10th Maths Sample Question Paper PDF 2025

dsoy vH;kl gsrq uewuk iz’u i= Sample question paper for practice only gkbZ Ldwy ijh{kk &2025 High School Examination - 2025 fo"k;&xf.kr...

dsoy vH;kl gsrq uewuk iz’u i= Sample question paper for practice only gkbZ Ldwy ijh{kk &2025 High School Examination - 2025 fo"k;&xf.kr Subject-MATHEMATICS (Hindi & English Version) Total Total Printed Pages Time Maximum Questions Marks 23 8 3 hours 75 funsZ’k& (𝑖) lHkh iz'u vfuok;Z gSaA (𝑖𝑖) iz'u Øekad 1 ls 5 rd ds izR;sd miiz’u ij 1-1 vad fu/kkZfjr gSA (𝑖𝑖𝑖) iz'u Øekad 6 ls 17 rd ds izR;sd iz’u 2 vad dk gSA (𝑖𝑣) iz'u Øekad 18 ls 20 rd ds izR;sd iz’u 3 vad dk gSA (𝑣) iz'u Øekad 21 ls 23 rd ds izR;sd iz’u 4 vad dk gSA Instructions% (i) All questions are compulsory. (ii) Sub-question of Question numbers 1 to 5 carry 1 mark each. (iii) Question numbers 6 to 17 carry 2 marks each. (iv) Question numbers 18 to 20 carry 3 marks each. (v) Question numbers 21 to 23 carry 4 marks each. 1 lgh fodYi pqudj fyf[k,% %& 1x6=6 (𝑖) (12, 16, 20) dk HCF gS& (𝑎) 1 (𝑏) 2 (𝑐) 3 (𝑑) 4 (𝑖𝑖) jSf[kd cgqin dh ?kkr gksrh gS& (𝑎) 0 (𝑏) 2 (𝑐) − 1 (𝑑) 1 (𝑖𝑖𝑖) lehdj.k fudk; 𝑎1 𝑥 + 𝑏1 𝑦 + 𝑐1 = 0 rFkk 𝑎2 𝑥 + 𝑏2 𝑦 + 𝑐2 = 0 ds ,d vf}rh; gy gksus dh 'krZ gS%& 𝑎 𝑏 𝑎 𝑏 𝑐 (𝑎) 1 ≠ 1 (𝑏) 1 = 1 = 1 𝑎2 𝑏2 𝑎2 𝑏2 𝑐2 𝑎1 𝑏1 𝑐1 𝑎1 𝑏1 (𝑐) = ≠ (𝑑) = 𝑎2 𝑏2 𝑐2 𝑎2 𝑏2 2 (𝑖𝑣) f}?kkr lehdj.k 𝑎𝑥 + 𝑏𝑥 + 𝑐 = 0, 𝑎 ≠ 0 esa nks cjkcj okLrfod ewy gksx a as ;fn& (𝑎) 𝑏 2 + 4𝑎𝑐 = 0 (𝑏) 𝑏 2 − 4𝑎𝑐 > 0 (𝑐) 𝑏 2 − 4𝑎𝑐 < 0 (𝑑) 𝑏 2 − 4𝑎𝑐 = 0 −1 (𝑣) 𝐴. 𝑃. − 3, 2 , 2, … …dk 11 oka in gS& (𝑎) 28 (𝑏) 22 (𝑐) − 38 (𝑑) − 22 1  (𝑣𝑖) fcanq 𝑃(−7 ,7) vkSj 𝑄(−2, −3) ds chp dh nwjh gS& (𝑎) 5√5 (𝑏) 5√6 (𝑐)6√5 (𝑑) 4√5 Choose the correct option and write it - (𝑖) 𝐻𝐶𝐹 𝑜𝑓(12, 16, 20) 𝑖𝑠 - (𝑎) 1 (𝑏) 2 (𝑐) 3 (𝑑) 4 (𝑖𝑖) Degree of linear polynomial is - (𝑎) 0 (𝑏) 2 (𝑐) − 1 (𝑑) 1 (𝑖𝑖𝑖) The condition for the systems of equations 𝑎1 𝑥 + 𝑏1 𝑦 + 𝑐1 = 0 𝑎𝑛𝑑 𝑎2 𝑥 + 𝑏2 𝑦 + 𝑐2 = 0 have a unique solution is - 𝑎 𝑏 𝑎 𝑏 𝑐 (𝑎) 1 ≠ 1 (𝑏) 1 = 1 = 1 𝑎 2𝑏 2 𝑎 𝑏 𝑐 2 2 2 𝑎1 𝑏1 𝑐1 𝑎1 𝑏1 (𝑐 ) =𝑏 ≠𝑐 (𝑑 ) =𝑏 𝑎2 2 2 𝑎2 2 2 (𝑖𝑣) The quadratic equation 𝑎𝑥 + 𝑏𝑥 + 𝑐 = 0, 𝑎 ≠ 0 will have two equal real roots, if (𝑎) 𝑏 2 + 4𝑎𝑐 = 0 (𝑏) 𝑏 2 − 4𝑎𝑐 > 0 (𝑐) 𝑏 2 − 4𝑎𝑐 < 0 (𝑑) 𝑏 2 − 4𝑎𝑐 = 0 −1 (𝑣) 11𝑡ℎ 𝑡𝑒𝑟𝑚 𝑜𝑓 𝑡ℎ𝑒 𝐴. 𝑃. − 3, , 2, … 𝑖𝑠 2 (𝑎) 28 (𝑏) 22 (𝑐) − 38 (𝑑) − 22 (𝑣𝑖) Distance between points 𝑃(−7 ,7) 𝑎𝑛𝑑 𝑄(−2, −3) 𝑖𝑠 − (𝑎) 5√5 (𝑏) 5√6 (𝑐)6√5 (𝑑) 4√5 2 fjDr LFkkuksa dh iwfrZ dhft, %& 1x6=6 (𝑖) f}?kkr lehdj.k 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0, 𝑎 ≠ 0 ds fy, fofoDrdj 𝐷 = -------------- (𝑖𝑖) 𝐴. 𝑃. ds izFke 𝑛 inksa dk ;ksx 𝑆 =----------------------- (𝑖𝑖𝑖) lHkh o`Ùk ------------------------- gksrs gSaA (𝑖𝑣) o`Ùk rFkk mldh Li’kZ js[kk ds mHk;fu"B fcanq ---------------------------------dks dgrs gSa (𝑣) fdlh iz;ksx dh lHkh izkjafHkd ?kVukvksa dh izkf;drkvksa dk ;ksx--------------------- gksrk gSA (𝑣𝑖) o`Ùk ds fdlh fcanq ij Li’kZ js[kk, Li’kZ fcanq ls tkus okyh f=T;k ij -----------------------------gksrh gSA Fill in the blanks : (𝑖) For a quadratic equation 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0, 𝑎 ≠ 0 discriminant 𝐷 = ……………….. (𝑖𝑖) Sum of first 𝑛 terms of an 𝐴. 𝑃. , 𝑆 =…………………… (𝑖𝑖𝑖) All circles are …………………………… (𝑖𝑣) The common point of a tangent to a circle and the circle is called ………………………….. (𝑣) The Sum of the probabilities of all the elementary events of an experiment is ………… (𝑣𝑖) The tangent at any point of a circle is …………………….to the radius through the point of contact. 2 3 lgh tksM+h feykb, %& 1x6=6 [k.M ^v^ [k.M ^c^ (𝑖) v/kZxksys dk oØ i`"Bh; {ks=Qy (𝑎) 0 (𝑖𝑖) csyu dk oØ i`"Bh; {ks=Qy (𝑏) 1 + 𝑐𝑜𝑡 2 𝐴 1 (𝑖𝑖𝑖) o`Ùk ds ,d f=T;k[k.M dk {ks=Qy (𝑐) 𝑡𝑎𝑛𝐴 (𝑖𝑣) 𝑐𝑜𝑡 𝐴 (𝑑) 2𝜋𝑟ℎ (𝑣) 𝑐𝑜𝑠𝑒𝑐 2 𝐴 (𝑒) 2𝜋𝑟 2 𝜃 (𝑣𝑖) 𝑠𝑖𝑛0° (𝑓) × 𝜋𝑟 2 360° Match the correct column : Section ‘A’ Section ‘B’ (𝑖) The curved surface area of the hemisphere (𝑎) 0 (𝑖𝑖) The curved surface area of the cylinder (𝑏) 1 + 𝑐𝑜𝑡 2 𝐴 1 (𝑖𝑖𝑖) Area of a sector of a circle (𝑐) 𝑡𝑎𝑛𝐴 (𝑖𝑣) 𝑐𝑜𝑡 𝐴 (𝑑) 2𝜋𝑟ℎ (𝑣) 𝑐𝑜𝑠𝑒𝑐 2 𝐴 (𝑒) 2𝜋𝑟 2 𝜃 (𝑣𝑖) 𝑠𝑖𝑛0° (𝑓) × 𝜋𝑟 2 360° 4 fuEufyf[kr esa lR;@vlR; fyf[k, %& 1x6=6 (𝑖) lehdj.k (𝑥 − 2)2 + 1 = 2𝑥 − 3 ,d f}?kkr lehdj.k ugha gSA (𝑖𝑖) 𝐴. 𝑃. 32 , 12 , −1 2 , −3 2 , …. dk lkoZUrj −2 gSA (𝑖𝑖𝑖) lHkh lef}ckgq f=Hkqt le:Ik gksrs gSaA (𝑖𝑣) fcUnqvksa 𝐴(3, −1) vkSj 𝐵(6, 4) dk e/; fcUnq (9, 3)gSA (𝑣) fdlh ?kVuk 𝐸 ds fy, 𝑃(𝐸̅) = 1 − 𝑃(𝐸) (𝑣𝑖) dsna zh; izo`fRr ds ekidksa esa ,d vkuqHkkfod laca/k gS] tks fuEufyf[kr gSA 3 माध्यक = बहुलक + 2 माध्य Write True/False in the following: (𝑖) Equation (𝑥 − 2)2 + 1 = 2𝑥 − 3 is not a quadratic equation. 3 1 −1 −3 (𝑖𝑖) The common difference of the 𝐴. 𝑃. , , , 2 , …. 𝑖𝑠 − 2 2 2 2 (𝑖𝑖𝑖) All isosceles triangles are similar. (𝑖𝑣) Mid point of points 𝐴(3, −1) 𝑎𝑛𝑑 𝐵(6, 4) 𝑖𝑠 (9, 3). (𝑣) For an event 𝐸, 𝑃(𝐸̅ ) = 1 − 𝑃(𝐸) (𝑣𝑖) There is an empirical relationship between the three measures of central tendency. 3 𝑀𝑒𝑑𝑖𝑎𝑛 = 𝑀𝑜𝑑𝑒 + 2 𝑀𝑒𝑎𝑛 5 izR;sd dk ,d 'kCn@okD; esa mRrj fyf[k, %& 1x6=6 (𝑖) dks.k&dks.k (𝐴𝐴) le:irk dlkSVh fyf[k,A (𝑖𝑖) fcUnqvks 𝑃(𝑥1 , 𝑦1 ) vkSj 𝑄(𝑥2 , 𝑦2 ) ds chp dh nwjh fyf[k,A (𝑖𝑖𝑖) n`f"V js[kk dh ifjHkk"kk fyf[k,A (𝑖𝑣) o`Ùk ds f=T;[k.M ds pki dh yEckbZ dk lw= fyf[k,A (𝑣) ,d o`Ùk dh fdruh Li’kZ js[kk,¡ gks ldrh gSaA (𝑣𝑖) voueu dks.k dh ifjHkk"kk fyf[k,A 3  Write the answer in one word/sentence of each : (𝑖) Write the angle-angle (AA) similarity criterion. (𝑖𝑖) Write the distance between the points 𝑃(𝑥1 , 𝑦1 ) and (𝑥2 , 𝑦2 ). (𝑖𝑖𝑖) Write the definition of line of sight. (𝑖𝑣) Write the formula for the length of the arc of a sector of a circle. (𝑣) How many tangents can a circle have? (𝑣𝑖) Write the definition of the angle of depression. 6 5005 dks vHkkT; xq.ku[k.M ds :Ik esa O;Dr dhft,A 2 Express 5005 as a product of its prime factor. vFkok@OR 8 ,9 ,oa 25 dk 𝐻𝐶𝐹 vkSj 𝐿𝐶𝑀 Kkr dhft,A Find the HCF and LCM of 8, 9 𝑎𝑛𝑑 25. 7 f}?kkr cgqin 𝑥 2 + 7𝑥 + 10 ds 'kwU;d Kkr dhft,A 2 Find the zeroes of the quadratic polynomial 𝑥 2 + 7𝑥 + 10. vFkok@ OR fdlh cgqin 𝑝(𝑥) ds fy,] 𝑦 = 𝑝(𝑥) dk xzkQ uhps fn;k x;k gSA 𝑝(𝑥) ds 'kwU;dksa dh la[;k Kkr dhft,A The graph of 𝑦 = 𝑝(𝑥) is given below for polynomial 𝑝(𝑥). Find the number of zeroes of 𝑝(𝑥). 8 f}?kkr cgqin 𝑥 2– 3 ds 'kwU;dksa dk ;ksxQy ,oa xq.kuQy Kkr dhft,A 2 2 Find the sum and product of the zeroes of quadratic polynomial 𝑥 – 3. vFkok@ OR −1 1 ,d f}?kkr cgqin Kkr dhft,] ftlds 'kwU;dksa dk ;ksx rFkk xq.kuQy Øe’k% , gSA 4 4 −1 1 Find a quadratic polynomial whose sum and product of the zeroes are , 4 respectively. 4 4  𝑎1 𝑏1 𝑐1 9 vuqikrksa , vkSj dh rqyuk dj Kkr dhft, fd fuEUk jSf[kd lehdj.k ;qXe laxr gSa ;k vlaxrA 𝑎2 𝑏2 𝑐2 2 3𝑥 + 2𝑦 = 5 2𝑥 − 3𝑦 = 7 𝑎 𝑏 𝑐1 On comparing the ratios 𝑎1 , 𝑏1 𝑎𝑛𝑑 , Find out whether the following pair of linear equations are 2 2 𝑐2 consistent or inconsistent. 3𝑥 + 2𝑦 = 5 2𝑥 − 3𝑦 = 7 vFkok@ OR fuEu jSf[kd lehdj.k ;qXe dks gy dhft,A 𝑥 + 𝑦 = 14 𝑥−𝑦 =4 Solve the following pair of linear equations. 𝑥 + 𝑦 = 14 𝑥−𝑦 =4 10 xq.ku[kaMu }kjk lehdj.k 2𝑥 2 − 5𝑥 + 3 = 0 ds ewy Kkr dhft,A 2 Find the roots of the equation 2𝑥 2 − 5𝑥 + 3 = 0 by factorisation. vFkok@ OR f}?kkr lehdj.k 2𝑥 + 𝑘𝑥 + 3 = 0, esa 𝑘 dk ,slk eku Kkr dhft, fd mlds nks cjkcj ewy gksaA 2 Find the value of 𝑘 for quadratic equation 2𝑥 2 + 𝑘𝑥 + 3 = 0, so that they have two equal roots. 11 nks vadks okyh fdruh la[;k,¡ 3 ls foHkkT; gSa ? 2 How many two digit numbers are divisible by 3? vFkok@ OR ,d 𝐴. 𝑃. esa 𝑎 = 5, 𝑑 = 3 vkSj 𝑎𝑛 = 50 gS, 𝑛 Kkr dhft,A In an 𝐴. 𝑃. 𝑎 = 5, 𝑑 = 3 𝑎𝑛𝑑 𝑎𝑛 = 50, Find 𝑛. 12 ;fn ∆𝐴𝐵𝐶 esa 𝐷𝐸 || 𝐵𝐶 gS] rks 𝐸𝐶 Kkr dhft,A 2 If in ∆𝐴𝐵𝐶, 𝐷𝐸 ||𝐵𝐶 then Find EC. 5  vFkok@ OR vk/kkjHkwr lekuqikfrdrk ize; s dk dFku fyf[k,A Write the statement of Basic Proportionality Theorem. 13 fcUnqvksa 𝑃(−1,7) vkSj 𝑄(4, −3) dks feykus okys js[kk[k.M dks 2: 3 esa foHkkftr djus okys fcUnq ds funsZ'kkad Kkr dhft,A 2 Find the co-ordinates of the points which divides the line segment joining the points 𝑃(−1,7) and 𝑄(4, −3) in the ratio 2: 3. vFkok@ OR ;fn fcUnq 𝐴(6, 1), 𝐵(8, 2), 𝐶(9, 4) vkSj 𝐷 (𝑝, 3) ,d lekarj prqHkqZt ds 'kh"kZ blh Øe esa gk]sa rks 𝑝 dk eku Kkr dhft,A If the points 𝐴(6, 1), 𝐵(8, 2), 𝐶(9, 4)𝑎𝑛𝑑 𝐷 (𝑝, 3) are the vertices of a parallelogram, taken in order, find the value of 𝑝. 3 14 ;fn 𝑠𝑖𝑛𝐴 = 4 , rks 𝑐𝑜𝑠𝐴 vkSj 𝑡𝑎𝑛𝐴 dk eku ifjdfyr dhft,A 2 3 If 𝑠𝑖𝑛𝐴 = 4 , then find the value of 𝑐𝑜𝑠𝐴 and tan 𝐴 vFkok@ OR fuEufyf[kr dk eku fudkfy,& 𝑠𝑖𝑛60° 𝑐𝑜𝑠30° + 𝑠𝑖𝑛30° 𝑐𝑜𝑠60° Evaluate the following. 𝑠𝑖𝑛60° 𝑐𝑜𝑠30° + 𝑠𝑖𝑛30° 𝑐𝑜𝑠60° 15 ,d fcUnq 𝐴 ls tkss ,d o`Ùk ds dsUnz ls 5𝑐𝑚 nwjh ij gS] o`Ùk ij Li’kZ js[kk dh yEckbZ 4𝑐𝑚 gSA o`Ùk dh f=T;k Kkr dhft,A 2 The length of the tangent from a point A at distance 5 cm from the center of the circle is 4 cm. Find the radius of the circle. vFkok@ OR fl) dhft, fd ckg~; fcUnq ls o`Ùk ij [khaph xbZ Li’kZ js[kkvksa dh yEckb;k¡ cjkcj gksrh gSaA Prove that, the lengths of tangents drawn from an external point to a circle are equal. 16 lfork vkSj gehnk nks fe= gSa bldh D;k izkf;drk gS fd nksuksa 2 (𝑖) ds tUe&fnu fHkUu fHkUUk gksa \ (𝑖𝑖) dk tUefnu ,d gh gks \ ¼yhi dk o"kZ dks NksM+rs gq,½ Savita and Hamida are two friends. What is the probability that both will have (i) different birthdays ? (ii) The same birthday ? (ignoring a leap years) vFkok@ OR ;fn 𝑃(𝐸) = 0.05 gS] rks ‘𝐸 ugh ’ dh izkf;drk D;k gSA If 𝑃(𝐸) = 0.05, what is the probability of ‘not E’ 6 17 vPNh izdkj ls QsaVh xbZ 52 iRrksa dh ,d xM~Mh esa ls ,d iRrk fudkyk tkrk gSA bldh izkf;drk ifjdfyr dhft, fd ;g iRrk % (𝑖) ,d bDdk gksxk , (𝑖𝑖) ,d bDdk ugha gksxkA 2 One card is drawn from a well- shuffled deck of 52 cards. Calculate the probability that the card will (i) be an ace, (ii) not be an ace. vFkok@ OR ,d FkSys esa 3 yky vkSj 5 dkyh xsna sa gSaA bl FkSys esa ls ,d xsna ;n`PN;k fudkyh tkrh gSA bldh izkf;drk D;k gS fd xsna (𝑖) yky gks \ (𝑖𝑖) yky ugha gks \ A bag contains 3 red balls and 5 black balls. A ball is drawn at random from this bag. What is the probability that the ball drawn is (i) red ? (ii) not red ? 18 fl) dhft, fd 3 + √5 ,d vifjes; la[;k gSA 3 Prove that 3 + √5 is an irrational number vFkok@ OR tkWp dhft, fd D;k fdlh izkd`r la[;k 𝑛 ds fy,] la[;k 6𝑛 vad 0 ij lekIr gks ldrh gS ? Check whether 6𝑛 can end with the digit 0 for any natural number 𝑛 ? 19 Hkwfe ij ,d fcUnq ls] ehukj dk ikn fcUnq 30𝑚 dh nwjh ij gS] ehukj ds f’k[kj dk mUu;u dks.k 30° gSA ehukj dh Å¡pkbZ Kkr dhft,A 3 The angle of elevation of the top of the tower from a point on the ground, which is 30𝑚 away from the foot of the tower, is 30°. Find the height of the tower. vFkok@ OR 1.5𝑚 yEck ,d izs{kd ,d fpeuh ls 28.5𝑚 dh nwjh ij gSA mldh vk¡[kks ls fpeuh ds f’k[kj dk mUu;u dks.k 45° gSA fpeuh dh Å¡pkbZ Kkr dhft,A An observer 1.5𝑚 tall is 28.5 𝑚 away from a chimney. The angle of elevation of the top of the chimney from his eyes is 45°.Find the height of the chimney. 20 6 𝑐𝑚 f=T;k okys ,d o`Ùk ds ,d f=T;k[k.M dk {ks=Qy Kkr dhft,] f=T;k[k.M dk dks.k 60° gSA 3 Find the area of a sector of a circle with radius 6 𝑐𝑚, If angle of the sector is 60° vFkok@ OR ,d ?kM+h dh feuV dh lqbZ ftldh yEckbZ 14 𝑐𝑚 gSA bl lqbZ }kjk 5 feuV esa jfpr {ks=Qy Kkr dhft,A The length of the minute hand of a clock is 14 𝑐𝑚. Find the area swept by the minute hand in 5 minutes. 21 nks vadks dh ,d la[;k ,oa mlds vadks dks myVus ij cuh la[;k dk ;ksx 66 gSA ;fn la[;k ds vadks dk varj 2 gks] rks la[;k Kkr dhft,A 4 The sum of a two digit number and the number obtained by reversing the digits is 66. If the digits of the number differ by 2. Find the number. vFkok@ OR ;fn ge va’k esa 1 tksM+ nsa rFkk gj esa ls 1 ,d ?kVk ns]a rks fHkUUk 1 esa cny tkrh gSA ;fn gj esa 1 tksM+ ns]a 1 rks ;g 2 gks tkrh gSA og fHkUu D;k gS \ If we add 1 to the numerator and subtract 1 from the denominator, a fraction redues to 1. It 1 becomes 2 , If we only add 1 to the denominator. What is that fraction? 7 22 ,d f[kykSuk f=T;k 3.5 𝑐𝑚 okys ,d 'kadq ds vkdkj dk gS] tks mlh f=T;k okys ,d v)Zxksys ij v/;kjksfir gSA bl f[kykSus dh lEiw.kZ Å¡pkbZ 15.5 𝑐𝑚 gSA bl f[kykSus dk lEiw.kZ i`"Bh; {ks=Qy Kkr dhft,A 4 A toy is in the form of a cone of radius 3.5 𝑐𝑚, mounted on a hemisphere of same radius. The total height of this toy is 15.5 𝑐𝑚. Find the total surface area of this toy vFkok@ OR ,d Bksl] ,d v)Zxksys ij [kMs+ ,d 'kadq ds vkdkj dk gS ftudh f=T;k,¡ 1 𝑐𝑚 gSa rFkk 'kadq dh Å¡pkbZ mldh f=T;k ds cjkcj gSA bl Bksl dk vk;ru 𝜋 ds inksa esa Kkr dhft,A A solid is in the shape of a cone standing on a hemisphere with both their radii being to 1𝑐𝑚 and the height of the cone is equal to its radius. Find the volume of this solid in terms of π. 23 fuEUkfyf[kr lkj.kh 35 uxjksa dh lk{kjrk nj ¼izfr'kr esa½ n'kkZrh gSA ek/; lk{kjrk nj Kkr dhft,A 4 lk{kjrk nj ¼izfr'kr es½a 45 − 55 55 − 65 65 − 75 75 − 85 85 − 95 uxjksa dh la[;k 3 10 11 8 3 The following table gives the literacy rate (in percentage) of 35 cities, Find the mean literacy rate Literacy rate (in %) 45 − 55 55 − 65 65 − 75 75 − 85 85 − 95 Number of cities 3 10 11 8 3 vFkok@ OR ,d LFkkuh; VsyhQksu funsZf’kdk ls 100 dqyuke fy, x, vkSj muesa iz;qDr vaxzsth o.kZekyk ds v{kjksa dh la[;k dk fuEufyf[kr ckjackjrk caVu izkIr gqvk % v{kjksa dh la[;k 1−4 4−7 7 − 10 10 − 13 13 − 16 16 − 19 dqyukeksa dh la[;k 6 30 40 16 4 4 dqy ukeksa dk cgqyd Kkr dhft,A 100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabet in the surnames was obtained as follows: Number of 1−4 4−7 7 − 10 10 − 13 13 − 16 16 − 19 letters Number of 6 30 40 16 4 4 surnames Find the mode size of the surnames. ------------------X--------------------X------------------------X--------------------------X-----------------X---------------X------------ 8