Solution SR 15 Main Test 7

Batch: Seniors-15RAO ALL INDIA TEST SERIES

MAIN FULL TEST [7]Date:

ANSWER SHEET

PHYSICS1. (C) 2. (B) 3. (D) 4. (D) 5. (B)6. (C) 7. (B) 8. (B) 9. (A) 10. (C)11. (D) 12. (D) 13. (C) 14. (B) 15. (D)16. (D) 17. (A) 18. (B) 19. (A) 20. (D)21. (A) 22. (A) 23. (C) 24. (B) 25. (A)26. (C) 27. (A) 28. (D) 29. (A) 30. (B)

CHEMISTRY31. (C) 32. (D) 33. (B) 34. (D) 35. (C)36. (C) 37. (D) 38. (A) 39. (B) 40. (B)41. (C) 42. (D) 43. (A) 44. (D) 45. (C)46. (B) 47. (B) 48. (D) 49. (B) 50. (A)51. (A) 52 (C) 53 (C) 54 (D) 55. (A)56 (D) 57 (B) 58. (A) 59. (C) 60. (C)

MATHEMATICS61. (B) 62. (A) 63 (C) 64. (B) 65. (B)

66. (C) 67. (C) 68. (A) 69. (D) 70. (B)71. (A) 72. (C) 73. (B) 74. (A) 75. (C)76. (D) 77. (C) 78. (D) 79. (A) 80. (A)81. (A) 82. (A) 83. (A) 84. (A) 85. (A)86. (B) 87. (B) 88. (A) 89. (C) 90. (B)

Rao All India Test Series_Sr-2015 Batch_MAIN Full Test - [7]_SOLUTIONS

2SANTACRUZ | ANDHERI | GOREGAON | KANDIVALI (E) | KANDIWALI (W) | BORIVALI | BHAYANDER | VASAI | POWAI | DADAR |SION | THANE | LOKPURAM (THANE) | DOMBIVLI | KALYAN | PANVEL | KAMOTHE | NERUL | SANPADA | KHARGHAR |

PART-A: PHYSICS= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =1. (C)

99. 1 1 1100

L C MSD VSD mm mm

Topic:- Units & Dimension_(Least count)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_NSp sir.

2. (B)

1 130 , 60r A i , 1

1

sin,sin

ir

Topic:- Light waves_(Prism)_L-2_IIT-JEE_Sr-15_Full Test-7_Main Level_NSp sir.

3. (D)

1 2

2 sd kdt

30 220 10 2

x

Topic:- Newtons Law of Cooling_(Heat transfer)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_NSp sir.

4. (D)The two identical metal plates set up fields with intensities 1 2E and E as shown in fig.

Q1 Q2

E1 E2

11

0

,2QE

A

22

02QE

A

1 2E E E

Or 1 20

12

E Q QA

V Ed

1 2 1 202 2

Q Q d Q QVA C

Topic:- Electrostatics_(Capacitors)_L-2_IIT-JEE_Sr-15_Full Test-7_Main Level_NSp sir.

5. (B)Using ,g

g

IS G we get

I I

2 12 8

5 2

Shunt is used in parallel.

Topic:- Current Electricity_(Ammeter)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_NSp sir.



6. (C)

Maximum energy stored 2012

LI

1 80 16 6402

J Topic:- Current Electricity _(RL Circuit)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_NSp sir.

7. (B)cos cos(90 )

cotu v

V u

At P 2 2 2cot

sinc

V uRa g

Topic:- Projectile Motion_(Projectile from ground)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_NSp sir.

8. (B)Let 1 2m m m (constant)

If

1 2

[ ( )] (1)

2 ( ) (2)

m x m m xx m x ga

mx m x gT

m

From (1) & (2) 2 2( )2mT g ag

Topic:- NLM_(Pulley block problem)_L-2_IIT-JEE_Sr-15_Full Test-7_Main Level_NSp sir.

9. (A)

Area under P x graph mdvPdx vdxdt

3

2

1

3 3 1

10 1307 3

30 211 64 410

V vmv dv

v v v ms

Topic:- Work energy & power_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_NSp sir.

10. (C)

0

4 90 360 3 3120 120 3

24060

m i m J mv

v i Jv kmph

Topic:- Collision & C.O.M._(Conservation of Linear momentum)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_NSp sir.



11. (D)

h

l

mg

O

2

2

2

12

1sin2

2 sinc

mgh mv

mgl mv

va gl

And 2 2 2

cos

3sin 1t

R c t

a g

a a a g

Topic:- Work Power Energy_(Conserve mechanical energy)_L-2_IIT-JEE_Sr-15_Full Test-7_Main Level_NSp sir.

12. (D)

2

2

sin ;1

gakr

The time taken by the bodies to roll down a distance l is 2lta

2

2

2 1sin

l kg r

2

21ktr

For hollow sphere 2

2 22

2 23 3

kI mr mkr

For solid cylinder 2

2 22

1 12 2

kI mr mkr

21 5 2 1033 3 911

2

n

c

tt

Topic:- Rotation_(Motion down inclined plane)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_NSp sir.



13. (C)

2

2

2

GMmEr

dE GMm drdt r dt

2 2 22 2 2

t R

o r

GMm dr GMm dr GMm drC dt dtr dt C r C r

1 1 12 2

R

r

GMm GMmt tC r C R r

Topic:- Gravitation_L-2_IIT-JEE_Sr-15_Full Test-7_Main Level_NSp sir.

14. (B)

2

2

2

2

2

2

1 ( )2

y ktd ya kdt

k ms givena ms

2

212

2 1

1 10 2 610 5

gTTT gg

Topic:- SHM_(Simple Pendulum)__L-2_IIT-JEE_Sr-15_Full Test-7_Main Level_NSp sir.

15. (D)If is density of water then the velocity with which the water coming out from the hole is

2v gh and

Force exerted by liquid on container 22s gh acceleration of container2 2sgh vg sha g

v v

But shv

sha gv

Topic:- Fluids_(Velocity of ejection)_L-2_IIT-JEE_Sr-15_Full Test-7_Main Level_NSp sir.

16. (D)3

rmsRTVM

If rmsV is same then TM is same

T MM for oxygen is moreoxygen is at higher temperature.

Topic:- Thermodynamics_(RMS velocities)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_NSp sir.



17. (A)(1)U a bpv

In adiabatic process 2 1( )1 1nR nRdTdU dw T T

(2)1 1 1

nR nRT pvU dU dT U a a

By comparing (1) & (2) 1 11

bbb

Topic:- Laws of thermodynamics_(Adiabatic process)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_NSp sir.

18. (B)

Frequency of first overtone in closed pipe 1 1

3 (1)4

pnl

Frequency of first overtone in open pipe 12 2

1 (2)pnl

From (1) & (2)

1 1 2 2

1 12

2

3 14

43

p pl l

ll

Topic:- Sound waves_(Open closed pipes)_L-2_IIT-JEE_Sr-15_Full Test-7_Main Level_NSp sir.

19. (A)(1)r Rq q Q

2 2

2 2

4 (2)4

r

R

q r rq R R

From (1) & (2) 2

2 2rQrq

R r

and

2

2 2RQRq

R r

So , 2 2

0 0 04 4 4r Rq q Q r RV

r R r R

Topic:- Electrostatics_(Potential due to charge system)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_NSp sir.

20. (D)

Fundamental frequency 1

2Tn

L

20( 1)1

2k bVdUT

dx d

20 ( 1)1

2 2bV kn

L d

Topic:- Electrostatics_(Capacitors)_L-2_IIT-JEE_Sr-15_Full Test-7_Main Level_NSp sir.



21. (A)

2; 2dQQ at bt i a btdt

0 2 02ai a bt tb

Heat produced / 2

2

0

a b

i Rdt

/ 2 / 22 2 2 2

0 0

( 2 ) ( 4 4 )a b a b

a bt Rdt a R b t R abtR dt

/ 22 22 / 2 3 / 2

0 00

4( ) ( ) 43 2

a ba b a bb R ta R t t abR

2 3 22

3 22

4 42 3 8 2 4a b R a abR aa Rb b b

3 3 3 3

2 6 2 6a R a R a R a R

b b b b

Topic:- Current electricity_(Heating effect)_L-2_IIT-JEE_Sr-15_Full Test-7_Main Level_NSp sir.

22. (A)

Area of the polygon 1 2 sin cos2 2 2

A R R n

221 2sin sin

2 2nRnR

n

2 2sin2

BnRE BAn

Resistance 1 ; 2 sin2

lR l n RA

12 2

2 sin( / ) 2 sin( / ) ;nR n Rn nRr r

2

1

cos( / )2

E r RB nIR

Topic:- Magnetism_(Flux)_L-2_IIT-JEE_Sr-15_Full Test-7_Main Level_NSp sir.

23. (C)For +vely charged particle in(i) Force due to electric field is in the +ve x-direction(ii) Force due to magnetic field is ( )F q V B



( ) ( )q Vi Bk qVB J For - vely charged particle(i) Force due to electric field is in the ve x-direction(ii) Force due to magnetic field is ( )F q V B

[ ]q Vi Bk [ ] ( )qVB i k qVB J

Topic:- Magnetism_(Force on a charge particle in magnetic field)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_NSp sir.

24. (B)

1E d B dAIR R dt R dt

12

B d hbR dt

2 2Bb dh Bbv

R dt R

b t I t Topic:- Magnetism_(Change in flux)_L-2_IIT-JEE_Sr-15_Full Test-7_Main Level_NSp sir.

25. (A)

Charge oscillates simple harmonic motion 2

01sin ,2

qq q t UC

0

422

8 8 4

qq t

Tt LC LC

Topic:- Current Electricity_(LC Circuit)_L-2_IIT-JEE_Sr-15_Full Test-7_Main Level_NSp sir.

26. (C)The top portion of the rod is at a distance 2 f . So v is less than 2 f for this portion. So the imagewould lean towards the lens. The image would not be a straight line as the lateral magnification is notsame as the longitudinal magnification.

Topic:- Ray optics_(Convex lens)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_NSp sir.

27. (A)Optical path difference between the waves 3 2( )n n t

Phase difference 3 2 3 21 1

2 ( ) 2 ( )n n t n n tvaccum n

Topic:- Light Waves_(YDSE)_L-2_IIT-JEE_Sr-15_Full Test-7_Main Level_NSp sir.



28. (D)

2 2

1 1 11 1

RR nn R

Topic:- Modern Physics _(Hydrogen atom)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_NSp sir.

29. (A)

minhceV

2 1 1

1 2 2

34

V VV V

2 2 1

1 1

4 1001003 3

V V VV V

Topic:- Modern Physics_(X-rays)_L-2_IIT-JEE_Sr-15_Full Test-7_Main Level_NSp sir.

30. (B)

0tN N e

/0

t RCq q e

0

0

ttRCNN e

q q

Nq is constant if

1 200tt RRC RC

Topic:- Radioactivity_(Radioactivity disintegration)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_NSp sir.



PART-B: CHEMISTRY= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =31. (C)

Equivalent weight of 3 4 98 / 3H PO

Equivalent weight of 2 58.3 / 2Mg OH Suppose x g of phosphoric acid would be needed then milliequivalent of 3 4H PO milliequivalent

of 2Mg OHmassNumber of equivalents

equivalent mass

3 100 2 10001000 112 .98 58.3

x x g

Topic:- Mole concept-2_(Equivalent weight)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_PDch sir.

32. (D)Flux is used to remove some earthy impurities like silica and undersirable metal oxide.

Topic:- Metallurgy_(Process)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_PDch sir.

33. (B)

8 2 2 2 2 38mole 2mole1mole 2mole

8 8 , 2 2S O SO SO O SO

Molar ratio of 8 2S and SO 8 2: 1:8S SO Molar ratio of 2 3SO and SO 2 3: 1:1SO SO Molar ratio of 8 3S and SO 8 3: 1:8S SO It means 1 mole of 8S will give 8 moles of 3SO .i.e. 8 80 640 .g (Molecular weight of 3 80)SO

Topic:- Mole concept-1_(Stoichiometric)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_PDch sir.

34. (D)B2H6 is electron deficient. It consists 3 centre 2 electron bond.

Topic:- Chemical bonding_(Hydrides)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_PDch sir.

35. (C)3. .2

K E RT

3 8.314 300 3741 3.741 .2

J kJ

Topic:- Gaseous state_(Ideal gas)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_PYch sir.

36. (C)Polyhalides of alkali metals have alkali metals in monopositive state.

Topic:- Chemical bonding_(Ionic compounds)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_PYch sir.37. (D)

Electron deficient species acts as an electrophile.Topic:- P-block_(Electron deficient compounds)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_PYch sir.



38. (A)At triple point, all the three states of a substance coexist. Pressure and temperature at triple point is

273.16 or 0.01Temp k CPressure = 0.006 atm.

Topic:- Gaseous state_(Temperature scale)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_PYch sir.

39. (B)

3 28 3

48 32rmsRT RTO u O

3

2

8 32 1648 3 9rms

O RTu O RT

Topic:- Gaseous state_(Velocities of gas)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_PYch sir.

40. (B)

2SnCl is not linearTopic:- Chemical bonding_(VSEPRT)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_PDch sir.

41. (C)Heat released in the formation of 2 ( ) 1. .,gH O i e H is lesser than heat released in the formation of

2 ( ) 2. .,lH O i e H 1 2( )H H . This is because some additional amount of heat is released in the

formation of 2 ( )lH O form 2 ( ) .gH OTopic:- Thermodynamics_(Thermochemistry)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_PYch sir.

42. (D) lnG RT K 2.303logG K

RT

Topic:- Chemical equilibrium_(Free energy)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_PYch sir.

43. (A)

Nesslers reagent 2 4K HgI is used for detection of 4NH ion.Topic:- Qualitative analysis_(Cations)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_PDch sir.

44. (D)3 2 3 3

strong acidweak base saltCH NH HCl CH NH Cl

Initial moles 0.1 0.08Resulting solution contains [salt] = 0.08

[base] 0.1 0.08moles lefttotal volume 1

0.02litreM

Applying

logbsalt

pOH pKbase



4log log5 10 4 log 5 3.30b bpK K

0.083.30 log 3.30 0.602 3.900.02

pOH

14, 14 3.90 10.1pH pOH pH

Applying logpH H 118 10H

Topic:- Ionic equilibrium_(pH)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_PYch sir.

45. (C)In BF3, B is sp

2 hybridised and has a vacant 2p-orbital which overlaps laterally with a filled 2p-orbital of F forming p p bond. However in CF4, C does not have any vacant p-orbitals toundergo -bonding.Thus . . . .B F C FB E B E .

Topic:- P-block_(Boron and Carbon family)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_PDch sir.

46. (B)Oxidation state of Cr in

32 6 3Cr H O

3 324 3Cr Z d i.e., three d-electrons are present.Topic:- D-block_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_PDch sir.

47. (B)

Butyric Acid HA Notationn + -HA H + A

-5a

0.01K = 1.610

5

2

1.6 1010

aKC

24 10

2 44 10 380 10

3 11.52 10 Sm k M

3 31.52 10 0.01 10 21.52 10

Topic:- Electrochemistry_L-2_IIT-JEE_Sr-15_Full Test-7_Main Level_PYch sir.

48. (D)

Theoretical 0.52b bT K m K



Actual Theoreticalb bT i T 3+ 2-

2 2A B 2A + 3Bat t 0, Cat eq. C C 2C 3C

C+ 4Ci = 0.6C

1 4 i = 3.4Actual 3.4 0.052 1bT 1.76

373 1.76bT 374.76

Topic:- Solution_L-2_IIT-JEE_Sr-15_Full Test-7_Main Level_PYch sir.

49. (B)

3 2 5

23 gm+ 27 gmHNO N O

2 5 2 3N O + H O 2 HNO

27 27moles 2 moles108 108

272 63gm

108

31.5 gm

total mass of 3HNO Retrievable 31.5 23 54.5 gm

54.5% labelling 10050

109%Topic:- Volumetric_L-2_IIT-JEE_Sr-15_Full Test-7_Main Level_PYch sir.

50. (A)

AgI

A+ A+

A+

A+

A+A+A+ A+

A+ A+

A+

g

g

g gg

g

g

ggg

g Positive charged sol.

Topic:- Surface Chemistry_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_PYch sir.



51. (A)

1

31 2 3

; 577.5 kJ/m

3 ; 5140 kJ m

Al Al e IE

Al Al e IE IE IE

2

3

23

IEIE

2 32 ; 3IE x IE x

5 577.5 5140x 912.5kJx 2 2 1825 kJIE x

3 3 2737.5 kJIE x Topic:- Periodic Properties_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_PYch sir.

52 (C)DNA mRNA (Transcription) m RNA proteins (Translation)

DNA daughter DNA (Replication)Topic:- Polymers_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_NGch sir.

53 (C) 22 3 3 3 3 32

Ca OHhydrolysis Dry distillationCO CH MgCl CH COOH Ca CH COO CH COCH

Topic:- Ether & Grignard Reagent_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_NGch sir.

54 (D)Phenol 10,apK 4- Methyl Phenol 10.2,apK

3-nitro phenol 8.3,apK

4- Nitro phenol 7.1,apK Consider following effects4-Nitrophenol = M, I3-Nitrophenol = only M4-Methylphenl = +MSo, greater the stability of conjugate base. i.e. lesser the basic it is, more will be the aK of the acid.

Topic:- GOC_(Acidic strength)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_NGch sir.

55. (A)Reactivity will be governed by collision frequency and there by the mass.

Topic:- GOC_(Substitution redox)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_NGch sir.

56 (D)Polyester have the function group RCOOR

Topic:- Polymer_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_NGch sir.



57 (B)

2 3 23 3 4 3 2 3, , , ,A B C D E

CH C H OH C H COOH CH COO NH CH CO N H CH N HTopic:- Amines_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_NGch sir.

58. (A)Formic acid can reduce Tollens reagent but not acetic acid .All carboxylic acids liberates 2CO from

2 3Na COTopic:- Carboxylic acid_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_NGch sir.

59. (C)In fact products of reaction d are 3 2 53CH C I C H OH it follows

1SN mechanismTopic:- Ether_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_NGch sir.

60. (C)Effective no.of atoms of 6A

Effective no. of atoms of C 2 26 of total octahedral Voids3 3

4 6 2 3or CC A ATopic:- Solid State_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_PYch sir.



PART-C: MATHEMATICS= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =61. (B)

If 1 2 3, ,z z z are collinear and 1 2 3 0az bz cz then a+b+c =0 .Hence

1 sin cos 1 2 0 sin cos 2

3 5 7, , ,

4 4 4 4

Topic:- Complex No._(Linearly dependent and independent)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_AMm sir.

62. (A)

5

1

1 2 3 4 5x x x x x dx

Put 3x t

2

2

2 1 1 2t t t t t dt

2

2 2

2

4 1t t t dt

2 2( ) 4 1f t t t t is odd 2

2

( ) 0f t dt

Topic:- Definite integration_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_AMm sir.

63 (C)Differentiate the given equations for 2 times and eliminate A, B

Topic:- Differential equation_(Order & degree)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_AMm sir.

64. (B)

Required area 2 12

4 2r ab

Topic:- Area under the curve_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_AMm sir.

65. (B)

Centre , 3, 3r r Topic:- Circle_(Definition of circle)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_AMm sir.



66. (C)

A(1,1)

C(5,3)B(-3,3)

G=(1,7/3)

(1,2) (3,2)

Topic:- Straight line_(Section formula)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_AMm sir.

67. (C)

d.rs of normal 2, 3,6

d.rs of X-axis 1,0,0 find cos 90 Topic:- 3-D_(Plane)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_AMm sir.

68. (A)planes are parallel

Ans=0Topic:- Vectors_(Cross product)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_AMm sir.

69. (D)

Let m be slope of common tangent

Then m 2 1,x and m 23 2 2,x x So, infinite common tangents

Topic:- Application of derivatives_(Tangent & normal)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_AMm sir.

70. (B)

1 1 2 4 4 6 9 9 12 16 .... 361 380 400

=

22 1 1 1

1

r r r r r r

r r

= 3 319

1

11

1r

r r

= 3 3 3 3 3 3 31 2 3 4 ...... 20 1 2 3 ...... 19



2 22 220 21 19 204 4

220 441 361 8000

4

Topic:- Progression Series_(Miscellaneous)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_AMm sir.

71. (A)

4 3 12 0 3, 4xy x y x y ______________ 1

3 4 12 0 4, 3xy x y x y _____________ 2

From 1 & 2 we find that the vertices of square are 3,3 , 4,3 4, 4 3, 4A B C and D

equation of diagonal AC is 0,x y equation of diagonal BD is 1 0x y

required equation is 2 2 0x y x y Topic:- St. Lines_(Pair of St. Lines)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_AMm sir.

72. (C)

3 2 22 9 12 1f x x ax a x '( ) 0 , 2f x x a x a

'' 12 18f x x a ''( ) 0 ( )f a f x has maximum when ,x a P a ''(2 ) 0 ( )f a f x has minimum when 2 2x a q a

But 2 2P q a Topic:- Application of Derivatives _(Max. & Min.)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_AMm sir.

73. (B)

Let 0, , 0,x x a y y a be the equations of the sides of a square and ,P h k be a point in thelocus. Given condition,

2 22 2 22c h h a k k a 2 2 2 2 0h k ah ak a c

locus of ,h k x 2 2 2 2 0x y ax ay a c Topic:- Co-ordinate Geometry_(Locus)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_AMm sir.

74. (A)The locus of points of trisection of double ordinate PQ is 2 4

9y ax

Which is the parabola whose length of latusrectum =49a

19

(length of latusrectum of given parabola)

Topic:- Parabola_(Definition of Parabola)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_AMm sir.



75. (C)

0

2

tan30

2 2 3log 2

1z z

z

2 2 3 03 22

z z

z or z

Topic:- Complex numbers_(Locus)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_AMm sir.

76. (D)

1 2 .log 2

2

x

x

y g x f x dx

y g x dx

y x c

It passes through 11,2

1 11 12 2

c c

2 1xy x If meets y axis at (0, 2)

Topic:- Application of Derivatives_(Tangent and normal)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_AMm sir.

77. (C)

3 / 2 5 / 6 7 / 6 3 / 2

/ 2 / 2 5 / 6 7 / 6

2sin 1 1 22

x dx dx odx dx dx

Topic:- Definite Integrtion_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_AMm sir.

78. (D)

2

2

2

33

1, 1, 2 12 1 2 1 2 1 1 1

22 1 1

1

n

n

n

a p d n ppS p p

S p p p

S p p

Topic:- Progression, A. P._L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_AMm sir.



79. (A)

Let 3 2f x ax bx cx d

Clearly f x is continuous on 0,1 and derivable on 0,1on and 0f d

21

' 3 2

f a b c d d

f x ax bx c

By rolles theorem

There exists 0,1 such that 2'( ) 0 3 2 0f a b c 23 2 0ax bx c has a root in (0, 1)

Topic:- Quadratic equation_(Location of roots)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_AMm sir.

80. (A)

1.2 2 1 2sin1 4 4. 4 11 23 3 54 553

Topic:- 3-D_(Plane & St. line)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_AMm sir.

81. (A)

Roots of 2 22 1 0x mx m are 2 22 4 4 1

2

m m mx

1x m

Given, 2 1, 1 4m m 1, 3m m

1 3m Topic:- Quadratic equation_(Location of roots)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_AMm sir.

82. (A)

We have 50

100!10050!50!C

The exponent of 7 in 50! is 250 50 7 1 87 7

The exponent of 7 in 100! is 2100 100 14 2 16

7 7

The exponent of 7 in 50

100C is 16 2 8 0 Topic:- Binomial theorem_(Exponent of prime)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_AMm sir.



83. (A)Let A be the first term and R be the common ratio of the G.P

1 1 1. , . , .P q ra A R b A R c A R

log 1 log 1 log 1log 1 log 1 log 1log 1 log 1 log 1

a p A p R pb q B q R qc r C r R r

1 1 3logC C A C

1 lo g 1 1 11 lo g 1 lo g 1 1 01 lo g 1 1 1

p R p p pq R q R q qr R r r r

Topic:- Progression_(G.P.)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_AMm sir.

84. (A)

21

4 3 4 3 2 4 23 2 3 2

nnn n

n

a aLt a Lt a a aa a

Topic:- Limits_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_AMm sir.

85. (A)

0 1f

0

( ) ( )'( )h

f x h f xf x Lth

0 0

( 0) ( ) ( ) ( ) (0) ( )h h

f x h f x f x f h f f xLt Lth h

1'( ) ( ). (0)f x f x f '(2) 12f

Topic:- Functions_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_AMm sir.

86. (B)0180A B C

1 1 0tan 2 tan 3 180C

1 2 3tan1 6

C

1tan 1 0C

4C

Topic:- Inverse Trigonometry_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_AMm sir.



87. (B)2 2 2sin sin & 2cos 3cosA B A B 2 22 2sin 3 3sinA B

22sin 3sin 1 0A A

2sin 1 sin 1 0A A 0 030 90A or A

If 0 0 030 45 105A B C

if 0 090 90A B (if is not possible)Topic:- Trigonometric ratios & Identities_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_AMm sir.

88. (A)

.a b c a b c

sin , cos ,a b c a b a b c a b c

sin , .cos , 1a b a b c

0, , , 02a b a b c

, &a b a c b c

. . . 0a b b c c a Topic:- Vectors_(Box product)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_AMm sir.

89. (C)

2

' '

2'' ' ''

''' ' '' '''

3 ''

3 ''' '' 2 '

2 ''' ' ''

'''

2

2

2 3 .

2 .

2 . .3 .

2. . 3 .

.

y p x

yy p x

yy y p x

yy y y p x

d y ydxy y y y y

y y y y y

p x p x

Topic:- Differentiation_(Higher order Derivative)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_AMm sir.



90. (B)

1 01 0

1 0

c b xc a yb a z

Given equation has non zero solution

11 0

1

c bc ab a

2 2 2 2 1a b c abc

Topic:- Determinants_(Solution of equations)_L-1_IIT-JEE_Sr-15_Full Test-7_Main Level_AMm sir.

Documents

Solution SR 15 Main Test 7