SRIGAYATRI EDUCATIONAL INSTITUTIONS...2020/04/25 · SRIGAYATRI EDUCATIONAL INSTITUTIONS INDIA (UT1+UT2) Date: 25-04-2020 Time: 3 Hours Max. Marks: 186 PHYSICS Syllabus: Mechanics

SRIGAYATRI EDUCATIONAL INSTITUTIONS

INDIA

(UT1+UT2) Date: 25-04-2020

Time: 3 Hours Max. Marks: 186

PHYSICS

Syllabus: Mechanics ( Kinematics (1D and 2D), Laws of Motion, Work, Energy and Power and

Rotational Motion, Gravitation, Oscillations and waves.

Section – 1 : (Maximum Marks : (15)

This section contains FIVE questions

Each question has FOUR options (A), (B), (C) and (D). ONLY ONE of these four options is

correct.

For each question, darken the bubble corresponding to the correct option in the ORS.

For each questions, marks will be awarded in one of the following categories :

Full Marks : +3 If only the bubble corresponding to the correct option is darkened.

Zero Marks : 0 If none of the bubbles is darkened.

Negative Marks : –1 In all other cases.

1. The relation between time t and displacement x is 2t x x , where and are constants.

The retardation is

A) 32 v B) 32 v C) 32 v D) 2 32 v

2. In the figure, the minimum value of a at which the cylinder starts rising up the inclined

surface is

A) tang B) cotg C) sing D) cosg

3. Initially the system shown in figure is in equilibrium. At the moment, the string is cut the

downward acceleration of blocks A and B are respectively a1 and a2. The magnitudes of a1 and

a2 are

A) zero and zero B) 2g and zero C) g and zero D) None of the above

4. Two satellites S1 and S2 are revolving round a planet in coplanar and concentric circular

orbits of radii R1 and R2 in the same direction respectively. Their respective periods of

JEE ADVANCE IIT 2016 PAPER-1 MODEL – (54 BITS)

(UT1+UT2)

revolution are 1 hr and 8 hr. The radius of the orbit of satellite S1 is equal to 104 km. Their

relative speed when they are closest, in kmph is

A) 4102

B) 410 C) 42 10 40 44 10

5. A particle of mass ‘m’ is rigidly attached at ‘A’ to a ring of mass ‘3m’ and radius ‘r’. The

system is released from rest and rolls without sliding. The angular acceleration of ring just

after release is

A) 4

g

r A)

6

g

r C)

8

g

r D)

2

g

r


This section contains EIGHT questions

Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of

these four option(s) is (are) correct.

For each question, darken the bubble(s) corresponding to all the correct option(s) in the ORS.


Full Marks : +4 If only the bubble(s) corresponding to all the correct option(s) is(are)

darkened.

Partial Marks : +1 For darkening a bubble corresponding to each correct option,

provided NO incorrect option is darkened.



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. A particle having a velocity 0v v at t=0 is decelerated at the rate a v , where a is

positive constant

A) The particle comes to rest at 02 v

t

B) The particle will come to rest at infinity

C) The distance travelled by the particle before coming to rest is 3/2

22v

D) The distance travelled by the particle before coming to rest is 3/2

22

3

v

7. Two particles A and B, each of mass m are kept stationary by applying a horizontal force=mg

on particle B as shown in figure. Then

A) tan 2tan B) 1 22 5T T C) 1 22 5T T D)

8. The potential energy of a particle is given by formula 2100 5 100U x x , where U and x are

in SI units. If mass of the particle is 0.1 kg then magnitude of it‟s acceleration

A) At 0.05 m from the origin is 50 ms-2

B) At 0.05 m from the mean position is 100 ms-2

C) At 0.05 m from the origin is 150 ms-2

D) At 0.05 m from the mean position is 200 ms-2

9. Two blocks A and B each of mass m are connected by a massless spring of natural length l

and spring constant K. The blocks are initially resting on a smooth horizontal floor with the spring

at its natural length as shown. A third identical block C also of mass m, moves on the floor with a

speed v along line joining B and A and collides with B elastically. Then

A) The frequency of oscillation of the system AB is 1 2

2

K

m

B) The K.E of the system at maximum compression of the spring is 2 / 4mv

C) The maximum compression of the spring is m

vK

D) The maximum compression of the spring is 2

mv

K

10. When a wave travels from a denser to rarer medium, then

A) speed of wave increases B) Wavelength of wave decreases

C) Amplitude of wave increases D) there is no change in phase angle

11. A solid cylinder is rolling down the inclined plane without slipping. Which of the following

is/are correct

A) The friction force is dissipative B) The friction force is necessarily changing

C) The friction force will aid rotation but opposes translation

D) The friction force is reduced if is reduced

12. A double star consists of two stars having masses M and 2M. The distance between their

centres is equal to r. They revolve under their mutual gravitational interaction. Then, which

of the following statements are not correct?

A) Heavier star revolves in orbit of radius 2r/3

B) Both the stars revolve with same speed, period of which is equal to 32 / r 22 / 3GM

C) Kinetic energy of the heavier star is twice that of the other star

D) Havier star revolves in orbit of radius r/3

13. Second overtone frequency of a closed pipe and fourth harmonic frequency of an open pipe

are same. Then, choose the correct options

A) Fundamental frequency of closed pipe is more than the fundamental frequency of open pipe

B) First overtone frequency of closed pipe is more than first overtone frequency of open pipe

C) Fifteenth harmonic frequency of closed pipe is equal to twelfth harmonic frequency of open pipe

D) Tenth harmonic frequency of closed pipe is equal to eighth harmonic frequency of open pipe



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.


Full Marks : +3 If only the bubble corresponding to the correct answer is darkened

Zero Marks : 0 In all other cases

14. In the given spring blocks system if 2 125k Nm , find time period of oscillation.

15. A rod of mass m and length l is released from rest from vertical position as shown in the figure.

The normal force as a function of , which is exerted on the rod by the ground as it falls

downward, assuming that it does not slip is

23cos 1

mgn

then n=

16. Figure shows a plot of the transverse displacement of the particle of a string at t=0 through which a

travelling wave is passing in the positive x-direction. The wave speed is 20 cm/s. Find the

frequency of the wave.

17. Two satellites of mass ratio 1:2 are revolving around the earth in circular orbits such that the

distance of the second satellite is four times as compared to the distance of the first satellite. Find

the ratio of their centripetal forces.

18. An infinite collection of equal masses of 2 kg are kept on a horizontal line (x-axis) at positions x=

1, 2, 4, 8, ……. Find the gravitational potential at x= 0 in GJ units.

CHEMISTRY

Syllabus: 1st and 2

nd year Organic Chemistry.




correct.






19. Hydrogenium and oxygenium combine to give two products A and B . The wt. ratio of one with the

fixed weight of the other is in the ratio of 1:2. They follow

A) Law of definite proportions B) Law of reciprocal proportions

C) Law of multiple proportions D) Law of fixed proportions

20. An allotrope of oxygenium reacts with potassium manganate(X) to give purple coloured

compound(Y) in aqueous medium. The folrmulae of X and y are:

A) MnO2, Mn2O7 B) K2MnO4,MnO2 C) MnO2,MnSO4 D) K2MnO4,KMnO4

21. Which of the following is highly explosive in nature ?

A) NF3 B) XeO3 C) NH3.NI3 D) PH3

22. Br2 reacts with hot and concentrated aqueous sodiumcarbonate solution to give X,Y and Z. Y is a

good oxidising agent. Y is:

A) NaOBr B) NaBrO4 C) NaBrO3 D) NaBr

23. The number of d-electrons in BF3 is

A) 10.0 B) 0.0 C) 11.0 D) 5.0








darkened.








24. The correct statements regarding HNO3 is /are

A) It is a good oxidising agent B) It is good nitrating agent

C) Very dilute HNO3 with Zn gives N2O D) Zn with Conc. HNO3 gives NO2

25. Which of the following reaction products are true?

A) 2Ca3(PO4)2 +6SiO2 + 10C6CaSiO3 + P4 + 10CO

B) 470 / 560 ,

( ) 4 r P PK under presure K inert atmosphere

black edP

C) P4 +20 AgNO3 + 16H2O 20Ag+20HNO3+4H3PO4

D) P and S combine to give P 2S3,P2S5, P4S3, P4S7 etc.

26. The correct products could be among the given:

A) 9O3 + 2I2 I4O9 + 9O2

B) O3 +2K4[Fe(CN)6]+H2O 2K3[Fe(CN)6]+2KOH+O2

C) FeS+CO2 ( at 10000C) FeO +CO+S

D) H2S+ SO2 (Fe2O3-Catalyst)(303K) 3/8 S8 + 2H2O

27. The correct statements among these:

A) S8 has puckered ring structure B) Ca(OH)2 +H2S CaS+ 2H2O

C) HgS,CuS,PbS, CoS, NiS, FeS are black ppt. ZnS- dirty white ppt. Sb2S3 –Orange ppt.

D) CdS, SnS2, As2S3 – yellow, SnS-Chocolate colur ppt. Bi2S3 –brown ppt.

28. The correct reactions among these are:

A) C2H5OH+6KOH+4I2 CHI3 + HCOOK+5KI+5H2O

B) 2HgO+2I2 HgI2.HgO+2HIO

C) 4Na2S2O3 + I2 2NaI + Na6S8O12

D) 8NH3.NI3 5N2+6NH4I+9I2

29. In which of the following reactions iodine is liberated?

A) CuSO4 +KI B) NaIO3+ NaI+H2SO4

C) KI+H2O+O3 D) KI+MnO2+H2SO4

30. The correct ones among these are:

A) I3-, I5

-, I7

-, I8

- ,Cl3

-.Br3

- are known and are stabilized by large cations.

B) 2KI+2Cl2 2KICl4 C) CsI3 CsI + I2

D) I(ClO4)3, I(CH3COO)3 , IPO4,ICl3, I(NO3)3 contain I3+

ion.

31. Which of the following pairs can be reduced by H2? A) CuO,MoO3 B) UO3, In2O3 C) Cr2O3 , Na2O D) Fe3O4,Ag2O




inclusive.





32. Hot /conc. NaOH reacts with Cl2 to give --- moles of NaClO3

33. The number of oxygens shared in frame work silicates is :

34. In the formation of inorganic benzene ---- moles of H2 is liberated.

35. The moles of sodiumtetrathionate produced when hypo reacts with one mole of I2 is ____

36. CaCO3 decomposes to give fire extinguisher. It is passed through BaO2(aq), the product formed

converts black lead sulphide to white lead sulphate. The moles of oxidising agent required for the

process is :

MATHEMATICS

Syllabus: MATHS: Ut-1 & 2 Syllabus




correct.






37. Let X be the universal set for sets A and B. If 200, 300n A n B and 100n A B , then

1 1 300n A B , provided n X =_______

A) 600 B) 700 C) 800 D) 900

38. If , 11

xf x x

x

, then ......fofofo of x is equal to ________

A) 1

x

x B)

19

1

x

x

C)

19

1

x

x D) x

39. In a right angled triangle, if the hypotenuse is four times as long as the perpendicular drawn

to it from the opposite vertex. One of the acute angle is_____________

A) 150 B) 30

0 C) 45

0 D) 60

0

40. If tan tanA B x and cot cotB A y then cot A B _______

A) 1 1

y x B)

1 1

x y C)

1 1

x y D) x y

41. If cos sin2 2

r r rx i

, then the value of 1 2 3.......x x x is _______

A) – 1 B) 1 C) 0 D)








darkened.








42. The number ways in which we can choose 2 distinct integers from 1 to 100, such that the

difference between them is atmost 10, is _____

A) 2 2

100 90C C B) 98 88

100 90C C C) 2 88

100 90C C D) 2

100C

43. Suppose 1 2 3, , ,......, 2nx x x x n are real numbers such that 1i n ix x for 1 i n . Consider

the sum 1 , ,i j kS x x x i j k N (I, j, k distinct), then which of the following is not

true?

A) 1 2!. . .... nS n x x x B) 3 4S n n

C) 3 4 5S n n n D) 0S for all n

44. Consider the equation 2 0,x x a a N . If equation has integral roots, then

A) a= 2 B) a =6 C) a = 12 D) a = 20

45. If 00 , 180x y and

1sin cos

2x y x y then x and y are given by

A) 0 045 , 15x y B) 0 045 , 135x y C) 0 0165 , 15x y D) 0 0165 , 135x y

46. If 2sin 3cos 6 11x x , 0 4 , n R then holds for

A) no value of x and B) one value of x and two values of

C) two values of x and two values of D) two pairs of values of ,x .

47. The equation 2 11 2 sin cos 0x x y is satisfied by x R

A) exactly one value of x B) exactly two values of x

C) exactly one value of y D) exactly two values of y

48. If sides of triangle ABC are a, b, c such that 2b a c then

A) 2

3

b

c B)

1

3

b

c C) 2

b

c D)

3

2

b

c

49. If 1 2 3, ,z z z and 4z are roots of the equation 4 3 2

0 1 2 3 4 0a z a z a z a z a where

0 1 2 4, , &a a a a are real, then

A) 1 2 3 4, , ,z z z z are also roots of equation

B) 1z is equal to atleast one of 1 2 3 4, , ,z z z z

C) 1 2 3 4, , ,z z z z are also roots of equation

D) None of the above




inclusive.





50. If the matrix

1 2 3 0

2 4 3 2

3 2 1 3

6 8 7

A

is of rank 3, then __________

51. The number of solutions of sec .cos5 1 0x x in the interval 0,2 is _____

52. If 5 7

sin sin sin18 18 18

K

then 1

K _________

53. If 2 2

sin cos cos secf ec , then minimum value of f is ____________

54. In ABC , 9

sin sin sin sin sin sin4

A B B C C A and a= 2, then the value of 3 , where is

area of triangle is ______

SRIGAYATRI EDUCATIONAL INSTITUTIONS

INDIA

(UT1+UT2) Date: 25-04-2020

Time: 3 Hours Max. Marks: 186

KEY SHEET

PHYSICS

1) A 2) A 3) B 4) B 5) B

6) A, D 7) A,C 8) A,B,C 9) A,B,D 10) A,C,D

11) C,D 12) A,C 13) B,C,D 14) 1 15) 2

16) 5 17) 8 18) 4

CHEMISTRY

19) C 20) D 21) B 22) C 23) B

24) A,B,D 25) A,B,C,D 26) A,B,C,D 27) A,B,C,D 28) A,B,D

29) A,B,C,D 30) A,B,C,D 31) A,B,D 32) 1 33) 4

34) 12 35) 1 36) 4

MATHS

37) B 38) A 39) A 40) B 41) A

42) A,B,C 43) A,B,C 44) A,B,C,D 45) A,D 46) B, D

47) A,C 48) A,C,D 49) A,B 50) 5 51) 8

52) 8 53) 9 54) 3

JEE ADVANCE (IIT 2016 PAPER-I MODEL – (54 BITS)

HINTS & SOLUTIONS

1. 2dt

xdx

1

2

dxv

dt x

2

12

2

dv dxa

dt x dt

2 32 2V V V

2. On the cylinder

If N = Normal reaction between cylinder and inclined plane

sinN horizontal component of N = ma………………..(1)

cosN vertical component of N mg ………………(2)

1 sin

2 cos

N ma

N mg

tana

g

tana g

3. T= 2 mg

As soon as string is cut T on A suddenly becomes zero. Therefore a force of 2 mg acting on upward

direction on A suddenly becomes zero

So net force on it will become 2 mg down wards

1

22

mga g

m

Spring force does not become instantly zero. So acceleration of B will not change a2 =0

4. 2 3

0

2,

RT R V

T

Rel velocity 1 20 0V V

5. The distance of CM from the ring centre O

3 0

3 4

m m n rx

m m

We can apply torque equation about point of contact as the ring is rolling

P PI

22 24 3

4

rmg mr mr m AP

2

24 2mgr mr m r

26mgr mr

26mgr mr

6. a) a v

dv

vdt

0

0 1

2

0

1

2

t

v

dt v dv

02 v

t

b) a v

dv

v vdt

0

0 1

2

0

1s

v

ds v dv

3

202

3

vS

7.

2 cosT mg

2 sinT mg

8. 5 200dV

F xdx

At origin, 0 5x F N

2550 / sec

0.1

Fa m

m

Mean position is at F=0

5

0.025200

x m

5 200

50 200000.1

F xa

m

………………(1)

At 0.05 m from the origin

0.05x m

0.05x m

Substitute in equation (1) we have

250 seca m

250 / secm

At 0.05 m from the mean position means

0.075 0.025x x m

Substitute in equation (1) we have

2100 / seca m 0

9. Let 1V is the velocity acquired by A and B then

1 1 1

2

VmV mV mV V

So, 2 2 2 2

1 1

1 1 1 1

2 2 2mV mV mV KX

L

Where x is displacement 2

Mx V

K

So (d) is correct.

At maximum compression, KE of A – B system is

2 2 2 2

1 1 1

1 1 1

2 2 2mV mV mV mV

(6) is correct

10. Conceptual

11. Conceptual

12. 2 2M r x Mx Mr Mx Mx

3

nl

13. Conceptual

14.

222

52

2

eff

kk

kK

kk

Refluxed mass of system 5 5 5

5 5 2

5122 2 5

2

5

Tkkeq k

2

15 1

25

15. At angle

1

1 cos2 2

lIW mg

2 31 cos

gW

l …………(1)

Difference ate w.r.to

2

1sin

3 sin2

2

3

mgg

ml l

21 31 cos

2 2n

ga

1 3

sin2 4

fa g

cos sinx f nf ma m a a

3 sin

sin cos 1 cos4 2

gm g

3 3

sin sin 12 2

mg

fN m g a

2 1 1

1 3cos cos4 3

mg

16. V f

17. Centripetal force 2

2

mv GMm

r r

Where m is the mass of the satellite and m is the mass of the satellite of eanks

2

1

2

418

2

rf

f r

18. 2 3

1 1 11 ........

2 2 2V Gm

2 41

12

GMV m

CHEMISTRY

19. 2 2 2 2 2

32

2H O H O H O

2 2 2H O:H O The wt. ratio of oxygen with fixed wt.of hydogen

is16:32=1:2 which is a simple multiple ratio hence it

follows law of multiple propotions

20. 2K2MnO4 (X) Green coloured)+O3+H2O 2KMnO4(Y)(purple colour)+2KOH+O2

Oxygenium(O2) allotrope is O3

21. XeO3 20 times more explosive than TNT(trinitrotoluene) 2XeO3 2Xe+3O2

22. 3Na2CO3(aq) (hot/conc.)+3Br2 5NaBr+NaBrO3 +3CO2 Y= NaBrO3 Br is in +5 oxidation state to

act like good oxidising agent

23. zero as there is no d-orbital in both B and F.

24. 4 Zn+10 HNO3(6%)(very dilute) 4 Zn(NO3)2 +NH4NO3 + 3H2O

25. They are experimental observations. Hence are true.

26. A and B oxidising power of O3, C and D are methods of preparation of “s”

27. A) S8 has puckered ring structure B) Ca(OH)2 +H2S CaS+ 2H2O

C) HgS,CuS,PbS, CoS, NiS, FeS are black ppt. ZnS- dirty white ppt. Sb2S3 –Orange ppt

D) CdS, SnS2, As2S3 – yellow, SnS-Chocolate colur ppt. Bi2S3 –brown ppt.

28. C) 2Na2S2O3 +I2 Na2S4O6+2NaI is correct. Remaining are correct

29. A) 2CuSO4+4KI 2K2SO4+Cu2I2+I2 B) NaIO3 + 5NaI+6H2SO4 6NaHSO4+3H2O+3I2

C) 2KI+H2O+O3 2KOH+ O2+I2 D) 2KI+MnO2+3H2SO4 2KHSO4+MnSO4+2H2O+2I2

30. A) KI+I2 KI3 =K+ + I3

- , KBr+Br2 KBr3 =K

+ + Br3

-

B) formation of polyhalogen compound C) CsI3 dissociates on heating to give I2

D) I(ClO4)3 I3+

+3ClO4- .

31. C) Cr2O3 +3H2 2Cr+3H2O , Na2O+H2 no reduction because sodium is highly

electropositive Na2O is strong oxide. A,B and D pairs are reduced by hydrogen.

32. 6NaOH(hot/Conc.) + 3Cl2 5NaCl +NaClO3 + 3H2O

33. Each silicon is surrounded by four Oxygens.

-O-Si-O-Si-

O O

O O

O -Si

Each Si is surrounded by 4-oxygens

34. 3B2H6.2NH3 2B3N3H6(inorganic benzene)+12H2

35. 2Na2S2O3 +I2 Na2S4O6(sodiumtetrathionate)+2NaI

36. CaCO3 CaO +CO2, BaO2+H2O+CO2 BaCO3 +H2O2

(oxidising agent) 4H2O2+PbS PbSO4+4H2O

MATHS

37. n A B n A n B n A B

200 300 100 400

And 11 1n A B n A B

300 n X n A B

300 400 700n X

38. 1

11

1

x

x xfof x f f x fxx

x

11

1

x

x xx x

x

Now, 1

xfofof x f fof x f x

x

(i.e., ) ........1

xfofo odd terms x

x

39. Let BP p then given

4AC P and ,AB x BC y

2 2 216x y p ……………………(1)

From .sinp

ABDx

cosx p ec

And from ,sin 90p

BCDy

secy p

Now from (1), 2 2 2 2 2cos sec 16p ec p p

2 2cos sec 16ec …………….(2)

015 .

40. Given tan tanA B x ;

1 1 tan tan

cot cottan tan tan tan

A By B A

B A A B

tan tantan tan

x xA B

A B y

Now

1 1 tan tancot

tan tan tan

A BA B

A B A B

1x

y xy

x xy

1 1

x y

41. Given 2

r rx cis

1 2 3 2 3. . ....... . . ......

2 2 2x x x cis cis cis

2 3

.........2 2 2

cis

1/ 2

11 1/ 2

cis cis

42. Let 1 2,x x be the choosen numbers.

Let „a‟ be the integer before te 1x , „b‟ be the integer between 1x and 2x and „c‟ be the integer after

2x .

98a b c , where 0, 10, 0a b c .

Now, we consider the choices, where difference is atleast 11, then the no. of solutions is

3 1 288 3 1 90C C

The no. of ways in which „b‟ is less than 10 is, 2 2100 90C C .

Options (A), (B), (C) are correct.

43. Since i, j, k are distinct.

1, 1, 1n i n j n k are also distinct and they lie between 1 to n.

Now . .i j kS x x x

1 1 1n i n j n kx x x

1 1 1. .n i n j n kx x x

, ,i j kx x x

S (they are also distinct)

0S for all n.

(A), (B), (C) are all not correct.

44. 1 1 4

2

ax

integer

1 4a should be a perfect square

But 1+4a is an odd number

2

1 4 2 1 ,a n n Z

24 4 4a n n

1a n n

2,6,12,20a all are possible

45. 1

sin cos2

x y x y

0 030 150x y or and 0 060 300x y or

0 0 0 045 165 125 105x or or or

0 0 0 015 135 95 75y or or or

But 00 , 180x y

0 0 0 045 , 15 165 , 135x y or x y

Satisfying given equations.

46. Given 2sin 3cos 6 11x x

sin 3 cos 2,2

And 2 26 11 6 11x x x x

2 6 9 2x x

2

3 2x

2 6 11 2 & sin 3 cos 2x x

(i.e., Both are equal to - 2.

But 2 6 11 2x x if 3x only

Now sin 3 cos 2

cos 1 cos cos36

or

36

or

7 19

6 6or

Two values for 0 4

47. Since „x‟ is real, 0

2

14 sin cos 4 0y

2

1sin cos 1 0y

2

1sin cos 1y

But 2

1 2sin cos 1 sin 0,1y

1sin cos 1y

1cos2

y

0y

Put 0y then the given equation is,

2 2 1 0 1x x x .

48. w. k.t. a + b >c

2 2b c b c b a c

3 2b c

2

3

b

c

Now 2b c a b c b c

2 2b

c bc

.

49. Since 0 1 2 3 4, , , &a a a a a are real and 1 2 3, ,z z z and 4z are the roots of the equation

1 2 3 4, , ,z z z z are also roots.

And w.k.t. if coefficients of the equation are real then the roots occurs pairwise.

1z is equal to atleast one of 1 2 3 4, , &z z z z .

50. 2 2 1 3 3 1 4 4 12 , 3 , 6R R R R R R R R R

1 2 3 0 1 2 3 0

0 0 3 2 0 4 11

0 4 8 3 0 4 8 3

0 4 11 0 0 3 2

2 4 3 3 2R R R R R

1 2 3 0 1 2 3 0

0 4 11 0 4 11

0 0 3 3 0 0 3 3

0 0 3 2 0 0 0 5

4 4 3R R R

Whose rank should be 3 if and only if 5 0 5

51. sec .cos5 1 0x x

2 12

x n

Now cos5 cos 0 cos 0x x x

2cos3 .cos2 0x x

cos3 0 cos2 0x or x

3 2 1 2 2 1 ,2 2

x n or x n n Z

2 1 2 1 ,6 4

x n or x n n Z

3 5 7 9 11

, , , , ,6 6 6 6 6 6

x

4

& 3 5 7

, , ,4 4 4 4

x

4

No. of solutions is 8 in 0,2

52. 5 7

sin sin sin18 18 18

K

5 7

cos cos cos2 18 2 18 2 18

8 4 2

cos cos cos18 18 18

2 4

cos .cos .cos9 9 9

Let 99

2cos .cos 2 .cos 2k

3

3

8sinsin 2 9

2 sin8sin

9

sin sin9 9

8sin 8sin9 9

1

8k

53. 2 2 2 2sin cos 2 cos sec 2f ec

2 25 cos secec

2 2 2

1 45 5

sin cos sin 2

2

2

10 sin 2 1 1

sin 2

2

44

sin

5 4 9f

the minimum value of f is 9.

54. Given 4sin sin 4sin sin 4sin sin 9A B B C C A

060A B C

Area of triangle 233

4a

3 3. 3 3

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SRIGAYATRI EDUCATIONAL INSTITUTIONS...2020/04/25 · SRIGAYATRI EDUCATIONAL INSTITUTIONS INDIA (UT1+UT2) Date: 25-04-2020 Time: 3 Hours Max. Marks: 186 PHYSICS Syllabus: Mechanics