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CBSE Class 10 Pre Board 2026 : Mathematics (Daly College, Indore)

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SET-5 Series AQ@QA Z-n H$moS> Q.P. Code amob Z . 30/B/5 narjmWu Z-n H$moS> H$mo C ma-nwp VH$m Ho$ _wI-n >na Ad ` {bIo & Roll No. Candidates must write the Q.P. Code on the title page of the answer-book. H $n`m Om M H$a b| {H$ Bg Z-n _o _w{ V n > 11 h & Z-n _| Xm{hZo hmW H$s Amoa {XE JE Z-n H$moS H$mo narjmWu C ma-nwp VH$m Ho$ _wI-n > > na {bI| & H $n`m Om M H$a b| {H$ Bg Z-n _| >14 Z h & H $n`m Z H$m C ma {bIZm ew $ H$aZo go nhbo, C ma-nwp VH$m _| Z H$m H $_m H$ Ad ` {bI| & 15 {_ZQ >H$m g_` {X`m J`m h & ZBg Z-n 10.15 ~Oo {H$`m OmEJm & 10.15 ~Oo go 10.30 ~Oo VH$ N>m Ho$db ZBg Ad{Y Ho$ Xm amZ do C ma-nwp VH$m na H$moB C ma Zht {bI|Jo & Please check that this question paper contains 11 printed pages. Q.P. Code given on the right hand side of the question paper should be written on the title page of the answer-book by the candidate. Please check that this question paper contains 14 questions. Please write down the serial number of the question in the answer-book before attempting it. 15 minute time has been allotted to read this question paper. The question paper will be distributed at 10.15 a.m. From 10.15 a.m. to 10.30 a.m., the students will read the question paper only and will not write any answer on the answer-book during this period. J{UV (_mZH$)$ (Ho$db { >~m{YV narjm{W `m| Ho$ {bE) MATHEMATICS (STANDARD) (FOR VISUALLY IMPAIRED CANDIDATES ONLY) :2 Time allowed : 2 hours 30/B/5 : 40 Maximum Marks : 40 Page 1 P.T.O. : : 14 (i) (ii) (iii) 6 1 6 2 (iv) 4 7 10 3 (v) 4 11 14 4 (vi) I S> H$ 6 1. 2 (H$) {Z Z{b{IV g_m Va lo r Ho$ nXm| H$s g `m kmV H$s{OE : 2 5, 11, 17, ....., 203 AWdm (I) Cg g_m Va lo Ho$ W_ 20 nXm| H$m `moJ\$b kmV H$s{OE {OgH$m ndm nX an = 5 3n mam X m h & 2. { KmV g_rH$aU 3. 18 30/B/5 9x2 6 2x+2=0 Ho$ _yb kmV H$s{OE & go_r 22 go_r 6 go_r {d_mAm| dmbo YmVw Ho$ EH$ R>mog KZm^ H$mo {nKbmH$a 3 go_r `mg dmbr {H$VZr JmobmH$ma Jmo{b`m ~ZmB Om gH$Vr h ? Page 2 2 2 2 General Instructions : Read the following instructions very carefully and strictly follow them : (i) This question paper contains 14 questions. All questions are compulsory. (ii) This question paper is divided into three sections and C. Section A, B (iii) Section A comprises of 6 questions (Q. no. 1 to 6) of 2 marks each. Internal choice has been provided in two questions. (iv) Section B comprises of 4 questions (Q. no. 7 to 10) of 3 marks each. Internal choice has been provided in one question. (v) Section C comprises of 4 questions (Q. no. 11 to 14) of 4 marks each. Internal choice has been provided in one question. It also contains two case study based questions. (vi) Use of calculator is not permitted. SECTION A This section contains 6 questions of 2 marks each. 1. (a) Find the number of terms in the following AP : 2 5, 11, 17, ....., 203 OR (b) Find the sum of the first 20 terms of an AP whose nth term is given as an = 5 3n. 2. Find the roots of the quadratic equation 9x2 3. How many spherical shots each having diameter 3 cm can be made by melting a cuboidal solid of dimensions 18 cm 22 cm 6 cm ? 30/B/5 Page 3 6 2 x + 2 = 0. 2 2 2 P.T.O. 4. 5. 6. {Z Z{b{IV ~ Q>Z H$m ~h bH$ 24 h VWm g^r ~ma ~maVmAm| H$m `moJ\$b bw V ~ma ~maVmE x VWm y Ho$ _mZ kmV H$s{OE : 0 10 4 10 20 x 20 30 20 30 40 y 40 50 6 Xmo g H$s ne -aoIm h & `{X N>moQ>o d m H$s { `m kmV H$s{OE & 48 50 h & 2 go_r h , N>moQ>o d m 7 2 (H$) Xmo H $_mJV {df_ YZ nyUm H$m| H$m JwUZ\$b 255 h & EH$ { KmV g_rH$aU Ho$ gy U H$s ghm`Vm go `o nyUm H$ kmV H$s{OE & AWdm 2 k Ho$ (I) do _mZ kmV H$s{OE {OZHo$ {bE { KmV g_rH$aU (k + 3) x2 + kx + 1 = 0 Ho$ Xmo _yb dm V{dH$ VWm ~am~a hm| & 2 I S> I 4 7. 30/B/5 3 4 go_r { `m Ho$ EH$ d m Ho$ H|$ O go 7 go_r H$s X ar na p WV EH$ q~X ItMr OmZo dmbr Xmo ne -aoImAm| H$s aMZm Ho$ nX {b{IE & Page 4 P go 3 4. The mode of the following distribution is 24 and the sum of all frequencies is 50. Find the missing frequencies x and y. Class 5. 2 Frequency 0 10 4 10 20 x 20 30 20 30 40 y 40 50 6 In two concentric circles, a chord of length 48 cm of the larger circle is a tangent to the smaller circle, whose radius is 7 cm. Find the radius of the larger circle. 6. (a) 2 The product of two consecutive odd positive integers is 255. Find the integers, by formulating a quadratic equation. 2 OR (b) Find the value(s) of k for the quadratic equation, (k + 3) x2 + kx + 1 = 0, to have two real and equal roots. 2 SECTION B This section contains 4 questions of 3 marks each. 7. Write the steps of construction for constructing a pair of tangents to a circle of radius 4 cm from a point P, at a distance of 7 cm from its centre O. 30/B/5 3 Page 5 P.T.O. 8. 9. (H$) g_w Vb go 60 _r. D $Mr bmBQ>-hmCg Ho$ {eIa go XoIZo na Xmo g_w r OhmOm| Ho$ AdZ_Z H$moU 45 VWm 60 h & `{X bmBQ>-hmCg Ho$ EH$ hr Amoa EH$ OhmO X gao OhmO Ho$ R>rH$ nrN>o hmo, Vmo XmoZm| OhmOm| Ho$ ~rM H$s X ar kmV H$s{OE & [ 3 = 1 732 br{OE] AWdm (I) 1 6 _r. b ~m -nmo Q> go 3 _r. ^y{_ na 4 _r. b ~r N>m`m ~ZmVm h , Vmo b n-nmo Q> H$s D $MmB kmV H$s{OE & {Z Z{b{IV ~ma ~maVm ~ Q>Z 50 _m `H$ Am`w kmV H$s{OE, `{X nm {bgr Ho$db C ht `{ $`m| H$mo Xr OmVr h , {OZH$s Am`w 18 df `m Cggo A{YH$ hmo, na Vw 60 df go H$_ hmo & 20 go H$_ 30 go H$_ 40 go H$_ 50 go H$_ 60 go H$_ 10. 30/B/5 3 3 3 1 12 39 46 50 50 n[admam| _| ^moOZ na h E X {ZH$ `` H$mo Xem Vr h & _m ` X {ZH$ `` kmV H$s{OE & 200 250 8 250 300 10 300 350 12 350 400 10 400 450 10 Page 6 3 8. (a) (b) 9. 10. As observed from the top of a lighthouse 60 m high from the sea level, the angles of depression of two ships are 45 and 60 . If one ship is exactly behind the other on the same side of the lighthouse, then find the distance between the two ships. [Use 3 = 1 732] OR A 1 6 m tall boy stands at a distance of 3 m from a lamp-post and casts a shadow of length 4 m on the ground. Find the height of the lamp-post. The following frequency distribution shows the ages of 50 policyholders. Calculate the median age, if policies are given only to persons having age 18 years onwards, but less than 60 years. Age (in years) Below 20 Number of Policyholders 1 Below 30 12 Below 40 39 Below 50 46 Below 60 50 The table below shows the daily expenditure on food of 50 households of a locality. Find the mean daily expenditure. Daily Expenditure (in ) 200 250 30/B/5 3 3 3 3 Number of Households 8 250 300 10 300 350 12 350 400 10 400 450 10 Page 7 P.T.O. I S> J 4 11. 4 (H$) `{X Xmo d m na na ~m ne H$aVo h , Vmo {g H$s{OE {H$ ne q~X , d mm| Ho$ H|$ m| H$mo {_bmZo dmbr aoIm na p WV h & AWdm (I) {g H$s{OE {H$ EH$ ~m q~X go d m na ItMr JB Xmo ne -aoImAm| H$s b ~mB`m g_mZ hmoVr h & 12. 4 g_Vb ^y{_ na p WV EH$ q~X go, EH$ D$ dm Ya C `Z H$moU 192 tan Bg H$ma nm`m J`m {H$ tan = _r. H$s X ar MbZo na ~Zm C `Z H$moU = 3 4 5 12 h & _rZma H$s Amoa Bg H$ma nm`m J`m {H$ h & _rZma H$s D $MmB kmV H$s{OE & H$aU A ``Z 13. 4 4 1 _H$mZ AWdm H$ma O gr _h Jr d Vw IarXZo Ho$ {bE EH$ _ `_-dJu` `{ $ Ho$ {bE ~ H$ go G$U boH$a Cgo AmgmZ {H$ Vm| _| `mO g{hV MwH$mZm AmgmZ hmo OmVm h & A_Z EH$ H$ma IarXZo Ho$ {bE ~ H$ go < 2,36,000 H$m G$U boVm h Am a Cgo _m{gH$ {H$ Vm| _| MwH$mZm ew $ H$aVm h & dh < 2,000 H$s nhbr {H$ V MwH$mVm h VWm CgHo$ ~mX {V _mh {H$ V _| < 500 & (H$) kmV H$s{OE {H$ dh 25dt (I) kmV H$s{OE {H$ dh nhbr 30/B/5 {H$ V _| {H$VZr am{e MwH$mVm h & 2 25 {H$ Vm| 2 Page 8 _| Hw$b {H$VZr am{e MwH$mVm h & SECTION C This section contains 4 questions of 4 marks each. 11. (a) (b) 12. If two circles touch each other externally, then prove that the point of contact lies on the line joining their centres. 4 OR Prove that the lengths of two tangents drawn from an external point to a circle are equal. 4 At a point on the level ground, the angle of elevation of the top 5 . On 12 walking 192 m towards the tower, the angle of elevation is of a vertical tower is found to be such that tan = , such that tan 3 . Find the height of the tower. 4 Case Study 13. = 4 1 While buying an expensive item like a house or a car, it becomes easier for a middle-class person to take a loan from a bank and then repay the loan along with interest in easy instalments. Aman buys a car by taking a loan of < 2,36,000 from the bank and starts repaying the loan in monthly instalments. He pays < 2,000 as the first instalment and then increases the instalment by < 500 every month. 30/B/5 (a) Find the amount he pays in the 25th instalment. 2 (b) Find the total amount paid by him in first 25 instalments. 2 Page 9 P.T.O. H$aU A ``Z 2 14. hmoVm h , C moJ _| ~h V bm^H$mar hmoVo h , {deofV`m V~, O~ Q> H$ go {ZH$mbr JB Am{Iar ~y X ^r ~h V _h d aIVr hmo & {dH$ AmYma dmbm Q> H$ ~Zm`m CgH$s { `m Ho$ ~am~a h VWm ~obZmH$ma ^mJ H$s D $MmB CgH$s { `m H$s X JwZr h & Q> H$ D$na go ~ X h & (H$) `{X ~obZmH$ma ^mJ H$s { `m H$s{OE & 3 _r. h , Vmo Q> H$ H$m Am`VZ kmV 2 (I) H$s{OE & 30/B/5 2 Page 10 Case Study 14. 2 Conical bottom tanks in which an inverted cone at the bottom is surmounted by a cylinder of same diameter, are very advantageous in industry, specially where getting every last drop from the tank is important. Vikas designed a conical bottom tank where the height of the conical part is equal to its radius and the height of the cylindrical part is two times of its radius. The tank is closed from the top. (a) If the radius of the cylindrical part is 3 m, then find the volume of the tank. (b) 2 Find the ratio of the volume of the cylindrical part to the volume of the conical part. 30/B/5 Page 11 2 P.T.O.

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