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HIMACHAL PRADESH MAR 2008 : Mathematics

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xf.kr le; % 3 ?k.Vs (MATHEMATICS) Time : 3 Hrs iw.kkZd% 85 a MM : 85 vko ;d funsZ k & 1 lHkh iz u vfuok;Z gSA a 2 iz u la[;k 1 ls 10 rd 2 & 2 vd okys] 11 ls 20 rd 3 &3 vd a a okys rFkk 21 ls 25 rd 5&5 vad okys gSA a 3 js[kkxf.kr okys iz uksa dh vkd`fr vfuok;Z gSA Important Instructions : 1) All questions are compulsory. 2) Q. Nos. 1 to 10 of 2 marks each, Q. No. 11 to 20 of 3 marks each and Q. No. 21 to 25 of 5 marks each. 3) Draw the diagrams of Geometrical questions. Hkkx &d Section -A iz0 1 867 vkSj 225 dk HCF ;qfDyM+ foHkktu ,YxksfjFe dk iz;ksx djds Kkr dhft,A Use Euclid s algorithm to find the HCF of 867 and 225. iz0 2 fl) dhft, fd 3 $ 2 5 ,d vifjes; la[;k gSA Prove that 3 + 2 5 is irrational. iz-0 3 fuEufyf[kr lehdj.k fudk; dks izfrLFkkfir fof/k ls gy dhft,A 3x - y = 3 9x - 3y = 9 Solve the following pair of Linear or Equation by the Substitution Method. 3x - y = 3 9x - 3y = 9 10 iz0 4 K dk eku Kkr dhft, ;fn f)?kkr lehdj.k 2x2 + Kx + 3 = 0 ds ewy cjkcj gksA a Find the value of K for the quadratic equation 2x2 + Kx + 3 = 0 have equal roots. iz0 5 x & v{k ij og fcUnq Kkr dhft, tks 2] &5 vkSj &2] 9 ls lenwjLFk gksA Find the point on the x - axis which is equidistant from (2, -5) and (-2, 9). iz0 6 5 cm f=T;k ds ,d o`r ij ,slh nks Li kZ js[kk,a [khafp, tks ijLij 60O ds dks.k ij >qdh gksA Draw a pair of tangents to a circle of radius 5 cm which are Inclined to each other at an angle of 60O. iz0 7 nks [kaHks ftudh apkbZ;ka 6 m vkSj 11 m gSa rFkk ls lery Hkwfe ij [kM+s gSA ;fn a buds fupys fljksa ds chp dh nwjh 12 m gks rks buds ijh fljksa ds chp dh nwjh Kkr dhft,A Two poles of Heights 6m and 11 m stands on a plane ground. If the distance between the feet of the poles is 12m. Find the distance between their tops. iz0 8 nks ladnzh; o`rksa dh f=T;k,a 5 cm rFkk 3 cm gSa A cM+s o`r dh ml thok dh s yEckbZ Kkr dhft, tks NksVs o`r dks Li kZ djrh gksA Two concentric circles are of radie 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle. iz0 9 ;fn P(E) = 0.05 gks rks E ugha*] dh izk;fdrk D;k gS \ If P(E) = 0.05, what is the probability of not E ? iz0 10 ,d ikls dks ,d ckj QSdk tkrk gS fuEufyf[kr dks izkIr djus dh izk;fdrk Kkr a dhft,A 1 ,d vHkkT; la[;k 2 ,d fo ke la[;k A die is thrown once. Find the probability of getting i) a prime number ii) an odd number. 11 Hkkx&[k Section B iz0 11 lehdj.k fudk; 2x + y - 6 = 10 4x - 2y - 4 = 0 dks xzkQh;fof/k ls gy dhft,A Solve the following system of linear equations graphically : 2x + y - 6 = 0 4x - 2y - 4 = 0 iz0 12 3x4 + 6x3 - 2x2 - 10x - 5 ds vU; lHkh kwU;d Kkr dhft, ;fn blds nks kwU;d 5 3 vkSj 5 3 gSA a Obtain all other zeroes of 3x4 + 6x3 - 2x2 - 10x - 5, if two of its zeroes are 5 3 and 5 3 . iz0 13 AP : 3, 15, 27, 39, ......................... dk dkSu lk in mlds 54osa in ls 132 vf/kd gksxk \ Which term of the AP : 3, 15, 27, 39, ............. will be 132 more than its 54th term? iz0 14 2 tan2 45O + Cos2 30O - Sin2 60O dk eku Kkr dhft,A Evaluate 2 tan2 45O + Cos2 30O - Sin2 60O. iz0 15 fl) dhft, CosA 1 + SinA Prove the identity iz0 16 $ CosA 1 + SinA 1 + SinA Cos A + = 1 + SinA Cos A 2 Sec A. = 2 Sec A. ml prqHkZqt dk {ks=Qy Kkr dhft, ftlds kh kZ blh e esa (-4, -2), (-3, - 5), (3, - 2) vkSj (2, 3) gA Sa Find the area of the quadrilateral whose vertics, taken in order are (-4, -2), (-3, -5), (3, -2) and (2, 3). 12 iz0 17 fcUnq A ds funsZ kkad Kkr dhft, tgka AB ,d o`r dk O;kl gS ftldk dsUnz O (2, -3) gS rFkk B ds funsZ kkad (1, 4) gSA a Find the coordinate of a point A, where AB is the diameter of a circle whose centre is O (2, -3) and B is (1, 4). iz0 18 ,d f=Hkqt ABC dh Hkqtk BC ij ,d fcUnq D bl izdkj fLFkr gS fd ADC = BAC gSA fn[kkb, fd CA2 = CB.CD gSA D is a point on the side BC of a triangle ABC such that ADC = BAC. Show that CA2 = CB.CD. iz0 19 15 cm f=T;k okys ,d o`r dh dksbZ thok dsUnz ij 60O dk dks.k varfjd djrh gSA laxr y?kq [kaM dk {ks=Qy Kkr dhft,A ( = 3.14 3 = 1.73 ) yhft,A A Chord of a circle of radius 15 cm subtends an angle of 60O at the centre. Find the areas of the corresponding minor segments of the circle. (Use = 3.14 and 3 = 1.73) iz0 20 Hkqtk 4 cm okys oxZ ds izR;sd dksus ls 1 cm f=T;k okys o`r dk ,d prq;kZ k a dkVk x;k gS rFkk chp esa 2 cm O;kl dk ,d o`r Hkh dkVk x;k gS tSlk fd vkd`fr esa n kkZ;k x;k gSA oxZ ds ks k Hkkx dk {ks=Qy Kkr dhft,A From each corner of a square of side 4 cm a quadrant of a circle of radius 1 cm is cut and also a circle of diameter 2 cm is cut as shown in fig. Find the area of the remaining portion of the square. 13 Hkkx & x Section - C iz0 21 ,d jsyxkM+h ,d leku pky ls 360 km dh nwjh r; djrh gSA ;fn og pky 5 km/h vf/kd gksrh rks og mlh ;k=k esa 1 ?kaVk de le; ysrhA jsyxkM+h dh pky Kkr dhft,A A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train. iz0 22 ehukj ds vk/kkj ls ,d ljy js[kk esa 4 m vkSj 9 m dh nwjh ij fLFkr nks fcUnqvksa ls ehukj ds f k[kj ds mUu;u dks.k iwjd ik, tkrs gaSA fl) dhft, fd ehukj dh mapkbZ 6 m gSA The Angles of Elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. Prove that the height of the tower is 6 m. iz0 23 ;fn fdlh f=Hkqt dh ,d Hkqtk dk oxZ vU; nks Hkqtkvksa ds oxksZa ds ;ksx ds cjkcj gks rks igyh Hkqtk dk leq[k dks.k ledks.k gksrk gSA fl) dhft,A In a triangle, if square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle. Prove it. iz0 24 ikuh ihus okyk ,d fxykl 14 cm mpkbZ okys ,d kadq ds fNUud ds vkdkj dk a gSA nksuksa o`rkdkj fljksa ds O;kl 4 cm vkSj 2 cm gSA bl fxykl dh /kkfjrk Kkr a dhft,A A drinking glass is in the shape of a frustum of a cone of height 14 cm. The diameter of its two circular ends are 4 cm and 2 cm. Find the capacity of the glass. 14 iz0 25 fuUufyf[kr vkadM+kas dk ek/;d 525 gSA ;fn okjaokjrkvksa dk ;ksx 100 gS] rks x vkSj y dk eku Kkr djsA a oxZ varjky okjaokjrk 0-100 2 100-200 5 200-300 x 300-400 12 400-500 17 500-600 20 600-700 y 700-800 9 800-900 7 900-1000 4 The median of the following data is 525. Find the value of x and y, if the total frequency is 100. Class Interval Frequcny 0-100 2 100-200 5 200-300 x 300-400 12 400-500 17 500-600 20 600-700 y 700-800 9 800-900 7 900-1000 4 15

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Additional Info : Model Question Papers Of Matric Examination March 2008 Mathematics
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