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CBSE Class X 2007 : MATHEMATICS FOR BLIND CANDIDATES [Set 2]

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CBSE 10
Kendriya Vidyalaya (KV), Kamla Nehru Nagar, Ghaziabad

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Roll No. jksy uaCode No. Series RKM 30(B) dksM ua- Please check that this question paper contains 13 printed pages. Code number given on the right hand side of the question paper should be written on the title page of the answer-book by the candidate. Please check that this question paper contains 25 questions. Please write down the serial number of the question before attempting it. i;k tk p dj ysa fd bl iz'u&i=k esa eqfnzr i`"B 13 gSaA iz'u&i=k esa nkfgus gkFk dh vksj fn, x, dksM uEcj dks Nk=k m kj&iqfLrdk ds eq[k&i`"B ij fy[ksaA i;k tk p dj ysa fd bl iz'u&i=k esa 25 iz'u gSaA i;k iz'u dk m kj fy[kuk 'kq: djus ls igys] iz'u dk ekad vo'; fy[ksaA MATHEMATICS (FOR BLIND CANDIDATES ONLY) xf.kr dsoy us=kghu ijh{kkfFkZ;ksa ds fy, Time allowed : 3 hours Maximum Marks: 80 fu/kkZfjr le; % 3 ?k.Vs 30(B) vf/kdre vad % 80 1 P.T.O. General Instructions : (i) All questions are compulsory. (ii) The question paper consists of 25 questions divided into three sections A, B and C. Section A contains 7 questions of 2 m arks each, Section B is of 1 2 q uestions of 3 m arks each and Section C is of 6 questions of 5 marks each. (iii) There is no overall choice. However, an internal choice has been provided in two questions of two marks each, two questions of three marks each and two questions of five marks each. (iv) Use of calculators is not permitted. lkekU; funsZ'k % (i) lHkh iz'u vfuok;Z gSaA (ii) bl iz'u&i=k esa 25 iz'u gSa tks rhu [k.Mksa v] c vkSj l esa c Vs gq, gSaA [k.M v esa nks & nks vad okys 7 iz'u] [k.M c esa rhu&rhu vad okys 12 iz'u rFkk [k.M l esa ik p&ik p vad okys 6 iz'u 'kkfey gSaA (iii) iz'u&i=k esa dksbZ lexz O;kid fodYi ugha gSA fQj Hkh nks&nks vadksa okys nks iz'uksa] rhu&rhu vadksa okys nks iz'uksa rFkk ik p&ik p vadksa okys nks iz'uksa esa vkarfjd fodYi fn, x, gSaA (iv) 30(B) dSydqysVjksa ds iz;ksx dh vuqefr ugha gSA 2 SECTION A [k.M v Questions number 1 to 7 carry 2 marks each. iz'u la[;k 1 ls 7 rd izR;sd iz'u ds 2 vad gSaA 1. Find the LCM of x3 + x2 + x + 1 and x4 1. x3 + x2 + x + 1 rFkk x4 1 dk y?kqre lekioR;Z Kkr dhft,A 2. Solve for x and y : ax by = a + b ax by = 2 OR Solve for x and y : 8x 9y = 6xy 10x + 6y=19xy x rFkk y ds fy, gy dhft, % ax by = a + b ax by = 2 vFkok v Fkok x rFkk y ds fy, gy dhft, % 8x 9y = 6xy 10x + 6y=19xy 3. In an. A.P., the sum of its first n terms is n 2 + 2 n. Find its 20th term. ,d lekUrj Js<+h ds izFke n inksa dk ;ksxQy n2 + 2n gSA bldk 20ok in Kkr dhft,A 30(B) 3 P.T.O. 4. Two circles touch each other externally at C. Prove that the common tangent at C bisects the other two common tangents. OR D is any point on the side BC of a ABC such that ADC = BAC. Prove that CA2 = BC.CD. nks o` k ck :i ls ,d&nwljs dks C ij Li'kZ djrs gSaA fl) dhft, fd fcUnq C ij mHk;fu"B Li'kZ js[kk vU; nks mHk;fu"B Li'kZ js[kkvksa dks lef}Hkkftr djrh gSA vFkok ,d ABC dh Hkqtk BC ij dksbZ fcUnq D bl izdkj fLFkr gS fd ADC = BAC. fl) dhft, fd CA2 = BC.CD. 5. Find the mean of the following distribution : Class Frequency 0-10 8 10-20 12 20-30 10 30-40 11 40-50 9 fuEu caVu dk ek/; Kkr dhft, % oxZ 0 - 10 8 10 - 20 12 20 - 30 10 30 - 40 11 40 - 50 30(B) ckjEckjrk 9 4 6. A ceiling fan is marked at Rs. 970 cash or for Rs. 210 as cash down payment followed by three equal monthly instalments of Rs. 260. Find the rate of interest charged under the instalment plan. ,d Nr ds ia[ks dk udn ewY; 970 #- gS vFkok og 210 #- ds udn Hkqxrku ds lkFk 260 #- dh rhu leku ekfld fdLrksa ij miyC/k gSA fdLr ;kstuk ds vUrxZr C;kt dh nj Kkr dhft,A 7. A box contains 5 red balls, 4 green balls and 7 white balls. A ball is drawn at random from the box. Find the probability that the ball drawn is (a) white. (b) neither red nor white. ,d ckWDl esa 5 yky xsansa] 4 gjh xsansa rFkk 7 lQsn xsansa gSaA ckWDl esa ls ,d xsan ;kn`PN;k fudkyh xbZA izkf;drk Kkr dhft, fd fudkyh xbZ xsan v lQsn gSA c u rks yky gS vkSj u gh lQsn gSA SECTION B [k.M c Questions number 8 to 19 carry 3 marks each. iz'u la[;k 8 ls 19 rd izR;sd iz'u ds 3 vad gSaA 8. The sum of the digits of a two-digit number is 8 and the difference between the number and that formed by reversing the digits is 18. Find the number. nks vadksa dh ,d la[;k ds vadksa dk ;ksxQy 8 gS vkSj ewy la[;k rFkk vad iyV dj cuus okyh la[;k dk vUrj 18 gSA la[;k Kkr dhft,A 30(B) 5 P.T.O. 9. Simplify : ljy dhft, % 10. The first term, common difference and last term of an A.P. are 12, 6 and 252 respectively. Find the sum of all terms of this A.P. ,d lekUrj Js<+h dk izFke in] lkoZ vUrj rFkk vfUre in e'k% 12] 6 rFkk 252 gSaA bl lekUrj Js<+h ds lHkh inksa dk ;ksxQy Kkr dhft,A 11. Prove that any four vertices of a regular pentagon are cyclic. OR A, B, C a nd D o f a cyclic quadrilateral ABCD are (4x + 10) , (x + 2y) , (3y + 20) and (4x + y) respectively. Find the values of x and y. fl) dhft, fd fdlh le iapHkqt ds dksbZ pkj 'kh"kZ fcUnq p h; gSaA vFkok p h; prqHkqZt ABCD ds A, B, C rFkk D ds e'k% eku (4x + 10) , (x + 2y) , (3y + 20) rFkk (4x + y) gSaA x rFkk y ds eku Kkr dhft,A 12. Prove that the angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle. fl) dhft, fd fdlh pki }kjk o` k ds dsUnz ij vUrfjr dks.k ml pki }kjk o` k ds 'ks"k Hkkx ij fLFkr fdlh fcUnq ij vUrfjr dks.k dk nqxquk gksrk gSA 30(B) 6 13. A toy is in the form of a cone mounted on a hemisphere with same radius. The diameter of the base of the conical portion is 7 cm and the total height of the toy is 14.5 cm. Find the volume of the toy. [Use ] ,d f[kykSuk v/kZxksys ij yxs leku f=kT;k okys 'kadq ds vkdkj dk gSA 'kadq Hkkx ds vk/kkj dk O;kl 7 lseh rFkk f[kykSus dh dqy pkbZ 14-5 lseh gSA f[kykSus dk vk;ru Kkr dhft,A [ dk iz;ksx dhft, ] 14. The expenditure on different heads of a household (in hundreds of rupees) is as follows : Head Expenditure Education Sports Entertainment Gardening Decoration 20 10 15 10 17 Find the central angles of expenditure on various heads for making a pie-chart. fdlh ifjokj dk O;; lSadM+ksa #i;ksa esa fofHk enksa ij fuEu gS % en f'k{kk [ksy euksjatu ckxokuh ltkoV [kpZ 20 10 15 10 17 ,d ikbZ pkVZ cukus ds fy, fofHk enksa ij O;; ds fy, dsUnzh; dks.k Kkr dhft,A 30(B) 7 P.T.O. 15. All the three face cards of spades are removed from a well-shuffled pack of 52 cards. A card is then drawn at random from the remaining pack. Find the probability of getting (a) a black face card, (b) a queen, (c) a black card. 52 i kksa dh ,d lqfefJr x h esa ls gqdqe (spades) ds rhuksa fp=k okys i ks (face cards) fudky fn, x,A fQj 'ks"k x h esa ls ;kn`PN;k ,d i kk fudkyk x;kA izkf;drk Kkr dhft, fd fudkyk x;k i kk v ,d dkyk fp=k okyk i kk gS] c ,d csxe gS] l ,d dkyk i kk gSA 16. Prove that OR Evaluate without using trigonometric tables fl) dhft, fd vFkok f=kdks.kferh; rkfydkvksa ds iz;ksx fcuk fuEu dk eku Kkr dhft, % 17. Three consecutive vertices of a parallelogram are ( 2, 1); (1, 0) and (4, 3). Find the coordinates of the fourth vertex. ,d lekUrj prqHkqZt ds rhu ekxr 'kh"kZ fcUnq ( 2, 1); (1,0) rFkk (4, 3) gSaA pkSFks 'kh"kZ ds funsZ'kkad Kkr dhft,A 30(B) 8 18. If the point C ( 1, 2) divides the line segment AB in the ratio 3 : 4, where the coordinates of A are (2, 5), find the coordinates of B. ;fn fcUnq C ( 1, 2) ,d js[kk [k.M AB dks 3 : 4 ds vuqikr esa ck Vrk gS] tgk A ds funsZ'kkad (2, 5) gSa] rks B ds funsZ'kkad Kkr dhft,A 19. A loan of Rs. 2550 is to be paid back in two equal half-yearly instalments. How much is each instalment if interest is compounded half-yealrly at 8% per annum ? 2550 #- dk _.k nks leku v/kZokf"kZd fdLrksa esa ykSVk;k tkuk gSA izR;sd fdLr dh jkf'k Kkr dhft, ;fn C;kt v/kZokf"kZd la;ksftr gksrk gS rFkk mldh nj 8% okf"kZd gSA SECTION C [k.M l Questions number 20 to 25 carry 5 marks each. iz'u la[;k 20 ls 25 rd izR;sd iz'u ds 5 vad gSaA 20. Prove that the ratio of the ireas of two similar triangles is equal to the ratio of the squares of their corresponding sides. Use the above for the following : If the areas of two similar triangles are equal, prove that they are congruent. fl) dhft, fd nks le:i f=kHkqtksa ds {ks=kQyksa dk vuqikr] f=kHkqtksa dh laxr Hkqtkvksa ds oxks ds vuqikr ds leku gksrk gSA fuEu ds fy, mi;qZ dk iz;ksx djsa % fl) dhft, fd ;fn nks le:i f=kHkqtksa dk {ks=kQy leku gS rks nksuksa f=kHkqt lok xle gksrs gSaA 30(B) 9 P.T.O. 21. If a line touches a circle and from the point of contact a chord is drawn, prove that the angles which this chord makes with the given line are equal respectively to the angles formed in the corresponding alternate segments. Use the above for the following : If ABC is isosceles with AB = AC, prove that the tangent at A to the circumcircle of ABC is parallel to BC. ;fn ,d js[kk ,d o` k dks Li'kZ djrh gS rFkk Li'kZ fcUnq ls o` k dh thok [khaph tkrh gS] rks fl) dhft, fd bl thok }kjk Li'kZ js[kk ds lkFk cuk, x, dks.k laxr ,dkUrj o` k [k.Mksa ds dks.kksa ds e'k% leku gksrs gSaA fuEu ds fy, mi;qZ dk iz;ksx djsa % ABC ,d lef}ckgq f=kHkqt gS ftlesa AB = AC rks fl) dhft, fd ABC ds ifjo` k ds fcUnq A ij [khaph xbZ Li'kZ js[kk BC ds lekUrj ;fn gSA 22. The numerator of.a fraction is one less than its denominator. If three is added to each of the numerator and denominator, the fraction is increased by . Find the fraction. OR The difference of squares of two natural numbers is 45. The square of the smaller number is four times the larger number. Find the numbers. ,d fHk dk va'k blds gj ls ,d de gSA ;fn va'k rFkk gj izR;sd esa 3 tksM+s tk, ] rks u;k fHk igys fHk ls c<+ tkrk gSA fHk Kkr dhft,A vFkok nks izk r la[;kvksa ds oxks dk vUrj 45 gSA NksVh la[;k dk oxZ cM+h la[;k dk pkj xquk gSA la[;k, Kkr dhft,A 30(B) 10 23. A hemispherical bowl of internal diameter 36 cm is full of some liquid. This liquid is to be filled in cylindrical bottles of radius 3 cm and height 6 cm. Find the number of bottles needed to empty the bowl. OR Water flows out through a circular pipe whose internal radius is 1 cm, at the rate of 80 cm/second into an empty cylindrical tank, the radius of whose base is 40 cm. By how much will the level of water rise in the tank in half an hour ? ,d v/kZxksyh; crZu ftldk vkUrfjd O;kl 36 lseh gS] fdlh rjy inkFkZ ls Hkjk gqvk gSA bl rjy inkFkZ dks csyukdkj cksryksa ls Hkjk tkuk gSA izR;sd cksry dh f=kT;k 3 lseh rFkk pkbZ 6 lseh gSA crkb, bl v/kZxksyh; crZu dks [kkyh djus ds fy, fdruh cksrysa pkfg, A vFkok ,d o` kkdkj ikbi ftldk vkUrfjd v/kZO;kl 1 lseh gS] esa ls ikuh 80 lseh izfr lsd.M dh xfr ls cgdj ,d [kkyh csyukdkj VSad esa fxj jgk gSA csyukdkj VSad ds vk/kkj dh f=kT;k 40 lseh gSA crkb, vk/ks ?kaVs ds i'pkr~ VSad esa ikuh dk Lrj fdruk c<+sxkA 24. A pole 5 m high is fixed on the top of a tower. The angle of elevation of the top of the pole observed from a point A on the ground is 60 and the angle of depression of point A from the top of the tower is 45 . Find the height of the tower. (Take = 1.732) 5 eh- pk [kEHkk ,d ehukj dh pksVh ij yxk gSA Hkwfe ry ij fLFkr fcUnq A ls [kEHks ds 'kh"kZ fcUnq dk m ;u dks.k 60 gS rFkk ehukj ds 'kh"kZ fcUnq ls fcUnq A dk voueu dks.k 45 gSA ehukj dh pkbZ Kkr dhft,A = 1.732 yhft, 30(B) 11 P.T.O. 25. The salary of Hukam Singh is Rs. 42,000 per month (exclusive of HRA). He donates Rs. 30,000 to Prime Minister s Relief Fund (100% exemption). He contributes Rs. 6,500 per month towards Provident Fund and Rs. 5,000 quarterly towards LIC premium. He also purchases NSC worth Rs. 10,000. He pays income tax of Rs. 5,100 per month for 11 months. Calculate the income tax he has to pay in the 12 month of the year. Use the following to calculate income tax : (a) Savings 100% exemption for permissible savings upto Rs. 1,00,000 (b) Rates of Income tax Slab Income tax (i) Upto Rs. 1,00,000 No tax (ii) From Rs. 1,00,001 to Rs. 1,50,000 10% of the taxable income exceeding Rs. 1,00,000 (iii) From Rs. 1,50,001 to Rs. 2,50,000 Rs. 5,000 + 20% of the amount exceeding Rs. 1,50,000 (iv) Rs. 2,50,001 and above Rs. 25,000 + 30% of the amount exceeding Rs. 2,50,000 (c) Education Cess 30(B) 2% of Income tax payable 12 gqdqe flag dk osru edku fdjk;k Hk kk NksM+dj 42]000 #- ekfld gSA og 30]000 #- iz/kku ea=kh jkgr dks"k 100% NwV esa nku nsrk gSA og 6]500 #- izfr ekg Hkfo"; fuf/k esa rFkk 5]000 #- =kSekfld thou chek izhfe;e nsrk gSA og 10]000 #- ds jk"V h; cpr i=k Hkh [kjhnrk gSA og 5]100 #- ekfld 11 ekg rd vk; dj nsrk gSA crkb, mls o"kZ ds 12osa ekg esa fdruk vk; dj nsuk iM+sxkA vk; dj dh x.kuk gsrq fuEu dk iz;ksx djsa % (v) cpr 1,00,000 vf/kdre #- dh vuqqer cprksa ij 100% NwV (c) vk; dj dh njsa LySc vk; dj (i) 1,00,000 #- rd dksbZ vk; dj ugha (ii) 1,00,001 #- ls 1,50,000 #- rd 1,00,000 #- ls vf/kd dj&;ksX; vk; dk 10% (iii) 1,50,001 #- ls 2,50,000 #- rd 5,000 #- + 1,50,000 #- ls vf/kd jkf'k dk 20% (iv) 2,50,001 #- vkSj vf/kd 25,000 #- + 2,50,000 #- ls vf/kd jkf'k dk 30% (l) f'k{kk midj 30(B) ns; vk; dj dk 2% 13 P.T.O.

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