Maths 10th Sample Paper 2023-24 PDF

dsoy vH;kl gsrq uewuk iz’u i= Sample question paper for practice only gkbZ Ldwy ijh{kk &2024 High School Examination - 2024 fo"k;&xf.kr Subject-M...

dsoy vH;kl gsrq uewuk iz’u i= Sample question paper for practice only gkbZ Ldwy ijh{kk &2024 High School Examination - 2024 fo"k;&xf.kr Subject-MATHEMATICS (Hindi & English Version) Total Total Printed Pages Time Maximum Question Marks 23 8 3 hours 75 funsZ’k& (𝑖) lHkh iz'u vfuok;Z gSaA (𝑖𝑖) iz'u Øekad 1 ls 5 rd oLrqfu"B izdkj ds iz'u gSaA (𝑖𝑖𝑖) iz'u Øekad 6 ls 23 esa vkarfjd fodYi fn, x, gSaA Instructions % (i) All questions are compulsory. (ii) Question numbers 1 to 5 are objective type questions. (iii) Internal options have been given in question numbers 6 to 23. 1 lgh fodYi pqudj fyf[k, % 1x6=6 (𝑖) 𝐻𝐶𝐹 (91, 21) gS& (𝑎) 91 (𝑏) 21 (𝑐) 13 (𝑑) 7 (𝑖𝑖) lehdj.k fudk; 𝑥 + 2𝑦 + 5 = 0 vkSj −3𝑥 − 6𝑦 + 1 = 0 dk gy gkssxk& (𝑎) vf}rh; gy (𝑏) dksbZ gy ugha (𝑐) vuarr% vusd gy (𝑑) nks gy (𝑖𝑖𝑖) f}?kkr cgqin 𝑎𝑥 + 𝑏𝑥 + 𝑐 ds 'kwU;dksa dk ;ksxQy gksxk& (𝑎) (𝑏) (𝑐) (𝑑) (𝑖𝑣) f}?kkr lehdj.k 𝑥 − 4𝑥 + 4 = 0 ds fofoDrdj dk eku gksxk& (𝑎) 4 (𝑏) 2 (𝑐) 0 (𝑑) 1 (𝑣) o`Ùk ds fdlh foUnq ij [khph xbZ Li'kZ js[kkvksa dh la[;k gksxh& (𝑎) 1 (𝑏) 2 (𝑐) 3 (𝑑) 0 (𝑣𝑖) foUnq (0, 5) ,oa (−5, 0) ds chp dh nwjh gS& (𝑎) 5 (𝑏) 5√2 (𝑐) 2√5 (𝑑) 2 1  Choose the correct option and write it: (𝑖) 𝐻𝐶𝐹 (91,21) 𝑖𝑠 − (𝑎) 91 (𝑏) 21 (𝑐) 13 (𝑑) 7 (𝑖𝑖) The pair of equation 𝑥 + 2𝑦 + 5 = 0 and −3𝑥 − 6𝑦 + 1 = 0 has - (𝑎) Unique Solution (𝑏) has no solutiona (𝑐) Infinitely many solutions (𝑑) two Solution (𝑖𝑖𝑖) The Sum of the zeros of quadratic Polynomial 𝑎𝑥 + 𝑏𝑥 + 𝑐 will be- (𝑎) (𝑏) (𝑐) (𝑑) (𝑖𝑣) The discriminant of the quadratic equation 𝑥 − 4𝑥 + 4 = 0 is- (𝑎) 4 (𝑏) 2 (𝑐) 0 (𝑑) 1 (𝑣) Number of tangents drawn at a point on circle (𝑎) 1 (𝑏) 2 (𝑐) 3 (𝑑) 0 (𝑣𝑖) The distance between the point (0, 5) and (−5, 0) is- (𝑎) 5 (𝑏) 5√2 (𝑐) 2√5 (𝑑) 2 2 fjDr LFkkuksa dh iwfrZ dhft, % 1x6=6 (𝑖) f=?kkr cgqin ds --------------------'kwU;d gksxsaA (𝑖𝑖) Jh/kjkpk;Z us ,d lw= izfrikfnr fd;k ftls vc -----------------------ds :i esa tkuk tkrk gSA (𝑖𝑖𝑖) lekarj Js.kh 5,10,15 … dk 10okW in -----------------gSA (𝑖𝑣) lHkh -------------------------f=Hkqt le:i gksrs gSaA (𝑣) ,d fuf'pr ?kVuk dh izkf;drk ----------------------gksrh gSA (𝑣𝑖) f=T;k 𝑟 okys o`Ùk dk {ks=Qy dk lw= ----------------------------gSA Fill in the blanks : (𝑖) ……… Zeros will be in a cubic polynomial. (𝑖𝑖) Shridharacharya derived a formula now known as the ……………… (𝑖𝑖𝑖) The 10th term of 𝐴. 𝑃. 5,10,15 … is……………. (𝑖𝑣) All …………… Triangles are similar. (𝑣) The Probability of a certain event is……….. (𝑣𝑖) Formula of area of the circle of radius 𝑟 is ………………. 2 3 lgh tksM+h feykb, % 1x6=6 [k.M ^v^ [k.M ^c^ (𝑖) 𝑠𝑖𝑛 𝐴 + 𝑐𝑜𝑠 𝐴 (𝑎) 5 (𝑖𝑖) tan (90° − 𝐴) (𝑏) 𝑎 (𝑖𝑖𝑖) 5𝑠𝑒𝑐 𝐴 − 5𝑡𝑎𝑛 𝐴 (𝑐) 𝑙𝑏ℎ (𝑖𝑣) ?kukHk dk vk;ru (𝑑) 1 (𝑣) oxZ dk {ks=Qy (𝑒) 0 (𝑣𝑖) 𝑃(𝐸) + 𝑃(Ē) dk eku D;k gksxk (𝑓) 9 (𝑔) 𝑐𝑜𝑡𝐴 (ℎ) 𝑎 (𝑖) 𝑐𝑜𝑠𝐴 (𝑗) 1 Match the correct column : Section ‘A’ Section ‘B’ (𝑖) 𝑠𝑖𝑛 𝐴 + 𝑐𝑜𝑠 𝐴 (𝑎) 5 (𝑖𝑖) tan (90° − 𝐴) (𝑏) 𝑎 (𝑖𝑖𝑖) 5𝑠𝑒𝑐 𝐴 − 5𝑡𝑎𝑛 𝐴 (𝑐) 𝑙𝑏ℎ (𝑖𝑣) Volume of a cuboid (𝑑) 1 (𝑣) Area of square (𝑒) 0 (𝑣𝑖) What will be the value of 𝑃(𝐸) + 𝑃(𝐸 ) (𝑓) 9 (𝑔) 𝑐𝑜𝑡𝐴 (ℎ) 𝑎 (𝑖) 𝑐𝑜𝑠𝐴 (𝑗) 1 4 izR;sd dk ,d 'kCn@okD; esa mRrj fyf[k, % 1x6=6 (𝑖) 'kwU;dksa dh la[;k fyf[k,A (𝑖𝑖) lokZf/kd ckjEckjrk okyk oxZ D;k dgykrk gS \ (𝑖𝑖𝑖) fdlh lekarj Js.kh ds izFke 𝑛 inksa dk ;ksx Kkr djus dk lw= fyf[k,A (𝑖𝑣) mUu;u dks.k dh ifjHkk"kk fyf[k,A (𝑣) Li'kZ js[kk vkSj o`Ùk ds mHk;fu"B foUnq dks D;k dgrs gSa \ (𝑣𝑖) 'kadq ds vk;ru dk lw= fyf[k,A 3  Write the answer in one word/sentence of each : (𝑖) Find the number of zeros. (𝑖𝑖) What is the class of maximum frequency is called. (𝑖𝑖𝑖) Write the formula to find the sum of the first 𝑛 terms of an A.P. (𝑖𝑣) Write the definition of angle of elevation. (𝑣) What is called the common point of the tangent and the circle? (𝑣𝑖) Write the formula for the volume of a cone. 5 fuEufyf[kr esa lR;@vlR; fyf[k, % 1x6=6 (𝑖) lekarj Js.kh 10,7,4, …. dk 10okW in −17 gSA (𝑖𝑖) le:i f=Hkqtksa dk {ks=Qy lnSo cjkcj gksrk gSA (𝑖𝑖𝑖) Li'kZ js[kk gh Nsnd js[kk gSA (𝑖𝑣) v)Zxksys dk vk;ru = 𝜋𝑟 gksxkA (𝑣) dks.k 𝜃 okys f=T;k[k.M ds laxr pki dh yEckbZ = × 2𝜋𝑟 (𝑣𝑖) nks le:i f=Hkqtksa dh laxr Hkqtk,W lekuqikrh gksrh gSaA Write True/False in the following: (𝑖) 10th term of the A.P. 10,7,4, …. is −17 (𝑖𝑖) The areas of similar triangles are always equal. (𝑖𝑖𝑖) The tangent line is the secant line. (𝑖𝑣) The Volume of hemisphere is = 𝜋𝑟 (𝑣) Length of an arc of a sector of angle 𝜃 = × 2𝜋𝑟 (𝑣𝑖) The corresponding sides of two similar triangles are proportional. 6 140 dks vHkkT; xq.ku[k.Mksa ds xq.kuQy ds :i esa O;Dr dhft,A 2 Express 140 as a product of its prime factors. vFkok@ OR 𝐻𝐶𝐹(306,657) = 9 fn;k gSA 𝐿𝐶𝑀(306,657) Kkr dhft,A Given that 𝐻𝐶𝐹(306,657) = 9, find 𝐿𝐶𝑀(306,657) 7 4𝑢 + 8𝑢 ds 'kwU;d Kkr dhft,A 2 Find the zeros of 4𝑢 + 8𝑢 vFkok@ OR cgqin 15𝑥 + 12𝑥 + 7 ds 'kwU;dksa dk xq.kuQy Kkr dhft,A Find the Product of zeros of polynomial 15𝑥 + 12𝑥 + 7 4 8 vuqikrksa , vkSj dh rqyuk dj Kkr dhft, fd fuEUk js[kk,W ,d foUnq ij izfrPNsn djrh gSa] 2 lekarj gSa vFkok laikrh gSa& 5𝑥 − 4𝑦 + 8 = 0 7𝑥 + 6𝑦 − 9 = 0 On Comparing the ratio , and find out whether the lines representing the following pair of linear equations intersect at a point are parallel or coincident. 5𝑥 − 4𝑦 + 8 = 0 7𝑥 + 6𝑦 − 9 = 0 vFkok@ OR jSf[kd lehdj.k ;qXe dks gy dhft,A 𝑥 + 𝑦 = 14 𝑥−𝑦 =4 Solve the pair of linear equations. 𝑥 + 𝑦 = 14 𝑥−𝑦 =4 9 lekarj Js.kh (𝐴. 𝑃. ) ds izFke pkj in fyf[k, ftldk izFke in 𝑎 = 10 rFkk lkoZvarj 𝑑 = 10 gSA 2 Write first four terms of an A.P. whose first term is 𝑎 = 10 and common difference is 𝑑 = 10. vFkok@ OR lekarj Js.kh −5, −1,3,7 …. dk izFke in rFkk lkoZvarj Kkr dhft,A Find the first term and common difference of 𝐴. 𝑃.: −5, −1,3,7 …. 10 nks f=Hkqtksa dh le:irk ds fy, vko';d izfrca/k fyf[k,A 2 Write the necessary conditions for the similarity of two triangle vFkok@ OR FksYl izes; dk dFku fyf[k,A Write the statement of Thales theorem. 11 foUnqvksa 𝑃(2, 3) vkSj 𝑄(4, 1) ds chp dh nwjh Kkr dhft,A 2 Find the distance between points 𝑃(2, 3) and 𝑄(4, 1). vFkok@ OR 𝑥 vkSj 𝑦 ds chp esa ,d laca/k LFkkfir dhft, rkfd foUnq (𝑥, 𝑦), foUnqvksa (7, 1) vkSj (3, 5) ls lenwjLFk gksA Find a relation between 𝑥 and 𝑦 such that the point (𝑥, 𝑦), is equidistant from the points (7, 1) and (3, 5). 12 foUnqvksa (𝑎, 𝑏) vkSj (−𝑎, −𝑏) dk e/; foUnq Kkr dhft,A 2 5  Find the mid point of the points (𝑎, 𝑏) and (−𝑎, −𝑏). vFkok@ OR ml foUnq ds funsZ'kkad Kkr dhft, tks foUnqvksa (−1, 7) vkSj (4, −3) dks feykus okys js[kk[k.M dks 2: 3 ds vuqikr esa foHkkftr djrk gSA Find the coordinates of the point which divides the line segment joining the points (−1, 7) and (4, −3) in the ratio 2:3. 13 ;fn 𝑠𝑖𝑛𝐴 = , rks 𝑐𝑜𝑠𝐴 vkSj 𝑡𝑎𝑛𝐴 dk eku ifjdfyr dhft,A 2 If 𝑠𝑖𝑛𝐴 = , then find the value of 𝑐𝑜𝑠𝐴 and 𝑡𝑎𝑛𝐴 vFkok@ OR ,d ledks.k f=Hkqt 𝐴𝐵𝐶 esa ftldk dks.k 𝐵 ledks.k gS] ;fn 𝑡𝑎𝑛𝐴 = 1 , rks lR;kfir dhft, fd 2𝑠𝑖𝑛𝐴. 𝑐𝑜𝑠𝐴 = 1 In a right angle triangle 𝐴𝐵𝐶, right angled at B,if 𝑡𝑎𝑛𝐴 = 1 , then verify that 2𝑠𝑖𝑛𝐴. 𝑐𝑜𝑠𝐴 = 1 14 5 lseh- f=T;k okys ,d o`Ùk ds foUnq 𝑃 ij Li'kZ js[kk 𝑃𝑄 dsUnz 𝑂 ls tkus okyh ,d js[kk ls foUnq 𝑄 ij bl izdkj feyrh gS fd 𝑂𝑄 = 12 lseh-A 𝑃𝑄 dh yEckbZ Kkr dhft,A 2 A tangent PQ at a point P of a circle of radius 5cm.meets a line through the centre O at a point Q so that 𝑂𝑄 = 12𝑐𝑚. Find the length of PQ vFkok@ OR ,d foUnq 𝐴 ls tks ,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 The length of the tangent from a point A at a distance of 5 cm. from the center of a circle, to the circle is 4 cm. find the radius of the circle. 15 6𝑐𝑚 f=T;k okys ,d o`Ùk ds ,d f=T;k[k.M dk {ks=Qy Kkr dhft, ftldk dks.k 60°gSA 2 Find the area of a sector of a circle with radius 6 cm. if angle of the sector is 60°. vFkok@ OR ,d o`Ùk ds prqFkkZa'k dk {ks=Qy Kkr dhft, ftldh ifjf/k 22 lseh- gSA Find the area of a quadrant of a circle whose circumference is 22 cm. 16 ,d ikals dks ,d ckj Qsadus ij vHkkT; la[;k vkus dh izkf;drk Kkr dhft,A 2 A die is thrown once. Find the probability of getting a prime number. vFkok@ OR ,d fMCCks esa 5 yky] 8 lQsn vkSj 4 gjs daps gSaA bl fMCcs esa ls ,d dapk ;kn`PN;k fudkyk tkrk gSA lQsn dapk fudkyus dh izkf;drk Kkr dhft,A A box contains 5 red, 8 white and 4 green marbles. one marble is taken out of the box random. Find the probability of getting a white marble. 17 ;fn 𝑃(𝐸) = 0.05 gS] rks ‘ 𝐸 ugh ’ dh izkf;drk D;k gS \ 2 If 𝑃(𝐸) = 0.05, then what is the probability of 𝐸 𝑛𝑜𝑡. vFkok@ OR ,d ikals dks ,d ckj Qsadus ij fo"ke la[;k vkus dh izkf;drk Kkr dhft,A 6  A die is thrown once. then Find the probability of getting an odd number. 18 n'kkZb, fd 3√2 ,d vifjes; la[;k gSA 3 Show that 3√2 is an irrational number. vFkok@ OR tkWp dhft, fd D;k fdlh izkd`r la[;k 𝑛 ds fy,] la[;k 6 vad 0 ij lekIr gks ldrh gSA Check whether 6 can end with the digit 0 for any natural number 𝑛 19 f}?kkr lehdj.k 2𝑥 − 3𝑥 + 5 = 0 ds ewyksa dh izd`fr Kkr dhft,A 3 Find the nature of roots of the quadratic equation 2𝑥 − 3𝑥 + 5 = 0 vFkok@ OR f}?kkr lehdj.k 6𝑥 − 𝑥 − 2 = 0 ds ewyksa dh izd`fr Kkr dhft,A Find the nature of roots of the quadratic equation 6𝑥 − 𝑥 − 2 = 0 20 nks ?kuksa ftuesa ls izR;sd dk vk;ru 64𝑚 gS] ds layXu Qydksa dks feykdj ,d Bksl cuk;k tkrk gSA blls izkIr ?kukHk dk i`"Bh; {ks=Qy Kkr dhft,A 3 Two cubes each of volume 64𝑚 are joined end to end. Find the surface area of the resulting cuboid vFkok@ OR ,d Bksl ,d v)Zxksys ij [kM+s ,d 'kadq ds vkdkj dk gS] ftudh f=T;k,W 1𝑐𝑚 gSa rFkk 'kadq dh ÅWpkbZ 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 equal to1 cm and the height of the cone is equal to its radius. Find the volume of this solid in terms of 𝜋 21 nks la[;kvksa dk varj 26 gS vkSj ,d la[;k nwljh la[;k dh rhu xquh gSA mUgs Kkr dhft,A 4 The difference of two numbers is 26 and one number is three times the other number. Find them. vFkok@ OR jSf[kd lehdj.k ;qXe dks gy dhft,A 3𝑥 − 5𝑦 − 4 = 0 9𝑥 = 2𝑦 + 7 Solve the pair of linear equations. 3𝑥 − 5𝑦 − 4 = 0 9𝑥 = 2𝑦 + 7 22 /kjrh ij ,d ehukj Å/okZ/kj [kM+h gSA /kjrh ds ,d ikn foUnq ls] tks ehukj ds ikn foUnq ls 15𝑚 nwj gS] ehukj ds f'k[kj dk mUu;u dks.k 60° gSA ehukj dh ÅWpkbZ Kkr dhft,A 4 A tower is standing vertically on the ground. From a point on the ground, which is 15m away from the foot of the tower, the angle of elevation of the top of the tower is found 60°. Find the height of the tower. 7  vFkok@ OR 7 𝑚 ÅWps Hkou ds f’k[kj ls ,d dscy VkWoj ds f’k[kj dk mUu;u dks.k 60°gS vkSj blds ikn dk voueu dks.k 45°gSA VkWoj dh ÅWpkbZ Kkr dhft,A From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Determine the height of the tower. 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 45 − 55 55 − 65 65 − 75 75 − 85 85 − 95 lk{kjrk nj ¼izfr'kr esa½ 3 10 11 8 3 uxjksa dh la[;k The following table gives the literacy rate (in percentage) of 35 cities, Find the mean literacy rate 45 − 55 55 − 65 65 − 75 75 − 85 85 − 95 Literacy rate (in %) 3 10 11 8 3 Number of cities vFkok@ OR fuEufyf[kr vkWdM+s 225 fctyh midj.kksa ds izsf{kr thou dky ¼?k.Vksa esa½ dh lwpuk nsrs gSa midj.kksa dk cgqyd thoudky Kkr dft,A thou dky ¼?k.Vksa 𝟎 − 𝟐𝟎 𝟐𝟎 − 𝟒𝟎 𝟒𝟎 − 𝟔𝟎 𝟔𝟎 − 𝟖𝟎 𝟖𝟎 − 𝟏𝟎𝟎 𝟏𝟎𝟎 − 𝟏𝟐𝟎 esa½ ckjEckjrk 10 35 52 61 38 29 The following data gives the information on the observed life times (in hours) of 225 electrical components. Determine the mode lifetimes of the components. Life times (in 𝟎 − 𝟐𝟎 𝟐𝟎 − 𝟒𝟎 𝟒𝟎 − 𝟔𝟎 𝟔𝟎 − 𝟖𝟎 𝟖𝟎 − 𝟏𝟎𝟎 𝟏𝟎𝟎 − 𝟏𝟐𝟎 hours) frequency 10 35 52 61 38 29 8