Master JEE CLASSES · Sec – I(Q.N : 19 – 23) Questions with Single Answer Type +3 -1 5 15 Sec...
Transcript of Master JEE CLASSES · Sec – I(Q.N : 19 – 23) Questions with Single Answer Type +3 -1 5 15 Sec...
SYLLABUS: Physics: Integration & its application, Complete vectors (Introduction to physical quantities like Position Vectors , displacement Vectors ,Velocity Vector, acceleration Vector and mathematical relation between
them), EXCLUDE ((Derivation of 2 2 21, , 22
v u at s ut at v u as ) Problems on acceleration due to
gravity ,Lammi's Theorem ,Projectile motion and relative motion ,Graphs Basic Mathematics: Algebra(logarithms, quadratic equations and expressions),Trigonometry, Co-ordinate geometry (Straight lines),Graphs: Straight-line, Parabola, Rectangular hyperbola, Circle, sine, cosine, exponential + Include expression for areas of standard geometrical figures like - cone, ellipse etc. Limits, Continuity & differentiation . Application of differentiation - Maxima, Minima, Integration & its application Chemistry: Gaseous State: Measurable properties of gases; Gas Laws - Ideal gas equation, Dalton's Law of Partial pressure: Graham's Law of diffusion, Kinetic theory of gases; Distribution of molecular velocities; Kinetic energy, Non ideality of gases; vander Waal's equaiton of state, Compressibility factor; liquifaction of gases & Critical state ,Methods of expressing concnetration of a solution - % by weight, Molarity, Molality, Normality, Mole fraction, ppm, % labelling of oleum, volume strength of hydrogen peroxide, stoichiometry-II:Titrations, Volumetric analysis: neutralisation titrations - simple titrations, double titrations and back titrations, Redox titrations: oxalic-acid vs KMnO4, Mohr’s salt vs KMnO4 ; iodometry , iodimetry, Degree of hardness of water ,Cumulative syllabus
Master JEE CLASSES Kukatpally, Hyderabad.
Max. Marks: 186
Mathematics: Complete Sequence & Series ; Measurement of Angles, Trigonometric Ratios & Identities, T- Ratio of Compound angle, Multiple, sub-multiple angles (Excluding graph, periodicity and extreme values) & some special angles ; Cumulative
JEE-ADVANCE-2016-P1-Model
PHYSICS:
Section Question Type +Ve
Marks
- Ve
Marks No.of Qs Total marks
Sec – I(Q.N : 1 – 5) Questions with Single Answer Type +3 -1 5 15
Sec – II(Q.N : 6 – 13) Questions with Multiple Correct Choice 4 -2 8 32
Sec – II(Q.N : 14-18) Questions with Integer Answer Type +3 0 5 15
Total 18 62
CHEMISTRY: Section Question Type
+Ve
Marks
- Ve
Marks No.of Qs Total marks
Sec – I(Q.N : 19 – 23) Questions with Single Answer Type +3 -1 5 15
Sec – II(Q.N : 24 –31) Questions with Multiple Correct Choice 4 -2 8 32
Sec – II(Q.N : 32-36) Questions with Integer Answer Type +3 0 5 15
Total 18 62
MATHEMATICS: Section Question Type
+Ve
Marks
- Ve
Marks No.of Qs Total marks
Sec – I(Q.N:37 – 41) Questions with Single Answer Type +3 -1 5 15
Sec – II(Q.N :42–49) Questions with Multiple Correct Choice 4 -2 8 32
Sec – II(Q.N : 50-54) Questions with Integer Answer Type +3 0 5 15
Total 18 62
JEE-ADVANCE-2016-P1-Model IMPORTANT INSTRUCTIONS Max Marks: 186
space for rough work Page 2
PHYSICS Max Marks: 62 SECTION-I
(SINGLE CORRECT CHOICE TYPE) This Section Contains FIVE questions, Each question has FOUR options (A), (B), (C) and (D). ONLY ONE of those four options is Correct For each question, darken the bubble corresponding to the correct option in the ORS, For each question, marks will be awarded in one of the following categories: Full Marks : +3 If only the bubble corresponding to the correct option in darkened, Zero Marks : 0 If none of the bubbles is darkened. Negative Marks: -1 In all other cases 1. How many minimum number of vectors in different planes can be added to give zero
resultant
A) 2 B) 3 C) 4 D) 5
2. The condition for A B A B
is that
A) A B B) B 0
C) A 0 D) B is unit vector
3. Given A B C 0
. Which of the following statements is not correct
A) A,B and C
each must be a null vector
B) the magnitude of A
equals to the magnitude of B C
C) the magnitude of A
can never be greater than that the sum of the magnitude of
B and C
D) A,Band C
must lie in the same plane
4. The value of dydx
for the curve 2x y at the point 1,1 is
A) 1 B) 2 C) 3 D) -2
5. Value of 2x 7 dx at x 3 is
A) 12 B) 6 C) 9 D) 12 SECTION-II
(MULTIPLE CORRECT CHOICE TYPE) This Section contains EIGHT question. Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four options(s) is
(are) correct. For each question, darken the bubble(s) corresponding to all the correct options(s) in the ORS. For each question, marks will be awarded in
one of the following categories: Full Marks : +4 If only the bubble(s) corresponding to all the correct options(s), is (are) darkened . Partial Marks : +1
For darkening a bubble corresponding to each correct option, Provided NO incorrect option is darkened. Zero Marks : 0 If none of the bubbles is
darkened. Negative Marks: -2 In all other cases. , For example, if (A), (C)and (D) are all the correct options for a question, darkening all these three will
result in +4 marks; darkening only (A) and (D) will result in +2 marks; and darkening (A) and(B) will result in -2 marks as a wrong option is also darkened.
6. Which of the quantity / quantities are vectors A) time B) velocity C) Flux density D) Magnetic field intensity space for rough work Page 3
7. Two forces, each equal to F, acts as show in figure, their resultant is
060
F
F A) F
2 B) 3F C) F D) 5F
8. Which of the following quantity / quantities are scalar A) mass B) acceleration C) distance D) temperature 9. Determine the sign of the slope and its nature of the following graph
O X
Y
1P
2P
A) positive B) constant C) 090 D)
2
2
d y 0dx
10. The forces which meet at one point but their lines of action do not lie in one plane are called
12. Given vector R 2i 3j . The angle between R
and y-axis is/are
A) 1 3tan2
B) 1 2cos3
C) 1 2tan3
D) 1 3cos13
13. Given y ln ax b , then dydx
A) aax b
B) aax b
C) abx a
D) ab ax
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A) Non-coplanar non-concurrent forces B) Coplanar concurrent forces C) Coplanar non-concurrent forces D) Non-coplanar concurrent forces 11. Which of the following statement(s) is/are true A) Speed, energy and angle are scalar quantities B) Distance is a scalar quantity but displacement is a vector quantity C) A vector has only magnitude, where as a scalar has both magnitude & direction D) Momentum, force, torque are vector quantities
SECTION 3 (INTEGER ANSWER TYPE)
This section contains FIVE questions. The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both inclusive For each question, darken the bubble corresponding to the correct integer in the ORS. For each question ,marks will be awarded in one of the following categories : Full Marks : +3 If only the bubble corresponding to the correct answer is darkened. Zero Marks : 0 In all other cases 14. If the area under the straight line y 2x 3 with x-axis between the lines x 2 & x 4 is
3n sq.units . Find the value of n
15. Find the minimum value of the function 2y 25x 5 10x
16. The position vectors of two balls are given by 1 2r 2i 7 j m, r 2i 4j m . What will be
the distance between the two balls ( in meters)?
17. The projection of a vector r 3i j 2k on the x y plane has magnitude 5n , then n is
18. Two equal forces have their resultant equal to either and they are inclined at an angle
2n , then n is
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CHEMISTRY Max Marks: 62 SECTION-I
(SINGLE CORRECT CHOICE TYPE) This Section Contains FIVE questions, Each question has FOUR options (A), (B), (C) and (D). ONLY ONE of those four options is Correct For each question, darken the bubble corresponding to the correct option in the ORS, For each question, marks will be awarded in one of the following categories: Full Marks : +3 If only the bubble corresponding to the correct option in darkened, Zero Marks : 0 If none of the bubbles is darkened. Negative Marks: -1 In all other cases
19. 0.84g of an acid (mol.wt.150) was dissolved in water and the volume was made up to
100 ml. 25 ml of this solution required 28 ml (N/10) NaOH solution for neutralization.
The equivalent weight and basicity of the acid
A) 75,2 B) 150 ,1 C) 75,4 D) 150,2
20. 20 ml of 0.1 M 2 4FeC O solution is titrated with 40.1M KMnO is acidic medium. Volume
of 4KMnO solution required to oxidize 2 4FeC O completely is
A) 20 ml B) 12 ml C) 8 ml D) 4 ml
21. Which among the following indicates change in the chemical composition due to
dissociation
A)
logV
logP B)
PV
T
C) T
PV/T
D)
P
V
22. At what temperature the RMS velocity of 2O molecules will have the same RMS
velocity as 2SO at 047 C ?
A) 0113 C B) 0160 C C) 0113 C D) 0160 C
23. The gas that is heated up during Joule Thomson effect at ordinary temperature is
A) 2O B) 2CO C) 2H D) 2SO
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SECTION-II (MULTIPLE CORRECT CHOICE TYPE)
This Section contains EIGHT question. Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four options(s) is (are) correct. For each question, darken the bubble(s) corresponding to all the correct options(s) in the ORS. For each question, marks will be awarded in one of the following categories: Full Marks : +4 If only the bubble(s) corresponding to all the correct options(s), is (are) darkened . Partial Marks : +1 For darkening a bubble corresponding to each correct option, Provided NO incorrect option is darkened. Zero Marks : 0 If none of the bubbles is darkened. Negative Marks: -2 In all other cases. , For example, if (A), (C)and (D) are all the correct options for a question, darkening all these three will result in +4 marks; darkening only (A) and (D) will result in +2 marks; and darkening (A) and(B) will result in -2 marks as a wrong option is also darkened.
24. The angular momentum of electron can have the value(s)
A) h2
B) h
C) 2h
D) 5 h2 2
25. Heisenberg’s uncertainty principle is not valid for A) moving electron B) motor car C) stationary particles D) all of these 26. With regard to the gaseous state of matter which of the following statements are
correct? A) complete order of molecules B) complete disorder of molecules C) random motion of molecules D) fixed position of molecules 27. Which of the following figures does not represent 1 mole of dioxygen gas at STP ? A) 16 grams of gas B) 22.7 litres of gas C) 236.022 10 dioxygen molecules D) 11.2 litres of gas 28. Under which of the following two condition applied together, gas deviates most from
the ideal behavior ? A) low pressure B) high pressure C) low temperature D) high temperature 29. Which of the following changes decreases the vapour pressure of water kept in a sealed
vessel ? A) Decreasing the quantity of water B) Adding salt to water C) Decreasing the volume of the vessel to one-half D) Decreasing the temperature of water 30. Which is a dimensionless quantity ? A) Mole fraction B) Molality C) % by wt. of solvent D) % by wt. of solution 31. 100ml of each of 2 21NH O and 11.2 V 2 2H O solutions are mixed, then the resultant
solution will be A) 2 23M H O B) 2 20.5 N H O C) 2 225.5g / LH O D) 2 22.55g / LH O
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SECTION III (INTEGER ANSWER TYPE)
This section contains FIVE questions. The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both inclusive For each question, darken the bubble corresponding to the correct integer in the ORS. For each question ,marks will be awarded in one of the following categories : Full Marks : +3 If only the bubble corresponding to the correct answer is darkened. Zero Marks : 0 In all other cases 32. In how many acids among the following, the basicity is greater than 1 ?
3 4 3 3 3 2 3 3H PO , H PO ,H PO , H BO
33. What volume of 0.1 M HCl will be oxidised by 1 mL of 0.1 M 4KMnO
34. 3.2 g of oxygen and 0.2 g of hydrogen are placed in 1.12 litre flask at 00 C . The total
pressure in atm of the gas mixture will be
35. At 400 K, the root mean square (rms) speed of gas X (molecular mass = 40) is equal to
the most probable speed of gas Y at 60 K. The molecular mass of the gas Y is
36. Compressibility factor for ideal gas will be equal to
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MATHEMATICS Max Marks: 62 SECTION-I
(SINGLE CORRECT CHOICE TYPE) This Section Contains FIVE questions, Each question has FOUR options (A), (B), (C) and (D). ONLY ONE of those four options is Correct For each question, darken the bubble corresponding to the correct option in the ORS, For each question, marks will be awarded in one of the following categories: Full Marks : +3 If only the bubble corresponding to the correct option in darkened, Zero Marks : 0 If none of the bubbles is darkened. Negative Marks: -1 In all other cases
37. If 1 etan tan , then cos2 1 e 2
A) 1 ecoscos e
B) 1 ecos
cos e
C) 1 ecos
cos e
D) cos e
1 ecos
38. If sin x 3 3sin x , then
A) tan x tan B) 2tan x tan C) 3tan x tan D) tan x 3tan 39. If 2 3sin x sin x sin x 1 ¸then 6 4 2cos x 4cos x 8cos x A) 8 B) 4 C) 2 D) 0
40. If 2
2 2 2
1 1 1 ....1 2 3 6
, then 2 2 2
1 1 1 ....1 3 5
A) 2
8 B)
2
12 C)
2
3 D)
2
2
41. If n1 1 1H 1 .....2 3 n
, then the value of 503 5 99S 1 ......2 3 50
is
A) 50H 50 B) 50100 H C) 5049 H D) 50H 100 SECTION-II
(MULTIPLE CORRECT CHOICE TYPE) This Section contains EIGHT question. Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four options(s) is (are) correct. For each question, darken the bubble(s) corresponding to all the correct options(s) in the ORS. For each question, marks will be awarded in one of the following categories: Full Marks : +4 If only the bubble(s) corresponding to all the correct options(s), is (are) darkened . Partial Marks : +1 For darkening a bubble corresponding to each correct option, Provided NO incorrect option is darkened. Zero Marks : 0 If none of the bubbles is darkened. Negative Marks: -2 In all other cases. , For example, if (A), (C)and (D) are all the correct options for a question, darkening all these three will result in +4 marks; darkening only (A) and (D) will result in +2 marks; and darkening (A) and(B) will result in -2 marks as a wrong option is also darkened.
42. If 1 1 1S ........ terms2 5 5 8 8 11
n
, then the value of the above expression is
A) 3n 2 23
B) n2 3n 2
C) less than n D) less than n3
43. For 02
¸if 2n 2n
n 0 n 0
x cos , y sin
and 2n 2n
n 0
z cos cos
, then xyz
A) xy z B) xz y C) x y z D) yz x
44. In a PQR, R2
, if P Qtan , tan2 2
are the roots of the equation 2ax bx c 0 a 0 , then
A) a b c B) b c a 0 C) a c b 0 D) c a b
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45. For the series 2 21 2 1 2 3S 1 .......
1 3 1 3 5
A) th7 term is 16 B) th7 term is 18 C) sum of first 10 terms is 505
4 D) sum of first 10 terms is 405
4 46. If 3 5cos ,cos
5 13 , then
A) 33cos65
B) 56sin65
C) 2 1sin2 65
D) 63cos65
47. If sin cos cos sin , then sin 2
A) 14 B) 3
4 C) 1
4 D) 3
4
48. If cos is the geometric mean between sin and cos where 0 ,2
, then cos 2
A) 22sin4
B) 22cos
4
C) 22sin
4
D) 22cos
4
49. If x, y, z are three consecutive odd numbers, then log xz 4 A) 2log y B) log y C) 2log y 3 D) 2log y
SECTION III (INTEGER ANSWER TYPE)
This section contains FIVE questions. The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both inclusive For each question, darken the bubble corresponding to the correct integer in the ORS. For each question ,marks will be awarded in one of the following categories : Full Marks : +3 If only the bubble corresponding to the correct answer is darkened. Zero Marks : 0 In all other cases
50. If 0
01 2 3 4 5 6
14cos36 cot 7 n n n n n n2
, then the product of the digits in
621
i 1
n
51. If 2 x x3 3 3
7log ,log 2 5 , log 22
are in A.P, then the value of x is
52. If 0 01 sin 2 cos 2f , then 8f 11 .f 342cos 2
53. If the angle between the minute hand and the hour hand of a clock when the time is 7 : 20 A.M is 020 .K , then K =
54. Let 0 A,B,C,D , where B,C are not complementary such that 2cos A 6cos B 7cosC 9cos D 0 and 2sin A 6sin B 7sin C 9sin D 0 , then the value of
3cos A Dcos B C
space for rough work Page 10
KEY & SOLUTION PHYSICS
1 C 2 B 3 A 4 B 5 D 6 BD
7 C 8 ACD 9 ABCD 10 D 11 ABD 12 CD
13 B 14 6 15 4 16 5 17 2 18 3
CHEMISTRY
19 A 20 B 21 C 22 C 23 C 24 ABC
25 BC 26 BC 27 AD 28 BC 29 BD 30 ACD
31 C 32 2 33 5 34 4 35 4 36 1
MATHS
37 D 38 C 39 B 40 A 41 B 42 ABCD
43 AC 44 AD 45 AC 46 BCD 47 BD 48 AB
49 AD 50 9 51 3 52 4 53 5 54 7
Master JEE CLASSES Kukatpally, Hyderabad.
JEE-ADVANCE-2016-P1-Model Max. Marks: 186
Page 1
PHYSICS 1. The resultant of any three vectors will be cancel out by fourth vector 2. Conceptual 3. As A B C 0
,so A B C
. They must be in a plane. Also A B C
4. 2y x
dy 2xdx
At point 1,1
dy 2 1 2dx
5. 3
2 xx 7 dx 7x3
33 7 3 9 21 12
3
6. Conceptual 7. 0120
RF 2Fcos2
022Fcos60 F
8. Conceptual
9. 0dyslope tan ve 90dx
and 2
2
d y 0 slopeiscons tan tdx
10. Conceptual 11. Conceptual 12.
13
R
2
3
12 2tan tan
3 3
13 3cos cos13 13
13. dy d ln ax bdx dx
d ln ax b d ax bd ax b dx
a
ax b
14.
x 2 x 4
y 2x 3
Y
XO
3
4
2
Area y dx 4
2
2x 3 dx 42
2
2x 3x2
16 4 12 6
A 18
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3n 18 n 6
15. For maximum and minimum value dy 0dx
dy 150x 10 0 xdx 5
2
2
d y 50dx
2
2
d ydx
has +ve value at 1x5
y has minimum value at 1x5
2
min1 1y 25 5 10 45 5
16. 1 2s r r 2 2 7 4 j 4i 3j
2 2s 4 3 5m
17. Consider only x and y components : 2 23 1 10 5 2 n 2 18. 2 2 2F F F 2F cos 1 2 1 cos
01cos 1202
23
n 3
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CHEMISTRY
19. 1 1 2 2N V N V 1N 100 0.1 28
21
0.1 28N 2.8 10100
1W 1000N
GEW 100
2 0.842.8 10 10150
'n ' factor
2 0.842.8 10 10 n150
n 2 So 150eq.wt 75
2
20. 2 4FeC ON n M 3 0.1 0.3
4KMnON n M 5 0.1 0.5
2 4 4FeC O KMnO
NV NV 0.3 20 0.5 V
4KMnO
0.3 20V 12ml0.5
21. PV PRnR nT T
So after dissociation number of moles increases and PVT
also increases
22. 2 2O SO
3RT 3R 320M M
2 2O SO
T 32032 64
0T 320 T 160K or 160 273 113 C32 64
23. Gases which shows large positive deviation are heated up during Joule Thomson effect
24. nhmvr n 1, 2,3,......2
25. Uncertainty principle applicable only for moving electrons 26. Gaseous molecules are always random motion and disordrly arranged 27. 1 mole of dioxygen represent 32 g of 2O , 22.7 lit of 2O or 236.022 10 molecules of 2O gas 28. At high pressure and low temperature gases deviates from ideal behavior 29. Vapour pressure does not depend upon the quantity of water or size of the vessel 30. Mole fraction and weight percent has no units.
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31. 2 2 2 2 2 211.211.2V H O NH O i.e 2NH O5.6
1 1 2 2 R 1 2N V N V N V V R1 100 2 100 N 200 RN 1.5 Strength = N Equation of mass 1.5 17 25.5g / L 32. 3 4H PO Basicity = 3 3 3H PO Basicity = 2 3 2H PO Basicity = 1 3 3H BO Basicity = 0 33. 1 1 2 2N V N V
34. T 1 2RTP n nV
0.0821 2730.1 0.11.12
35. x y
3RT 2RTM M
400 603R 3R M 440 M
36. Z 1 for Ideal gases
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MATHEMATICS 37.
2
2
1 tan / 2cos1 tan / 2
2
2
1 e1 tan1 e 21 e1 tan1 e 2
2 2
2 2
1 tan e 1 tan2 2
1 tan e 1 tan2 2
cos e1 ecos
38. sin x cos 3 cos x sin 3 3 sin cos x cos sin x sin x cos3 3cos cos x 3sin x sin 3
3
3
4sin xtan x4cos x
3tan x tan 39. 2 2sin x 1 sin x cos x
22 2 41 cos x 2 cos x cos x
2 4 2 44 4cos x cos x 1 cos x cos x
2 2 4 4 6 44 4cos x 4cos x 4cos x cos x cos x cos x 6 4 2cos x 4cos x 8cos x 4
40. 2 2 2 2 2 2 2 2 2
1 1 1 1 1 1 1 1 1..... ...... .....1 3 5 1 2 3 2 4 6
2 2 2 21 3.
6 4 6 24 8
41. 501 1 1S 2 1 2 2 .... 22 3 50
1 1 1100 1 ......2 3 50
50100 H
42. 1 1 1 1S .......2 5 5 8 8 11 3n 1 3n 2
5 2 8 5 11 8 3n 2 3n 1.......3 3 3 3
1 3n 2 23
3n
3 3n 2 2
n3n 2 2
It is less than n and less than n3
43. 2 4x 1 cos cos ......
22
1 cosec1 cos
2 4y 1 sin sin .....
22
1 sec1 sin
2 2 4 4z 1 sin cos sin cos ......
2 2
11 sin cos
1 xyz1 1 xy 11x y
xyz xy z 2 2cosec .sec z 2 2cosec sec z xyz x y z
Page 6
44. P Q btan tan2 2 a
and P Q ctan .tan
2 2 a
P Q b / atan 1 12 2 1 c / a
b a c a b c
45. 2
7
1 2 3 ..... 7 28.28t 161 3 5 ..... 13 7.7
2 22
n 2
n n 1 n 1t
4.n 4
2n
1S n 2n 14
n n 1 2n 11 n n 1 n4 6
101 10.11.21 505S 10.11 104 6 4
46. 3 5cos ,cos5 13
4 12sin ,sin5 13
cos cos cos sin sin 3 5 4 12. .5 13 5 13
3365
4 5 3 12sin . .5 13 5 13
5665
63cos65
2
631 165sin2 2 65
47. sin cos cos sin sin sin2
cos sin2
1 1cos sin 1 sin 22 4
3 3sin 2 or4 4
48. 2cos sin .cos 22cos sin 2 2cos 2 2cos 1 sin 2 1
2sin cos 22sin4
22cos
4
49. x y 2, z y 2 log xz 4 log y 2 y 2 4 2log y 2log y
50. 1 2 3 4 5 6n 1,n 2,n 3,n 4,n 5, n 6 2
1n 1 4 9 16 25 36 91
Page 7
Product of the digits = 1.9 = 9
51. x 2 x3 3 3
72log 2 5 log log 22
2x x 72 5 2 22
2x x x2 10.2 25 2.2 7
2x x2 12.2 32 0
x x2 8 2 4 0 x 3 or 2 But x 2 not satisfies x 3 52. 1 sin 2 cos 2f
2cos 2
2 2 2
2 2
cos sin cos sin
2 cos sin
1
1 tan
0 00 0
1 1f 11 f 341 tan11 1 tan 34
0 0 01 11 34 452
0 08 f 11 f 34 4
53. Hours hand, 12 hrs = 0360
227 : 20hrs hr3
Angle made by hrs hand 0
022 360 2203 12
Minutes hand, 1hr = 0360 20 minutes = 0120 Angle between them 0 0 0 0220 120 100 20 .K K 5 54. 2 cos A 9 cos D 6 cos B 7 cos C 1 2sin A 9sin D 6sin B 7 sin C 2
2 2 2 21 2 2cos A 9cos D 2sin A 9sin D
2 26 cos B 7 cos C 6sin B 7 sin C 4 81 36 cos A D 36 49 84cos B C
cos A D 7cos B C 3
3cos A D7
cos B C
8
*******
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