XY is a line parallel to side BC of DABC. BE ?? AC and CF ?? AB meets XY is E and F respectively. Show that ar(ABE)5ar(ACF). OR In figure, ABCD is a trapezium in which AB ?? DC. E is the mid point of AD and F is a point on BC such that EF ?? DC. Prove that F is the mid point of BC. 24. From a right circular cylinder with height 8 cm and radius 6 cm, a right circular cone of the same height and base is removed. Find the total surface area of the remaining solid. 25. How many spherical lead shots each 4.2 cm diameter can be obtained from a solid cuboid of lead with dimensions 66 cm, 42 cm and 21 cm. OR An iron pipe 20 cm long has external diameter equal to 25 cm. If the thickness of the pipe is 1 cm, find the total surface area of the pipe.
5. 5. w w w .edurite.com 5041/IX/SA2/30/A1 26. Three unbiased coins are tossed together. Find the probability of getting (i) two heads (ii) at least two heads (iii) no head OR A bag contains 12 balls out of which x are white. If one ball is taken out from the bag, find the probability of getting a white ball. If 6 more white balls are added to the bag and the probability now for getting a white ball is double the previous one, find the value of x. 27. The marks obtained by 40 students of class IX in Mathematics are given below : 81, 55, 68, 79, 85, 43, 29, 68, 54, 73, 47, 35, 72, 64, 95, 44, 50, 77, 64, 35, 79, 52, 45, 54, 70, 83, 62, 64, 72, 92, 84, 76, 63, 43, 54, 38, 73, 68, 52, 54 Prepare a frequency distribution table with class - size of 10 marks. 28. Find the median of the following data 19, 25, 59, 48, 35, 37, 30, 32, 51. If 25 is replaced by 52 what will be the new median. SECTION - D Question numbers 29 to 34 carry 4 marks each 29. Solve for x, ( )4 23 5 25 7 3 5 15 xx x 1 5 12 1 OR A and B are friends. A is elder to B by 5 years. Bs sister C is half the age of B while As father D is 8 years older than twice the age of B. If the present age of D is 48 years, find the present ages of A, B and C. 30. Prove that the parallelograms on the same base and beween the same parallels are equal in area. OR Diagonals AC and BD of a trapezium ABCD with AB ?? DC intersect each other at O. Prove that ar(DAOD) 5 ar(DBOC) 31. Draw a histogram of frequency polygon for the following data Marks 10 - 15 15 - 20 20 - 25 25 - 30 30 - 40 40 - 60 60 - 80 No. of students 7 9 8 5 12 12 8
6. 6. w w w .edurite.com 6041/IX/SA2/30/A1 32. In figure, diagonals AC and BD of quadrilateral ABCD intersect at O, such that OB5OD. If AB5CD show that (i) ar (DOC) 5 ar (AOB) (ii) ar (DCB) 5 ar (ACB) (iii) ABCD is a parallelogram. 33. In figure, two circles intersect at B and C. Through B two line segments ABD and PBQ are drawn to intersect the circles at A, D, and P, Q respectively. Prove that ACP QCD∠ ∠5 . 34. A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior. The diameter of the pencil is 7 mm and the diameter of graphite is 1 mm. If the length of the pencil is 14 cm. Find the volume of wood and that of graphite. - o O o -
7. 7. w w w .edurite.com 7041/IX/SA2/30/A1 ¹ÇU - ·¤ ÂýàÙ â´Øæ 1 âð10 Ì·¤ ÂýØð·¤ ·ð¤ çÜ° 1 ¥´·¤ ãñÐ 1 âð10 Ì·¤ ÂýØð·¤ ÂýàÙ ·ð¤ çÜ° ¿æÚU çß·¤ËÂ çÎ° ãé° ãñ´ çÁÙ×ð´ âð °·¤ çß·¤ËÂ âãè ãñÐ ¥æÂ·¤æð âãè çß·¤ËÂ ·¤æ ¿ØÙ ·¤ÚUÙæ ãñÐ 1. çÙÙçÜç¹Ì ×ð´ âð ·¤æñÙ ÚñUç¹·¤ â×è·¤ÚUæ Ùãè´ ãñ? (A) ax1by1c50 (B) 0x10y1c50 (C) 0x1by1c50 (D) ax10y1c50 2. çÙÙçÜç¹Ì ×ð´ âð ·¤æñÙ, â×è·¤ÚUæ 4x13y516 ·¤æ °·¤ ãÜ ãñ? (A) (2, 3) (B) (1, 4) (C) (2, 4) (D) (1, 3) 3. Îè ãé§ü ¥æ·ë¤çÌ ×ð´ PQRS °·¤ ¥æØÌ ãñÐ ØçÎ RPQ 30∠ 5 8 , Ìæð (x 1 y) ·¤æ ×æÙ ãñ Ñ (A) 908 (B) 1208 (C) 1508 (D) 1808 4. ¥æ·ë¤çÌ ×ð´ Îæð ÕãéÖéÁæð´ ·¤æ ÿæðæÈ¤Ü â×æÙ ãñÐ (A) (a) (B) (b) (C) (c) (D) (d) 5. °·¤ â×æ´ÌÚU ¿ÌéÖüéÁ ·ð¤ Îæð ·ý¤×æ»Ì ·¤æðææð´ ·¤æ ¥ÙéÂæÌ 1 : 3 ãñÐ ÀUæðÅðU ·¤æðæ ·¤æ ×æÂ ãñ Ñ (A) 508 (B) 908 (C) 608 (D) 458 6. ¥æ·ë¤çÌ ×ð´ PQRS °·¤ â×æ´ÌÚU ¿ÌéÖüéÁ ãñ çÁâ×ð´ ∠PSR 1255 8 , RQT∠ ·¤æ ×æÂ ãñ Ñ (A) 758 (B) 658 (C) 558 (D) 1258
8. 8. w w w .edurite.com 8041/IX/SA2/30/A1 7. °·¤ â×¿ÌéÖüéÁ ·ð¤ çß·¤æü 12 âð×è °ß´ 16 âð×è ãñÐ â×¿ÌéÖüéÁ ·¤è ÖéÁæ ·¤è ÜÕæ§ü ãñ Ñ (A) 10 âð×è (B) 12 âð×è (C) 16 âð×è (D) 8 âð×è 8. °·¤ ß»ü ·ð¤ çß·¤æü ·¤è ÜÕæ§ü 10 âð×è ãñ, Ìæð ©â ß»ü ·¤æ ÿæðæÈ¤Ü ãñ Ñ (A) 20 ß»ü âð×è (B) 100 ß»ü âð×è (C) 50 ß»ü âð×è (D) 70 ß»ü âð×è 9. °·¤ ·¤×ÚðU ·¤è çß×æ°¡ 10 ×è.310 ×è.35 ×è. ãñ´Ð ©â ×ð´ ÚU¹ð Áæ â·¤Ùð ßæÜð ¹Õð ·¤è ¥çÏ·¤Ì× ÜÕæ§ü ãñ Ñ (A) 15 ×è (B) 16 ×è (C) 10 ×è (D) 12 ×è 10. ¥æ¡·¤Ç¸æð´ 25.7, 16.3, 2.8, 21.7, 24.3, 22.7, 24.9 ·¤è ÂýâæÚU ãñ Ñ (A) 22 (B) 22.9 (C) 21.7 (D) 20.5 ¹ÇU - ¹ ÂýàÙ â´Øæ 11 âð 18 Ì·¤ ÂýØð·¤ ·ð¤ çÜ° 2 ¥´·¤ ãñ´Ð 11. 24 ·ð¤ »éæÙ¹´ÇUæð´ ·¤æ ×æØ ææÌ ·¤èçÁ°Ð 12. °·¤ ·¤×ÚðU ·¤è ÜÕæ§ü, ¿æñÇ¸æ§ü °ß´ ª¡¤¿æ§ü ·ý¤×àæÑ 5 ×è, 4 ×è °ß´ 3 ×è ãñ´Ð 50 L¤Â° ÂýçÌ ß»ü ×èÅUÚU ·¤è ÎÚU âð ·¤×ÚðU ·¤è ÀUÌ °ß´ ÎèßæÚUæð´ ÂÚU ÂðÅU ·¤ÚUæÙð ·¤æ ÃØØ ææÌ ·¤èçÁ°Ð 13. °·¤ Âæ§üÂ ·ð¤ ¥ÙéÂýSÍ ÂçÚUÀðUÎ ·¤æ ÿæðæÈ¤Ü 5 ß»ü âð×è ãñÐ ØçÎ ©â Âæ§Â ×ð´ ÂæÙè ·ð¤ ÕãÙð ·¤è »çÌ 30 âð×è ÂýçÌ âð·¤ÇU ãñ, Ìæð ææÌ ·¤èçÁ° ç·¤ 1 ç×ÙÅU ×ð´ ©â Âæ§üÂ âð ç·¤ÌÙð ÜèÅUÚU ÂæÙè Õãð»æ? 14. 13 âð×è ÃØæâ ßæÜð ßëæ ·¤è Îæð â×æ´ÌÚU Áèßæ°´ ·ý¤×àæÑ 5 âð×è °ß´ 12 âð×è ãñ´Ð ØçÎ Áèßæ°¡ ·ð¤Îý çÕÎé ·ð¤ â×é¹ (çßÂÚUèÌ) Âÿææð´ ×ð´ çSÍÌ ãñ, Ìæð ©Ù·ð¤ Õè¿ ·¤è ÎêÚUè ææÌ ·¤èçÁ°Ð 15. çâh ·¤èçÁ° ç·¤ °·¤ â×æ´ÌÚU ¿ÌéÖüéÁ ·ð¤ Îæð â´ÜÙ ·¤æðææð´ ·ð¤ ·¤æðæ â×çmÖæÁ·¤ ÂÚUSÂÚU â×·¤æðæ ÂÚU ÂýçÌÀðUÎ ·¤ÚUÌð ãñ´Ð 16. °·¤ â×æ´ÌÚU ¿ÌéÖüéÁ ·ð¤ ¥çÏ·¤ ·¤æðæ ßæÜð àæèáü âð ÕÙæ° »° Îæð Ü´Õæð´ ·ð¤ Õè¿ ·¤æ ·¤æðæ 508 ãñÐ â×æ´ÌÚU ¿ÌéÖüéÁ ·ð¤ ·¤æðæ ææÌ ·¤èçÁ°Ð ¥Íßæ °·¤ çæÖéÁ ABC ×ð´ D ÌÍæ E ·ý¤×àæÑ BC °ß´ AD ·ð¤ ×Ø çÕÎé ãñ´, Ìæð çâh ·¤èçÁ° ç·¤ ÿæðæÈ¤Ü (BED) 5 1 4 ÿæðæÈ¤Ü (ABC) 17. Îæð âßæZ»â× ßëæ ÂÚUSÂÚU çÕÎé¥æð´ A ÌÍæ B ÂÚU ÂýçÌÀðUÎ ·¤ÚUÌð ãñ´Ð çÕÎé A âð °·¤ ÚðU¹æ¹´ÇU PAQ §â Âý·¤æÚU ÕÙæØæ ÁæÌæ ãñ ç·¤ çÕÎé P ÌÍæ Q çßçÖóæ ßëææð´ ÂÚU çSÍÌ ãñ´Ð çâh ·¤èçÁ° ç·¤ BP 5 BQ. 18. â×è·¤ÚUæ 2x23y512 ·¤è âãæØÌæ âð y ·¤æð x ·ð¤ M¤Â ×ð´ ÃØÌ ·¤èçÁ°Ð ©Ù çÕÎé¥æð´ ·ð¤ çÙÎðüàææ´·¤ ææÌ ·¤èçÁ° Áãæ¡ ÂÚU §â â×è·¤ÚUæ mæÚUæ çÙM¤çÂÌ ÚðU¹æ x-¥ÿæ °ß´ y-¥ÿæ ·¤æð ·¤æÅUÌè ãñÐ
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