Page 1 1JD39IH ?????? ??? ? â€“ I, 2016-17 SUMMATIVE ASSESSMENT â€“ I, 2016 â€“ 17 ???? / MATHEMATICS ? ? â€“ X / CLASS â€“ X ?????? ???:3 ?? ?????? ???:90 Time Allowed : 3 hours Maximum Marks: 90 ???? ???? : 1. ??? ?????? ? | 2. ?? ? ? 31 ?, ?? ??? ??? ?, ?, ? ??? ? ? ????? ??? ?? | ?- ? ? 4 ? ???? ?? 1 ??? ?? ??; ?-? ? 6 ? ???? ?? ?? 2 ??? ??; ?-? ? 10 ? ???? ?? ?? 3 ??? ?; ??? ?-? ? 11 ? ???? ?? ?? 4 ??? ? | 3. ?? ? ? ??? ??? ???? ?? | 4. ????????? ?? ??? ???$? ?? | General Instructions: 1. All questions are compulsory. 2. The question paper consists of 31 questions divided into four sections A, B, C and D. Sectionâ€“A comprises of 4 questions of 1 mark each; Section- B comprises of 6 questions of 2 marks each; Sectionâ€“C comprises of 10 questions of 3 marks each and Sectionâ€“D comprise of 11 questions of 4 marks each. 3. There is no overall choice in this question paper. 4. Use of calculator is not permitted. ? - ? / SECTION â€“ A ??%? 1 ?? 4 ? ?? 1 ??? ?? | Question numbers 1 to 4 carry one mark each. 1. ? ??? PQR ?, ?????? PQ ??? PR ?? (??? ??+?? S ??? T ?? ??? -.?? ? ?? ST||OR ? | ??? PS=4 cm, PQ=9 cm ??? PR=4.5 cm ??, ?? PT /?? ????? | In PQR, ? S and T are points on the sides PQ and PR respectively such that ST||QR. If PS = 4cm, PQ = 9cm and PR = 4.5cm, then find PT. 2. cosec48 o + tan88 o ?? 0 o ?? 45 o ?? ??? ?? ????? ?? tâ€“???????? ?? ???? ? 34 ????? | Express cosec48 o + tan88 o in terms of t â€“ ratios of angles between 0 o and 45 o . 3. ??? ? ?? ??? 0 o ?? 90 o ?? ???? ??, ?? sin? ?? ??? ?? 6? ???? ??? Page 2 1JD39IH ?????? ??? ? â€“ I, 2016-17 SUMMATIVE ASSESSMENT â€“ I, 2016 â€“ 17 ???? / MATHEMATICS ? ? â€“ X / CLASS â€“ X ?????? ???:3 ?? ?????? ???:90 Time Allowed : 3 hours Maximum Marks: 90 ???? ???? : 1. ??? ?????? ? | 2. ?? ? ? 31 ?, ?? ??? ??? ?, ?, ? ??? ? ? ????? ??? ?? | ?- ? ? 4 ? ???? ?? 1 ??? ?? ??; ?-? ? 6 ? ???? ?? ?? 2 ??? ??; ?-? ? 10 ? ???? ?? ?? 3 ??? ?; ??? ?-? ? 11 ? ???? ?? ?? 4 ??? ? | 3. ?? ? ? ??? ??? ???? ?? | 4. ????????? ?? ??? ???$? ?? | General Instructions: 1. All questions are compulsory. 2. The question paper consists of 31 questions divided into four sections A, B, C and D. Sectionâ€“A comprises of 4 questions of 1 mark each; Section- B comprises of 6 questions of 2 marks each; Sectionâ€“C comprises of 10 questions of 3 marks each and Sectionâ€“D comprise of 11 questions of 4 marks each. 3. There is no overall choice in this question paper. 4. Use of calculator is not permitted. ? - ? / SECTION â€“ A ??%? 1 ?? 4 ? ?? 1 ??? ?? | Question numbers 1 to 4 carry one mark each. 1. ? ??? PQR ?, ?????? PQ ??? PR ?? (??? ??+?? S ??? T ?? ??? -.?? ? ?? ST||OR ? | ??? PS=4 cm, PQ=9 cm ??? PR=4.5 cm ??, ?? PT /?? ????? | In PQR, ? S and T are points on the sides PQ and PR respectively such that ST||QR. If PS = 4cm, PQ = 9cm and PR = 4.5cm, then find PT. 2. cosec48 o + tan88 o ?? 0 o ?? 45 o ?? ??? ?? ????? ?? tâ€“???????? ?? ???? ? 34 ????? | Express cosec48 o + tan88 o in terms of t â€“ ratios of angles between 0 o and 45 o . 3. ??? ? ?? ??? 0 o ?? 90 o ?? ???? ??, ?? sin? ?? ??? ?? 6? ???? ??? What happens to value of sin? when ? increase from 0 o top 90 o . 4. ?? ??????? ????? ?? ??? ???? 9?, ?????? ?? ??<? /?? ????? ???? ?9?? = 12.4 ?? ??< = 10.5 ???? ?? | Find median of the data, using an empirical relation when it is given that mode = 12.4 and mean = 10.5. ? â€“ ? / SECTION B ??%? 5 ?? 10 ? ?? ?? 2 ??? ? | Question numbers 5 to 10 carry two marks each. 5. ???$?? ?? ??? ???=? ???? ????A? ?? B? 4q+1 ?? 4q+3 ?? B? ?? ???? ??, ???? q ??? ???=? ????A? ?? | Show that any positive odd integer is of the form 4q + 1 or 4q + 3, where q is some positive integer. 6. ??C ????? ?? 3 2 4 ?? ??D???? ??%? ?? | Prove that 3 2 4 is an irrational number. 7. /?? ????? ?? ??E ????? ?????? ??G ?? ??H??? ???????? ??? ?????? ?? ??+?? ?? ??I?? ???? ?, ?????? ? ???? ?????? ?: 2x â€“ 3y + 6 = 0 4x â€“ 5y + 2 = 0 Find whether the lines representing the following pair of linear equations intersect at a point are parallel or coincident: 2x â€“ 3y + 6 = 0 4x â€“ 5y + 2 = 0 8. ????? ?, AD /?? ?????, AB = BC = 1cm ??? CD = 2cm ?? | In the figure, find AD if AB = BC = 1cm CD = 2cm. Page 3 1JD39IH ?????? ??? ? â€“ I, 2016-17 SUMMATIVE ASSESSMENT â€“ I, 2016 â€“ 17 ???? / MATHEMATICS ? ? â€“ X / CLASS â€“ X ?????? ???:3 ?? ?????? ???:90 Time Allowed : 3 hours Maximum Marks: 90 ???? ???? : 1. ??? ?????? ? | 2. ?? ? ? 31 ?, ?? ??? ??? ?, ?, ? ??? ? ? ????? ??? ?? | ?- ? ? 4 ? ???? ?? 1 ??? ?? ??; ?-? ? 6 ? ???? ?? ?? 2 ??? ??; ?-? ? 10 ? ???? ?? ?? 3 ??? ?; ??? ?-? ? 11 ? ???? ?? ?? 4 ??? ? | 3. ?? ? ? ??? ??? ???? ?? | 4. ????????? ?? ??? ???$? ?? | General Instructions: 1. All questions are compulsory. 2. The question paper consists of 31 questions divided into four sections A, B, C and D. Sectionâ€“A comprises of 4 questions of 1 mark each; Section- B comprises of 6 questions of 2 marks each; Sectionâ€“C comprises of 10 questions of 3 marks each and Sectionâ€“D comprise of 11 questions of 4 marks each. 3. There is no overall choice in this question paper. 4. Use of calculator is not permitted. ? - ? / SECTION â€“ A ??%? 1 ?? 4 ? ?? 1 ??? ?? | Question numbers 1 to 4 carry one mark each. 1. ? ??? PQR ?, ?????? PQ ??? PR ?? (??? ??+?? S ??? T ?? ??? -.?? ? ?? ST||OR ? | ??? PS=4 cm, PQ=9 cm ??? PR=4.5 cm ??, ?? PT /?? ????? | In PQR, ? S and T are points on the sides PQ and PR respectively such that ST||QR. If PS = 4cm, PQ = 9cm and PR = 4.5cm, then find PT. 2. cosec48 o + tan88 o ?? 0 o ?? 45 o ?? ??? ?? ????? ?? tâ€“???????? ?? ???? ? 34 ????? | Express cosec48 o + tan88 o in terms of t â€“ ratios of angles between 0 o and 45 o . 3. ??? ? ?? ??? 0 o ?? 90 o ?? ???? ??, ?? sin? ?? ??? ?? 6? ???? ??? What happens to value of sin? when ? increase from 0 o top 90 o . 4. ?? ??????? ????? ?? ??? ???? 9?, ?????? ?? ??<? /?? ????? ???? ?9?? = 12.4 ?? ??< = 10.5 ???? ?? | Find median of the data, using an empirical relation when it is given that mode = 12.4 and mean = 10.5. ? â€“ ? / SECTION B ??%? 5 ?? 10 ? ?? ?? 2 ??? ? | Question numbers 5 to 10 carry two marks each. 5. ???$?? ?? ??? ???=? ???? ????A? ?? B? 4q+1 ?? 4q+3 ?? B? ?? ???? ??, ???? q ??? ???=? ????A? ?? | Show that any positive odd integer is of the form 4q + 1 or 4q + 3, where q is some positive integer. 6. ??C ????? ?? 3 2 4 ?? ??D???? ??%? ?? | Prove that 3 2 4 is an irrational number. 7. /?? ????? ?? ??E ????? ?????? ??G ?? ??H??? ???????? ??? ?????? ?? ??+?? ?? ??I?? ???? ?, ?????? ? ???? ?????? ?: 2x â€“ 3y + 6 = 0 4x â€“ 5y + 2 = 0 Find whether the lines representing the following pair of linear equations intersect at a point are parallel or coincident: 2x â€“ 3y + 6 = 0 4x â€“ 5y + 2 = 0 8. ????? ?, AD /?? ?????, AB = BC = 1cm ??? CD = 2cm ?? | In the figure, find AD if AB = BC = 1cm CD = 2cm. 9. ??? 1 cos(A+B) sin(A-B) 2 = = ?, ?? A ?? B /?? ?????, ???? ???? ??? ?? ?? A + B ?? A â€“ B K?? ??? ? | If 1 cos(A+B) sin(A-B), 2 = = then find A and B, when it is given that A + B and A â€“ B are acute angles. 10. ???? ?? ????? ????????? ???? ???? ??? ?? | ???? ???? ?? ?????? ????????? ???? ????? | x Cf 600 ?? ?? 60 500 ?? ?? 58 400 ?? ?? 54 300 ?? ?? 35 200 ?? ?? 22 100 ?? ?? 10 Given below is a cumulative frequency distribution. Corresponding to it, make an ordinary frequency distribution. x Cf Below 600 60 Below 500 58 Below 400 54 Below 300 35 Below 200 22 Below 100 10 ? - ? / SECTION C ??%? 11 ?? 20 ? ?? ?? 3 ??? ?? | Question numbers 11 to 20 carry three marks each. 11. 306 ?? 657 ?? HCF /?? ????? | HCF ?? ????? ???? ???? LCM ?? /?? ????? | Find HCF of 306 and 657. Also find their LCM using their HCF. Page 4 1JD39IH ?????? ??? ? â€“ I, 2016-17 SUMMATIVE ASSESSMENT â€“ I, 2016 â€“ 17 ???? / MATHEMATICS ? ? â€“ X / CLASS â€“ X ?????? ???:3 ?? ?????? ???:90 Time Allowed : 3 hours Maximum Marks: 90 ???? ???? : 1. ??? ?????? ? | 2. ?? ? ? 31 ?, ?? ??? ??? ?, ?, ? ??? ? ? ????? ??? ?? | ?- ? ? 4 ? ???? ?? 1 ??? ?? ??; ?-? ? 6 ? ???? ?? ?? 2 ??? ??; ?-? ? 10 ? ???? ?? ?? 3 ??? ?; ??? ?-? ? 11 ? ???? ?? ?? 4 ??? ? | 3. ?? ? ? ??? ??? ???? ?? | 4. ????????? ?? ??? ???$? ?? | General Instructions: 1. All questions are compulsory. 2. The question paper consists of 31 questions divided into four sections A, B, C and D. Sectionâ€“A comprises of 4 questions of 1 mark each; Section- B comprises of 6 questions of 2 marks each; Sectionâ€“C comprises of 10 questions of 3 marks each and Sectionâ€“D comprise of 11 questions of 4 marks each. 3. There is no overall choice in this question paper. 4. Use of calculator is not permitted. ? - ? / SECTION â€“ A ??%? 1 ?? 4 ? ?? 1 ??? ?? | Question numbers 1 to 4 carry one mark each. 1. ? ??? PQR ?, ?????? PQ ??? PR ?? (??? ??+?? S ??? T ?? ??? -.?? ? ?? ST||OR ? | ??? PS=4 cm, PQ=9 cm ??? PR=4.5 cm ??, ?? PT /?? ????? | In PQR, ? S and T are points on the sides PQ and PR respectively such that ST||QR. If PS = 4cm, PQ = 9cm and PR = 4.5cm, then find PT. 2. cosec48 o + tan88 o ?? 0 o ?? 45 o ?? ??? ?? ????? ?? tâ€“???????? ?? ???? ? 34 ????? | Express cosec48 o + tan88 o in terms of t â€“ ratios of angles between 0 o and 45 o . 3. ??? ? ?? ??? 0 o ?? 90 o ?? ???? ??, ?? sin? ?? ??? ?? 6? ???? ??? What happens to value of sin? when ? increase from 0 o top 90 o . 4. ?? ??????? ????? ?? ??? ???? 9?, ?????? ?? ??<? /?? ????? ???? ?9?? = 12.4 ?? ??< = 10.5 ???? ?? | Find median of the data, using an empirical relation when it is given that mode = 12.4 and mean = 10.5. ? â€“ ? / SECTION B ??%? 5 ?? 10 ? ?? ?? 2 ??? ? | Question numbers 5 to 10 carry two marks each. 5. ???$?? ?? ??? ???=? ???? ????A? ?? B? 4q+1 ?? 4q+3 ?? B? ?? ???? ??, ???? q ??? ???=? ????A? ?? | Show that any positive odd integer is of the form 4q + 1 or 4q + 3, where q is some positive integer. 6. ??C ????? ?? 3 2 4 ?? ??D???? ??%? ?? | Prove that 3 2 4 is an irrational number. 7. /?? ????? ?? ??E ????? ?????? ??G ?? ??H??? ???????? ??? ?????? ?? ??+?? ?? ??I?? ???? ?, ?????? ? ???? ?????? ?: 2x â€“ 3y + 6 = 0 4x â€“ 5y + 2 = 0 Find whether the lines representing the following pair of linear equations intersect at a point are parallel or coincident: 2x â€“ 3y + 6 = 0 4x â€“ 5y + 2 = 0 8. ????? ?, AD /?? ?????, AB = BC = 1cm ??? CD = 2cm ?? | In the figure, find AD if AB = BC = 1cm CD = 2cm. 9. ??? 1 cos(A+B) sin(A-B) 2 = = ?, ?? A ?? B /?? ?????, ???? ???? ??? ?? ?? A + B ?? A â€“ B K?? ??? ? | If 1 cos(A+B) sin(A-B), 2 = = then find A and B, when it is given that A + B and A â€“ B are acute angles. 10. ???? ?? ????? ????????? ???? ???? ??? ?? | ???? ???? ?? ?????? ????????? ???? ????? | x Cf 600 ?? ?? 60 500 ?? ?? 58 400 ?? ?? 54 300 ?? ?? 35 200 ?? ?? 22 100 ?? ?? 10 Given below is a cumulative frequency distribution. Corresponding to it, make an ordinary frequency distribution. x Cf Below 600 60 Below 500 58 Below 400 54 Below 300 35 Below 200 22 Below 100 10 ? - ? / SECTION C ??%? 11 ?? 20 ? ?? ?? 3 ??? ?? | Question numbers 11 to 20 carry three marks each. 11. 306 ?? 657 ?? HCF /?? ????? | HCF ?? ????? ???? ???? LCM ?? /?? ????? | Find HCF of 306 and 657. Also find their LCM using their HCF. 12. ??? ?9?? 3 2 6 6 x x x k - + + , ?9?? x- 3 ?? ???$??? ??? ?? ??? ?? k ?? ??? /?? ?????| If 3 2 6 6 x x x k - + + is completely divisible by x- 3, then find the value of k. 13. ?M???? ?9?? 2 6 9 x x + + ?? ??K? ??? a ??? ß ??? ?? ?M???? ?9?? /?? ????? ????? ??K? a - ??? ß - ? | If a and ß are zeroes of a polynomial 2 6 9, x x + + then form a polynomial whose zeroes are a - and . ß - 14. ??E ??-?? ?????? ??G ?? ?O-???? ???? ?? ?? ?????: x + 2y = 2 x â€“ 3y = 7 Solve the following pair of linear equations by the cross multiplication method: x + 2y = 2 x â€“ 3y = 7 15. ABC ? ?? ????? ? ??? ??, ???? 90 o B ? = ?? | AB ??? BC ?? (??? ?? ??+?? D ??? E -.?? ? | ??C ????? ?? 2 2 2 2 AE CD AC DE + = + ?? | ABC ? is a right angled triangle in which 90 . o B ? = D and E are any points on AB and BC respectively. Prove that 2 2 2 2 . AE CD AC DE + = + 16. ?? ? ABC ? ?? ????9 ? ??? ??, ????? ?? ???? x ???? ?? ?? | ???? ?? BC ?? ?? ????? P ?? Q ?? ??? ? ?? PB = BC = CQ ?? | ??C ????? ?? (a) PQ PA PA PB = (b) 2 2 3 PA x = In given figure ABC ? is an equilateral triangle, whose each side measure x units. P and Q are two points on BC produced such that PB = BC = CQ. Page 5 1JD39IH ?????? ??? ? â€“ I, 2016-17 SUMMATIVE ASSESSMENT â€“ I, 2016 â€“ 17 ???? / MATHEMATICS ? ? â€“ X / CLASS â€“ X ?????? ???:3 ?? ?????? ???:90 Time Allowed : 3 hours Maximum Marks: 90 ???? ???? : 1. ??? ?????? ? | 2. ?? ? ? 31 ?, ?? ??? ??? ?, ?, ? ??? ? ? ????? ??? ?? | ?- ? ? 4 ? ???? ?? 1 ??? ?? ??; ?-? ? 6 ? ???? ?? ?? 2 ??? ??; ?-? ? 10 ? ???? ?? ?? 3 ??? ?; ??? ?-? ? 11 ? ???? ?? ?? 4 ??? ? | 3. ?? ? ? ??? ??? ???? ?? | 4. ????????? ?? ??? ???$? ?? | General Instructions: 1. All questions are compulsory. 2. The question paper consists of 31 questions divided into four sections A, B, C and D. Sectionâ€“A comprises of 4 questions of 1 mark each; Section- B comprises of 6 questions of 2 marks each; Sectionâ€“C comprises of 10 questions of 3 marks each and Sectionâ€“D comprise of 11 questions of 4 marks each. 3. There is no overall choice in this question paper. 4. Use of calculator is not permitted. ? - ? / SECTION â€“ A ??%? 1 ?? 4 ? ?? 1 ??? ?? | Question numbers 1 to 4 carry one mark each. 1. ? ??? PQR ?, ?????? PQ ??? PR ?? (??? ??+?? S ??? T ?? ??? -.?? ? ?? ST||OR ? | ??? PS=4 cm, PQ=9 cm ??? PR=4.5 cm ??, ?? PT /?? ????? | In PQR, ? S and T are points on the sides PQ and PR respectively such that ST||QR. If PS = 4cm, PQ = 9cm and PR = 4.5cm, then find PT. 2. cosec48 o + tan88 o ?? 0 o ?? 45 o ?? ??? ?? ????? ?? tâ€“???????? ?? ???? ? 34 ????? | Express cosec48 o + tan88 o in terms of t â€“ ratios of angles between 0 o and 45 o . 3. ??? ? ?? ??? 0 o ?? 90 o ?? ???? ??, ?? sin? ?? ??? ?? 6? ???? ??? What happens to value of sin? when ? increase from 0 o top 90 o . 4. ?? ??????? ????? ?? ??? ???? 9?, ?????? ?? ??<? /?? ????? ???? ?9?? = 12.4 ?? ??< = 10.5 ???? ?? | Find median of the data, using an empirical relation when it is given that mode = 12.4 and mean = 10.5. ? â€“ ? / SECTION B ??%? 5 ?? 10 ? ?? ?? 2 ??? ? | Question numbers 5 to 10 carry two marks each. 5. ???$?? ?? ??? ???=? ???? ????A? ?? B? 4q+1 ?? 4q+3 ?? B? ?? ???? ??, ???? q ??? ???=? ????A? ?? | Show that any positive odd integer is of the form 4q + 1 or 4q + 3, where q is some positive integer. 6. ??C ????? ?? 3 2 4 ?? ??D???? ??%? ?? | Prove that 3 2 4 is an irrational number. 7. /?? ????? ?? ??E ????? ?????? ??G ?? ??H??? ???????? ??? ?????? ?? ??+?? ?? ??I?? ???? ?, ?????? ? ???? ?????? ?: 2x â€“ 3y + 6 = 0 4x â€“ 5y + 2 = 0 Find whether the lines representing the following pair of linear equations intersect at a point are parallel or coincident: 2x â€“ 3y + 6 = 0 4x â€“ 5y + 2 = 0 8. ????? ?, AD /?? ?????, AB = BC = 1cm ??? CD = 2cm ?? | In the figure, find AD if AB = BC = 1cm CD = 2cm. 9. ??? 1 cos(A+B) sin(A-B) 2 = = ?, ?? A ?? B /?? ?????, ???? ???? ??? ?? ?? A + B ?? A â€“ B K?? ??? ? | If 1 cos(A+B) sin(A-B), 2 = = then find A and B, when it is given that A + B and A â€“ B are acute angles. 10. ???? ?? ????? ????????? ???? ???? ??? ?? | ???? ???? ?? ?????? ????????? ???? ????? | x Cf 600 ?? ?? 60 500 ?? ?? 58 400 ?? ?? 54 300 ?? ?? 35 200 ?? ?? 22 100 ?? ?? 10 Given below is a cumulative frequency distribution. Corresponding to it, make an ordinary frequency distribution. x Cf Below 600 60 Below 500 58 Below 400 54 Below 300 35 Below 200 22 Below 100 10 ? - ? / SECTION C ??%? 11 ?? 20 ? ?? ?? 3 ??? ?? | Question numbers 11 to 20 carry three marks each. 11. 306 ?? 657 ?? HCF /?? ????? | HCF ?? ????? ???? ???? LCM ?? /?? ????? | Find HCF of 306 and 657. Also find their LCM using their HCF. 12. ??? ?9?? 3 2 6 6 x x x k - + + , ?9?? x- 3 ?? ???$??? ??? ?? ??? ?? k ?? ??? /?? ?????| If 3 2 6 6 x x x k - + + is completely divisible by x- 3, then find the value of k. 13. ?M???? ?9?? 2 6 9 x x + + ?? ??K? ??? a ??? ß ??? ?? ?M???? ?9?? /?? ????? ????? ??K? a - ??? ß - ? | If a and ß are zeroes of a polynomial 2 6 9, x x + + then form a polynomial whose zeroes are a - and . ß - 14. ??E ??-?? ?????? ??G ?? ?O-???? ???? ?? ?? ?????: x + 2y = 2 x â€“ 3y = 7 Solve the following pair of linear equations by the cross multiplication method: x + 2y = 2 x â€“ 3y = 7 15. ABC ? ?? ????? ? ??? ??, ???? 90 o B ? = ?? | AB ??? BC ?? (??? ?? ??+?? D ??? E -.?? ? | ??C ????? ?? 2 2 2 2 AE CD AC DE + = + ?? | ABC ? is a right angled triangle in which 90 . o B ? = D and E are any points on AB and BC respectively. Prove that 2 2 2 2 . AE CD AC DE + = + 16. ?? ? ABC ? ?? ????9 ? ??? ??, ????? ?? ???? x ???? ?? ?? | ???? ?? BC ?? ?? ????? P ?? Q ?? ??? ? ?? PB = BC = CQ ?? | ??C ????? ?? (a) PQ PA PA PB = (b) 2 2 3 PA x = In given figure ABC ? is an equilateral triangle, whose each side measure x units. P and Q are two points on BC produced such that PB = BC = CQ. Prove that (a) PQ PA PA PB = (b) 2 2 3 PA x = 17. ??? 5 cosec = 3 ? ??, ?? ??? ??????? : 4sec 2tan 5sin 20cos 3cosec +9cot ? ? ? ? ? ? - + - If 5 cosec = , 3 ? evaluate: 4sec 2tan 5sin 20cos 3cosec +9cot ? ? ? ? ? ? - + - 18. ??C ????? ?? : (1 + tan A + cot A). (sin A â€“ cos B) = sin A. tan B â€“ cot A. cos B Prove that: (1 + tan A + cot A). (sin A â€“ cos B) = sin A. tan B â€“ cot A. cos B 19. ?? ?P? ???? ?, ?? ??(??? ???-??? ??%? ???? ????? ?? ??S?? ? ?? ??? ??? ?? | ??E ????????? ???? ? ????T ????? ?? ??%? ???? ??S?? ?? ??%? ???$? ?? ?? : ?? ??S? ? ????? ?? ??%? 10-12 12-14 14-16 16-18 18-20 ??S?? ?? ??%? 12 25 13 10 20 ??-????? ???? ??, ?? ??S? ? ??? ?? ????? ?? ??%? ?? ??< /?? ????? | In a subji mandi, fruit vendors were selling apples on boxes, which carried varying number of apples. The following frequency distribution shows apples according to the number of boxes: No. of apples in a box 10-12 12-14 14-16 16-18 18-20 No. of boxes 12 25 13 10 20 Find the mean number of apples kept in a packing box, using step deviation method. 20. 50 ??U???$??? M??? ?V ????? ?? ??E??-?? ????????? ???? ?? ?9?? /?? ????? | ?V ??? 0-10 10-20 20-30 30-40 40-50 ??U???$??? ?? ??%? 5 12 20 10 3Read More

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