SECTION - A Question numbers 1 to 10 carry 1 mark each A2

Size: px

Start display at page:

Download "SECTION - A Question numbers 1 to 10 carry 1 mark each A2"

Eustace Hines
5 years ago
Views:

1 A Class - X MATHEMATICS Time : 3 to 3½ hours Maximum Marks : 80 â Ø : 3 âð 3½ ƒæ ÅUð çï Ì : 80 General Instructions : 1. All questions are compulsory. Total No. of Pages : 13 é Ü ÂëcÆUæð è â Øæ : 13. 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 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 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. â ÂýàÙ-Â 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 ãñ, ¹ ÇU - Õ ð 8 ÂýàÙ ãñ æñúu ÂýˆØð ÂýàÙ æð ð ãñ, ¹ ÇU - â ð 10 ÂýàÙ ãñ æñúu ÂýˆØð ÂýàÙ 3 æð æ ãñ, 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 ËÂ éùð Ð 4. â ð æð ü Öè âßæðüâçúu çß ËÂ Ùãè ãñ, Üðç Ù æ ÌçÚU çß ËÂ 1 ÂýàÙ æð ð, 3 ÂýàÙ 3 æð ð æñúu ÂýàÙ 4 æð ð çî» ãñ Ð æâ çî» çß ËÂæð ð âð çß ËÂ æ ØÙ Úð UÐ 5. ñ Ü é ÜðÅUÚU æ ÂýØæð» ßçÁüÌ ãñð 6. â ÂýàÙ-Â æ æð ÂÉ Ùð ð çü 15 ç ÙÅU æ â Ø çîøæ»øæ ãñð â ßçÏ ð ÎæñÚUæÙ ÀUæ æ ð ßÜ ÂýàÙ-Â æ æð ÂÉ ð»ð æñúu ßð žæúu-âéçsì æ ÂÚU æð ü žæúu Ùãè çü¹ð»ðð 1 P.T.O.

2 SECTION - A Question numbers 1 to 10 carry 1 mark each. 1. If sin u5cos(u68) where T and (u68) are both acute angles then the vlaue of u is : (A) 168 (B) 38 (C) 488 (D) 458. Given that cos 1 M the value of secm 1 tan M is : (A) 1 (B) (C) 1 (D) 0 3. In figure 1, AD53cm, BD54cm and CB51 cm them tan u equals : figure 1 (A) 3 4 (B) 5 1 (C) 4 3 (D) In figure, if DE??BC then x equals to : (A) 3 cm (B) 4 cm (C) 7 cm (D) 4.7 cm A

3 5. In figure 3, the graph of a polynomial p(x) is shown. The number of zeroes of p(x) is : figure 3 (A) 3 (B) 4 (C) 1 (D) 6. According to Euclid s division algorithms HCF of any two positive integers a and b with a > b is obtained by applying Euclid s division lemma to a and b to find q and r such that a5bq1r where r must satisfy. (A) 1 < r < b (B) 0 < r < b (C) 0 [ r < b (D) 0 < r [ b 7. The decimal expansion of will terminate after how many places of decimal? (A) 1 (B) (C) 3 (D) will not terminate 8. The pair of linear equations xy50 and 3x14y50 have : (A) One solution (B) Two solutions (C) Many solutions (D) No solution 9. If 13 seca cos ec B then 1 A B is equal to : (A) Zero (B) >908 (C) 908 (D) < For a given data with 40 observations the less than ogive and the more than ogive interest at (0.5,15). The median of the data is : (A) 5.5 (B) 0.5 (C) 15 (D) A 3 P.T.O.

4 SECTION - B Question numbers 11 to 18 carry marks each. 11. Is a composite number? Give reason for your answer. 1. Can (x13 ) be the remainder on the division of a polynomial p(x) by (x5)? Justify your answer. 13. In figure 4 ABCD is a rectangle. Find the values of x and y. figure If tan (A1B)5 3, tan (AB) = 1, where A > B and A, B are acute angles. Find the values of A and B. 15. Find the mode of the following distribution of marks obtained by 60 students. Marks Obtained No. of Students The following distribution gives the production of wheat in 100 farms of a village per hectare : Production (kg/ha) No. of Farms Write the above distribution as less than type cumulative frequency distribution A 4

5 17. In figure 5, DE AC and DF AE. Prove that EF BF 5 EC BE. 18. In a right angled triangle if hypotenuse is 0 cm and the ratio of other two sides is 4:3, find the sides. OR In an isosceles triangle ABC if AB5AC513 cm and the altitude from A on BC is 5 cm. Find BC. SECTION - C Question numbers 19 to 8 carry 3 marks each. 19. Show that any positive odd integer is of the form 6q11 or 6q13 where q is a positive integer. 0. Prove that ( 5 3 ) is an irrational number. 1 The age of a father is equal to sum of the ages of his 6 children. After 15 years, twice the age of the father will be the sum of ages of his children. Find the age of the father. OR The auto fare for the first kilometer is fixed and is different from the rate per km for the remaining distance. A man pays Rs.57 for the distance of 16 km and Rs. 9 for a distace of 6 km. Find the auto fare for the first kilometer and for each successive kilometer.. If A is an acute angle of a right angled triangle, prove that 1sinA sec AtanA 1sinA 3. If a, b are the zeroes of the polynomial x x8 then form a quadratic polynomial whose zeroes are 3a and 3b A 5 P.T.O.

6 4. Find the median of the following data. Classes Frequency If sec u 5 x 1 1 4x then prove that sec u1tan u 5x or 1 x. 6. Find mean of the following frequency distribution using step deviation method. Classes Frequency OR The mean of the following frequency distribution is 54. Find the value of p : Classes Frequency 7 p In figure 6, OA.OB5OC.OD. Show that A5 C and B5 D. 8. The diagonals of a trapezium ABCD, in which AB??DC, intersect at O. If AB5CD, then find the ratio of areas of triangles AOB and COD. OR In a triangle ABC, the mid points of sides AB, BC and CA are D,E and F respectively. Find the ratio of areas of triangles DEF and DABC A 6

7 SECTION - D Question numbers 9 to 34 carry 4 marks each : 9. Solve graphically the pair of linear equations : 3x1y350 ; xy1850 Write the co-ordinates of the vertices of the triangle formed by two lines with x - axis. 30. Find all the zeroes of the polynomial x 4 10 x 3 15x 115x1, if it is given that two of its zeros are 3 and If sin FRV S and sec FRVHF T then prove that q( p 1 ) p 3. Prove that : 4 4 cos FRV VLQ VLQ OR Prove that : cosec ( 90 ) WDQ FRV ( ) FRV 33. The following distribution gives the daily income of 50 workers of a factory. Daily income (in rupees) Number of Workers Change the above distribution to more than type distribution and draw its ogive. 34. Prove that if a line is drawn parallel to one side of a triangle to intersect the other sides in distinct points, 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 sides then the angles opposite to the first side is a right angle. - o 0 o A 7 P.T.O.

8 ¹ ÇU- ÂýàÙ â Øæ 1 âð 10 Ì ÂýˆØð ÂýàÙ æð æ ãñð 1. ØçÎ sin u5cos(u68) ãæð, Áãæ u æñúu (u68) ØêÙ æð æ ãæð Ìæð u æ æù ãæð»æ Ñ (A) 168 (B) 38 (C) 488 (D) 458. ØçÎ cos 1 M Ìæð secm 1 tan M æ æù ãæð»æ Ñ (A) 1 (B) (C) 1 (D) 0 3. æ ë çì-1 ð, AD53 âð. è., BD54 âð. è. æñúu CB51 âð. è. ãæð Ìæð tan u æ æù ãñð æ ë çì-1 (A) 3 4 (B) 5 1 (C) 4 3 (D) æ ë çì- ð, ØçÎ DE??BC Ìæð x æ æù ãñ Ñ (A) 3 âð. è. (B) 4 âð. è. (C) 7 âð. è. (D) 4.7 âð. è A 8

9 5. æ ë çì-3 ð ÕãéÂÎ p(x) æ»ýæè ÎàææüØæ»Øæ ãñð p(x) ð àæê Ø æð è â Øæ ãñ Ñ æ ë çì-3 (A) 3 (B) 4 (C) 1 (D) 6. Øêç ÜÇU çßöæáù Ë»æðçÚU ð ÙéâæÚU Îæð ÏÙæˆ Âê ææz æð a æñúu b æ HCF ææì ÚUÙð ð çü, Áãæ a>b, a æñúu b ð çü Øéç ÜÇU çßöæáù Âý ðçø æ æ ÂýØæð» ÚU ã â Âý æúu q æñúu r ææì ÚUÌð ãñ ç a5bq1r Áãæ r ãæð»æ Ñ (A) 1 < r < b (B) 0 < r < b (C) 0 [ r < b (D) 0 < r [ b æ Îàæ Üß ÂýâæÚU Îàæ Üß ð ç ÌÙð SÍæÙæð ð ÂÚUæ Ì âæ Ì ãñð (A) 1 (B) (C) 3 (D) âæ Ì Ùãè ãæð»æð 8. ÚñU¹èØ â è ÚU æ Øé x y 0 æñúu 3 x 4 y 0 æ Ñ (A) ãü ãæð»æð (B) Îæð ãü ãæð»ððð (C) Ùð ãü ãæð»ðð (D) æð ü ãü Ùãè ãæð»æð 9. ØçÎ 13 seca cosec B ÌÕ 1 A B æ æù ãñ Ñ (A) àæê Ø (B) > 908 (C) 908 (D) < ç ãè çî» 40 Âýðÿæ ææð ð çü Ò Âý æúu æ ÌæðÚU æó æñúu Ò çï Âý æúu æ ÌæðÚU æ æ ÂýçÌ ÀðUÎ çõ Îé (0.5, 15) ãñð æšø æ æù ãñ Ñ (A) 5.5 (B) 0.5 (C) 15 (D) A 9 P.T.O.

10 ¹ ÇU-Õ ÂýàÙ â Øæ 11 âð 18 Ì ÂýˆØð ÂýàÙ ð ãñ Ð 11. Øæ Öæ Ø â Øæ ãñ? æúu æ ÎèçÁ Ð 1. U Øæ ÕãéÂÎ p(x) æð (x5) âð Öæ» ÎðÙð ÂÚU (x13) àæðá Âýæ# ãæð â Ìæ ãñ? ØæØæðç Ì žæúu Îð Ð 13. æ ë çì-4 ð ABCD æøì ãñð x æñúu y æ æù ææì èçá Ð æ ë çì ØçÎ tan (A1B)5 3, tan (AB)51 æñúu A > B Áãæ A, B ØêÙ æð æ ãæð Ìæð A æñúu B æ æù ææì èçá Ð 15. çù ÙçÜç¹Ì âæúu æè ð 60 çßlæçíüøæð mæúuæ ÂýæŒÌ ÎàææüØð» ãñ Ð ÕãéÜ ææì èçá Ð Œ ž ÎÆSÍÎ ã Í ž ÏÉ h Í çù ÙçÜç¹Ì âæúu æè ç âè»æ ß ð 100 È æ æðz ð ãé æ ÂýçÌ ãñ ÅðUØÚUU (ha)»ðãê æ ˆÂæÎÙ ÎàææüÌð ãñ Ð o ÍµÀ (kg/ha) Í¾Í Až ÏÉ h Í ÂÚUæð Ì Õ ÅUÙ æð Âý æúu ð â Øè ÕæÚ UÕæÚUÌæ Õ ÅUÙ ð ÕÎÜ ÚU çüç¹ Ð A 10

11 17. æ ë çì 5 ð, DE AC æñúu DF AE. çâh èçá ç EF BF 5 EC BE. 18. â æð æ ç æöéá ð æü è Ü Õæ ü 0 âð. è. ãñð ØçÎ â è Ø ÖéÁæ æð æ ÙéÂæÌ 4 : 3 ãæð Ìæð ÖéÁæ ææì èçá Ð Íßæ â çmõæãé ç æöéá ABC ð ØçÎ AB5AC513 âð. è. æñúu àæèáü A âð BC ÂÚU Ü Õ 5 âð. è. ãæð Ìæð ÖéÁæ BC è Ü Õæ ü ææì èçá Ð ¹ ÇU-â ÂýàÙ â Øæ 19 âð 8 Ì ÂýˆØð ÂýàÙ ð 3 ã ñð 19. Îàææü ç æð ü Öè ÏÙæˆ çßá Âê ææz 6q11 Øæ 6q13 ð M Â æ ãæðìæ ãñ, Áãæ q æð ü ÏÙæˆ Âê ææz ãñð 0. çâh èçá ( 5 3 ) ÂçÚU ðø â Øæ ãñð 1 çâìæ è æøé â ð 6 Õ ææð è æøé ð Øæð» ð ÕÚUæÕÚU ãñð 15 ßáü Âà æì çâìæ è æøé, â ð Õ ææð è æøé ð Øæð» è, Îé»éÙè ãæð»èð çâìæ è ßÌü æù æøé ææì èçá Ð Íßæ ØçÎ ÂãÜð ç Üæð èåuúu ð çü S ê ÅUÚU ÖæÇ æ é ÀU çùøì L ÂØð ãñ æñúu çè ÚU ÂýçÌ ç Üæð èåuúu â è ÎÚU Ü» ãñð ØçÎ ÃØç Ì 16 ç Üæð èåuúu ÎêÚUè ÌØ ÚUÙð ÂÚU 57 L. æñúu 6 ç Üæð èåuúu ÎêÚUè ð çü 9 L. ÎðÌæ ãæð Ìæð ææì ÚUæð ç S ê ÅUÚU ÖæÇ ð è çùøì ÎÚU æñúu ÂýçÌ ç Üæð èåuúu ç ÚUæØæ ç ÌÙè ãñð. ØçÎ â æð æ ç æöéá ð, A ØêÙ æð æ ã ñ Ìæð çâh èçá 1sinA secatana 1sinA. 3. ØçÎ a, b ÕãéÂÎ x x 8 ð àæê Ø ãæð Ìæð ßã ÚñUç¹ ÕãéÂÎ ææì èçá çáâ ð àæê Ø 3a æñúu 3b ãæð Ð A 11 P.T.O.

12 4. æšø ææì èçá Ð Á Þ ¼7È¾ È¼ 7 È¼7 È ØçÎ sec u 5 x 1 1 4x Ìæð çâh èçá sec u1tan u 5x Øæ 1 x. 6. Â»-çß ÜÙ çßçï mæúuæ çù Ù ÕæÚ UÕæÚUÌæ Õ ÅUÙ æ æšø ææì èçá Ð Á Þ ¼7È¾ È¼ 7 È¼7 È Íßæ çù Ù ÕæÚU ÕæÚUÌæ Õ ÅUÙ æ æšø 54 ãñð p æ æù ææì èçá Ð Á Þ È¼ 7 È¼7 È 7 p æ ë çì 6 ð, OA.OB5OC.OD Îàææü ç A5 C æñúu B5 D. 8. â Ü Õ ABCD çáâ ð AB??DC ãñ, ð çß æü ÂÚUSÂÚU çõ Îé O ÂÚU ÂýçÌ ÀðUÎ ÚUÌð ãñ Ð ØçÎ AB5CD ãæð Ìæð ç æöéáæð AOB æñúu COD ð ÿæð æè Üæð æ ÙéÂæÌ ææì èçá Ð Íßæ ç æöéá ABC è ÖéÁæ æð AB, BC æñúu CA ð ŠØ çõ Îé ý àæñ D, E æñúu F ãñð DDEF æñú DABC ð ÿæð æè Üæð æ ÙéÂæÌ ææì èçá Ð A 1

13 ¹ ÇU-Î ÂýàÙ â Øæ 9 âð 34 Ì ÂýˆØð ÂýàÙ ð 4 ãñ Ð 9. çî» ÚñU¹èØ â è ÚU æ Øé æð»ýæè mæúuæ ãü èçá Ð 3 x y 3 0 ; xy 8 0 ÎæðÙæð ÚðU¹æ æð æñúu x- ÿæ ð Õè ÕÙð ç æöéá ð àæèáæðz ð çùîðüàææ çüç¹ Ð ÕãéÂÎ x 10x 5 x 15x 1 ð âöè àæê Ø ææì èçá ; ØçÎ â ð Îæð àæê Ø 3 æñúu 3 ãñ Ð 31. ØçÎ sin Mcos M p æñúu secmcosec MqÌæð çâh èçá q( p 1 ) p 3. çâh èçá Ñ 4 4 cos Mcos Msin sin M Íßæ çâh èçá Ñ cosec (90 M) tan Mcos (90 M) cos M 33. çù ÙçÜç¹Ì Õ ÅUÙ ç âè Èñ ÅUÚUè ð 50 Ÿæç æð è ÎñçÙ æø ÎàææüÌæ ãñð ÓÉ» Èº. ºÈÒ ¹Ò ÈÉ¹ ÈÒ ÊÄ cºè â Õ ÅUÙ æð çï Âý æúu ð Õ ÅUÙ ð ÕÎçÜ æñúu çè ÚU â æ ÌæðÚU æ ¹è ç Ð 34. çâh èçá ç ç æöéá è ÖéÁæ ð â æ ÌÚU ¹è è» ü ÚðU¹æ Áæð ç Ø Îæð ÖéÁæ æð æð æåuìè ãñ Ù Îæð ÖéÁæ æð æð â æù ÙéÂæÌ ð çßöæçáì ÚUÌè ãñð Íßæ çâh èçá ç æöéá ð ØçÎ ÖéÁæ æ ß»ü Ø Îæð ÖéÁæ æð ð ß»æðZ ð Øæð»È Ü ð ÕÚUæÕÚU ãæð Ìæð ÂãÜè ÖéÁæ ð âæ Ùð æ æð æ â æð æ ãæðìæ ãñð - o 0 o A 13 P.T.O.

CBSE QUESTION PAPER CLASS-X. MATHEMATICS i1fu1a

CBSE QUESTION PAPER CLASS-X. MATHEMATICS i1fu1a 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