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SEE Question paper of Optional Mathematics 2075

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