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CBSE Class X 2007 : MATHEMATICS

11 pages, 64 questions, 10 questions with responses, 12 total responses,

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

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Code No. Series : RKM/1 dksM ua- Roll No. 30/1/1 Candidates must write the Code on the title page of the answer-book. jksy ua- ijh{kkFkhZ dksM dks m kj&iqfLrdk ds eq[k i`"B ij vo'; fy[ksaA 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 dj ysa fd bl iz'u&i=k esa eqfnzr i`"B 11 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 xf.kr Time allowed : 3 Hours ] fu/kkZfjr le; % 3 ?k.Vs ] [ Maximum Marks: 80 [ vf/kdre vad % 80 General Instuctions : 1. All questions are compulsory. 2. 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. 3. 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. 4. In question on construction, the drawing should be neat and exactly as per the given measurements. 5. Use of calculators is not permitted. However, you may ask for Mathematical tables. 30/1/1 1 [P.T.O. lkekU; funsZ'k % 1. lHkh iz'u vfuok;Z gSaA 2. 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 v 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 3. 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 4. jpuk okys iz'u esa vkjs[ku LoPN gks vkSj fn, x, ekiu ds loZFkk vuq:i gksA 5. 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. If x + k is the GCD of x2 _ 2x _ 15 and x3 + 27, find the value of k. ;fn x + k e-l- (GCD) gS x2 _ 2x _ 15 rFkk x3 + 27 dk] rks k dk eku Kkr dhft,A 2. Solve for x and y : OR Solve for x and y : x rFkk y ds fy, gy dhft, % vFkok vFkok x rFkk y ds fy, gy dhft, % 30/1/1 2 3. Find the sum of first 25 terms of an A.P. whose nth term is 1 _ 4n. ml lekUrj Js.kh ds izFke 25 inksa dk ;ksx Kkr dhft, ftldk nok in 1 _ 4n gSA 4. P and Q are points on sides CA and CB respectively of Prove that AQ2 + BP2 = AB2 + PQ2 OR In Fig. 1, DE | | AB and FE | | DB. Prove that DC2 = CF.AC ABC, right angled at C. ABC dh Hkqtkvksa CA rFkk CB ij e'k% fcUnq P rFkk Q fLFkr gSaA ;fn ABC esa fcUnq C ij ledks.k gS] rks fl) dhft, fd AQ2 + BP2 = AB2 + PQ2 vFkok v Fkok vk fr 1 esa] DE | | AB rFkk FE | | DB fl) dhft, fd DC2 = CF.AC 5. The mean of the following frequency distribution is 62.8. Find the missing frequency x. Class Frequency 0-20 20-40 40-60 60-80 80-100 100-120 5 8 x 12 7 8 fuEu ckjackjrk caVu dk ek/; 62.8 gSA yqIr ckjackjrk x Kkr dhft, % oxZ ckjackjrk 30/1/1 0-20 20-40 40-60 60-80 80-100 100-120 5 8 x 12 7 8 3 [P.T.O. 6. Cards marked with numbers 3, 4, 5, ......, 50 are placed in a box and mixed thoroughly. One card is drawn at random from the box. Find the probability that number on the drawn card is (i) divisible by 7. (ii) a number which is a perfect square. ,d cDls esa 3, 4, 5, ......, 50 }kjk vafdr dkMZ j[ks x;s gSaA dkMks dks Hkyh izdkj feykdj cDls esa ls ,d dkMZ ;kn`PN;k fudkyk x;kA izkf;drk Kkr dhft, fd fudkys x;s dkMZ ij (i) (ii) 7. 7 ls iw.kZr;k foHkkftr gksus okyh la[;k vafdr gSA ,d iw.kZ oxZ la[;k vafdr gSA A washing machine is available for Rs. 13,500 cash or Rs. 6,500 as cash down payment followed by three monthly instalments of Rs. 2,500 each. Find the rate of interest charged under instalment plan. ,d diM+s /kksus dh e'khu 13]500 #- udn ij vFkok 6]500 #- ds udn Hkqxrku ds lkFk 2]500 #ekfld dh rhu leku fdLrksa esa miyC/k gSA fdLr ;kstuk ds vUrxZr C;kt dh nj Kkr dhft,A 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 equations graphically : 2x + 3y = 8 ; x + 4y = 9 fuEu lehdj.k fudk; dks xzkQ+ dh lgk;rk ls gy dhft, % 2x + 3y = 8 ; x + 4y = 9 9. Simplify : ljy dhft, % 30/1/1 4 10. Which term of the A.P. 3, 15, 27, 39,....... will be 132 more than its 54th term ? lekUrj Js.kh 3, 15, 27, 39,....... dk dkSu lk in blds 54osa in ls 132 vf/kd gksxk \ 11. In Fig. 2, TA is a tangent to the circle from a point T and TBC is a secant to the circle. If AD is the bisector of CAB, prove that ADT is isosceles. In ABC, AD OR BC and AD = BD.DC. Prove that 2 BAC is a right angle. vk fr 2 esa] TA o` k dh fcUnq T ls Li'kZ js[kk gS rFkk TBC ,d Nsnd gSA ;fn AD, CAB dk lef}Hkktd gS] rks fl) dhft, fd ADT ,d lef}ckgq f=kHkqt gSA vFkok ABC esa AD 2 BC gS rFkk AD = BD.DC A fl) dhft, fd BAC ,d ledks.k gSA 12. Draw a PQR with base QR = 6 cm, vertical angle P = 60 and median through P to the base is of length 4.5 cm. PQR dh jpuk dhft, ftldk vk/kkj QR = 6 lseh] 'kh"kZ dks.k P = 60 rFkk fcUnq P ls vk/kkj ij [khaph xbZ ekf/;dk dh yEckbZ 4.5 lseh gSA 13. A toy is in the form of a cone mounted on a hemisphere of common base radius 7 cm. The total height of the toy is 31 cm. Find the total surface area of the toy. (Use ) ,d f[kykSuk ,d v/kZxksys ij yxs 'kadq ds vkdkj dk gS] ftuds leku vk/kkj dh f=kT;k 7 lseh gSA ;fn f[kykSus dh dqy pkbZ 31 lseh gS] rks f[kykSus dk dqy i`"Bh; {ks=kQy Kkr dhft,A 30/1/1 dk iz;ksx dhft,A 5 [P.T.O. 14. The enrolment of a secondary school in different classes is given below : Class VI VII VIII IX X Enrolment 600 500 400 700 200 Draw a pie chart to represent the above data. ,d mPp ek/;fed fo|ky; dh fofHk d{kkvksa esa fo|kfFkZ;ksa dh la[;k fuEu gS % VI VII VIII IX X fo|kfFkZ;ksa dh la[;k 600 500 400 700 200 d{kk mijksDr vk dM+ksa dks iznf'kZr djrk ,d ikbZ pkVZ cukb,A 15. A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball from the bag is thrice that of a red ball, find the number of blue balls in the bag. ,d FkSys esa 5 yky vkSj dqN uhyh xsansa gSaA ;fn FkSys esa ls uhyh xsan dks fudkyus dh izkf;drk] yky xsan dks fudkyus dh izkf;drk ls frxquh gks rks FkSys esa j[kh uhyh xsanksa dh la[;k Kkr dhft,A 16. Prove that : OR Evaluate without using trigonometric tables : fl) dhft, vFkok v Fkok f=kdks.kferh; rkfydkvksa ds iz;ksx fcuk eku Kkr dhft, % 30/1/1 6 17. Show that the points (7, 10), (_ 2, 5) and (3, _ 4) are the vertices of an isosceles right triangle. fl) dhft, fd fcUnq (7, 10), (_ 2, 5) rFkk (3, _ 4) ,d ledks.k lef}ckgq f=kHkqt ds 'kh"kZ fcUnq gSaA 18. In what ratio does the line x _ y _ 2 = 0 divides the line segment joining (3, _ 1) and (8, 9) ? fcUnq (3, _ 1) rFkk (8, 9) dks feykus okys js[kk[kaM dks js[kk x _ y _ 2 = 0 fdl vuqikr esa ck Vrh gS \ 19. A man borrows money from a finance company and has to pay it back in two equal half-yearly instalments of Rs. 7,396 each. If the interest is charged by the finance company at the rate of 15% per annum, compounded semi-annually, find the principal and the total interest paid. ,d O;f fdlh fo k dEiuh ls dqN jkf'k _.k ysrk gS vkSj og mls nks leku v/kZokf"kZd fdLrksa esa ykSVkrk gS tcfd izR;sd fdLr 7,396 #- gSA ;fn dEiuh 15% okf"kZd dh nj ls v/kZokf"kZd la;ksftr p o`f) C;kt ysrh gS] rks ewy/ku rFkk dqy fn;k x;k C;kt Kkr dhft,A 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. If a line is drawn parallel to one side of a triangle, to intersect the other two sides in distinct points, prove that the other two sides are divided in the same ratio. Using the above, prove the following : In Fig. 3, DE | | BC and BD = CE. Prove that ABC is an isosceles triangle. 30/1/1 7 [P.T.O. ;fn fdlh f=kHkqt dh ,d Hkqtk ds lekUrj vU; nks Hkqtkvksa dks dkVrs gq, dksbZ js[kk [khaph tk,] rks fl) dhft, fd og f=kHkqt dh vU; nksuksa Hkqtkvksa dks leku vuqikr esa foHkkftr djrh gSA mijks dk iz;ksx dj fuEu fl) dhft, % vk fr 3 esa] DE | | BC rFkk BD = CE fl) dhft, fd ABC ,d lef}ckgq f=kHkqt gSA 21. Prove that the sum of either pair of opposite angles of a cyclic quadrilateral is 180 . Using the above, find x and y in Fig. 4. fl) dhft, fd p h; prqHkqZt ds lEeq[k dks.kksa ds fdlh Hkh ;qXe dk ;ksx 180 gksrk gSA mijksDr dk iz;ksx dj vk fr 4 esa x rFkk y ds eku Kkr dhft,A 22. The difference of two numbers is 5 and the difference of their reciprocals is numbers. OR 30/1/1 8 . Find the By increasing the list price of a book by Rs. 10 a person can buy 10 less books for Rs. 1,200. Find the original list price of the book. nks la[;kvksa dk vUrj 5 gS rFkk muds O;qR eksa dk vUrj gSA la[;k, Kkr dhft,A vFkok ,d iqLrd ds vafdr ewY; esa 10 #- o`f) djus ij 1]200 #- esa 10 iqLrdsa de [kjhnh tkrh gSaA iqLrd dk okLrfod vafdr ewY; Kkr dhft,A 23. A sphere, of diameter 12 cm, is dropped in a right circular cylindrical vessel, partly filled with water. If the sphere is completely submerged in water, the water level in the cylindrical vessel rises by cm. Find the diameter of the cylindrical vessel. OR A solid right circular cone of diameter 14 cm and height 8 cm is melted to form a hollow sphere. If the external diameter of the sphere is 10 cm, find the internal diameter of the sphere. 12 lseh O;kl okys ,d xksys dks ,d yEc o` kh; csyukdkj crZu esa] tks vkaf'kd :i ls ikuh ls Hkjk gS] esa Mkyk x;k gSA ;fn xksyk iwjh rjg ls ikuh esa Mwc tk,] rks csyukdkj crZu esa ikuh dk Lrj lseh c<+ tkrk gSA csyukdkj crZu dk O;kl Kkr dhft,A vFkok ,d Bksl yEc o` kh; 'kadq dk O;kl 14 lseh rFkk pkbZ 8 lseh gSA bldks fi?kyk dj ,d [kks[kyk xksyk cuk;k x;kA ;fn xksys dk ck O;kl 10 lseh gS] rks xksys dk vkUrfjd O;kl Kkr dhft,A 24. A boy standing on a horizontal plane finds a bird flying at a distance of 100 m from him at an elevation of 30 . A girl standing on the roof of 20 metre high building, finds the angle of elevation of the same bird to be 45 . Both the boy and the girl are on opposite sides of the bird. Find the distance of bird from the girl. {kSfrt ry ij [kM+k ,d yM+dk 100 ehVj dh nwjh ij ,d i{kh dks 30 ds m ;u dks.k ij ns[krk gSA ,d yM+dh tks fd 20 ehVj ps Hkou ij [kM+h gS] mlh i{kh dks 45 ds m ;u dks.k ij ns[krh gSA ;fn yM+dh i{kh dh foijhr fn'kk esa gSa] rks i{kh dh yM+dh ls nwjh Kkr dhft,A 30/1/1 9 [P.T.O. 25. Ms. Shahnaz earns Rs. 35,000 per month (excluding HRA). She donates Rs. 30,000 to Prime Minister Relief Fund (100% exemption) and Rs. 40,000 to a Charitable Hospital (50% exemption). She contributes Rs. 5,000 per month to Provident Fund and Rs. 25,000 per annum towards LIC premium. She purchases NSC worth Rs. 20,000. She pays Rs. 2,300 per month towards income tax for 11 month. Find the amount of income tax she has to pay in 12th month of the year. Use the following to calculate income tax : (a) Saving : (b) 100% exemption for permissible savings upto Rs. 1,00,000 Rates of income tax for ladies Slab Income tax (i) Upto Rs. 1,35,000 No tax (ii) From Rs. 1,35,001 to Rs. 1,50,000 10% of taxable income exceeding Rs. 1,35,000 (iii) From Rs. 1,50,001 to Rs. 2,50,000 Rs. 1,500 + 20% of the amount excedding Rs. 1,50,000 (iv) From Rs. 2,50,001 and above (c) Rs. 21,500 + 30% of the amount exceeding Rs. 2,50,000 Education Cess : 2% of Income tax payable Jherh 'kgukt= dk ekfld osru 35]000 #- edku fdjk;k Hk kk NksM+dj gSA og iz/kkueU=kh lgk;rk dks"k esa 30]000 #- 100% NwV rFkk /kekZFkZ [kSjkrh vLirky dks 40]000 #- 50% NwV nku nsrh gSA og 5]000 #- izfr ekl Hkfo"; fuf/k esa rFkk 25]000 #- okf"kZd thou chek izhfe;e nsrh gSA og 20]000 #- ds jk"V h; cpr i=k [kjhnrh gS rFkk 2]300 #- izfr ekl igys 11 ekl rd vk;dj nsrh gSA Kkr dhft, fd 12osa ekl esa mls fdruk vk;dj nsuk gksxkA 30/1/1 10 vk; dj x.kuk gsrq fuEu dk iz;ksx djsa % v cpr % vf/kdre 1]00]000 #- rd cpr ij 100% NwV c efgykvksa ds fy, vk;dj dh njsa % LyS c vk; dj (i) 1]35]000 #- rd dksbZ vk; dj ugha (ii) 1]35]001 #- ls 1]50]000 #- rd 1]35]000 #- ls vf/kd dj ;ksX; vk; dk 10% (iii) 1]50]001 #- ls 2]50]000 #- rd 1]500 #- + 1]50]000 #- ls vf/kd jkf'k dk 20% (iv) 2]50]001 #- vkSj vf/kd 21]500 #- + 2]50]000 #- ls vf/kd jkf'k dk 30% ns; vk;dj dk 2% l 'kSf{kd izHkkj 30/1/1 11 [P.T.O.

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