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CBSE Class X 2007 : MATHEMATICS

11 pages, 64 questions, 14 questions with responses, 15 total responses,

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

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Roll No. jksy uaCode No. Series RKM dksM ua- 30/1 Please check that this question paper contains 11 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 condidate. 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 iz'u&i=k esa i;k tk p i;k iz'u dj ysa fd bl iz'u&i=k esa eqfnzr i`"B 11 gSaA nkfgus gkFk dh vksj fn, x, dksM uEcj dks Nk=k m kj&iqfLrdk ds eq[k&i`"B ij fy[ksaA dj ysa fd bl iz'u&i=k esa 25 iz'u gSaA dk m kj fy[kuk 'kq: djus ls igys] iz'u dk ekad vo'; fy[ksaA MATHEMATICS xf.kr Time allowed : 3 hours Maximum Marks: 80 fu/kkZfjr le; % 3 ?k.Vs vf/kdre vad % 80 General Instuctions : (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 marks each, Section B is of 12 questions of 3 marks 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) In question on construction, the drawing should be neat and exactly as per the given measurements. (v) Use of calculators is not permitted. However, you may ask for Mathematical tables. lekU; funsZ'k % (i) 30/1 lHkh iz'u vfuok;Z gSaA 1 P.T.O. (ii) (iii) (iv) (v) bu 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 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 jpuk okys iz'u esa vkjs[ku LoPN gks vkSj fn, x, ekiu ds loZFkk vuq:i gksA dSydqysVj ds iz;ksx dh vuqefr ugha gSA ysfdu ;fn vko';drk gks rks vki xf.krh; lkjf.k;ksa dh ek x dj ldrs gSaA 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 rFkk 2. and . dk y?kqre lekioR;Z Kkr dhft,A Solve for x and y : 8x 9y = 6xy 10x + 6y = 19xy OR Solve for x and y : x rFkk y ds fy, gy dhft, % 8x 9y = 6xy 10x + 6y = 19xy vFkok vFkok x rFkk y ds fy, gy dhft, % 3. In an A.P., the sum of its first n terms is n2 + 2n. Find its 18th term. ,d lekUrj Js<+h ds izFke n inksa dk ;ksxQy n2 + 2n gSA bldk 18ok in Kkr dhft,A 30/1 2 4. In Figure 1, 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 CA2 = BC.CD. ABC such that ADC = BAC. Prove that vk fr 1 esa] nks o` k ijLij fcUnq C ij ck r% Li'kZ djrs gSaA fl) dhft, fd fcUnq C ls 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 dhft, fd CA2 = BC.CD. 5. BAC. fl) Find the mean of the following distribution : Class Frequency 0-10 8 10-20 12 20-30 10 30-40 11 40-50 30/1 ADC = 9 3 P.T.O. fuEu caVu dk ek/; Kkr dhft, % oxZ 0-10 8 10-20 12 20-30 10 30-40 11 40-50 6. ckjEckjrk 9 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 30/1 4 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. Solve the following system of linear equations graphically : 2x + 3y = 12 2y 1 = x fuEu jSf[kd lehdj.k fudk; dks xzkQ+ }kjk gy dhft, % 2x + 3y = 12 2y 1 = x 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 BC is a chord of a circle with centre O. A is a point on arc BAC as shown in Figure 2. Prove that BAG + OBC = 90 . 30/1 5 P.T.O. fl) dhft, fd fdlh le iapHkqt ds dksbZ pkj 'kh"kZ fcUnq p h; gSaA vFkok dsUnz O okys o` k dh BC ,d thok gSA pki BAC ij ,d fcUnq A gS tSlk fd vk fr 2 esa n'kkZ;k x;k gSA fl) dhft, fd BAG + OBC = 90 . 12. Draw a circle of radius 4.5 cm. At a point A on it, draw a tangent to the circle without using the centre. 4.5 lseh f=kT;k dk ,d o` k [khafp,A bl o` k ds fcUnq A ls] dsUnz dk iz;ksx fd, fcuk] o` k ij ,d Li'kZ js[kk [khafp,A 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 ij 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 Games Entertainment Gardening Decoration 20 10 15 10 17 Draw a pie diagram to represent the above data. fdlh ifjokj dk [kpZ lSadM+ksa #i;ksa esa fofHk enksa ij fuEu gS % en f'k{kk [ksy euksjatu ckxokuh ltkoV [kpZ 20 10 15 10 17 mi;qZ vk dM+ksa dks ikbZ vkjs[k }kjk iznf'kZr dhft,A 30/1 6 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 v Fkok 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 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-yearly 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 30/1 7 P.T.O. 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 areas 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 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 : In Figure 3, ABCD is a cyclic quadrilateral and PQ is the tangent to the circle at C. If BD is the diameter and DCQ = 40 and ABD = 60 , find (i) ADB (ii) BCP. 30/1 8 ;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 % vk fr 3 esa] ABCD ,d p h; prqHkqtZ gS rFkk PQ o` k ds fcUnq C ij Li'kZ js[kk gSA ;fn BD o` k dk O;kl rFkk DCQ = 40 rFkk ABD = 60 gks] rks (i) ADB (ii) BCP Kkr dhft,A 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 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 ? 30/1 9 P.T.O. ,d v/kZxksyh; crZu ftldk vkfUrfjd O;kl 36 lseh gS] fdlh rjy inkFkZ ls Hkjk gqvk gSA bl rjy inkFkZ dks csyukdkj cksryksa esa 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, 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 12th month of the year. Use the following to calculate income tax : (a) Savings (b) 100% exemption for permissible savings upto Rs. 1,00,000 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 (c) 30/1 Rs. 25,000 + 30% of the amount exceeding Rs. 2,50,000 Education Cess 2% of Income tax 10 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 vf/kdre 1]00]000 #- dh vuqer 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 #dk 20% (iv) 2]50]001 #- vkSj vf/kd 25]000 #dk 30% + 1]50]000 #- ls vf/kd jkf'k 2]50]000 #- ls vf/kd jkf'k vk; dj dk 2% l f'k{kk midj 30/1 + 11 P.T.O.

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