Mathematics Past Paper VIII PDF

class (d{kk) % VIII MATHEMATICS (xf.kr) PAPER I section - 'a' ([kaM&^v*) Max. Marks...

class (d{kk) % VIII MATHEMATICS (xf.kr) PAPER I section - 'a' ([kaM&^v*) Max. Marks 90 1. Write the degree of polynomial (x2 + 1)(x + 2). 1 cgqin (x2 + 1)(x + 2) dh ?kkr fyf[k,A 1 2. Simplify (50 + 60 + 7 0 + 80 )2 1 1 ljy dhft, (50 + 60 + 70 + 80 )2 3. Name the geometrical shape which has unlimited lines of symmetry. 1 ml T;kfefr vkÑfr dk uke crkb,] ftlesa vlhfer js[kkvksa dh lefefr gSA 4. In the word 'MATHS' which letter shows rotational symmetry of order 2 ? 1 fn, x, 'kCn 'MATHS' esa dkSu&lk v{kj ?kw.kZu lefefr dk ?kw.kZu Øe 2 n'kkZrk gS\ SECTIon - 'b' ([kaM&^c*)  1  −5  1 7  1  2 x −1  5. Find x so that   ×   =    2  3   3   3    1  −5  1 7  1  2 x −1  x Kkr dhft,] rkfd   ×   =     3   3   3   2 Evaluate : (0.01024 ) − 6. 5 2 2 eku Kkr dhft, % (0.01024 ) − 5 VIII-MATHEMATICS (1) 7. Divide 2 2 x 4 + 6 2 x 3 + x 2 by 2 2x 2 2 2 2 x 4 + 6 2 x3 + x 2 dks 2 2x 2 ls Hkkx dhft,A 8. Using factor method, divide the polynomial (y2 – y – 42) by (y – 7). 2 xq.ku[kaM fofèk dk iz;ksx djds cgqin (y2 – y – 42) dks (y – 7) ls Hkkx dhft,A 9. The sum of two positive integers is 120. The integers are in the ratio 2 : 3. Find the integers. 2 nks le iw.kk±dksa dk ;ksx 120 gSA mu iw.kk±dksa esa vuqikr 2 % 3 gSA iw.kk±d Kkr dhft,A 10. Write the order and angle of rotational symmetry of equilateral triangle. 2 leckgq f=kHkqt dk ?kw.kZu lefefr Øe vkSj ?kw.kZu lefefr dks.k fyf[k,A section - 'c' ([kaM&^l*) 11. Rehana received a sum of Rs. 40,000 as a loan from a finance company at the rate of 7% p.a. Find the compound interest paid by Rehana after 2 years. 3 jsgkuk dks ,d foRr daiuh ls 40]000 :i;s dk dtZ 7% okf"kZd C;kt nj ls feykA Kkr dhft, fd nks lky esa jsgkuk n~okjk fdruk pØo`f¼ C;kt fn;k tk,xk\ 1   1 1 34 12. Evaluate : 7  64 + 27 3   3 3     1   1 1 34 eku Kkr dhft, % 7  64 3 + 27 3       13. Using long division method, show that x+2 is a factor of x3 + 8. 3 yach Hkkx fofèk dk iz;ksx djds] n'kkZb, fd x+2] x3 + 8 dk xq.ku[kaM gSA 14. Solve the following equation and verify your answer. 3 fn;k x;k lehdj.k gy dhft, vkSj vius mÙkj dk lR;kiu dhft, & 2 − 7x 3 + 7x = 1 − 5x 4 + 5x VIII-MATHEMATICS (2) 15. The sum of the digits of a two digit number is 10. The number obtained by interchanging the digits exceeds the original number by 36. Find the original number. 3 nks vadksa dh la[;k esa vadksa dk ;ksx 10 gSA vadksa ds ijLij iyVus ls izkIr la[;k ewy la[;k ls 36 cydrs gSa\ 27. A pair of adjacent sides of a rectangle is in the ratio of 5 : 12. If the length of the diagonal is 26 cm. Find the lengths of sides and perimeter of the rectangle. 4 ,d vk;r dh vklUu Hkqtkvksa ds ,d ;qXe esa 5 % 12 dk vuqikr gSA ;fn bldk fod.kZ 26 ls-eh- gS rks vk;r dh Hkqtkvksa dh yEckbZ vkSj ifjeki Kkr dhft,A VIII-MATHEMATICS (5) 28. ABCD is a rectangle in which DP D C and BQ are perpendiculars from Q D and B respectively on diagonal AC. Show that : 4 (i) DADP @ DCBQ P (ii) ∠ADP = ∠CBQ A B (iii) DP = BQ ABCD ,d vk;r gS ftlds fod.kZ AC ij D vkSj B ls Øe'k% yEc DP vkSj BQ [khaps x;s gSa n'kkZb, % (i) DADP @ DCBQ (ii) ∠ADP = ∠CBQ (iii) DP = BQ 29. Using ruler and compass, construct a quadrilateral ABCD in which AB = CD = 5 cm, BC = 4.5 cm, B = 60, C = 120. Which type of quadrilateral is this? 4 iqQVs vkSj ijdkj dk iz;ksx djds prqHkqZt ABCD dh jpuk dhft, ftlesa AB = CD = 5 cm, BC = 4.5 cm, B = 60, C = 120 gSA ;g fdl izdkj dk prqHkqZt gS\ Alternate question for visually challenged students in lieu of Q. No. 29 ç-la- 29 ds LFkku ij n`f"V ckfèkr fo|kfFkZ;ksa ds fy, oSdfYid iz'u A money box contains one rupee and 2 rupee coins in ratio 3 : 5. If the total value of coins in the money box is Rs. 78, find the number of one rupee coins. ,d xqYyd esa ,d #i;s vkSj 2 #i;s ds flDds 3 % 5 ds vuqikr esa gSA ;fn xqYyd esa iwjs flDdksa dk eku 78 #i;s gS] mlesa ,d #i;s ds flDdksa dh la[;k Kkr dhft,A 30. A card is drawn from a well shuffled deck of cards, find the probability that 4 the card drawn is (i) a black 9 (ii) a king of spade (iii) an ace (iv) a diamond VIII-MATHEMATICS (6)  52 iRrksa dh rk'k dh xM~Mh esa ls ,d iRrk ;kn`PN;k fudkyk tkrk gS] izkf;drk Kkr dhft, fd fudkyk x;k iRrk gS (i) ,d dkyk (ii) ,d gqdqe dk ckn'kkg (iii) ,d bDdk (iv) ,d b±V 31. A box contains 24 marbles of different colours. The following table shows number of marbles of these different colours. Draw a pie chart for the data. Colour of marble Red Green Yellow Blue No. of marbles 5 3 6 10 ,d cDls esa 24 fofHkUu jax ds iRFkj gS] fuEufyf[kr lkj.kh esa fofHkUu jaxksa ds iRFkjksa dh la[;k nh xbZ gS bls ,d o`Rr fp=k ls n'kkZb, & iRFkj dk jax yky gjk ihyk uhyk iRFkkjksa dh la[;k 5 3 6 10 4 or (vFkok) The following is the distribution of weights (in kg) of 50 persons. Weight (in kg) 50-55 55-60 60-65 65-70 70-75 75-80 80-85 85-90 No. of persons 8 5 12 4 5 7 6 3 Draw the histogram. (i) How many persons have weight more than 80 Kg? (ii) In which group, maximum no. of persons exit? fuEufyf[kr rkfydk esa 50 yksxksa ds Hkkj (fdyksxzke esa) fn;s x, gSa & otu (fd-xzk- esa) 50-55 55-60 60-65 65-70 70-75 75-80 80-85 85-90 yksxksa dh la[;k 8 5 12 4 5 7 6 3 ,d vk;r fp=k cukb, (i) fdrus yksxksa dk Hkkj 80 fd-xzk- ls T;knk gS\ (ii) fdl lewg esa T;knk yksx gSa\ VIII-MATHEMATICS (7)  Alternate question for visually challenged students in lieu of Q. No. 31 ç-la- 31 ds LFkku ij n`f"V ckfèkr fo|kfFkZ;ksa ds fy, oSdfYid iz'u Divide 3x(5x2+3x3+2) – (2x2+8–x) by (–2+3x). Write quotient and remainder. 3x(5x2+3x3+2) – (2x2+8–x) dks (–2+3x) ls Hkkx dhft,A HkkxiQy o 'ks"kiQy fyf[k,A VIII-MATHEMATICS (8)  PAPER II Max. Marks 90 section - 'a' ([kaM&^v*) Question numbers 1 to 4 carry 1 mark each. ç'u la[;k 1 ls 4 rd izR;sd iz'u 1 vad dk gSA −2 1. Find the value of 3 × (64 ) 3 1 −2 3 × (64 ) 3 dk eku Kkr dhft,A 2. Write the polynomial x 5 − 7 x9 + x 7 + 6 in standard form. Also write its degree. 1 cgqin x5 − 7 x9 + x 7 + 6 dks ekud :i esa fyf[k,A bldh ?kkr Hkh fyf[k,A 3. Name a triangle which has line symmetry but do not have rotational symmetry. 1 ,d ,sls f=kHkqt dk uke crk,¡ ftlesa js[kk lefefr rks gksrh gS ijarq ?kw.kZu lefefr ugha gksrhA 4. In the word 'STUDENT' which letters show rotational symmetry of order 2? 1 fn, x, 'kCn 'STUDENT' esa dkSu ls v{kj ?kw.kZu lefefr dk ?kw.kZu Øe 2 n'kkZrs gSa\ SECTIon - 'b' ([kaM&^c*) Question numbers 5 to 10 carry 2 marks each. 2 ç'u la[;k 5 ls 10 rd izR;sd iz'u 2 vad dk gSA Find the value of (3 + 4 )× 2 0 −1 2 5. (30 + 4−1 )× 22 dk eku Kkr dhft,A 6. Find the value of x, if 22x–1 = 8x–3 2 ;fn 22x–1 = 8x–3 gks rks] x dk eku Kkr dhft,A VIII-MATHEMATICS (1) 7. Divide 3a 4 + 2a 3 − 6a by 3a. 2 3a 4 + 2a 3 − 6a dks 3a ls Hkkx dhft,A 8. Using factor method, divide the polynomial a 2 + 14a + 48 by (a+8). 2 xq.ku[kaM fofèk dk iz;ksx djds cgqin a 2 + 14a + 48 dks (a+8) ls Hkkx dhft,A 9. Solve the following equation : 2 fuEu lehdj.k dks gy dhft, % 11(7 y + 2 ) =5 (6 y − 2 ) 10. Write the order and angle of rotation of a regular hexagon.. 2 ,d fu;fer "kV~Hkqt dk ?kw.kZu lefefr Øe rFkk ?kw.kZu lefefr dks.k fyf[k,A section - 'c' ([kaM&^l*) Question numbers 11 to 20 carry 3 marks each. ç'u la[;k 11 ls 20 rd izR;sd iz'u 3 vad dk gSA 11. Evaluate (ljy dhft,) % 3 12. Compute the Amount for H 65,536 invested for 1½ years at 12½% p.a., the interest being compounded Semi-annually. 3 H 65]536dh jkf'k ds fy, 1½ o"kZ dk 12½% okf"kZd nj ls fuos'k djus ij feJ/u Kkr dhft, tcfd C;kt vèkZokf"kZd la;ksftr gksrk gSA 13. Using long division method, show that (x–3) is a factor of 6+x–4x2+x3. 3 yEch Hkkxfofèk dk ç;ksx djds n'kkZb;s fd (x–3)] 6+x–4x2+x3 dk xq.ku[k.M gSA 14. A number consists of two digits whose sum is 8. If 18 is added to the number, its digits are reversed. Find the number. 3 nks vadksa dh ,d la[;k ds nksuksa vadksa dk ;ksx 8 gSA ;fn bl la[;k esa 18 tksM+k tkrk gS rks blds vadksa dk LFkku iyV tkrk gSA ewy la[;k Kkr dhft,A or (vFkok) VIII-MATHEMATICS (2)  The numerator of a fraction is 4 less than the denominator. If 1 is added to both its numerator and denominator, it becomes ½. Find the fraction. 3 ,d fHkUu dk va'k mlds gj ls 4 de gSA ;fn ml fHkUu ds va'k rFkk gj nksuksa esa 1 tksM+k tk, rks ;g ½ cu tkrh gSA og fHkUu Kkr dhft,A 15. Arvind has a piggy bank. It is full of one rupee and fifty paise coins. It contains 3 times as many fifty paise coins as one rupee coins. The total amount of the money in the piggy bank is H 35. How many coins of each kind are there in the piggy bank? 3 vjfoan ds ikl ,d fiXxh cSad gSA ;g ,d :i;s rFkk ipkl iSls ds flDdksa ls Hkjk gqvk gSA blesa ipkl iSls ds flDdksa dh la[;k] ,d #i;s ds flDdksa dh la[;k ls rhu xquh gSA fiXxh cSad esa j[kh dqy /ujkf'k 35 #i;s gSA izR;sd izdkj ds fdrus flDds fiXxh cSad esa j[ks gq, gSa\ 16. In the given figure ABCD is a parallelogram. D C If ∠DAB= 750 and ∠DBC= 600, Calculate ∠CDB and ∠ADB 3 nh xbZ vkÑfr esa] ABCD ,d lekarj prqHkqZt gSA vxj ∠DAB= 750, ∠DBC= 600 gS rks ∠CDB rFkk 600 750 ∠ADB ds eku Kkr dhft,A A B 17. The lengths of one pair of adjacent sides of a D C rectangle ABCD are in the ratio 3 : 4. If one of its diagonal measures 10 cm, find the lengths 10 cm of the sides of rectangle. 3 ,d vk;r dh nks layXu Hkqtkvksa dh yackbZ 3 % 4 ds vuqikr esa gSaA ;fn blds ,d fod.kZ dh eki A B 10 cm gS rks bldh Hkqtkvksa dh yackbZ Kkr dhft,A 18. Construct a quadrilateral ABCD in which sides AB = 4 cm, BC = 5 cm, CD = 4.5 cm, AD = 5.5 cm and diagonal AC = 7.5 cm. 3 ,d prqHkqZt ABCD dh jpuk dhft, ftlesa AB = 4 cm, BC = 5 cm, CD = 4.5 cm, AD = 5.5 cm rFkk fod.kZ AC = 7.5 cm gSA VIII-MATHEMATICS (3)  Alternate question for visually challenged students in lieu of Q. No. 18 ç-la- 18 ds LFkku ij n`f"V ckfèkr fo|kfFkZ;ksa ds fy, oSdfYid iz'u In a factory, the production of scooters has risen to 48400 from 40000 in 2 years. Find the rate of growth per annum. ,d dkj[kkus esa 2 o"kks± esa LdwVjksa dk mRiknu 40000 ls c