RBSE Class 10 Maths Question Paper 2015 PDF

RBSE Class 10 Maths Question Paper 2015 ŸÊ◊Ê¢∑§ Roll No. No. of Questions — 30 S—09—Mathematics No. of Printed Pages — 7 ◊ÊäÿÁ◊∑§ ¬⁄UˡÊÊ, 2015 SECONDARY EXAMINATION, 2015...

RBSE Class 10 Maths Question Paper 2015 ŸÊ◊Ê¢∑§ Roll No. No. of Questions — 30 S—09—Mathematics No. of Printed Pages — 7 ◊ÊäÿÁ◊∑§ ¬⁄UˡÊÊ, 2015 SECONDARY EXAMINATION, 2015 ªÁáÊà MATHEMATICS ‚◊ÿ — 3 41 ÉÊá≈U ¬ÍáÊÊZ∑§ — 80 ¬⁄UˡÊÊÁÕ¸ÿÊ¥ ∑§ Á‹∞ ‚Ê◊Êãÿ ÁŸŒ¸‡Ê — GENERAL INSTRUCTIONS TO THE EXAMINEES : 1. ¬⁄UˡÊÊÕ˸ ‚fl¸¬˝Õ◊ ¬Ÿ ¬˝‡Ÿ¬òÊ ¬⁄U ŸÊ◊Ê¢∑§ ÁŸflÊÿ¸Ã— Á‹π¥ – Candidate must write first his / her Roll No. on the question paper compulsorily. 2. ‚÷Ë ¬˝‡Ÿ ∑§⁄UŸ ÁŸflÊÿ¸ „Ò¥ – All the questions are compulsory. 3. ¬˝àÿ∑§ ¬˝‡Ÿ ∑§Ê ©UûÊ⁄U ŒË ªß¸ ©UûÊ⁄U ¬ÈÁSÃ∑§Ê ◊¥ „UË Á‹π¥ – Write the answer to each question in the given answer-book only. 4. Á¡Ÿ ¬˝‡ŸÊ¥ ◊¥ ÊãÃÁ⁄U∑§ πá«U „Ò¥U, ©UŸ ‚÷Ë ∑§ ©UûÊ⁄U ∞∑§ ‚ÊÕ „UË Á‹π¥ – For questions having more than one part, the answers to those parts are to be written together in continuity. 5. ¬˝‡Ÿ ¬òÊ ∑§ Á„UãŒË fl ¢ª˝¡Ë M§¬Ê¢Ã⁄U ◊¥ Á∑§‚Ë ¬˝∑§Ê⁄U ∑§Ë òÊÈÁ≈U / ¢Ã⁄U / Áfl⁄UÊœÊ÷Ê‚ „UÊŸ ¬⁄U Á„UãŒË ÷Ê·Ê ∑§ ¬˝‡Ÿ ∑§Ê „UË ‚„UË ◊ÊŸ¥ – If there is any error / difference / contradiction in Hindi and English versions of the question paper, the question of Hindi version should be treated valid. S—09—Maths. S – 4009 [ Turn over  2 6. πá«U ¬˝‡Ÿ ‚¢ÅÿÊ ¢∑§ ¬˝àÿ∑§ ¬˝‡Ÿ A 1 – 10 1 B 11 – 15 2 C 16 – 25 3 D 26 – 30 6 Part Question Nos. Marks per question A 1 – 10 1 B 11 – 15 2 C 16 – 25 3 D 26 – 30 6 7. ¬˝‡Ÿ ∑˝§◊Ê¢∑§ 28 fl 30 ◊¥ ÊãÃÁ⁄U∑§ Áfl∑§À¬ „Ò¥U – There are internal choices in Question Nos. 28 and 30. 8. ¬ŸË ©UûÊ⁄U ¬ÈÁSÃ∑§Ê ∑§ ¬ÎcΔUÊ¥ ∑§ ŒÊŸÊ¥ Ê⁄U Á‹Áπ∞ – ÿÁŒ ∑§Ê߸ ⁄U»§ ∑§Êÿ¸ ∑§⁄UŸÊ „UÊ, ÃÊ ©UûÊ⁄U-¬ÈÁSÃ∑§Ê ∑§ ÁãÃ◊ ¬ÎcΔUÊ¥ ¬⁄U ∑§⁄¥U ÊÒ⁄U ßã„¥U ÁÃ⁄U¿UË ‹ÊߟÊ¥ ‚ ∑§Ê≈U∑§⁄U ©UŸ ¬⁄U “⁄U»§ ∑§Êÿ¸” Á‹π Œ¥ – Write on both sides of the pages of your answer-book. If any rough work is to be done, do it on last pages of the answer-book and cross with slant lines and write ‘Rough Work’ on them. 9. ¬˝‡Ÿ ∑˝§◊Ê¢∑§ 26 ∑§Ê ‹πÊÁøòÊ ª˝Ê»§ ¬¬⁄U ¬⁄U ’ŸÊß∞ – Draw the graph of Question No. 26 on graph paper. π¢«U– A PART – A 1. ‚◊ÊãÃ⁄U üÊ…∏UË 7, 5, 3, 1, – 1, – 3,..... ∑§Ê ‚Êfl¸ ãÃ⁄U ôÊÊà ∑§ËÁ¡∞ – Write the common difference of the A.P. 7, 5, 3, 1, – 1, – 3,...... 2. Á’ãŒÈ ( – 5, 4 ) ∑§Ë x– ˇÊ ‚ ŒÍ⁄UË Á‹Áπ∞ – Write the distance of the point ( – 5, 4 ) from x-axis. 3. ⁄ÒUÁπ∑§ ‚◊Ë∑§⁄UáÊ ÿÈÇ◊ 4x + 2y = 5 ÃÕÊ x – 2y = 0 ∑§Ê „U‹ Á‹Áπ∞ – Write the solution of the pair of linear equations 4x + 2y = 5 and x – 2y = 0. 4. ÷ÊÖÿ ªÈáÊŸπá«U ÁflÁœ mÊ⁄UÊ 96 ÊÒ⁄U 404 ∑§Ê HCF ôÊÊà ∑§ËÁ¡∞ – Find the HCF of 96 and 404 by the Prime Factorisation Method. 5. ë¿UË ¬˝∑§Ê⁄U ‚ »¥§≈UË ªß¸ 52 ¬ûÊÊ¥ ∑§Ë ∞∑§ ªaÔUË ◊¥ ‚ ∞∑§ ¬ûÊÊ ßÄ∑§Ê Ÿ„UË¥ „UÊŸ ∑§Ë ¬˝ÊÁÿ∑§ÃÊ ôÊÊà ∑§ËÁ¡∞ – One card is drawn from a well-shuffled deck of 52 cards. Calculate the probability that the card will not be an ace. 6. ÿÁŒ K ( 5, 4 ) ⁄UπÊπ¢«U PQ ∑§Ê ◊äÿ Á’ãŒÈ „ÒU ÃÕÊU Q ∑§ ÁŸŒ¸‡ÊÊ¢∑§ ( 2, 3 ) „ÒU, ÃÊ P ∑§ ÁŸŒ¸‡ÊÊ¢∑§ ôÊÊà ∑§ËÁ¡∞ – If K ( 5, 4 ) is the mid-point of the line segment PQ and co-ordinates of Q are ( 2, 3 ), then find the co-ordinates of point P. 7. ÿÁŒ Á’ãŒÈ R ‚ O ∑§ãº˝ flÊ‹ Á∑§‚Ë flÎûÊ ¬⁄U RA fl RB S¬‡Ê¸ ⁄UπÊ∞° ¬⁄US¬⁄U θ ∑§ ∑§ÊáÊ ¬⁄U ¤ÊÈ∑§Ë „UÊ¥ ÃÕÊ ∠ AOB = 40˚ „UÊ ÃÊ ∑§ÊáÊ θ ∑§Ê ◊ÊŸ ôÊÊà ∑§⁄¥U – If tangents RA and RB from a point R to a circle with centre O are inclined to each other at an angle of θ and ∠ AOB = 40˚ then find the value of θ. S—09—Maths. S – 4009  3 8. 4 ‚◊Ë ÁòÊÖÿÊ flÊ‹ flÎûÊ ¬⁄U ÁSÕà Á∑§‚Ë Á’ãŒÈ ¬⁄U Á∑§ÃŸË S¬‡Ê¸ ⁄UπÊ Ê¥ ∑§Ë ⁄UøŸÊ ∑§Ë ¡Ê ‚∑§ÃË „ÒU ? How many tangents can be constructed to any point on the circle of radius 4 cm ? 9. 14 ‚◊Ë √ÿÊ‚ flÊ‹ flÎûÊ ∑§Ë ¬Á⁄UÁœ ôÊÊà ∑§ËÁ¡∞ – Find the circumference of a circle whose diameter is 14 cm. 10. ÁòÊÖÿÊ r flÊ‹ flÎûÊ ∑§ ∞∑§ ÁòÊÖÿπ¢«U, Á¡‚∑§Ê ∑§ÊáÊ ¢‡ÊÊ¥ ◊¥ θ „ÒU, øʬ ∑§Ë ‹ê’Ê߸ ôÊÊà ∑§ËÁ¡∞ – Write the length of an arc of a sector of circle with radius r and angle with degree measure θ. π¢«U – B PART – B 11. ÁŒπÊß∞ Á∑§sin 28˚ cos 62˚ + cos 28˚ sin 62˚ = 1. Show that sin 28˚ cos 62˚ + cos 28˚ sin 62˚ = 1. tan 67˚ 12. cot 23˚ ∑§Ê ◊ÊŸ ôÊÊà ∑§ËÁ¡∞ – tan 67˚ Find the value of. cot 23˚ 1 – tan 2 A 13. ÿÁŒ 3 cot A = 4, ÃÊ ∑§Ê ◊ÊŸ ôÊÊà ∑§ËÁ¡∞ – 1 + tan2 A 1 – tan 2 A If 3 cot A = 4, then evaluate. 1 + tan2 A 14. ∑§Ê߸ ’øŸ ∞∑§ πÊπ‹ œ¸ ªÊ‹ ∑§ Ê∑§Ê⁄U ∑§Ê „ÒU Á¡‚∑§ ™§¬⁄U ∞∑§ πÊπ‹Ê ’‹Ÿ äÿÊ⁄UÊÁ¬Ã „Ò –U œ¸ ªÊ‹ ∑§Ë ÁòÊÖÿÊ 7 ‚ ◊ Ë „ÒU ÊÒ⁄U ß‚ ’øŸ ( ¬ÊòÊ ) ∑§Ë ∑ȧ‹ ™°§øÊ߸ 13 ‚◊Ë „ÒU – ß‚ ’øŸ ∑§Ê ÊãÃÁ⁄U∑§ ¬ÎcΔUËÿ ˇÊòÊ»§‹ ôÊÊà ∑§ËÁ¡∞ – A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The radius of the hemisphere is 7 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel. 15. Ê∑ΧÁà ◊¥ ∑§ÊáÊÊ¥ ∠OKS fl ∠ROP ∑§Ê ◊ÊŸ ôÊÊà ∑§ËÁ¡∞, ÿÁŒ ÁòÊ÷È¡ Δ OPR ~ Δ OSK ÃÕÊ ∠ POS = 125˚ ÊÒ⁄U ∠ PRO = 70˚ „ÒU – R P 70˚ O 125˚ K S S—09—Maths. S – 4009 [ Turn over  4 In the figure, Δ OPR ~ Δ OSK , ∠ POS = 125˚ and ∠ PRO = 70˚. Find the values of ∠ OKS and ∠ ROP. R P 70˚ O 125˚ K S π¢«U – C PART – C ⎡⎢ 1 – tan A ⎤⎥ 2 16. Á‚h ∑§ËÁ¡∞ Á∑§ ⎢⎣ 1 + cot A ⎥⎦ = tan 2 A. ⎡⎢ 1 – tan A ⎤⎥ 2 Prove that ⎢⎣ 1 + cot A ⎥⎦ = tan 2 A. 17. 3x 3 + x 2 + 2x + 5 ∑§Ê 1 + 2x + x 2 ‚ ÷ʪ ŒËÁ¡∞ – Divide 3x 3 + x 2 + 2x + 5 by 1 + 2x + x 2. 18. Á‚h ∑§ËÁ¡∞ Á∑§ ⎯√⎯2 ∞∑§ ¬Á⁄U◊ÿ ‚¢ÅÿÊ „ÒU – Prove that ⎯ √⎯2 is an irrational number. 19. A.P. 17, 15, 13,...... ∑§ Á∑§ÃŸ ¬Œ Á‹∞ ¡Ê∞° ÃÊÁ∑§ ©UŸ∑§Ê ÿÊª 81 „UÊ ? How many terms of the A.P. 17, 15, 13,...... must be taken, so that their sum is 81 ? 20. ∞∑§ ŸŒË ∑§ ¬È‹ ∑§ ∞∑§ Á’ãŒÈ ‚ ŸŒË ∑§ ‚ê◊Èπ Á∑§ŸÊ⁄UÊ¥ ∑§ flŸ◊Ÿ ∑§ÊáÊ ∑˝§◊‡Ê— 30˚ ÊÒ⁄U 45˚ „ÒU – ÿÁŒ ¬È‹ Á∑§ŸÊ⁄UÊ¥ ‚ 4 ◊Ë≈U⁄U ∑§Ë ™°§øÊ߸ ¬⁄U „UÊ, ÃÊ ŸŒË ∑§Ë øÊÒ«∏UÊ߸ ôÊÊà ∑§ËÁ¡∞ – From a point on a bridge across a river the angles of depression of the banks on opposite sides of the river are 30˚ and 45˚ respectively. If the bridge is at a height of 4 m from the banks, find the width of the river. 21. ŒË ªß¸ Ê∑ΧÁà ◊¥ O ∞∑§ flÎûÊ ∑§Ê ∑§ãº˝ „ÒU Á¡‚∑§ ’ÊsÔ Á’ãŒÈ K ‚ flÎûÊ ¬⁄U ŒÊ S¬‡Ê¸ ⁄UπÊ∞° KR, KS πË¥øË ªß¸ „Ò¥U, ÃÊ Á‚h ∑§ËÁ¡∞ Á∑§ KR = KS. S O K R S—09—Maths. S – 4009  5 In the given figure, O is the centre of a circle and two tangents KR, KS are drawn on the circle from a point K lying outside the circle. Prove that KR = KS. S O K R 22. 4 ‚◊Ë, 5 ‚◊Ë ÊÒ⁄U 6 ‚◊Ë ÷È¡Ê Ê¥ flÊ‹ ∞∑§ ÁòÊ÷È¡ ∑§Ë ⁄UøŸÊ ∑§⁄U ß‚∑§ ‚◊M§¬ ∞∑§ ãÿ ÁòÊ÷È¡ ∑§Ë ⁄UøŸÊ ∑§ËÁ¡∞ Á¡‚∑§Ë ÷È¡Ê∞° ÁŒÿ ªÿ ÁòÊ÷È¡ ∑§Ë ‚¢ªÃ ÷È¡Ê ∑§Ë 35 ªÈŸË „UÊ¥ – Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle 3 similar to it whose sides are time of the corresponding sides of the 5 given triangle. 23. 7 ‚◊Ë ÁòÊÖÿÊ flÊ‹ flÎûÊ ◊¥ ∑§ÊáÊ 120˚ ∑§ ‚¢ªÃ ŒËÉʸ ÁòÊÖÿπá«U ∑§Ê ˇÊòÊ»§‹ ôÊÊà ∑§ËÁ¡∞ – Find the area of corresponding major sector of a circle with radius 7 cm and angle 120˚. 24. 1 ‚◊Ë ÁòÊÖÿÊ ÊÒ⁄U 2 ‚◊Ë ‹ê’Ë ÃÊê’ ∑§Ë ∞∑§ ¿U«∏U ∑§Ê ∞∑§ ‚◊ÊŸ øÊÒ«∏UÊ߸ flÊ‹ 18 ◊Ë≈U⁄U ‹ê’ ∞∑§ ÃÊ⁄U ∑§ M§¬ ◊¥ ’Œ‹Ê ¡ÊÃÊ „ÒU – ÃÊ⁄U ∑§Ë ◊Ê≈UÊ߸ ôÊÊà ∑§ËÁ¡∞ – A copper rod of radius 1 cm and length 2 cm is drawn into a wire of length 18 m of uniform thickness. Find the thickness of the wire. 25. ŸË⁄U¡ ÊÒ⁄U œË⁄U¡ Á◊òÊ „Ò¥U – ©UŸ∑§ ¡ã◊ ÁŒfl‚ ∑§Ë ¬˝ÊÁÿ∑§ÃÊ∞° ôÊÊà ∑§ËÁ¡∞ — (i) ¡’ ¡ã◊ ÁŒfl‚ Á÷ÛÊ-Á÷ÛÊ „UÊ¥ (ii) ¡’ ¡ã◊ ÁŒfl‚ ‚◊ÊŸ „UÊ – Neeraj and Dheeraj are friends. Find the probability of their birthdays when (i) birthdays are different. (ii) birthdays are same. π¢«U – D PART – D 26. 5 ‚flÊ¥ ÊÒ⁄U 3 ‚ãÃ⁄UÊ¥ ∑§Ê ∑ȧ‹ ◊ÍÀÿ 35 L§¬ÿ „ÒU ¡’Á∑§ 2 ‚flÊ¥ ÊÒ⁄U 4 ‚ãÃ⁄UÊ¥ ∑§Ê ∑ȧ‹ ◊ÍÀÿ 28 L§¬ÿ „ÒU – ß‚ ‚◊SÿÊ ∑§Ê ’Ë¡ªÁáÊÃËÿ M§¬ ◊¥ √ÿQ§ ∑§⁄U ª˝Ê»§ ÁflÁœ ‚ „U‹ ∑§ËÁ¡∞ – The cost of 5 apples and 3 oranges is Rs. 35 and the cost of 2 apples and 4 oranges is Rs. 28. Formulate the problem algebraically and solve it graphically. S—09—Maths. S – 4009 [ Turn over  6 27. ∞∑§ ◊Ê≈U⁄U ’Ê≈U Á¡‚∑§Ë ÁSÕ⁄U ¡‹ ◊¥ øÊ‹ 18 Á∑§◊Ë / ÉÊá≈UÊ „ÒU – ©U‚ ’Ê≈U Ÿ 12 Á∑§◊Ë œÊ⁄UÊ ∑§ ¬˝ÁÃ∑ͧ‹ ¡ÊŸ ◊¥, fl„UË ŒÍ⁄UË œÊ⁄UÊ ∑§ ŸÈ∑ͧ‹ ¡ÊŸ ∑§Ë ¬ˇÊÊ 12 ÉÊá≈UÊ Áœ∑§ ‹ÃË „ÒU – œÊ⁄UÊ ∑§Ë øÊ‹ ôÊÊà ∑§ËÁ¡∞ – 1 The speed of a boat in still water is 18 km/h. It takes an hour extra 2 in going 12 km upstream instead of going the same distance downstream. Find the speed of the stream. 28. Êÿà ABCD ∑§ ãŒ⁄U ÁSÕà O ∑§Ê߸ Á’ãŒÈ „ÒU, Á‚h ∑§ËÁ¡∞ — OB 2 + OD 2 = OA 2 + OC 2 A D P R O B C O is any point inside rectangle ABCD. Prove that OB 2 + OD 2 = OA 2 + OC 2 A D P R O B C ÕflÊ PK PT ÁŸêŸ ◊¥ ŒË ªß¸ Ê∑ΧÁà ◊¥KS = TR „Ò¥U ÃÕÊ ∠ PKT = ∠ PRS „ÒU – Á‚h ∑§ËÁ¡∞ Á∑§ Δ PSR ∞∑§ ‚◊Ám’Ê„ÈU ÁòÊ÷È¡ „ÒU – P K T S R S—09—Maths. S – 4009  7 PK PT In the given figure, = and ∠ PKT = ∠ PRS. Prove that Δ PSR KS TR is an isosceles triangle. P K T S R 29. K ∑§Ê ◊ÊŸ ôÊÊà ∑§ËÁ¡∞, ÿÁŒ Á’ãŒÈ A ( 2, 3 ), B ( 4, k ) ÊÒ⁄U C ( 6, – 3 ) ‚¢⁄UπË „ÒU – Find the value of k if the points A ( 2, 3), B ( 4, k ) and C ( 6, – 3 ) are collinear. 30. ÁŸêŸ ’¢≈UŸ ∑§Ê ∑§ÁÀ¬Ã ◊Êäÿ ◊ÊŸ∑§⁄U ◊Êäÿ x– ôÊÊà ∑§ËÁ¡∞ — flª¸ ¢Ã⁄UÊ‹ 10 – 25 25 – 40 40 – 55 55 – 70 70 – 85 85 – 100 ’Ê⁄¢U’Ê⁄UÃÊ 2 3 7 5 6 7 ÕflÊ ÁŸêŸ ’¢≈UŸ ∑§Ê ’„ÈU‹∑§ ôÊÊà ∑§ËÁ¡∞ — flª¸ ¢Ã⁄UÊ‹ 0 – 20 20 – 40 40 – 60 60 – 80 80 – 100 100 – 120 ’Ê⁄¢U’Ê⁄UÃÊ 10 35 52 61 38 20 – In the following distribution calculate mean x from assumed mean : Class- 10 – 25 25 – 40 40 – 55 55 – 70 70 – 85 85 – 100 interval Frequency 2 3 7 5 6 7 OR Find the mode of the following distribution : Class- 0 – 20 20 – 40 40 – 60 60 – 80 80 – 100 100 – 120 interval Frequency 10 35 52 61 38 20 S—09—Maths. S – 4009 [ Turn over