RBSE Class 10 Maths I Question Paper 2010

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1 RBSE Class 0 Maths I Question Paper 00 ŸÊ Ê Roll No. No. of Questions 6 No. of Printed Pages 7 S 09 Maths. I ÊäÿÁ UˡÊÊ, 00 SECONDARY EXAMINATION, 00 ªÁáÊà ó Õ òê MATHEMATICS First Paper ÿ 3 4 ÉÊá appleu ÍáÊÊZ 40 UˡÊÊÁÕ ÿêapple apple Á Ê Êãÿ ÁŸŒapple Ê GENERAL INSTRUCTIONS TO THE EXAMINEES :. UˡÊÊÕË fl Õ Ÿapple Ÿ òê U ŸÊ Ê ÁŸflÊÿ à Á πapple Candidate must write first his / her Roll No. on the question paper compulsorily.. Ë Ÿ UŸapple ÁŸflÊÿ Ò U All the questions are compulsory. 3. àÿapple Ÿ Ê UûÊ U ŒË ªß UûÊ U- ÈÁSÃ Ê apple UË Á πapple Write the answer to each question in the given answer-book only. 4. Á Ÿ apple apple Áœ ÊŸ UflÊ apple ʪ Ò U, UŸ Ë ÊªÙ Ê U ÊÕ Ãà Á πapple For questions having more than one part carrying similar marks, the answers of those parts are to be written together in continuity. 5. ŸË UûÊ U- ÈÁSÃ Ê apple Îc UÊapple apple ŒÊappleŸÊapple Êapple U Á Áπ ÿᜠÊappleß U$» Êÿ UŸÊ UÊapple, ÃÊapple UûÊ U- ÈÁSÃ Ê apple Áà Îc UÊapple U apple U ÊÒ U ßã apple U Áà U UË ÊߟÊapple apple Ê U U UŸ U U$» 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 Rough Work on them. S 09 Maths. I S [ Turn over

2 S 09 Maths. I S 6. Ÿ Ê 3 fl 5 apple ÊãÃÁ U Áfl À Ò U There are internal choices in Question Nos. 3 and Ÿ Ê apple 7 à Áà ÉÊÍûÊ UÊà Ÿ Ò U Question Nos. to 7 are Very Short Answer type. 8. Ÿ Ê apple øê U ʪ ( i, ii, iii, iv ) Ò U ÊÒ U àÿapple ʪ apple øê U Áfl À A, B, C ÊÒ U D ÁŒ ª Ò U UË UûÊ UÊˇÊ U UûÊ U- ÈÁSÃ Ê apple ÁŸêŸÊŸÈ Ê U ÃÊÁ Ê ŸÊ U Œapple There are four parts ( i, ii, iii, iv ) in Question No.. Each part has four alternatives A, B, C and D. Write the letter of the correct alternative in the answer-book at a place by making a table as mentioned below : Ÿ Ê Question No.. (i). (ii). (iii). (iv) Ë UûÊ U Ê ÊˇÊ U Correct letter of the Answer. (i) 7,500 L ÿapple Ê 4% ø flîáh éÿê Ë Œ U apple fl Ê Á üêœÿ ÒU (A) 7,800 L ÿapple (B) 8,00 L ÿapple (C) 8, L ÿapple (D) 8,08 L ÿapple (ii) The compounded amount of Rs. 7,500 for years at the rate of 4% compound interest per annum is (A) Rs. 7,800 (B) Rs. 8,00 (C) Rs. 8, (D) Rs. 8,08. ÿᜠ3 + a 3 apple ( + a ) Ê Êª ÁŒÿÊ Êÿ ÃÊapple Êapple» UÊappleªÊ (A) + a (B) + a (C) a (D) 0. If 3 + a 3 is divided by ( + a ) then the remainder is (A) + a (B) + a (C) a (D) 0.

3 (iii) (iv) 3 «U apple Ë ÊÿÈ Ë ŸË ÊÃÊ Ë ÊÿÈ Ë Áà UÊß ÒU ÿᜠÊÃÊ Ë flã ÊŸ ÊÿÈ fl ÒU, ÃÊapple fl øêã «U apple Ë ÊÿÈ UÊappleªË (A) 3 + (B) + 3 (C) + 4 (D) 3. A boy is now one third as old as his mother. What will be the age of the boy after years if mother s present age is? (A) 3 + (B) + 3 (C) + 4 (D) 3. Ê ø ÅÿÊ Êapple Ê Êäÿ 8 ÒU ÿᜠÅÿÊ U UÊ ŒË ÊÃË ÒU, ÃÊapple Êäÿ 6 UÊapple ÊÃÊ ÒU U UÊß ªÿË ÅÿÊ ÒU (A) 0 (B) 8 (C) 6 (D) 6. The mean of 5 numbers is 8. If one number is ecluded, then mean becomes 6. Ecluded number is (A) 0 (B) 8 (C) 6 (D) 6.. ÁfllÊÕË Ê Ê U 4 fl Ë ÊÿÈ apple ãã apple 36 Á ª Ê ÕÊ 5 fl Ë ÊÿÈ apple à apple ÿ U U U 45 Á ª Ê UÊapple ªÿÊ 5 flapple fl Ë flîáh Œ U ôêêã ËÁ The weight of a student at the end of 4 years of his age was 36 kg. It increased to 45 kg at the end of 5 years of his age. Find the rate of growth in 5th year y 343y apple ªÈáÊŸπá«U ËÁ Factorise 8 3 y 343y. 4. ÊÿÃ Ê Á U Ê 40 apple Ë ÒU U Ë È Ê Êapple Ê ŸÈ Êà : 3 ÒU ÊÿÃ Ë ê Êß ÃÕÊ øêò«uêß ôêêã ËÁ The perimeter of a rectangle is 40 cm. The ratio of its sides is : 3. Find the length and breadth of the rectangle. 5. Ë UáÊ 8 = 0 Êapple U ËÁ Solve the equation 8 = 0. S 09 Maths. I S [ Turn over

4 6. ÁmÉÊÊÃ Ë UáÊ ôêêã ËÁ Á apple Í + 5 ÊÒ U 5 Ò U S 09 Maths. I S 4 Find the quadratic equation whose roots are + 5 and UŸ, 3, 4, 7, 5, Ë ÊÁäÿ Ê ôêêã ËÁ Find median of the following distribution :, 3, 4, 7, 5,. 8. ßc U ÅÿÊ ÁflÁœ apple 39 Ê flª ôêêã ËÁ Find out the square of 39 by the favourite number method. 9. ÍòÊ UÊflàÿ ÿêapple ÿappleã mê UÊ Ë UáÊ ( + ) ( + ) = ( 3 ) ( 4 ) Êapple U ËÁ Solve the equation ( + ) ( + ) = ( 3 ) ( 4 ) by the Sutra Paravartya Yojayet. 0. flsãè Êapple ŸªŒ π UËŒ Ãapple Ò U ÿê 90 L ÿapple Ãà Ê ŒÊÿªË ÃÕÊ 60 L ÿapple Ë 6 ÊÁ Á SÃÊapple apple π UËŒÊ Ê ÃÊ ÒU éÿê Ë UÊÁ Ê 50 L 0 UÊapple, ÃÊapple flsãè Ê Ÿ Œ ÍÀÿ ôêêã ËÁ An article can be purchased on a cash payment or a cash down payment of Rs. 90 and 6 equal monthly instalments of Rs. 60 each. If the amount of interest is Rs. 50, find the cash price of the article.. a b a 3 + b 3 apple ªÈáÊŸπá«U ËÁ Factorise a b a 3 + b 3.. Ë UáÊ ÁŸ Êÿ = Solve the system of equation = y, y = Êapple U ËÁ y, y =. 3. Ë UáÊ = 0 apple Í Êapple Ë Î Áà ôêêã ËÁ Comment on the nature of the roots of the equation = UŸ 8, 7, 9, 6, 5 Ê Êäÿ Áflø Ÿ ôêêã ËÁ Find the mean deviation of the following distribution : 8, 7, 9, 6, mãm ÿêappleª ÁflÁœ apple mê UÊ Ê flª Í ôêêã ËÁ Find the square root of by Dwandwa Yoga method. 6. Ÿ appleu㺠ÊÒ U È appleuãº Ê 4,500 L 0 ÊÒ U 6,000 L 0 ªÊ U ÿê Ê U UÃapple Ò U Ÿ appleu㺠Êapple Á ÿ Ê ÊappleŒÊ U UÊappleŸapple apple Ê UáÊ Ê Ê 40% ÁÃÁ Q U Á ÃÊ ÒU ÿáœ È Ê 3,500 L ÿapple ÈU Ê UÊapple, ÃÊapple àÿapple Ê Ê ôêêã ËÁ Narendra and Surendra started a business by investing Rs. 4,500 and Rs. 6,000 respectively. Narendra being an active partner, gets an additional 40% of the profit. If the total profit is Rs. 3,500, find the profit of each.

5 5 7. Ÿ ŒÊ Ÿapple 5,000 L ÿapple ªÊ U»Ò Ë S UÊapple U πêapple Ê ÊÃ Ê ÊŒ, Êflapple UË È U Í Ë ªÊ U Ÿ ŒÊ apple ÊÕ ÿfl Êÿ apple Áê Á à UÊapple ªÿË ÿᜠfl apple ãã apple UŸ apple Ê Ê ŸÈ Êà 0 : 7 ÕÊ, ÃÊapple Êflapple UË Ë Í Ë ôêêã ËÁ Narmada started a fancy store by investing Rs. 5,000. After 7 months, Kaveri joined Narmada in the business by investing a certain amount. At the end of the year, if the ratio of their profits was 0 : 7, then find the capital of Kaveri apple ªÈáÊŸπá«U ËÁ Factorise ÿ Êapple 3 + ÃÕÊ Ê 0 0 ôêêã ËÁ Find the L.C.M. of the epressions 3 + and Ê appleπëÿ ÁflÁœ apple ÁŸêŸ Ë UáÊ ÁŸ Êÿ Êapple U ËÁ + y = 4, = y. Solve the following system of equations graphically : + y = 4, = y.. ŒÊapple ÅÿÊ Êapple Ê ÿêappleª 48 ÒU ÃÕÊ UŸ Ê ªÈáÊŸ» 43 ÒU ÅÿÊ ôêêã ËÁ The sum of two numbers is 48 and their product is 43. Find the numbers.. ÁŸêŸÁ ÁπÃ Ê «UÊapple apple fl 000 Êapple ÊœÊ U ÊŸÃapple ÈU fl 005 apple Á ÁŸflÊ U πø Íø Ê ôêêã ËÁ ÊòÊÊ Áà Á ª Ê ÍÀÿ ( L ÿêapple apple ) flsãè ( Á ª Ê apple ) fl 000 fl 005 A B C D E F S 09 Maths. I S [ Turn over

6 6 Taking 000 as base year, find the cost of living inde for the year 005 from the following data : Quantity Per kg price ( in Rs. ) Items ( in kg ) Year 000 Year 005 A B C D E F Í U 3,400 L ÿapple ŸªŒ ÿê,000 L ÿapple Ãà Ê ŒÊÿªË ÊÒ U Êapple UÊÁ Ê ÃËŸ ÊŸ flêá Á SÃÊapple apple U éœ ÒU Á àÿapple Á Sà apple ÊÕ Êapple UÊÁ Ê U 9% flêá ÊœÊ UáÊ éÿê apple éÿê Œappleÿ ÒU ÿᜠŸË Á Sà ÿêapple ŸÊ apple Í U π UËŒÃÊ ÒU, ÃÊapple U apple ŸªŒ ÍÀÿ apple Á ÃŸË UÊÁ Ê Áœ ŒappleŸË «UÃË ÒU? ÕflÊ ÿáq ø flîáh éÿê U È U UÊÁ Ê UœÊ U appleãê ÒU, Á apple fl U ÃËŸ ÊŸ flêá Á SÃÊapple apple ÊÒ UÊÃÊ ÒU ÿᜠø flîáh éÿê Ë Œ U 0% UÊapple ÃÕÊ àÿapple Á SÃ Ë UÊÁ Ê,33 L ÿapple UÊapple, ÃÊapple UœÊ U Ë ªß Í UÊÁ Ê ôêêã ËÁ A cooler is available on a cash payment of Rs. 3,400 or a cash down payment of Rs.,000 and the remaining amount is to be paid in three equal yearly instalments. A simple interest at 9% per annum on the remaining amount is to be paid along with each instalment. If Manish purchases a cooler under instalment scheme, what amount he pays in ecess of the cost price of the cooler? OR A person borrows some money on compound interest and returns it in three equal annual instalments. If the rate of compound interest is 0% and the amount of each instalment is Rs.,33, then find the principal amount borrowed Á ßapple Áà Êà ø flîáh éÿê Ë Œ U apple 8,000 L ÿapple Ê 3 fl Ê éÿê,6 L ÿapple UÊapple ÊÿappleªÊ, Á éÿê flêá Œappleÿ ÒU? At what rate of compound interest will the interest on Rs. 8,000 for 3 years be Rs.,6, when the interest is payable annually? 3 S 09 Maths. I S

7 7 5. ŒÊapple Uê ËŒflÊ U A fl B ÿêfl ÊÁÿ ÊÚ apple apple flapple Ê appleuãè ÁflÁ ÛÊ Áfl ÿêapple apple ÁŸêŸÊŸÈ Ê U Ê# UÃapple Ò U, Á Ÿ apple Ê U ÊÕ apple ÁŒ ªÿapple Ò U 0 0 Áfl ÿ A apple B apple Ê U. ª apple Ë ªÁáÊà ÊÒÁà ÁflôÊÊŸ U ÊÿŸ ÁflôÊÊŸ ÊÁ Uà Êäÿ ôêêã U ÃÊßÿapple Á U A ÊÒ U B apple apple ÊÒŸ Áœ ÿêappleçÿ ÒU ÕflÊ ÁŸêŸ Ê Uê Ê UÃÊ UŸ Ë ÊÁäÿ Ê ôêêã ËÁ flª à UÊ f i For admission to a professional college, the marks obtained by two candidates A and B, in different subjects are given below, with the weightage of each subject is given : S. No. Subjects Marks of A Marks of B Weightage. English Mathematics Physics Chemistry By calculating the weightage mean, state who of A and B is more suitable. 3 OR Find the median of the following frequency distribution : 3 Class-interval f i ÁŸêŸ Ê Uê Ê UÃÊ UŸ Ê Êäÿ Áflø Ÿ ôêêã ËÁ flª Ê Uê Ê UÃÊ Find the mean deviation of the following distribution : 3 Class Frequency S 09 Maths. I S [ Turn over