SEE Question paper of Optional Mathematics 2075

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Apr 06, 2020

  • 0 Symbol No. SEE 2075 (2019) RE-231 tee vay afre Rewer Preece araret arat defer Resiarere oat Rah war: 3 ater Yige - qoo wa vereal gat Pratt (Answer all the questions) wag ‘&' (Group 'A‘) {8x(2+2)=32] 4. aR for) = 2x - A OCD) SAT Te TTR If f(x) = 2x - I then find the value of f-1). (@ afe user sere p(x) = 2x? - 6x? - Sn - 2 WaT TUS x -2 et Am wl AT Te STENT | If a factor of a polynomial p(x) = 2x5 - 6x? - Sm - 2 is x - 2, find the value of m. mH) 4T 16 areata Fe eee ae Prater Calculate the arithmetic mean and geometric mean between 4 and 16, (&) Pratta Afgaaat wearer creqere | er eraeare Prater afew ofeentina ger 7 meter | Write the definition of inverse matrix. In which condition the inverse matrix cannot be defined? Write it. 2 oo ak [T]o-[ 4 ava Cum amet Nef 8 2) sna in | If fo7l2 3) ind the matrix C. @) WA y=mxtec, Cyomaxt oc, tae ST TT TTA wo TEE wed fi Rares arraar area et ore OPT ETT | Write down the formula to find the angle between the lines y=mx +c, and y = mx + c,. Also write the condition of perpendicularity of these lines. x, () ate BART 16x? - doy + Oy? = OF TATSA Taree Bea BAL TT k BT TT Wa AUST! If the lines represented by /6x? - kxy + 9y? = 0 are coincident, find the value of k. (@ Er Frat Ger MAH se Gwar PEE (0, 6) t (8, 0) SL TT WT Fat where tar TSE | The end points of a diameter of a circle are (0, 6) and (8, 0). Find the tion of the circle. equation of the circle. aa:
  • 1 RE-231 Q) X. (@) Presrorierciter anfercar ar sareaetet FANT ATE sin 165° Bt AM TAT AMSA | Find the vaiue of sin 165° without using a trigonometric table or a calculator. cw att sin’ Has +) at sina —3{@ = 3) a of ee a _A If 1 . 1 If sin Hart), prove that sioax—3{ +4) &_ @&) warftra wHetq (Prove that): sin‘B + 008‘B = 1~ >sin?2B @) FA THT (Solve): 2cos0 = secd [or <6 < 90°] = 2V3 WHET pt q frrat arr 30° p A TS If pq =6, ia| =2¥3 unit and the angle between P and q is 30°, find the length of P- A (@) feavat Prat AD = DCT Rrg GPP ABC Ft RE B Br ake Rages B CD a fend Aaecee are: BPAT7 D X37 27 Bet G a Rafe Feet Tear HTT A In the given figure, AD = DC and the point G is the centroid of the triangle ABC. If the position vectors of the points B and D are 37, 477 and 37, 37 respectively, find the position vector of G. 5.) Pz AG, -S) arg tar x + y = ORT Teas ata Ta Paget afeatk +900 ay Ufa TEseT wed EA Vater Peegase ToS ATA | Find the coordinates of the image of a point A(3, -5) after reflection on the line x+-y=0 followed by the rotation through +90° about the origin. 0 +1 @) afer [ | A ATSA STARTET Tat TSAR Find the transformation represented by the matrix wag ‘@’ (Group ‘B’) 17x4=68 &. ARE gGe)= 2x - 3 T fog) = Ox -11 A f(a) TeT TTR | If g(x)= 2x -3 and fog(x) = 6x -11, then find /-"¢x). qo. aa Wigtq (Solve): 2x°- 97 + 7x + 6=0. c 0 -1 RAT,
  • 2 GB) RE- 231 49. User Toba sole see ot Teeeat THe 243 | ale sae ae Se hret Sat oe Geer ware Aolhat aah Tee TTT AY SRT TATRA Sata VET 19 qeeeat ATH TA MTT | The product of the first five terms of a geometric series is 243. If the third term of the geometric series is equal to the tenth term of an arithmetic ~ series, find the sum of the first 19 terms of the arithmetic series. 9. at aeieem 2? - 3x = 10 ay Aare Bar TET Solve graphically the quadratic equation x? - 3x = 10. 93, Hear faftrere ger wera (Solve by matrix method): Ss=4+2, —- 22) yx xy ay. fry (4, -1) Te OTA T Rar 2x -3y = 5 AT 45° at aT aaTTA | Twat Srarearet Bet Te ATS TET | Find the equation of any one straight line passing through the point (4, -1) and making an angle of 45° with the line 2x -3y = 5. qx. ate aetleret 2x? + kay + 3 = OF Ulatiirer aH sitet Rareedthrat stot 45° WU k St are WT ToT we Wareee Area ates TH TT aT If an angle between the pair of lines represented by the equation 2x? + kxy + 37° = 0 is 45°, then find the positive value of k and also find the separate equations of the lines. 9 Reeve fran drag X neal at A Ge B a aehirg Yume AYO 12-0 TT Ft AS TI BA AAT x? + py? de + Gy-12=0T Z X @ fieurewes (-4, 5) GL wT aT A fee TAT TSAR In the given figure, the circle A with centre X passes through the centre Y of the circle B. If the equation of circle B_ is x? + y? -dx + 6y - 12 =0 and the co-ordinates of X are (-4, 5), then find the equation of the circle A. Q9, FRTESSE Sera AT TfeteeTaT PAT TT ATT TT TSAR | Without using the calculator or table, find the value of: sin] 00°.sin120°.sin140°.sin160° ge, aft P, QX R Wer APOR FF Bes FT Vara aeAeTe If P, Qand R are the angles of a APQR, prove that: 2| sin 2 +.sin® sin. — sin ® -cosP =1-4c0s?.cos2 sin 2 2 2 2 2 2 2 BAT:
  • 3 RE-231 (4) 48. BH wgte (Solve). [email protected] (0°<@ <360°) 20, UsaT ARAL BT CHEATS TAT VIAT STAT TA Sly KSAT SST HAH: 60° t 30° al afe waa Sug 15 Phe Ae Ua SATE THT TTR | From the roof and foot of a house, the angles of depression and elevation - of the top of a tree are 60° and 30° respectively. If the height of the tree is 15 ft, find the height of the house. M1. SRT AB wat Wer siquat shire ACB we araty ge wT Tee fafuare veattre were Prove by vector method that the circumference angle ACB of a semi- circle with a diameter AB is a right-angle. 33. eidfrgse AQ, 3), B(2, 6)% C(3, 4) aUat Pt ABC ad T= EG & frearrt nel art viaferaens BECO, 0), 2] 3 rerdtrer afeeer gi rad grat aki eteeaT ‘eittrgeear Préengqes aet AABC Tt aaar aa sfafararee Usd aearhearaT FEET were! A triangle ABC with vertices A(2, 3), B(2, 6) and CQ, 4) is translated by [7] and the image so obtained is enlarged by E[(0, 0), 2]. Write the co-ordinates of the vertices of the images so formed and represent AABC and its both images in the same graph. 3. fares AG, 1) t B(7, 5) Het Wares AB ae ST Tal A4, DT BY-7, 5) frags Stet Taras A'B aa Te ITT CTATS Wahrirer WA 2x2 Hear var wars yey | Aline segment AB joining the points A(4, 1} and B(7, 5) is transformed to the line segment A'B' joining the points A'(-4, 1} and B(-7, 5). Find the 2x2 matrix that represents this transformation. Qs, Tet Rearat Tear aparare were HAT Tear TS Te ATS ARR Find the mean deviation and its coefficient from median of the data given below: 10, 50, 60, 40, 30, 20 Ww. dat Reva werrgepare Prareorefterareat Pores Tra AST | Calculate the coefficient of variation from the data given below. SUT AAT (Class-interval) 0-10 | 10-20) 20-30 | 30-40] 40-50 Aa (Frequency) 5 8 15 16 6 CR