ê·ÂŒÈ : πÂä  PAPERS/MATHS/81-T.pdf߈πÀπ¬ËπU 20. SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ...
Transcript of ê·ÂŒÈ : πÂä  PAPERS/MATHS/81-T.pdf߈πÀπ¬ËπU 20. SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ...
![Page 1: ê·ÂŒÈ : πÂä  PAPERS/MATHS/81-T.pdf߈πÀπ¬ËπU 20. SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A ´∂Èœ ß‹ÒΩ˪Uÿ SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A](https://reader034.fdocumento.com/reader034/viewer/2022042114/5e90e4e79fab8867ad113582/html5/thumbnails/1.jpg)
Roll No.
Serial No. of Q. C. A. B.
912490 [ Turn over
≤¡ÈJ …ÂX‡Rπ› ‚¢z W : 58 ] [ ≤¡ÈJ ÆÂÈÈåX∆ …ÂÏ¡π› ‚¢z W : 40
Total No. of Questions : 58 ] [ Total No. of Printed Pages : 40
‚¢xË∆ ‚¢zW : 81-T ê·ÂŒÈ : πÂä∆Â
Code No. : 81-T Subject : MATHEMATICS (∆ÂêÈ›ÂÈÔ üÊ·Ê¢∆¬ / Tamil Version )
å»Ê¢∑ : 08. 04. 2013 ] [ Date : 08. 04. 2013
‚ÂÆÂÈŒÈ : üúπB 9-30 ࢫ ÆÂÈ«ÊW„ÂR 12-45 ¬ÂÕ¬π ] [ Time : 9-30 A.M. to 12-45 P.M.
…¬ÂÆÂ⁄ÕÂå˘ •¢∑π ›ÂÈ : 100 ] [ Max. Marks : 100
FOR OFFICE USE ONLY
Q. No. Marks
Q. No. Marks
Q. No. Marks
Q. No. Marks
Q. No. Marks
1. 14. 27. 40. 53.
2. 15. 28. 41. 54.
3. 16. 29. 42. 55.
4. 17. 30. 43. 56.
5. 18. 31. 44. 57.
6. 19. 32. 45. 58.
7. 20. 33. 46. ×
8. 21. 34. 47. ×
9. 22. 35. 48. ×
10. 23. 36. 49. ×
11. 24. 37. 50. ×
12. 25. 38. 51. ×
13. 26. 39. 52. ×
Total Marks
Total Marks in
words
Grand Total
1.
2.
Signature of Evaluators Registration No. Signature of the Deputy Chief
Signature of the Room Invigilator
![Page 2: ê·ÂŒÈ : πÂä  PAPERS/MATHS/81-T.pdf߈πÀπ¬ËπU 20. SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A ´∂Èœ ß‹ÒΩ˪Uÿ SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A](https://reader034.fdocumento.com/reader034/viewer/2022042114/5e90e4e79fab8867ad113582/html5/thumbnails/2.jpg)
81-T 2
( SPACE FOR ROUGH WORK ) 912490
ÒøËQµË∂ A«Èfié∑‰ : i) ß›Ω µÏ∂Ë-µÏˆª‹Ωˉ ÒΩËAfiøÏœ øœµˆ∑ µÏˆª-µÏ∂Ë µˆ∑ ( Objective type )
µÏ∂Ë»∑‰ ¿◊^à µÏˆª∑ˆ∆ ´ZQà µˆ∑ µÏ∂Ë»∑‰ ( Subjective type ) ´∂ Ò¿Ë‹Ωà 58 µÏ∂Ë»∑‰ ©‰∆∂.
ii) øœµˆ∑ µÏˆª-µÏ∂Ë µˆ∑ µÏ∂Ë»∑e»A ( Objective type questions ) µÏˆª ´ZQµΩ◊∑Ë∂ ߪà ÆQ»∑fiøflH‰∆Q. æÍ…∑‰ ÆQ»∑fiøflH‰∆ ߪ‹ΩÈ◊A‰∆Ë∑µ µÏˆª¡∆È»∑ µ¤HÃ.
iii) µÏˆª∑ˆ∆ ´ZQà µˆ∑ µÏ∂Ë»∑e»Ò∑∂ ( Subjective type questions ) ƇҵËW µÏ∂˵Ï◊Aà ߪà ÆQ»∑fiøflH‰∆Q. æÍ…∑‰ ÆQ»∑fiøflª ߪ‹ΩÈ√¡ µÏˆª¡∆È»∑ µ¤HÃ.
iv) øœµˆ∑ µÏˆª-µÏ∂Ë µˆ∑ ( Objective type ) ¿◊^à ´ZQà µˆ∑ µÏ∂Ë»∑e» ( Subjective type ) Ò∑∂ µ≈…∑fiøflH‰∆ A«Èfié∑ˆ∆ ∑µ∂¿Ë∑ ∑ˆªfiøÏF»∑ûÃ.
v) ¿ËºË»∑Œ∑‰ µÏˆª∑ˆ∆ ÒøÿπÈ√Ëœ ´ZQΩœ BªËQ ( µˆ¬øª…∑‰, øª…∑‰, ¿fié∑ˆ∆ ΩµÏ¬ ). ߇µÏΩȈ¡ ¿Í«È ÒøÿπÈ√Ëœ ´ZΩfiøflª µÏˆª∑‰ ¿ΩÈfiøÍH ÒπÕ¡fiøª ¿ËflªËQ.
vi) øœµˆ∑ µÏˆª-µÏ∂Ë µˆ∑ µÏ∂Ë»∑‰, ∑ËFflª ߪ…∑ˆ∆ æȬfiéΩœ, ¿◊^à ÒøËW‹Q∑ øËÿ« µÏ∂Ë»∑∆Èœ •≈È‹Q ´ZQΩœ / C¬¤HΩœ / A«È¡ÏHΩœ∑‰ øËÿ«ˆµ •a¿ΩÈ»∑fiøª¿ËflªËQ. ߇µÏΩȈ¡ ¿Í«È∂Ëœ ¿ΩÈfiøÍH ÒπÕ¡fiøª¿ËflªËQ.
vii) ¿ËºË»∑Œ∑e»A µÏ∂Ë‹Ωˈ∆ øFfiøΩ◊Ò∑∂ 15 æȿȪ…∑‰ BHΩ√Ë∑ µ≈…∑fiøflH‰∆Q.
viii) ƇҵËW ø»∑‹ΩÈÿ •F¡ÏYà ∑º»A∑ˆ∆ ÒπÕQ øËŒfiøΩ◊Ò∑∂ ߪà ( Space for Rough Work ) ÆQ»∑fiøflH‰∆Q.
I. ∑ Í÷µWà ƇҵËW µÏ∂˵Ï◊Aà / SZˆ¿ Òø«ËΩ B◊^∑e»Aà ( Incomplete
statements ) æËÿA ¿Ë◊^ µÏˆª∑‰ Ω¬fiøflH‰∆∂. ßµ◊^‰ Æÿ^ ¿flH¿ ¿È∑À πU¡Ë∂Q •œ√Q ÒøËW‹Ω¿Ë∂Q. πU¡Ë∂ µÏˆªˆ¡‹ ΩŒ›ÒΩH‹Q, •Ω◊Ò∑∂ Ω¬fiøflH‰∆ A«È¡ÍflH ´Z‹Qªÿ SZˆ¿¡Ë∑ ´ZΩ µ¤HÃ. 20 × 1 = 20
1. A, B ¿◊^à C ¶∑È¡ˆµ∑‰ Òµ◊«œ√ËΩ ∑º…∑‰ ´∂Èœ, ë∑º…∑∆Èÿ ÒµflªË∂Q ∑º…∑∆Èÿ πŒ»ˆ∑¡Ïÿ ¿ÍQ ø¬µÏú‰∆Qí Ô ÿøQ ´…∏∂à A«ÈfiøϪfiøHà ?
(A) A ∩ ( B ∪ C ) = ( A ∩ B ) ∪ ( A ∩ C )
(B) A ∩ ( B ∩ C ) = ( A ∩ B ) ∩ ( A ∩ C )
(C) ( A ∪ B ) ∪ C = ( A ∩ C ) ∪ ( B ∪ C )
(D) ( A ∩ B ) ∪ C = ( A ∪ C ) ∩ ( B ∪ C ).
µÏˆª :
![Page 3: ê·ÂŒÈ : πÂä  PAPERS/MATHS/81-T.pdf߈πÀπ¬ËπU 20. SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A ´∂Èœ ß‹ÒΩ˪Uÿ SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A](https://reader034.fdocumento.com/reader034/viewer/2022042114/5e90e4e79fab8867ad113582/html5/thumbnails/3.jpg)
3 81-T
( SPACE FOR ROUGH WORK ) 912490 [ Turn over
2. ßW Ω∂È¡Ë∂ ´¤∑∆Èÿ BflHÀπ¬ËπU ¿◊^à ߈πÀπ¬ËπU Sˆ«¡ 5 ¿◊^à 2
´∂Èœ •µ◊«Èÿ ÒøW»∑œ π¬ËπU
(A) 3 (B) 7
(C)
!
10 (D) 10.
µÏˆª :
3.
!
A + B = 2 3
4 5
"
# $
%
& ' ¿◊^Ã
!
A = 1 2
0 3
"
# $
%
& ' ´∂Èœ •ºÈ B
(A)
!
1 1
4 2
"
# $
%
& ' (B)
!
1 4
1 2
"
# $
%
& '
(C)
!
2 4
1 1
"
# $
%
& ' (D)
!
4 2
1 1
"
# $
%
& ' .
µÏˆª :
4.
!
nC
8 =
nC
5 ´∂Èœ n-ÿ ¿ΩÈfié
(A) 2 (B) 3
(C) 1 (D) 13.
µÏˆª :
5.
!
5 x2
y3 ¿◊^Ã
!
10 x3
y2 ÿ ©.ÒøË.¿ ( H.C.F. )
(A)
!
10 x3
y3 (B)
!
5 x2
y2
(C) 5 xy (D)
!
5 x3
y3.
µÏˆª :
![Page 4: ê·ÂŒÈ : πÂä  PAPERS/MATHS/81-T.pdf߈πÀπ¬ËπU 20. SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A ´∂Èœ ß‹ÒΩ˪Uÿ SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A](https://reader034.fdocumento.com/reader034/viewer/2022042114/5e90e4e79fab8867ad113582/html5/thumbnails/4.jpg)
81-T 4
( SPACE FOR ROUGH WORK ) 912490
6.
!
p2
p , q , r
" ´ÿøΩÿ µÏUµË»∑Ã
(A)
!
p2
q2
r2 (B) pqr
(C)
!
p2 (D)
!
p2
+ q2
+ r2
.
µÏˆª :
7.
!
a b" c( )a , b , c
# ´ÿøΩÿ ¿ΩÈfié
(A) 2 ( ab + bc + ca ) (B) ab + bc + ca
(C) 0 (D) a + b + c.
µÏˆª :
8.
!
a3
+ b3 ´ÿøΩÿ ÆW T√à ( a + b ) ´∂Èœ ¿◊Ò«ËW T√Ã
(A)
!
a3
+ b3
+ ab (B) a – b + ab
(C)
!
a2
+ b2
" ab (D)
!
a2
+ b2
+ ab .
µÏˆª :
9.
!
x y = 80 ´∂Èœ y-¡Ïÿ ¿ΩÈfié
(A) 5 (B) 16
(C) 4 (D) 20.
µÏˆª :
10. ´ÿøΩÿ ´∆È¡ µFµÃ
(A) (B)
!
2 x
(C) (D)
!
18 x .
µÏˆª :
![Page 5: ê·ÂŒÈ : πÂä  PAPERS/MATHS/81-T.pdf߈πÀπ¬ËπU 20. SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A ´∂Èœ ß‹ÒΩ˪Uÿ SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A](https://reader034.fdocumento.com/reader034/viewer/2022042114/5e90e4e79fab8867ad113582/html5/thumbnails/5.jpg)
5 81-T
( SPACE FOR ROUGH WORK ) 912490 [ Turn over
11.
!
4 x = 81
x ´∂Èœ x-ÿ ¿ΩÈfié
(A) – 4·5 (B) ± 4·5
(C) 4·5 (D) ± 0·45.
µÏˆª :
12.
!
2 + 3( ) ¿◊^Ã
!
2 " 3( ) ¶∑È¡µ◊ˆ« T√…∑∆Ë∑ Ò∑ˤª ßWøFÀ π¿ÿøËH
(A)
!
x2" 4 x + 1 = 0 (B)
!
x2
+ 4 x " 1 = 0
(C)
!
x2" 4 x " 1 = 0 (D)
!
x2
+ 4 x + 1 = 0 .
µÏˆª :
13. 3 y ≡ 2 ( ¿flH 6 ) ´∂Èœ y-ÿ ¿ΩÈfié
(A) 2 (B) 4
(C) 5 (D) 6.
µÏˆª :
14. øÏÿµWà ∑º…∑∆Èœ
!
Z4 ´ÿøQ
(A) 0, 1, 2 (B) 0, 1, 2, 3
(C) 0, 1, 2, 3, 4 (D) 1, 2, 3, 4 .
µÏˆª :
![Page 6: ê·ÂŒÈ : πÂä  PAPERS/MATHS/81-T.pdf߈πÀπ¬ËπU 20. SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A ´∂Èœ ß‹ÒΩ˪Uÿ SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A](https://reader034.fdocumento.com/reader034/viewer/2022042114/5e90e4e79fab8867ad113582/html5/thumbnails/6.jpg)
81-T 6
( SPACE FOR ROUGH WORK ) 912490
15. Δ ABC ¡Ïœ, D ¿◊^à E ¶∑È¡ˆµ∑‰ Sˆ«¡ AB ¿◊^à AC ¡Ïÿ æHfié‰∆È∑‰
´∂Èœ Δ ADE ¡Ïÿ ø¬fiø∆û
(A) 4 Δ ABC (B)
!
1
4 Δ ABC
(C) 2 Δ ABC (D)
!
1
2 Δ ABC.
µÏˆª :
16. Ò∑ËH»∑fiøflH‰∆ øª‹ΩÈœ XY || BC ´∂Èœ
!
AX
BX=
(A)
!
AY
AC (B)
!
YC
AY
(C)
!
AX
AB (D)
!
AY
CY.
µÏˆª :
17. Δ ABC, ∠ ABC = 90°, AC = ( x + y ) ¿◊^à BC = ( x – y ) ´∂Èœ AB ¡Ïÿ æÍ∆Ã
(A)
!
x2" y
2 (B) 2 xy
(C)
!
2 xy (D)
!
x2
+ y2.
µÏˆª :
![Page 7: ê·ÂŒÈ : πÂä  PAPERS/MATHS/81-T.pdf߈πÀπ¬ËπU 20. SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A ´∂Èœ ß‹ÒΩ˪Uÿ SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A](https://reader034.fdocumento.com/reader034/viewer/2022042114/5e90e4e79fab8867ad113582/html5/thumbnails/7.jpg)
7 81-T
( SPACE FOR ROUGH WORK ) 912490 [ Turn over
18. Ò∑ËH»∑fiøflH‰∆ øª‹ΩÈœ AC, CE ¿◊^à EH ¶∑È¡ˆµ∑‰ ÆW µflª‹ΩÈÿ
Sˆ«¡ B, D ¿◊^à F ´ÿ« é‰∆È»A µˆ¬¡fiøflª ÒΩËH∑ËH∑‰ : CB = 5 Òπ.¿Í
¿◊^à EF = 3 Òπ.¿Í ´∂Èœ CE ¡Ïÿ æÍ∆Ã
(A) 2 Òπ.¿Í (B) 5 Òπ.¿Í
(C) 3 Òπ.¿Í (D) 8 Òπ.¿Í.
µÏˆª :
19. ¿Ë^øËflH Aº∑‹ˆΩ ∑˺ ©Ωûà N‹ΩȬÃ
(A)
!
"
X # 100 (B)
!
X
" # 100
(C)
!
X
100 " # (D)
!
"
100 # X .
µÏˆª :
20. ÆW ©Wˆ∆¡Ïÿ •FfiøË∑‹ΩÈÿ C◊«∆û 44 Òπ.¿Í, •Ωÿ ©¡¬Ã 20 Òπ.¿Í ´∂Èœ
•Ωÿ ø»∑µËflH é«fiø¬fié
(A) 440 πQ¬ Òπ.¿Í (B) 880 πQ¬ Òπ.¿Í
(C) 88 πQ¬ Òπ.¿Í (D) 44 πQ¬ Òπ.¿Í.
µÏˆª :
![Page 8: ê·ÂŒÈ : πÂä  PAPERS/MATHS/81-T.pdf߈πÀπ¬ËπU 20. SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A ´∂Èœ ß‹ÒΩ˪Uÿ SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A](https://reader034.fdocumento.com/reader034/viewer/2022042114/5e90e4e79fab8867ad113582/html5/thumbnails/8.jpg)
81-T 8
( SPACE FOR ROUGH WORK ) 912490
II. ∑ËFflª ߪ…∑ˆ∆ ΩA›Ω µÏˆª∑ˆ∆» Ò∑ˤH æȬfié∑ : 10 × 1 = 10
21. A ¿◊^à B ¶∑È¡ˆµ •ˆ∂‹Q ∑º¿Ë∂ U µÏÿ ©fl∑º…∑‰ ´∂Èœ
!
A " B( )l = …………… .
µÏˆª :
22. A ´ÿ« •ºÈ¡Ïÿ µUˆπ ( m × n ) ¿◊^à B ´ÿ« •ºÈ¡Ïÿ µUˆπ ( n × p ) ´∂Èœ
AB-¡Ïÿ µUˆπ …………… .
µÏˆª :
23.
!
nP
o ´ÿøΩÿ ¿ΩÈfié …………… .
µÏˆª :
24.
!
x + y( ) ´ÿøΩÿ µÏ∑ÈΩS^ ∑ˬºÈ …………… .
µÏˆª :
25. ßWøFÀ π¿ÿøËflFÿ ΩÈflª µFµÃ ( Standard form ) …………… .
µÏˆª :
![Page 9: ê·ÂŒÈ : πÂä  PAPERS/MATHS/81-T.pdf߈πÀπ¬ËπU 20. SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A ´∂Èœ ß‹ÒΩ˪Uÿ SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A](https://reader034.fdocumento.com/reader034/viewer/2022042114/5e90e4e79fab8867ad113582/html5/thumbnails/9.jpg)
9 81-T
( SPACE FOR ROUGH WORK ) 912490 [ Turn over
26.
!
ax2
+ bx + c = 0 ´ÿ« ßWøFÀ π¿ÿøËflFÿ ø¤é∑ËflF¡Ïÿ ( Discriminant )
¿ΩÈfié 0 ˆµ µÏª Aˆ«û ´∂Èœ •Ωÿ T√…∑∆Èÿ ß¡œé …………… .
µÏˆª :
27. ßW µflª…∑∆Èÿ ˆ¿¡…∑‰ d Òπ.¿Í ÒΩˈ√µÏœ ©‰∆∂, ¿Yà •µ◊«Èÿ ¶¬…∑‰
R ¿◊^à r ´∂Èœ •µ◊^»A µˆ¬¡fiøHà ÒøËQ‹ ÒΩËH∑ËflFÿ
æÍ∆à …………… .
µÏˆª :
28. ÆW S»∑˺‹ΩÈÿ ÆW ø»∑‹ΩÈÿ ßW¿F»A ¿◊« ßW ø»∑…∑∆Èÿ ßW¿F∑∆Èÿ
BHΩœ π¿¿Ë∂Ëœ, •›Ω ßW ø»∑…∑eà …………… ≠ Ò∑ˤªˆµ.
µÏˆª :
29. ÆW 挵flª ©Wˆ∆¡Ïÿ ( Right circular cylinder ) Ò∑ˉ∆∆ˆµ ∑˺ ©ΩûÃ
N‹ΩȬà …………… .
µÏˆª :
30. ªËÒª»∑ËÒ|fl¬Ëÿ ( ø∂ÈÒ¬¤HS∑È ) ( Dodecahedron )-ßÿ ƇҵËW
S∑‹ΩÈÿ µFµÃ …………… .
µÏˆª :
![Page 10: ê·ÂŒÈ : πÂä  PAPERS/MATHS/81-T.pdf߈πÀπ¬ËπU 20. SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A ´∂Èœ ß‹ÒΩ˪Uÿ SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A](https://reader034.fdocumento.com/reader034/viewer/2022042114/5e90e4e79fab8867ad113582/html5/thumbnails/10.jpg)
81-T 10
( SPACE FOR ROUGH WORK ) 912490
III. 31.
!
2, 2 2 , 4 , ..... ´ÿ« ÒøW»A‹ÒΩ˪Œ µUˆπ¡Ïœ 64 ´‹Ωˆ∂¡ËµQ ©^fié ? 2
![Page 11: ê·ÂŒÈ : πÂä  PAPERS/MATHS/81-T.pdf߈πÀπ¬ËπU 20. SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A ´∂Èœ ß‹ÒΩ˪Uÿ SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A](https://reader034.fdocumento.com/reader034/viewer/2022042114/5e90e4e79fab8867ad113582/html5/thumbnails/11.jpg)
11 81-T
( SPACE FOR ROUGH WORK ) 912490 [ Turn over
32. 1 + 2 + 4 + ..... ´ÿ« ÒΩ˪Uœ 9 ©^fié∑‰ µˆ¬ BHΩœ ∑ˤ∑. ( N‹ΩȬ‹ˆΩ ø¡ÿøH‹Q∑ ) 2
![Page 12: ê·ÂŒÈ : πÂä  PAPERS/MATHS/81-T.pdf߈πÀπ¬ËπU 20. SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A ´∂Èœ ß‹ÒΩ˪Uÿ SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A](https://reader034.fdocumento.com/reader034/viewer/2022042114/5e90e4e79fab8867ad113582/html5/thumbnails/12.jpg)
81-T 12
( SPACE FOR ROUGH WORK ) 912490
33. Tÿ^ ´¤∑‰ ߈π‹ÒΩ˪Uœ ©‰∆∂. SΩœ ¿◊^à Tÿ«ËµQ ´¤ºÈÿ ߈πÀπ¬ËπU 20. SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A ´∂Èœ ß‹ÒΩ˪Uÿ Tÿ^ ©^fié»∑ˆ∆úà ∑ˤ∑. 2
![Page 13: ê·ÂŒÈ : πÂä  PAPERS/MATHS/81-T.pdf߈πÀπ¬ËπU 20. SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A ´∂Èœ ß‹ÒΩ˪Uÿ SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A](https://reader034.fdocumento.com/reader034/viewer/2022042114/5e90e4e79fab8867ad113582/html5/thumbnails/13.jpg)
13 81-T
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34. •ºÈˆ¡ ߪ¿Ë◊«Ã ÒπÕΩœ ( Transposing of matrix ) ´ÿ«Ëœ ´ÿ∂ ? ÆW ©ΩˬºÃ ΩW∑. 2
![Page 14: ê·ÂŒÈ : πÂä  PAPERS/MATHS/81-T.pdf߈πÀπ¬ËπU 20. SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A ´∂Èœ ß‹ÒΩ˪Uÿ SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A](https://reader034.fdocumento.com/reader034/viewer/2022042114/5e90e4e79fab8867ad113582/html5/thumbnails/14.jpg)
81-T 14
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35. a) ´¤ºÈ»ˆ∑¡Ïÿ •Ffiøˆª Ω‹QµÃ ( Fundamental counting principle )
´ÿ«Ëœ ´ÿ∂ ?
b)
!
nP
r ´ÿøΩÿ ÒøËW‰ ´ÿ∂ ? 2
![Page 15: ê·ÂŒÈ : πÂä  PAPERS/MATHS/81-T.pdf߈πÀπ¬ËπU 20. SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A ´∂Èœ ß‹ÒΩ˪Uÿ SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A](https://reader034.fdocumento.com/reader034/viewer/2022042114/5e90e4e79fab8867ad113582/html5/thumbnails/15.jpg)
15 81-T
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36. ÆW Bˆª¡Ïœ 3 Òµ‰ˆ∆ ¿◊^à 5 πȵfié ¬ËmË è»∑‰ ©‰∆∂. ´‹Ωˆ∂ µˆ∑∑∆Èœ 2 πȵfié è»∑‰ Bˆª¡Ïœ ßW»A¿Ë^ 4 è»∑ˆ∆ æÍ»∑ SFúà ? 2
![Page 16: ê·ÂŒÈ : πÂä  PAPERS/MATHS/81-T.pdf߈πÀπ¬ËπU 20. SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A ´∂Èœ ß‹ÒΩ˪Uÿ SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A](https://reader034.fdocumento.com/reader034/viewer/2022042114/5e90e4e79fab8867ad113582/html5/thumbnails/16.jpg)
81-T 16
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37. ßW ∑ˈµ∑∆Èÿ ©.ÒøË.¿ ( H.C.F. ) ¿◊^à ¿Í.ÒøË.¿. ( L.C.M. ) Sˆ«¡ ( a – 7 )
¿◊^Ã
!
a3" 10 a
2+ 11a + 70( ) . ∑ˈµ∑∆Èœ Æÿ^
!
a2" 12a + 35( ) ´∂Èœ
¿◊Ò«Ëÿˆ« ∑ˤ. 2
![Page 17: ê·ÂŒÈ : πÂä  PAPERS/MATHS/81-T.pdf߈πÀπ¬ËπU 20. SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A ´∂Èœ ß‹ÒΩ˪Uÿ SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A](https://reader034.fdocumento.com/reader034/viewer/2022042114/5e90e4e79fab8867ad113582/html5/thumbnails/17.jpg)
17 81-T
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38. ÒΩËAΩȈ¡ µÏ∑ÈΩS«À ÒπÕQ ´∆Ȉ¿fiøH‹Q∑.
!
5 + 2
5 " 2 2
![Page 18: ê·ÂŒÈ : πÂä  PAPERS/MATHS/81-T.pdf߈πÀπ¬ËπU 20. SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A ´∂Èœ ß‹ÒΩ˪Uÿ SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A](https://reader034.fdocumento.com/reader034/viewer/2022042114/5e90e4e79fab8867ad113582/html5/thumbnails/18.jpg)
81-T 18
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39. ÆW µºÈ∑Œ ÆW ÒøËWˆ∆ X. 18·75 »A µÏ◊øΩÿ T√à •Ωÿ •ª»∑ µÏˆ√ˆ¡ Æ‹Ω πΩµÍΩà 淪¿ˆª∑Èÿ«ËŒ. ´∂Èœ •fiÒøËW∆Èÿ •ª»∑ µÏˆ√ ´ÿ∂ ? 2
![Page 19: ê·ÂŒÈ : πÂä  PAPERS/MATHS/81-T.pdf߈πÀπ¬ËπU 20. SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A ´∂Èœ ß‹ÒΩ˪Uÿ SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A](https://reader034.fdocumento.com/reader034/viewer/2022042114/5e90e4e79fab8867ad113582/html5/thumbnails/19.jpg)
19 81-T
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40.
!
x2" 8 x + 1 = 0 ´ÿ« π¿ÿøËflˆª N‹ΩȬ‹ˆΩ ø¡ÿøH‹ΩÈ ΩÍŒ»∑. 2
![Page 20: ê·ÂŒÈ : πÂä  PAPERS/MATHS/81-T.pdf߈πÀπ¬ËπU 20. SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A ´∂Èœ ß‹ÒΩ˪Uÿ SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A](https://reader034.fdocumento.com/reader034/viewer/2022042114/5e90e4e79fab8867ad113582/html5/thumbnails/20.jpg)
81-T 20
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41. Qı¡ ßWøFÀ π¿ÿøËH ´ÿ«Ëœ ´ÿ∂ ? ÆW ´H‹Q»∑ËflH ΩW∑. 2
![Page 21: ê·ÂŒÈ : πÂä  PAPERS/MATHS/81-T.pdf߈πÀπ¬ËπU 20. SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A ´∂Èœ ß‹ÒΩ˪Uÿ SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A](https://reader034.fdocumento.com/reader034/viewer/2022042114/5e90e4e79fab8867ad113582/html5/thumbnails/21.jpg)
21 81-T
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42.
!
kx2
+ 6 x + 1 = 0 ´ÿ« π¿ÿøËflFœ k-¡Ïÿ ´Ã¿ΩÈfiøÏ◊A •Q π¿¿Ë∂ T√…∑ˆ∆ Ò∑ˤFW»Aà ? 2
![Page 22: ê·ÂŒÈ : πÂä  PAPERS/MATHS/81-T.pdf߈πÀπ¬ËπU 20. SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A ´∂Èœ ß‹ÒΩ˪Uÿ SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A](https://reader034.fdocumento.com/reader034/viewer/2022042114/5e90e4e79fab8867ad113582/html5/thumbnails/22.jpg)
81-T 22
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43. 3·5 Òπ.¿Í ¶¬Ã Ò∑ˤª ÆW µflª‹ΩÈ◊A 4·5 Òπ.¿Í ÒΩˈ√µÏœ ©‰∆ ÆW é‰∆È¡Ïœ ßW›Q ßW ÒΩËH∑ËH∑ˆ∆ •ˆ¿»∑. 2
![Page 23: ê·ÂŒÈ : πÂä  PAPERS/MATHS/81-T.pdf߈πÀπ¬ËπU 20. SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A ´∂Èœ ß‹ÒΩ˪Uÿ SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A](https://reader034.fdocumento.com/reader034/viewer/2022042114/5e90e4e79fab8867ad113582/html5/thumbnails/23.jpg)
23 81-T
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44. ABCD ´ÿøQ ÆW πËÕπQ¬Ã ( Rhombus ) ´∂Èœ
!
AC2
+ BD2
= 4 AB2 ´∂ æÈ^û∑. 2
![Page 24: ê·ÂŒÈ : πÂä  PAPERS/MATHS/81-T.pdf߈πÀπ¬ËπU 20. SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A ´∂Èœ ß‹ÒΩ˪Uÿ SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A](https://reader034.fdocumento.com/reader034/viewer/2022042114/5e90e4e79fab8867ad113582/html5/thumbnails/24.jpg)
81-T 24
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45. Ò∑ËH»∑fiøflH‰∆ øª‹ΩÈœ TP ¿◊^à TQ ¶∑È¡ˆµ O-ˆµ ˆ¿¡¿Ë∑ Ò∑ˤª µflª‹ΩÈ◊A µˆ¬¡fiøflª ÒΩËH∑ËH∑‰ ´∂Èœ ∠PTQ = 2 ∠OPQ ´∂ æÈ^û∑. 2
![Page 25: ê·ÂŒÈ : πÂä  PAPERS/MATHS/81-T.pdf߈πÀπ¬ËπU 20. SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A ´∂Èœ ß‹ÒΩ˪Uÿ SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A](https://reader034.fdocumento.com/reader034/viewer/2022042114/5e90e4e79fab8867ad113582/html5/thumbnails/25.jpg)
25 81-T
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46. ÆW æÈ√ •∆ˆµ¡Ë∆Uÿ ∑∆fié‹Ω∑‹ΩÈ√ÈW›Q øΩÈû∑‰ Ω¬fiøflH‰∆∂. ßΩ◊A ÆW ΩÈflªÃ µˆ¬¡ûÃ. 2
[ •∆û ( Scale ) : 20 ¿Í = 1 Òπ.¿Í ]
D »A ( ¿ÍflªUœ )
160 E »A 80 120 C »A 60
100 B »A 40 60
A ¡Ï√ÈW›Q
![Page 26: ê·ÂŒÈ : πÂä  PAPERS/MATHS/81-T.pdf߈πÀπ¬ËπU 20. SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A ´∂Èœ ß‹ÒΩ˪Uÿ SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A](https://reader034.fdocumento.com/reader034/viewer/2022042114/5e90e4e79fab8867ad113582/html5/thumbnails/26.jpg)
81-T 26
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47. øÏÿµWà •ºÈ»A ÆW µˆ√¡ˆ¿fié µˆ¬∑. 2
!
0 1 2
1 2 1
2 1 0
"
#
$ $ $
%
&
' ' '
![Page 27: ê·ÂŒÈ : πÂä  PAPERS/MATHS/81-T.pdf߈πÀπ¬ËπU 20. SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A ´∂Èœ ß‹ÒΩ˪Uÿ SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A](https://reader034.fdocumento.com/reader034/viewer/2022042114/5e90e4e79fab8867ad113582/html5/thumbnails/27.jpg)
27 81-T
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48. Ò∑ËH»∑fiøflH‰∆ ΩȤ¿‹ΩÈ◊A ¶Õ√Uÿ N‹ΩȬ‹ˆΩ πUøËŒ»∑. ( Verify the
Euler’s formula ) 2
![Page 28: ê·ÂŒÈ : πÂä  PAPERS/MATHS/81-T.pdf߈πÀπ¬ËπU 20. SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A ´∂Èœ ß‹ÒΩ˪Uÿ SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A](https://reader034.fdocumento.com/reader034/viewer/2022042114/5e90e4e79fab8867ad113582/html5/thumbnails/28.jpg)
81-T 28
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IV. 49. ÆW ΩŒµÏœ 82% µÏ¤ºfiøΩˬŒ∑‰ ∑ºÈΩ‹ΩÈYÃ, 72% µÏ¤ºfiøΩˬŒ∑‰ •«ÈµÏ¡√ÈYà 55% µÏ¤ºfiøΩˬŒ∑‰ ߬¤FY¿ ΩŒÀπÈ Òø◊^‰∆∂Œ ´∂Èœ,
߬¤H ø˪…∑∆ÈYà ΩËœµÏú◊«µŒ∑∆Èÿ πΩµÍΩà ´‡µ∆û ? ( Òµÿ µˆ¬øªÃ ( Venn diagram ) µˆ¬›Q πUøËŒ»∑ ) 3
![Page 29: ê·ÂŒÈ : πÂä  PAPERS/MATHS/81-T.pdf߈πÀπ¬ËπU 20. SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A ´∂Èœ ß‹ÒΩ˪Uÿ SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A](https://reader034.fdocumento.com/reader034/viewer/2022042114/5e90e4e79fab8867ad113582/html5/thumbnails/29.jpg)
29 81-T
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50. ∑ Í÷»∑ËPà ø¬µY»A π¬ËπU ¿◊^à ΩÈflª µÏ√»∑à ∑ˤ∑. 3
AZ ߈ªÒµ∆È
Class Interval
•ˆ√Òµ¤
frequency
0 – 4 2
5 – 9 3
10 – 14 10
15 – 19 3
20 – 24 2
![Page 30: ê·ÂŒÈ : πÂä  PAPERS/MATHS/81-T.pdf߈πÀπ¬ËπU 20. SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A ´∂Èœ ß‹ÒΩ˪Uÿ SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A](https://reader034.fdocumento.com/reader034/viewer/2022042114/5e90e4e79fab8867ad113582/html5/thumbnails/30.jpg)
81-T 30
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51.
!
x3" 2 x
2" 13 x " 10 ¿◊^Ã
!
x3" x
2" 10 x " 8 ¶∑È¡µ◊«Èÿ ¿Í.ÒøË.¿. ( L.C.M )
∑ˤ∑. 3
![Page 31: ê·ÂŒÈ : πÂä  PAPERS/MATHS/81-T.pdf߈πÀπ¬ËπU 20. SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A ´∂Èœ ß‹ÒΩ˪Uÿ SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A](https://reader034.fdocumento.com/reader034/viewer/2022042114/5e90e4e79fab8867ad113582/html5/thumbnails/31.jpg)
31 81-T
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![Page 32: ê·ÂŒÈ : πÂä  PAPERS/MATHS/81-T.pdf߈πÀπ¬ËπU 20. SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A ´∂Èœ ß‹ÒΩ˪Uÿ SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A](https://reader034.fdocumento.com/reader034/viewer/2022042114/5e90e4e79fab8867ad113582/html5/thumbnails/32.jpg)
81-T 32
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52. a + b + c = abc ´∂Èœ
!
a b2
c2" 1( )
bc + 1 +
b c2
a2" 1( )
ca + 1 +
c a2
b2" 1( )
ab + 1 = 2abc ´∂ ∑ˤøÏ»∑ûÃ. 3
![Page 33: ê·ÂŒÈ : πÂä  PAPERS/MATHS/81-T.pdf߈πÀπ¬ËπU 20. SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A ´∂Èœ ß‹ÒΩ˪Uÿ SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A](https://reader034.fdocumento.com/reader034/viewer/2022042114/5e90e4e79fab8867ad113582/html5/thumbnails/33.jpg)
33 81-T
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53. ߬¤H µflª…∑‰ Æÿˆ«Ò¡Ëÿ^ Òµ∆Èfié«¿Ë∑ ÒΩËflH» Ò∑ˤFW›ΩËœ
•µ◊«Èÿ ÒΩËHé‰∆È∑‰ ¿◊^à •‡µflª…∑∆Èÿ ˆ¿¡…∑‰ æŒ∑ËflFœ •ˆ¿›ΩÈW»Aà ´∂ æÈ^û∑. 3
![Page 34: ê·ÂŒÈ : πÂä  PAPERS/MATHS/81-T.pdf߈πÀπ¬ËπU 20. SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A ´∂Èœ ß‹ÒΩ˪Uÿ SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A](https://reader034.fdocumento.com/reader034/viewer/2022042114/5e90e4e79fab8867ad113582/html5/thumbnails/34.jpg)
81-T 34
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54. 12 Òπ.¿Í ¶¬SÃ, 6 Òπ.¿Í ©¡¬Sà Ò∑ˤH‰∆ ÆW BÃøÏÿ ∑∂ •∆ˆµ øËÿ« ∑∂•∆ˆµ Ò∑ˤª ÆW ∑Ë∆‹ΩÈÿ Ò¿Ë‹Ω é«fiø¬fiˆø ∑ˤ∑. 3
![Page 35: ê·ÂŒÈ : πÂä  PAPERS/MATHS/81-T.pdf߈πÀπ¬ËπU 20. SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A ´∂Èœ ß‹ÒΩ˪Uÿ SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A](https://reader034.fdocumento.com/reader034/viewer/2022042114/5e90e4e79fab8867ad113582/html5/thumbnails/35.jpg)
35 81-T
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V. 55. ÆW BflH‹ÒΩ˪Œ µUˆπ¡Ïœ SΩœ ©^fié 2 ¿◊^à SΩœ ≠›Q ©^fié∑∆Èÿ BHΩœ •H‹Ω ≠›Q ©^fié∑∆Èÿ BHΩ√Èÿ æËÿ∑Èœ ÆW ø…A. ´∂Èœ 20 µQ ©^fié – 112 »AÀ π¿Ã ´∂ ∑ˤøÏ»∑. 4
![Page 36: ê·ÂŒÈ : πÂä  PAPERS/MATHS/81-T.pdf߈πÀπ¬ËπU 20. SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A ´∂Èœ ß‹ÒΩ˪Uÿ SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A](https://reader034.fdocumento.com/reader034/viewer/2022042114/5e90e4e79fab8867ad113582/html5/thumbnails/36.jpg)
81-T 36
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56. 4 Òπ.¿Í ¿◊^à 2 Òπ.¿Í ¶¬…∑‰ Ò∑ˤª ßW µflª…∑∆Èÿ ˆ¿¡…∑e»∑Ȉª¡ 10 Òπ.¿Í ߈ªÒµ∆Èú‰∆Q. ßW ÒøËQ‹ ÒΩËH∑ËH∑‰ µˆ¬›Q •µ◊«Èÿ æÍ∆‹ˆΩ •∆›Q ´ZQ∑. 4
![Page 37: ê·ÂŒÈ : πÂä  PAPERS/MATHS/81-T.pdf߈πÀπ¬ËπU 20. SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A ´∂Èœ ß‹ÒΩ˪Uÿ SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A](https://reader034.fdocumento.com/reader034/viewer/2022042114/5e90e4e79fab8867ad113582/html5/thumbnails/37.jpg)
37 81-T
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57. ßW S»∑˺…∑∆Èÿ ∑˺…∑‰ π¿Ã ´∂Èœ Æ‹Ω ø»∑…∑∆Èÿ •∆ûà µÏ∑ÈΩ π¿¿Ë∑ ßW»Aà ´∂ æÈ^û∑. 4
![Page 38: ê·ÂŒÈ : πÂä  PAPERS/MATHS/81-T.pdf߈πÀπ¬ËπU 20. SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A ´∂Èœ ß‹ÒΩ˪Uÿ SΩœ ´¤ Tÿ«ËµQ ´¤ºÈÿ ßW¿ª…A](https://reader034.fdocumento.com/reader034/viewer/2022042114/5e90e4e79fab8867ad113582/html5/thumbnails/38.jpg)
81-T 38
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58.
!
y = x2 ¿◊^à y = 3 – 2x ´ÿøΩ◊A µˆ¬øªÃ ( graph ) µˆ¬›Q •Ωÿ T√Ã
!
x2
+ 2 x " 3 = 0 ´ÿ« π¿ÿøËflˆª ΩÍŒ»∑ûÃ. 4
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