CBSE QUESTION PAPER CLASS-X. MATHEMATICS i1fu1a
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1 CBSE QUESTION PAPER CLASS-X MATHEMATICS i1fu1a Time : 3 to 3½ hours Maximum Marks : 80 çï Ì â Ø : 3 âð 3½ ƒæ ÅUð çï Ì : 80 Total No. of Pages : 14 é Ü ÂëcÆUæð è â Øæ : 14 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, 3 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 calculator 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 æ ð 34 ÂýàÙ ãñ, Áæð æúu ¹ ÇUæð ð, Õ, â ß Î ð çßöæçáì ãñð ¹ ÇU - ð 10 ÂýàÙ ãñ æñúu ÂýˆØð ÂýàÙ 1 æ ãñð ¹ ÇU - Õ ð 8 ÂýàÙ ãñ æñúu ÂýˆØð ÂýàÙ 2 æð ð ãñ Ð ¹ ÇU - â ð 10 ÂýàÙ ãñ æñúu ÂýˆØð ÂýàÙ 3 æð æ ãñð ¹ ÇU - Î ð 6 ÂýàÙ ãñ æñúu ÂýˆØð 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 Ë éùð Ð 4. â ð æð ü Öè âßæðüâçúu çß Ë Ùãè ãñ, Üðç Ù æ ÌçÚU çß Ë 1 ÂýàÙ 2 æð ð, 3 ÂýàÙ 3 æð ð æñúu 2 ÂýàÙ 4 æð ð çî» ãñ Ð æâ çî» çß ËÂæð ð âð çß Ë æ ØÙ Úð UÐ 5. ñ Ü é ÜðÅUÚU æ ÂýØæð» ßçÁüÌ ãñð 6. â ÂýàÙ- æ æð ÂÉ Ùð ð çü 15 ç ÙÅU æ â Ø çîøæ»øæ ãñð â ßçÏ ð ÎæñÚUæÙ ÀUæ æ ð ßÜ ÂýàÙ- æ æð ÂÉ ð»ð æñúu ßð žæúu-âéçsì æ ÂÚU æð ü žæúu Ùãè çü¹ð»ðð
2 SECTION - A Question numbers 1 to 10 carry one mark each : 1. Which of the following numbers has terminating decimal expansion? (A) (B) (C) (D) The value of p for which the polynomial x 3 14x 2 2px18 is exactly divisible by (x22) is (A) 0 (B) 3 (C) 5 (D) DABC and DPQR are similar triangles such that A=328 and R=658 then B is (A) 838 (B) 328 (C) 658 (D) In fig. 1, the value of the median of the data using the graph of ogive and more than ogive is (A) 5 (B) 40 (C) 80 (D) If u5458, the value of cosec 2 u is (A) 1 2 (B) 1 (C) 1 2 (D) 2 6. sin (6081u)2cos (3082u) is equal to (A) 2 cosu (B) 2 sinu (C) 0 (D) 1
3 7. The [HCF3LCM] for the numbers 50 and 20 is (A) 10 (B) 100 (C) 1000 (D) The value of k for which the pair of linear equations 4x16y2150 and 2x1ky2750 represents parallel lines is (A) k53 (B) k52 (C) k54 (D) k If sina1sin 2 A51, then the value of cos 2 A1cos 4 A is (A) 2 (B) 1 (C) 22 (D) The value of [(seca1tana) (12sinA)] is equal to (A) tan 2 A (B) sin 2 A (C) cosa (D) sina SECTION - B Question numbers 11 to 18 carry 2marks each. 11. Find a quadratic polynomial with zeroes 31 2 and In figure 2, ABCD is a parallelogram. Find the values of x and y. 13. If sec4a5cosec (A2208) where 4A is an acute angle, find the value of A. OR If 5 tanu=4, find the value of 5 sin M 3 cos M 5 sin M 2 cos M.
4 AQ AR 14. In figure 3, PQ??CD and PR??CB. Prove that. QD RB 15. In figure 4, two triangles ABC and DBC are on the same base BC in which A5 D5908. If CA and BD meet each other at E, show that AE3CE5BE3DE. 16. Check whether 6 n can end with the digit 0 for any natural number n? 17. Find the mean of the following frequency distribution : Class Frequency Find the mode of the following data : Class Frequency
5 SECTION - C Question number 19 to 28 carry 3 marks each. 19. Prove that 7 is an irrational number. OR Prove that 3+ 5 is an irrational number. 20. Use Euclid s division algorithm to find the HCF of and If a and b are zeroes of the quadratic polynomial x 2 26x1a; find the value of a if 3a+2b= Solve for x and y. y 8 4 x 3 3 x 3 y OR The sum of the numerator and the denominator of a fraction is 8. If 3 is added to both the numerator and the denominator, the fraction becoms 3. Find the fraction Prove that tan M cot M 2 2 tan M cot M sin M cos M. 24. In figure 5, DABC is right angled at B, BC57cm and AC2AB51cm. Find the value of cosa2sina.
6 25. In figure 6, P and Q are the midpoints of the sides CA and CB respectively of DABC right angled at C. Prove that 4 (AQ 2 1BP 2 )55AB The diagonals of a trapezium ABCD with AB?? DC intersect each other at point O. If AB52CD, find the ratio of the areas of triangles AOB and COD. 27. The mean of the following frequency distribution is 50. Find the value of p. Classes Frequency p Compute the median for the following cumulative frequency distribution : Weight in (kg) Number of students OR Find the missing frequencies in the following frequency distribution table, if N=100 and median is 32. Marks obtained Total No. of Students 10? 25 30?
7 SECTION - D Question number 29 to 34 carry 4 marks each. 29. Divide 30x 4 111x 3 282x 2 212x148 by (3x 2 +2x24) and verify the result by division algorithm. 30. If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, prove that the other two sides are divided in the same ratio. OR Prove that in a triangle if the square of one side is equal to the sum of the squares of the other two side then the angle opposite to the first side is a right angle. 31. Without using trigonometric tables, evaluate the following : sec 37 cosec 53 12cot 158 cot258 cot458 cot758 cot658-3 (sin2 188+sin 2 728) OR tan M cot M Prove that: 511secu cosecu. 1 cot M 1 tan M 32. If 2cosu2sinu5x and cosu23sinu5y. Prove that 2x 2 1y 2 22xy Check graphically whether the pair of linear equations 4x2y2850 and 2x23y1650 is consistent. Also, find the vertices of the triangle formed by these lines with the x-axis. 34. The following table shows the ages of 100 persons of a locality. Age (yrs) Number of persons o O o -
8 ÂýàÙ â Øæ 1 âð 10 ÂýˆØð ÂýàÙ 1 æ ãñð ¹ ÇU- 1. çù ÙçÜç¹Ì ð âð æñù âè â Øæ æ Îàæ Üß ÂýâæÚU âæ Ì ãæð»æ? (A) (B) (C) (D) p æ ßã æù çáâ ð çü ÕãéÂÎ x 3 14x 2 2px18, Âê æüìøæ çßöæçáì ãæð»æ (x22) âð, ãñ Ñ (A) 0 (B) 3 (C) 5 (D) DABC ÌÍæ DPQR â Âý æúu ð â M  ç æöéá ãñ ç A=328 ÌÍæ R=658 ãñ, Ìæð B æ æù ãñ Ñ (A) 838 (B) 328 (C) 658 (D) æ ë çì 1 ð, çî¹æ»øð ÒÒâð Âý æúuóó ð ÌæðÚU æ ÌÍæ Òâð çï Âý æúu ð ÌæðÚU æó ð æüð¹ âð æ Ç æð æ æšø ãñ Ñ (A) 5 (B) 40 (C) 80 (D) ØçÎ u5458 ãñ, Ìæð cosec 2 u æ æù ãñ Ñ (A) 1 2 (B) 1 (C) 1 2 (D) 2
9 6. sin (6081u)2cos (3082u) ÕÚUæÕÚU ãñ Ñ (A) 2cosu (B) 2sinu (C) 0 (D) 1 7. â Øæ æð 50 ÌÍæ 60 æ [HCF3LCM] ãñ Ñ (A) 10 (B) 100 (C) 1000 (D) k æ ßã æù çáâ ð çü ÚñUç¹ â è ÚU æ Øé 4x16y2150 ÌÍæ 2x1ky2750 â æ ÌÚU ÚðU¹æ ÎàææüÌð ãñ; (A) k53 (B) k52 (C) k54 (D) k ØçÎ sina1sin 2 A51 ãñ, Ìæð cos 2 A1cos 4 A æ æù ãñ Ñ (A) 2 (B) 1 (C) 22 (D) (seca1tana) (12sinA) æ æù ÕÚUæÕÚU ãñ Ñ (A) tan 2 A (B) sin 2 A (C) cosa (D) sina ¹ ÇU-Õ ÂýàÙ â Øæ 11 âð 18 Ì ÂýˆØð ÂýàÙ 2 æð æ ãñð 11. ßã çmƒææì ÕãéÂÎ ææì èçá çáâ ð àæê Ø 31 2 ÌÍæ 32 2 ãñð 12. æ ë çì 2 ð ABCD â æ ÌÚU ÌéÖéüÁ ãñð x ÌÍæ y ð æù ææì èçá Ð
10 13. ØçÎ sec4a5cosec (A2208), Áãæ 4A ØêÙ æð æ ãñ, Ìæð A æ æù ææì èçá Ð Íßæ ØçÎ 5 tanu54 Ìæð 5 sin M 3 cos M 5 sin M 2 cos M æ æù ææì èçá Ð 14. æ ë çì 3 ð, PQ??CD ÌÍæ PR??CB ãñð çâh èçá ç AQ AR. QD RB 15. æ ë çì 4 ð, Îæð ç æöéáð ABC ÌÍæ DBC ãè æïæúu BC ÂÚU ãñ çáù ð A5 D5908 ãñð ØçÎ CA ÌÍæ BD çõ Îé D ÂÚU ÂÚUSÂÚU ç ÜÌð ãñ, Ìæð Îàææü ç AE3CE5BE3DE. 16. Áæ èçá ç ç âè Âýæ ë Ì â Øæ n ð çü Øæ 6 n æ æ ü æ àæê Ø ãæð â Ìæ ãñ? 17. çù ÙçÜç¹Ì ÕæÚ UÕæÚUÌæ Õ ÅUÙ æ æšø ææì èçá Ð Æ ã ¼ÍÁ <¼ÍÁ<³Í
11 18. çù ÙçÜç¹Ì æ Ç æð æ ÕãéÜ ææì èçá Ð Æ ã ¼ÍÁ <¼ÍÁ<³Í ¹ ÇU-â ÂýàÙ â Øæ 19 âð 28 Ì ÂýˆØð ÂýàÙ 3 æð æ ãñð 19. çâh èçá ç 7 ÂçÚU ðø â Øæ ãñð Íßæ çâh èçá ç 3+ 5 ÂçÚU ðø â Øæ ãñð 20. Øêç ÜÇU ð çßöæáù Ü»æðçÚUÍ æ ÂýØæð» ÚU ð ÌÍæ 9648 æ HCF ææì èçá Ð 21. ØçÎ çmƒææì ÕãéÂÎ x 2 26x1a ð a ÌÍæ b àæê Ø ãñ, Ìæð a æ æù ææì èçá ØçÎ 3a+2b=20 ãñð 22. x ÌÍæ y ð çüøð ãü èçá Ñ y 8 4 x 3 3 x 3 y Íßæ çöóæ àæ ÌÍæ ãúu æ Øæð» 8 ãñð ØçÎ àæ ÌÍæ ãúu ÎæðÙæð ð ÌèÙ-ÌèÙ ÁæðÇ çîøæ Áæ, Ìæð çöóæ 3 4 ææì èçá Ð ãæð ÁæÌè ãñð çöóæ 23. çâh èçá ç tan M cot M 2 2 tan M cot M sin M cos M.
12 24. æ ë çì 5 ð, D ABC ð B ÂÚU â æð æ ãñ, BC57 âð. è. ÌÍæ AC2AB51 âð. è. ãñð cosa2sina æ æù ææì èçá Ð 25. æ ë çì 6 ð DABC â æð æ ç æöéá ãñ çáâ ð C ÂÚU â æð æ ãñ P ÌÍæ Q ý àæñ ÖéÁæ æð CA ÌÍæ CB ð ŠØ çõ Îé ãñ Ð çâh èçá ç Ñ 4 (AQ 2 1BP 2 )55AB â Ü Õ ABCD ð, çáâ ð AB??DC ãñ, ð çß æü ÎêâÚðU æð çõ Îé O ÂÚU ÂýçÌ ÀðUÎ ÚUÌð ãñ Ð ØçÎ AB52 CD ãñ, Ìæð DAOB ÌÍæ DCOD ð ÿæð æè Üæð ð ÙéÂæÌ ææì èçá Ð 27. çù ÙçÜç¹Ì ÕæÚ UÕæÚUÌæ Õ ÅUÙ æ æšø 50 ãñ Ìæð p æ æù ææì èçá Ð Æ ã ¼ÍÁ <¼ÍÁ<³Í p 19
13 28. çù ÙçÜç¹Ì â Øè ÕæÚ UÕæÚUÌæ Õ ÅUÙ æ æšø ææì èçá Ð ½ÍÁ<Ξ äí¾ 38 É ž ¾ 40 É ž ¾ 42 É ž ¾ 44 É ž ¾ 46 É ž ¾ 48 É ž ¾ 50 É ž ¾ 52 É ž ¾ ÎÆSÍÎ ã Í ž Ï É h Í Íßæ ØçÎ n=100 ÌÍæ æšø 32 ãñ Ìæð çù ÙçÜç¹Ì ÕæÚ UÕæÚUÌæ Õ ÅUÙ ð ÜéŒÌ ÕæÚ UÕæÚUÌæ ææì èçá Ð äís³í ž žð à ÎÆSÍÎ ã Í ž ÏÉ h Í 10? 25 30? ¹ ÇU-Î ÂýàÙ â Øæ 29 âð 34 Ì ÂýˆØð ÂýàÙ 4 æ ãñð 29. ÕãéÂÎ 30x 4 111x 3 282x 2 212x148 æð (3x 2 12x24) âð Öæ» ÎèçÁ ÌÍæ ÂçÚU ææ æ âˆøæâù çßöæáù Ë»æðçÚUÍ âð èçá Ð 30. ØçÎ ç âè ç æöéá è ÖéÁæ ð â æ ÌÚU Ø Îæð ÖéÁæ æð æð çöóæ çõ Îé æð ÂÚU ÂýçÌ ÀðUÎ ÚUÙð ð çü ÚðU¹æ ¹è è Áæ ; Ìæð çâh èçá ç ßã Ø Îæð ÖéÁæ æð æð ãè ÙéÂæÌ ð çßöæçáì ÚUÌè ãñð Íßæ ØçÎ ç âè ç æöéá ð ÖéÁæ æ ß»ü, Ø Îæð ÖéÁæ æð ð ß»æðZ ð Øæð» ð ÕÚUæÕÚU ãæð, Ìæð çâh èçá ç ÂãÜè ÖéÁæ ð âæ Ùð æ æð æ â æð æ ãæðìæ ãñð 31. ç æ æð æç ÌèØ ÌæçÜ æ æð ð ÂýØæð» çõùæ, çù ÙçÜç¹Ì æ æù ææì èçá Ñ sec 37 cosec 53 12cot 158 cot258 cot458 cot758 cot65823(sin2 1881sin 2 728) Íßæ çâh èçá ç tan M cot M 511sec u cosec u. 1 cot M 1 tan M
14 32. ØçÎ 2cosu2sinu5x ÌÍæ cosu23sinu5y ãñ Ìæð çâh èçá ç Ñ 2x 2 1y 2 22xy æüð¹ mæúuæ Áæ èçá ç Øæ ÚñUç¹ â è ÚU æ Øé 4x2y2850 ÌÍæ 2x23y1650 â»ì ãñ Ð Ù ÚðU¹æ æð ÌÍæ x - ÿæ mæúuæ çùç üì ç æöéá ð àæèáü ææì èçá Ð 34. çù Ù ÌæçÜ æ ç âè Üæ ð ð 100 ÃØç ÌØæð è æøé ÎàææüÌæ ãñ Ñ ÈºËÁÃÈÒ<¹Ò ºÉb ºÈÒ ÊÄ cºè ÂÚUæð Ì Õ ÅUÙ æð ÒÒâð Âý æúu ð ÓÓ Õ ÅUÙ ð ÕÎÜ ÚU â æ ÌæðÚU æ ¹è ç Ð
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