RBSE Class 10 Maths Question Paper 2015

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1 BE Class 10 Maths Question aper 015 ŸÊ Ê oll No. No. of Questions 30 No. of rinted ages 7 09 Mathematics ÊäÿÁ UˡÊÊ, 015 ECNDAY EXAMINATIN, 015 ªÁáÊà MATHEMATIC ÿ ÉÊá appleu ÍáÊÊZ 80 UˡÊÊÁÕ ÿêapple apple Á Ê Êãÿ ÁŸŒapple Ê GENEAL INTUCTIN T THE EXAMINEE : 1. UˡÊÊÕË fl Õ Ÿapple Ÿ òê U ŸÊ Ê ÁŸflÊÿ à Á πapple Candidate must write first his / her oll No. on the question paper compulsorily.. Ë Ÿ UŸapple ÁŸflÊÿ Ò All the questions are compulsory. 3. àÿapple Ÿ Ê UûÊ U ŒË ªß UûÊ U ÈÁÃ Ê apple UË Á πapple Write the answer to each question in the given answer-book only. 4. Á Ÿ ŸÊapple apple ÊãÃÁ U πá«u Ò U, UŸ Ë apple UûÊ U ÊÕ UË Á πapple For questions having more than one part, the answers to those parts are to be written together in continuity. 5. Ÿ òê apple Á UãŒË fl ª apple Ë M Ê Ã U apple Á Ë Ê U Ë òêèá U / à U / Áfl UÊappleœÊ Ê UÊappleŸapple U Á UãŒË Ê Ê apple Ÿ Êapple UË UË ÊŸapple 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.

2 09 Maths πá«u Ÿ ÅÿÊ àÿapple Ÿ A B C D art Question Nos. Marks per question A B C D Ÿ Ê 8 fl 30 apple ÊãÃÁ U Áfl À Ò U There are internal choices in Question Nos. 8 and ŸË UûÊ U ÈÁÃ Ê apple ÎcΔUÊapple apple ŒÊappleŸÊapple Êapple U Á Áπ ÿᜠÊappleß U» Êÿ UŸÊ UÊapple, ÃÊapple UûÊ U- ÈÁÃ Ê apple Áãà ÎcΔUÊapple U apple U ÊÒ U ßã apple U Áà U UË ÊߟÊapple apple Ê U U UŸ U U» Êÿ Á π Œapple 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 ough Work on them. 9. Ÿ Ê 6 Ê appleπêáøòê ª Ê» apple U U ŸÊß Draw the graph of Question No. 6 on graph paper. π «U A AT A 1. Êãà U üêapple UË 7, 5, 3, 1, 1, 3,... Ê Êfl ãã U ôêêã ËÁ Write the common difference of the A.. 7, 5, 3, 1, 1, 3,..... Á ãœè ( 5, 4 ) Ë x ˇÊ apple ŒÍ UË Á Áπ Write the distance of the point ( 5, 4 ) from x-axis. 3. ÒUÁπ Ë UáÊ ÿèç 4x + y = 5 ÃÕÊ x y = 0 Ê U Á Áπ Write the solution of the pair of linear equations 4x + y = 5 and x y = ÊÖÿ ªÈáÊŸπá«U ÁflÁœ mê UÊ 96 ÊÒ U 404 Ê HCF ôêêã ËÁ Find the HCF of 96 and 404 by the rime Factorisation Method. 5. ë UË Ê U apple»apple UË ªß 5 ûêêapple Ë ªaÔUË apple apple ûêê ßÄ Ê Ÿ UË UÊappleŸapple Ë ÊÁÿ ÃÊ ôêêã ËÁ ne card is drawn from a well-shuffled deck of 5 cards. Calculate the probability that the card will not be an ace. 6. ÿᜠ( 5, 4 ) appleuπêπ «U Q Ê äÿ Á ãœè ÒU ÃÕÊU Q apple ÁŸŒapple ÊÊ (, 3 ) ÒU, ÃÊapple apple ÁŸŒapple ÊÊ ôêêã ËÁ If ( 5, 4 ) is the mid-point of the line segment Q and co-ordinates of Q are (, 3 ), then find the co-ordinates of point. 7. ÿᜠÁ ãœè apple apple 㺠flê apple Á Ë flîûê U A fl B Ê appleuπê U U θ apple ÊappleáÊ U ÊÈ Ë UÊapple ÃÕÊ AB = 40 UÊapple ÃÊapple ÊappleáÊ θ Ê ÊŸ ôêêã apple U If tangents A and B from a point to a circle with centre are inclined to each other at an angle of θ and AB = 40 then find the value of θ.

3 apple Ë ÁòÊÖÿÊ flê apple flîûê U ÁÕà Á Ë Á ãœè U Á ÃŸË Ê appleuπê Êapple Ë UøŸÊ Ë Ê ÃË ÒU? How many tangents can be constructed to any point on the circle of radius 4 cm? apple Ë ÿê flê apple flîûê Ë Á UÁœ ôêêã ËÁ Find the circumference of a circle whose diameter is 14 cm. 10. ÁòÊÖÿÊ r flê apple flîûê apple ÁòÊÖÿπ «U, Á Ê ÊappleáÊ ÊÊapple apple θ ÒU, øê Ë ê Êß ôêêã ËÁ Write the length of an arc of a sector of circle with radius r and angle with degree measure θ. π «U B AT B 11. ÁŒπÊß Á sin 8 cos 6 + cos 8 sin 6 = how that sin 8 cos 6 + cos 8 sin 6 = 1. tan 67 Ê ÊŸ ôêêã ËÁ cot 3 tan 67 Find the value of. cot ÿᜠ3 cot A = 4, ÃÊapple 1 tan A 1 + tan A Ê ÊŸ ôêêã ËÁ If 3 cot A = 4, then evaluate 1 tan A 1 + tan A. 14. Êappleß Ã Ÿ πêappleπ apple œ ªÊapple apple apple Ê Ê U Ê ÒU Á apple U πêappleπ Ê apple Ÿ äÿê UÊappleÁ Ã Ò U œ ªÊapple apple Ë ÁòÊÖÿÊ 7 apple Ë ÒU ÊÒ U ß Ã Ÿ ( ÊòÊ ) Ë È øêß 13 apple Ë ÒU ß Ã Ÿ Ê ÊãÃÁ U ÎcΔUËÿ ˇÊappleòÊ» ôêêã 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 Î Áà apple ÊappleáÊÊapple fl Ê ÊŸ ôêêã ËÁ, ÿᜠÁòÊ È Δ ~ Δ ÃÕÊ = 15 ÊÒ U = 70 ÒU 70 15

4 4 In the figure, Δ ~ Δ, = 15 and = 70. Find the values of and Á h ËÁ Á 1 tan A 1 + cot A rove that 1 tan A 1 + cot A π «U C AT C = tan A. = tan A x 3 + x + x + 5 Êapple 1 + x + x apple ʪ ŒËÁ Divide 3x 3 + x + x + 5 by 1 + x + x. 18. Á h ËÁ Á Á U appleÿ ÅÿÊ ÒU rove that is an irrational number. 19. A.. 17, 15, 13,... apple Á ßapple Œ Á Ê ÃÊÁ UŸ Ê ÿêappleª 81 UÊapple? How many terms of the A.. 17, 15, 13,... must be taken, so that their sum is 81? 0. ŸŒË apple È apple Á ãœè apple ŸŒË apple ê Èπ Á ŸÊ UÊapple apple flÿ Ÿ ÊappleáÊ Ê 30 ÊÒ U 45 ÒU ÿáœ È Á ŸÊ UÊapple apple 4 Ë U U Ë øêß U UÊapple, ÃÊapple ŸŒË Ë øêò«uêß ôêêã 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. 1. ŒË ªß Ê Î Áà apple flîûê Ê apple 㺠ÒU Á apple ÊsÔ Á ãœè apple flîûê U ŒÊapple Ê appleuπê, πë øë ªß Ò U, ÃÊapple Á h ËÁ Á =. 09 Maths. 4009

5 5 In the given figure, is the centre of a circle and two tangents, are drawn on the circle from a point lying outside the circle. rove that =.. 4 apple Ë, 5 apple Ë ÊÒ U 6 apple Ë È Ê Êapple flê apple ÁòÊ È Ë UøŸÊ U ß apple M ãÿ ÁòÊ È Ë UøŸÊ ËÁ Á Ë È Ê ÁŒÿapple ªÿapple ÁòÊ È Ë ªÃ È Ê Ë 3 5 ªÈŸË UÊapple Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it whose sides are 3 time of the corresponding sides of the 5 given triangle apple Ë ÁòÊÖÿÊ flê apple flîûê apple ÊappleáÊ 10 apple ªÃ ŒËÉÊ ÁòÊÖÿπá«U Ê ˇÊappleòÊ» ôêêã ËÁ Find the area of corresponding major sector of a circle with radius 7 cm and angle apple Ë ÁòÊÖÿÊ ÊÒ U apple Ë ê Ë ÃÊê apple Ë U«U Êapple ÊŸ øêò«uêß flê apple 18 Ë U U ê apple ÃÊ U apple M apple Œ Ê ÊÃÊ ÒU ÃÊ U Ë Êapple UÊß ôêêã ËÁ A copper rod of radius 1 cm and length cm is drawn into a wire of length 18 m of uniform thickness. Find the thickness of the wire. 5. ŸË U ÊÒ U œë U Á òê Ò U UŸ apple ã ÁŒfl Ë ÊÁÿ ÃÊ ôêêã ËÁ (i) ã ÁŒfl Á ÛÊ-Á ÛÊ UÊapple (ii) ã ÁŒfl ÊŸ UÊapple Neeraj and Dheeraj are friends. Find the probability of their birthdays when (i) (ii) birthdays are different. birthdays are same. π «U D AT D 6. 5 appleflêapple ÊÒ U 3 ãã UÊapple Ê È ÍÀÿ 35 L ÿapple ÒU Á appleflêapple ÊÒ U 4 ãã UÊapple Ê È ÍÀÿ 8 L ÿapple ÒU ß ÿê Êapple Ë ªÁáÊÃËÿ M apple ÿq U ª Ê» ÁflÁœ apple U ËÁ The cost of 5 apples and 3 oranges is s. 35 and the cost of apples and 4 oranges is s. 8. Formulate the problem algebraically and solve it graphically.

6 6 7. Êapple U U Êapple U Á Ë ÁÕ U apple øê 18 Á Ë / ÉÊá UÊ ÒU U Êapple U Ÿapple 1 Á Ë œê UÊ apple ÁÃ Í ÊŸapple apple, fl UË ŒÍ UË œê UÊ apple ŸÈ Í ÊŸapple Ë appleˇêê 1 ÉÊá UÊ Áœ appleãë ÒU œê UÊ Ë øê ôêêã ËÁ The speed of a boat in still water is 18 km/h. It takes 1 an hour extra in going 1 km upstream instead of going the same distance downstream. Find the speed of the stream. 8. Êÿà ABCD apple 㜠U ÁÕà Êappleß Á ãœè ÒU, Á h ËÁ B + D = A + C A D B is any point inside rectangle ABCD. rove that B + D = A + C A C D B ÁŸêŸ apple ŒË ªß Ê Î Áà apple = T T Δ Ám Ê ÈU ÁòÊ È ÒU ÕflÊ Ò U ÃÕÊ T = ÒU Á h ËÁ Á C T 09 Maths. 4009

7 In the given figure, = T T is an isosceles triangle. 7 and T =. rove that Δ T 9. Ê ÊŸ ôêêã ËÁ, ÿᜠÁ ãœè A (, 3 ), B ( 4, k ) ÊÒ U C ( 6, 3 ) appleuπë ÒU Find the value of k if the points A (, 3), B ( 4, k ) and C ( 6, 3 ) are collinear. 30. ÁŸêŸ UŸ Ê ÁÀ à Êäÿ ÊŸ U Êäÿ x ôêêã ËÁ flª à UÊ Ê U Ê UÃÊ ÕflÊ ÁŸêŸ UŸ Ê ÈU ôêêã ËÁ flª à UÊ Ê U Ê UÃÊ In the following distribution calculate mean x from assumed mean : Frequency Classinterval Classinterval Find the mode of the following distribution : Frequency