10. SECTION - B Question numbers 11 to 18 carry 2 marks each C1 P.T.O.
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1 C Class - X MATHEMATICS Time : to ½ hours Maximum Marks : 80 â Ø : âð ½ ƒæ ÅUð çï Ì : 80 General Instructions :. All questions are compulsory. Total No. of Pages : é Ü ÂëcÆUæð è â Øæ : 2. The question paper consists of 4 questions divided into four sections A, B, C and D. Section - A comprises of 0 questions of mark each, Section - B comprises of 8 questions of 2 marks each, Section - C comprises of 0 questions of marks each and Section - D comprises of 6 questions of 4 marks each.. Question numbers to 0 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 question of two marks, 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 5 minutes time has been allotted to read this question paper only. âæ æ Ø çùîðüàæ Ñ. âöè ÂýàÙ çùßæøü ãñ Ð 2. â ÂýàÙ- æ ð 4 ÂýàÙ ãñ, Áæð æúu ¹ ÇUæð ð, Õ, â ß Î ð çßöæçáì ãñð ¹ ÇU - ð 0 ÂýàÙ ãñ æñúu ÂýˆØð ÂýàÙ æ ãñ, ¹ ÇU - Õ ð 8 ÂýàÙ ãñ æñúu ÂýˆØð ÂýàÙ 2 æð ð ãñ, ¹ ÇU - â ð 0 ÂýàÙ ãñ æñúu ÂýˆØð ÂýàÙ æð æ ãñ, ¹ ÇU - Î ð 6 ÂýàÙ ãñ æñúu ÂýˆØð ÂýàÙ 4 æð æ ãñð. ÂýàÙ â Øæ âð 0 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 ÂýàÙ 2 æð ð, ÂýàÙ 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 5 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 P.T.O.
2 SECTION - A Question numbers to 0 are of mark each.. The decimal expansion of the rational number will terminate after : (A) one decimal place (B) two decimal places (C) three decimal place (D) more than decimal places 2. If the HCF of 65 and 7 is expressible in the form 65 m27, then the value of m is : (A) 4 (B) 2 (C) (D). The degree of the polynomial (x) (x 2 2x2x 4 ) is : (A) 2 (B) (C) 4 (D) 5 4. If a pair of linear equations is consistent, then the lines will be : (A) parallal (B) always coincident (C) intersecting or coincident (D) always intersecting. 5. A data has 25 observations (arranged in descending order). Which observation represents the median? (A) 2 th (B) th (C) 4 th (D) 5 th 6. If cosecu5 2, then 2(cosec2 ucot 2 u) is : (A) (B) 7 (C) 9 (D) 5 7. If sinusin 2 u5, the value of (cos 2 ucos 4 u) is : (A) (B) 2 (C) (D) 0 8. If DABC DDEF, BC54 cm, EF55 cm and ar (DABC)580 cm 2, the ar (DDEF) is : (A) 00 cm 2 (B) 25 cm 2 (C) 50 cm 2 (D) 200 cm C 2
3 9. In fig., if PS54 cm, the value of tan a is equal to : (A) 4 (B) 4 (C) 5 (D) 0. In fig. 2, if D is mid - point of BC, the value of o cot y o cot x is : (A) 2 (B) 4 (C) (D) 2 SECTION - B Question numbers to 8 carry 2 marks each.. Find the H.C.F of 455 and 84 using division algorithm. 2. Solve : 47xy56, x47y55. OR x 25y50, 2 x 2y C P.T.O.
4 . a, b are the roots of the quadratic polynomial p(x)5x 2 2(k26) x(2k). Find the value of k, if ab5ab. 4. If tanu , find the value of cosec VHF 2 2 cosec VHF. 5. Write the following distribution as less than type cumulative frequency distribution: C. I Frequency Find the modal class and the median class for the following distribution : C. I Frequency If the areas of two similar triangles are equal, prove that they are congruent. 8. From the given figure, find MLN. SECTION - C Question numbers 9 to 28 carry marks each. 9. Show that 52 is irrational. Show that 2 is irrational. OR C 4
5 20. Check whether 6 n can end with the digit zero for any natural number n. 2. If a, b are the two zeroes of the polynomial 25 p 2 25 p2, find a quadratic polynomial whose zeroes are 29 and 2:. 22. If A,B,C are interior angles of DABC, show that : cosec 2 B C 2 ¹ 2 tan 2 A 2 OR sec 2 ucot 2 (902u)52 cosec 2 (902u)2. 2. The sum of digits of a two digit number is. The number obtained by interchanging the digits of the given number exceeds that number by 6. Find the number. OR The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 0 km, the charge paid is Rs 05 and for a journey of 5 km, the charge paid Rs. 55. What are the fixed charges and the charge per km? 24. In fig (4), DPQR, right angled at Q, QR56 cm, QPR5608. Find the length of PQ and PR. 25. The mean of the following frequency distribution is 52. Find the missing frequency. C. I Frequency 5 4 f Find the mode of the following frequency distribution : C. I Frequency C 5 P.T.O.
6 27. In fig. 5, ABD is a triangle in which DAB5908and AC A BD. Prove that AD 2 5BDCD. 28. Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals. SECTION - D Question numbers 29 to 4 carry 4 marks each. 29. Solve the following system of equations graphically and find the vertices of the triangle bounded by these lines and the x-axis. 2x2y2450, x2y Draw more than ogive for the following frequency distribution and hence obtain the median C. I Frequency Prove the following : If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio. OR Prove that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. 2. Find all the zeroes of the polynomial x 4 x 29x 2 2x8, if two of its zeroes are, C 6
7 . Prove that cosmsinm 5cosecucotu. cosmsinm 4. If x5r sin A cosc, y5r sin A sin C, z5r cos A, prove that r 2 5x 2 y 2 z 2. OR Prove that cos A 5cosecAcotA. cos A - o 0 o C 7 P.T.O.
8 ¹ ÇU- ÂýàÙ â Øæ âð 0 Ì ÂýˆØð ÂýàÙ æ ãñð. ÂçÚU ðø â Øæ æ Îàæ Üß çßsìæúu âæ Ì ãæð»æ Ñ (A) Îàæ Üß ð ÕæÎÐ (B) Îæð Îàæ Üß ð ÕæÎÐ (C) ÌèÙ Îàæ Üß ð ÕæÎÐ (D) ÌèÙ ð çï Îàæ Üß ð ÕæÎÐ 2. ØçÎ 65 ÌÍæ 7 æ HCF 65 m - 7 ð M  ð ãñ Ìæð m æ æù ãñ Ñ (A) 4 (B) 2 (C) (D). ÕãéÂÎ (x) (x 2 2x2x 4 ) è ƒææì ãæð»è Ñ (A) 2 (B) (C) 4 (D) 5 4. ØçÎ ÚñUç¹ â è ÚU æ Øé â»ì ãæð Ìæð ÚðU¹æØð ãæð»è Ñ (A) â æùæ ÌÚU (B) ã ðàææ ÖØçÙcÅU (C) ÂýçÌ ÀðUÎè ÖØçÙcÅ (D) ã ðàææ ÂýçÌ ÀðUÎè æ Ç æð æð ƒæåuìð ãéøð ý ð ÚU¹æ»ØæÐ æñù âæ æ Ç æ æçšø æ æð Îàææü»æ? (A) 2 ßæ (B) ßæ (C) 4 ßæ (D) 5 ßæ 6. ØçÎ cosecu5 2, ÌÕ 2(cosec2 ucot 2 u) ãñ Ñ (A) (B) 7 (C) 9 (D) 5 7. ØçÎ sinusin 2 u5 Ìæð (cos 2 ucos 4 u) æ æù ãæð»æ Ñ (A) (B) 2 (C) (D) 0 8. ØçÎ DABC DDEF, BC54 âð. è., EF55 âð. è. ÿæð æè Ü (DABC)580 âð. è. 2 ÌÕ ÿæð æè Ü (DDEF) ãñ Ñ (A) 00 âð. è. 2 (B) 25 âð. è. 2 (C) 50 âð. è. 2 (D) 200 âð. è C 8
9 9. æ ë çì ð, ØçÎ PS54 âð. è. ãñ Ìæð tan a æ æù ãæð»æ Ñ (A) 4 (B) 4 (C) 5 (D) 0. æ ë çì 2 ð, D çõ Îé BC æ ŠØ çõ Îé ãñ o cot y o cot x æ æù ãæð»æ Ñ (A) 2 (B) 4 (C) (D) 2 ¹ ÇU-Õ ÂýàÙ â Øæ âð 8 Ì ÂýˆØð ÂýàÙ 2 æ ãñð. 455 ÌÍæ 84 æ HCF (.â.â.) çßöæáù Ë»æðçÚUÍ mæúuæ ææì èçá Ð 2. ãü ÚUæð 47xy56, x47y55. x 25y50, 2 x 2y50 Íßæ C 9 P.T.O.
10 . çmƒææì ÕãéÂÎ p(x)5x 2 2(k26) x(2k) ð àæê Ø a, b ãñ, Ìæð k æ æù ææì Úð U ØçÎ ab5ab ãæðð 4. ØçÎ tanu5 7 Ìæð æù ææì ÚUæð 2 2 cosec VHF 2 2 cosec VHF. 5. çù ÙçÜç¹Ì ÕæÚ UÕæÚUÌæ Õ ÅUÙ æ Òâð Âý æúu æó â Øè ÕæÚ UÕæÚUÌæ Õ ÅUÙ ÕÙæ ØðÐ Æ ãœr³á<íã ¼ÍÁ <¼ÍÁ<³Í çù ÙçÜç¹Ì ÕæÚ UÕæÚUÌæ Õ ÅUÙ æ ÕãéÜ ß»ü ÌÍæ æçšø æ ß»ü ææì èçá Ð Æ ãœr³á<íã ¼ÍÁ <¼ÍÁ<³Í ØçÎ Îæð â M  ç æöéáæð æ ÿæð æè Ü ÕÚUæÕÚU ãæð Ìæð çâh èçá ç ßð âßæz»â ãæð»ð Ð 8. æ ë çì Îð¹ ÚU MLN ææì èçáøðð C 0
11 ÂýàÙ â Øæ 9 âð 28 Ì ÂýˆØð ÂýàÙ æð æ ãñð 9. Îàææü Øð ç 52 ÂçÚU ðø â Øæ ãñð Îàææü Øð ç 2 ÂçÚU ðø â Øæ ãñð ¹ ÇU-â 20. Áæ èçá ç 6 n æ çßsìæúu àæê Ø ð â æœì ãæð»æ Áãæ n Âýæ ë Ì â Øæ ãñð Øæ 2. ØçÎ ÕãéÂÎ 25 p 2 25 p2 ð àæê Ø a, b ãæð Ìæð ßã çmƒææì ÕãéÂÎ ææì èçá çáâ ð àæê Ø ãæð Ð 29 ÌÍæ 2: 22. DABC ð A, B, C ÌÑ æð æ ãñð Îàææü Øð ç Ñ cosec 2 B C 2 ¹ 2tan 2 A 2 Øæ sec 2 ucot 2 (902u)52 cosec 2 (902u) æð âð ÕÙè â Øæ ð æð æ Øæð» ãñð â Øæ ð æð æð ÂÜÅUÙð âð ÕÙè ãé ü â Øæ ÂãÜè â Øæ âð 6 çï ãñð â Øæ ææì ÚUæðÐ Øæ Ù»ÚU ð ÅñU âè ð ÖæÇ ð ð çùøì ÖæÇ ð ð çìçúu Ì Üè» ü ÎêÚUè ÂÚU ÖæÇ æ âç çüì ç Øæ ÁæÌæ ãñð 0 ç. è. ÎêÚUè ð çüøð ÖæÇ æ 05 L. ãñ ÌÍæ 5 ç. è. ð çüøð ÖæÇ æ 55 L. ãñð çùøì ÖæÇ æ ÌÍæ ÂýçÌ ç. è. ÖæÇ æ Øæ ãñ? 24. æ ë çì 4 ð, DPQR ð Q â æð æ ãñð QR56 âð. è. QPR5608 Ìæð PQ ÌÍæ PR è Ü Õæ ü ææì ÚUæðÐ C P.T.O.
12 25. çù Ù ÕæÚ UÕæÚUÌæ âæúu æè æ æšø 52 ãñ, Ìæð ææì ÕæÚ UÕæÚUÌæ ææì èçáøðð Æ ãœr³á<íã ¼ÍÁ <¼ÍÁ<³Í 5 4 f çù Ù ÕæÚ UÕæÚUÌæ Õ ÅUÙ æ ÕãéÜ ææì ÚUæðÐ Æ ãœr³á<íã ¼ÍÁ <¼ÍÁ<³Í æ ë çì 5 ð, DABD ð, DAB5908 ãñ, ÌÍæ ACA BD çâh èçá Ñ AD 2 5BDCD. 28. çâh èçá ç ç âè â ÌéÖéüÁ ð ÖéÁæ ÂÚU ÕÙð ß»æðZ æ Øæð» â ð çß æü ÂÚU ÕÙð ãéøð ß»æðZ ð Øæð» ð ÕÚUæÕÚU ãæðìæ ãñð ÂýàÙ â Øæ 29 âð 4 Ì ÂýˆØð ÂýàÙ 4 æð æ ãñð ¹ ÇU-Î 29. çù Ù â è ÚU ææð æð»ýæè mæúuæ ãü èçá ÌÍæ x - ÿæ ß ÎæðÙæð ÚðU¹æ æð âð ÕÙð ãéøð ç æöéá ð àæèáü ð çùîðüàææ Öè ææì èçá Ð 2x2y2450, x2y çù Ù ÕæÚ UÕæÚUÌæ Õ ÅUÙ æ Òâð çï Âý æúu æó ÌæðÚU æ ¹è ç ÌÍæ ââð æçšø æ Öè ææì èçá Ð Æ ãœr³á<íã ¼ÍÁ <¼ÍÁ<³Í C 2
13 . çâh èçá, ØçÎ ç âè ç æöéá è ÖéÁæ ð â æ ÌÚU Ø Îæð ÖéÁæ æð æð çöóæ-çöóæ çõ Îé æð ÂÚU ÂýçÌ ÀðUÎ ÚUÙð ð çüøð ÚðU¹æ ¹è è ÁæØ Ìæð Øð Ø Îæð ÖéÁæ ãè ÙéÂæÌ ð çßöæçáì ãæð ÁæÌè ãñ Ð çâh èçá â æð æ ç æöéá ð æü æ ß»ü àæðá Ø Îæð ÖéÁæ æð ð ß»æðZ ð Øæð» ð ÕÚUæÕÚU ãæðìè ãñð Øæ 2. ÕãéÂÎ x 4 x 29x 2 2x8 ð âöè àæê Ø ææì ÚUæð ØçÎ â ð Îæð àæê Ø ÌÍæ ãæð Ð. çâh èçá cosmsinm 5cosecucotu. cosmsinm 4. ØçÎ x5r sin A cos C, y5r sin A sin C, z5r cos A, Ìæð çâh èçá r 2 5x 2 y 2 z 2. Øæ çâh èçá cos A 5cosecAcotA. cos A - o 0 o C P.T.O.
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