qp sr 15 main test 7

General Instructions :

(i) The test is of 3 hours duration. This Question Paper is of total 16 Pages

(ii) This paper consists of 90 questions. The maximum marks are 360.

(iii) There are THREE parts in the question paper.

The distribution of marks subjectwise in each part is as under for each correct response.

Part A – PHYSICS (+4, –1) (120 marks) – 30 questions

Part B – CHEMISTRY (+4, –1) (120 marks) – 30 questions

Part C – MATHEMATICS (+4, –1) (120 marks) – 30 questions

(iv) Each question has 4 choices (A), (B) ,(C) and(D), out of which ONLY ONE is correct.Candidates will be awarded FOUR marks each for indicating correct response of eachquestion. ONE mark will be deducted for indicating incorrect response of each question.

Useful DataGas Constant R = 8.314 J K1 mol1 1 Faraday = 96500 Coulomb

= 0.0821 Lit atm K1 mol1 1 calorie = 4.2 Joule= 1.987 2 Cal K1 mol1 1 amu = 1.66 10–27 kg

Avogadro’s Number Na = 6.023 1023 1 eV = 1.6 10–19 JPlanck’s constant h = 6.625 1034 J s

= 6.625 10–27 erg sAtomic No: H = 1, D = 1, Li = 3, Na = 11, K = 19, Rb = 37, Cs = 55, F = 9, Ca = 20, He = 2, O = 8, Au = 79, Ni = 28,

Zn = 30, Cu = 29, Cl = 17, Br = 35, Cr = 24, Mn = 25, Fe = 26, S = 16, P = 15, C = 6, N = 7, Ag = 47.Atomic Masses: He = 4, Mg = 24, C = 12, O = 16, N = 14, P = 31, Br = 80, Cu = 63.5, Fe = 56, Mn = 55, Pb = 207, Au = 197,

Ag = 108, F = 19, H = 1, Cl = 35.5, Sn = 118.6, Na = 23, D = 2, Cr = 52, K = 39, Ca = 40, Li = 7, Be = 4, Al = 27, S = 32.1

Name of the Student Roll Number

I have verified all the information filled in by the Candidate……………………………………………………..

Signature of the Invigilator

I have read all the instructions and shall abide by them……..……………………………………………………

Signature of the Candidate

Max. Marks : 360Max. Time : 3 hours

Date:Batch: Seniors-15

RAO ALL INDIA TEST SERIES

MAIN FULL TEST [7]

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

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

Space For Rough Work

PART-A: PHYSICS[Single Answer Choice Type]

This Section contains 30 multiple choice questions. Each question has 4 choices (A),(B),(C) and (D) out of which ONLY ONE is correct.= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =1. Each division on the main scale is 1mm. Which of the following vernier scales give vernier constant

equal to 0.01 mm?(A) 9 mm divided into 10 divisions (B) 90 mm divided into 100 divisions(C) 99 mm divided into 100 divisions (D) 9 mm divided into 100 divisions

2. One of the refracting surfaces of a prism of angle 30º is si lvered. A ray of l ight incident at an angle of60º retraces its path. The refractive index of the material of the prism is ,

(A) 2 (B) 3 (C) 32 (D) 2

3. It takes 10 minutes to cool a liquid from 61ºC to 59ºC. If room temperature is 30ºC , then time taken incooling from 51ºC to 49ºC is

(A) 10 minutes (B) 11 minutes (C) 13 minutes (D) 15 minutes

4. Two identical metal plates are given positive charges 1 2 1andQ Q Q respectively. If they are nowbrought close together to form a parallel plate capacitor with capacitance C, the potential differencebetween them is(A) 1 2( ) /(2 )Q Q C (B) 1 2( ) /Q Q C (C) 1 2( ) /Q Q C (D) 1 2( ) /(2 )Q Q C

5. An ammeter gives full scale deflection when a current of 2A flows through it. The resistance of ammeteris 12 . If the same ammeter is to be used for measuring a maximum current of 5A, then ammeter mustbe connected with a resistance of(A) 18 in parallel (B) 8 in parallel (C) 18 in series (D) 8 in series

6. If solenoid of resistance 50 , inductance 80H is connected to a 200V battery. Then the Maximumenergy stored is(A) 460 J (B) 604 J (C) 640 J (D) 406 J

7. If a particle is projected with speed u from ground at an angle with horizontal, then radius of curvatureof a point where velocity vector is perpendicular to initial velocity vector is given by

(A) 2 2cosu

g

(B) 2 2cot

sinug

(C)

2ug (D)

2 2tancos

ug




8. For the arrangement shown in the figure let ‘a’ and T be theacceleration of the blocks and tension in the string respectively.The string and the pulley are frictionless and massless. Which ofthe graphs show the correct relationship between ‘a’ and T forthe system in which sum of the two masses 1m and 2m is constant.

m2

m1

m1 > m2

(A)2a

T

(B)2a

T

(C)

T

21/ a

(D)

T

21/ a

9. A particle A of mass 10/7 kg is moving in the positive direction of x. Its initial position is 0x &initial velocity is 1 m/s. The velocity at 10x is: (use the graph given)

4

2

10 (in m)x

Power (in watts)

(A) 4 m/s (B) 2 m/s (C) 3 2 m/s (D) 100/3 m/s

10. A bomb travelling horizontally at 90 km/hr suddenly explodes into two parts of mass ratio 1:3.Immediately after explosion, the lighter mass is found to be travelling vertically upwards with speed360 3 km/hr. The heavier one must be travelling at(A) 240 km/hr vertically downwards

(B) 0240 3 / 30 ( )km hr downwards to horizontal initial direction

(C) 0240 / 60 ( )km hr downwards to horizontal initial direction

(D) 120 2 km/hr downwards 30° to horizontal




11. The given figure shows a small mass connected to a string, which moves in the vertical plane. If themass is released from rest when the string is horizontal as shown, the magnitude of the total accelerationof the mass as a function of the angle is

Initi alposi tion

(A) 2 sing (B) 2 cosg (C) 23cos 1g (D) 23sin 1g

12. A thin uniform spherical shell and a uniform solid cylinder of the same mass and radius are allowed toroll down a fixed incline, without slipping, starting from rest. The times taken by them to roll down thesame distance are in the ratio, :sph cylt t

(A) 1415 (B)

1514 (C)

310 (D)

109

13. A satellite of mass m is orbiting the earth in a circular orbit of radius r. It starts losing energy due tosmall air resistance at the rate of /C J s . Find the time taken for the satellite to reach the earth.

(Radius of earth R )

(A) 1 1GMm

C R r

(B) 1 12

GMmC R r

(C)

1 12

GMmC R r

(D)

2 1 1GMmC R r

14. A simple pendulum has time period 1T . The point of suspension is now moved upward according to

the relation 2 2, ( 1 / )y Kt K m s where y is the vertical displacement. The time period now becomes

2T . The ratio of 2

12

2

TT

is 2( 10 / )g m s

(A) 5 / 6 (B) 6 / 5 (C) 1 (D) 4 / 5




15. In the figure shown, a light container is kept on a horizontal rough surface of coefficient of frictionShV

. A very small hole of area S is made at depth h . Water of volume V is filled in the container..The friction is not sufficient to keep the container at rest. The acceleration of the container initially is

h

(A) V gSh (B) g (C) Zero (D)

Sh gV

16. If the molecules in a tank of hydrogen have the same RMS speed as the molecules in another tank ofoxygen, we may be sure that(A) the pressures are the same (B) the hydrogen is at the higher temperature(C) the temperatures are the same (D) the oxygen is at the higher temperature

17. The relation between U , P and V for an ideal gas in an adiabatic process is given by relation.U a bPV Find the value of adiabatic exponent ( ) of this gas.

(A) 1b

b

(B) 1b

a

(C) 1a

b

(D) a

a b

18. A pipe of length 1l , closed at one end is kept in a chamber of gas of density 1 . A second pipe open at

both ends is placed in a second chamber of gas of density 2 . The compressibility of both the gases isequal. Calculate the length of the second pipe if frequency of first overtone in both the cases is equal

(A) 2

11

43

l (B)

11

2

43

l (C)

21

1

l (D)

11

2

l

19. A charge Q is distributed over two concentric hollow spheres of radii r and R ( )R r such that the

surface densities are equal. The potential at the common centre is 0

14

times-

(A) 2 2

r RQr R

(B) 2 22

Q r Rr R

(C) 2 22 r RQr R

(D) zero




20. A dielectric slab is attached to a string of mass per unit length , whose other end is fixed to a wall.Capacitor has square plates of side b and separation between the plates is d . Find the fundamentalfrequency of vibration of the string. (Dielectric slab remains in equilibrium)

Lb

kd

V

(A) 2

0 ( 1)12 2

bV kL d

(B)

20 ( 1)1

2 2bV k

L d

(C) 0 ( 1)12 2

bV kL d

(D)

20 ( 1)1

2 2bV k

L d

21. The charge flowing through a resistance R varies with time t as 2Q at bt . The total heat producedin R by the time current ceases is

(A) 3 / 6a R b (B) 3 / 3a R b (C) 2

a Rb

(D)

3a Rb

22. An n sided regular polygon is inscribed in a circular region of radius R using a wire of crosssectional radius r and resistivity . If the magnetic field in the circular region has a time rate ofchange given by B then the current in the wire loop at any time is given by

(A) 2 cos( / )2

RBr n (B)

2 cos( / )2

RBr n (C)

2 sin( / )2

RBr n (D)

2 cos( / )3

RBr n

23. An ionized gas contains both positive and negative ions. If it is subjected simultaneously to an electricfield along the +x-direction and a magnetic field along the +z-direction, then(A) positive ions deflect towards + y -direction and negative ions towards- y direction(B) all ions deflect towards + y -direction(C) all ions deflect towards y -direction(D) positive ions deflect towards y -direction and negative ions towards y -direction.




24. An equilateral triangular loop ABC made of uniform thin wires is beingpulled out of a region with a uniform speed v , where a uniform magnetic

field B

perpendicular to the plane of the loop exists. At time 0t , thepoint A is at the edge of the magnetic field. The induced current (I) vstime ( )t graph will be as

A v

B C

(A) t

l

(B) t

l

(C) t

l

(D) t

l

25. A fully charged capacitor C with initial charge 0q is connected to a coil of self inductance L at t = 0.The time at which the energy is stored equally between the electric and the magnetic field is :

(A) 4LC

(B) 2 LC (C) LC (D) LC

26. A small straight rod is placed at an inclination with the opticalaxis of a thin lens as shown in the figure. The base of the rod is onthe optical axis and at a distance 2 (f f focal length of the lens)from the lens. The image of the rod would be

2f

(A) a straight line leaning towards the lens (B) a straight line leaning away from the lens

(C) a curve leaning towards the lens (D) a curve leaning away from the lens

27. In the figure shown in a YDSE , a parallel beam of light isincident on the slits from a medium of refractive index 1n .

The wavelength of light in this medium is 1 . A transparent

slab of thickness t and refractive index 3n is put in front ofone slit. The medium between the screen and the plane ofthe slits is 2n .The phase difference between the light wavesreaching point O (symmetrical, relative to the slit) is

O

1

1n3n

2n

(A) 3 21 1

2 ( )n n tn

(B) 3 21

2 ( )n n t

(C) 31

2 1 2

2 1nn t

n n

(D) 1

3 21

2( )

n n n t




28. A hydrogen atom is in an excited state of principal quantum number ( )n , it emits a photon of wavelength

( ) , when it returns to the ground state. The value of n is

(A) 1R

R

(B) ( 1)R

R

(C) ( 1)R (D) 1R

R

29. To decrease the cut-off wavelength of continuous X-rays by 25%, the potential difference acrossX-ray tube

(A) must be increased by 100 %3

(B) must be decreased by 100 %

3(C) must be increased by 25% (D) must be decreased by 25%

30. Average life of a radioactive sample is 4 ms. Initially the total number of nuclei is 0N . A charged

capacitor of capacity 20 F is connected across a resistor R . The value of R such that ratio ofnumber of nuclei remaining to charge on capacitor remains constant with time is

(A) 100 (B) 200 (C) 300 (D) 400

PART-B: CHEMISTRY[Single Answer Choice Type]

This Section contains 30 multiple choice questions. Each question has 4 choices (A),(B),(C) and (D) out of which ONLY ONE is correct.

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =31. How many grams of H3PO4 would be needed to neutralize 100 g of magnesium hydroxide?

(The molecular weights are 3 4 298 ( ) 58.3)H PO and Mg OH (A) 66.7 g (B) 252 g (C) 112 g (D) 168 g

32. Flux is used to(A) Remove all impurities from ores (B) Reduce metal oxide(C) Remove silica (D) Remove silica and undersirable metal oxide.

33. Sulphur trioxide is prepared by the following two reactions.

8( ) 2( ) 2( )8 8g g gS O SO

2( ) 2( ) 3( )2 2g g gSO O SO

How many grams of 3SO are produced from 1 mol of 8 ?S (Assume all SO2 produced in the firstreaction is used in the second reaction)(A) 1280.0 (B) 640.0 (C) 960.0 (D) 320.0




34. Which of the following hydrides is electron deficient?(A) NaH (B) CaH2 (C) CH4 (D) B2H6

35. Kinetic energy of one mole of an ideal gas at 300 K in kJ is(A) 34.8 (B) 3.48 (C) 3.741 (D) 348

36. Which of the following statements is correct for CsBr3?(A) It is a covalent compound (B) It contains Cs3+ and Br– ions

(C) It contains Cs+ and Br 3 ions (D) It contains Cs+, Br– and Br2 molecule.

37. Which is an electrophile?

(A) 4AlCl (B) 3NH (C) 3CH OH (D) 3BCl

38. Triple point of water is at temperature :(A) 273 K (B) 373 K (C) 203 K (D) 193 K

39. What is the ratio of mean speed of an O3 molecule to the rms speed of an O2 molecule at the same T?

(A) 1/ 23 / 7 (B) 1/ 216 / 9 (C) 1/ 23 (D) 1/ 24 / 9

40. 2CO is not isostructural with

(A) 2HgCl (B) 2SnCl (C) 2 2C H (D) 2ZnCl

41. The enthalpy of the reaction

2( ) 2( ) 2 ( ) 11 is2g g gH O H O H and that of

2( ) 2( ) 2 ( ) 21 is2g g lH O H O H . Both reactions are exothermic, then

(A) 1 2H H (B) 1 2 0H H (C) 1 2H H (D) 1 2H H

42. If equilibrium constant for a reaction is K, then standard free energy change is(A) º logG RT K (B) º lnG RT K

(C) º logG K

RT

(D) º 2.303logG K

RT

43. Which ion is detected by Nessler’s reagent?

(A) 4NH (B) 4MnO (C) 34PO (D) 2

4CrO




44. When 0.1 mole of 3 2CH NH (ionisation constant, 45 10 )bK is mixed with 0.08 mol HCl and thevolume is made up to 1 litre. Find the [H+] of resulting solution.

(A) 28 10 (B) 62 10 (C) 41.23 10 (D) 118 10

45. The bond dissociation energy of B – F in BF3 is 646 kJ mol–1 whereas that of C – F in CF4 is 515 kJ mol–1.The correct reason for higher B – F bond dissociation energy as compared to that of C – F is(A) smaller size of B-atom as compared to that of C-atom(B) stronger sigma bond between B and F in BF3 as compared to that between C and F in CF4(C) significant p p interaction between B and F in BF3 whereas there is no possibility of such interaction between C and F in CF4.(D) lower degree of p p interaction between B and F in BF3 than that between C and F in CF4.

46. The number of d-electrons in 32 6Cr H O

, [At. no. of Cr = 24] is

(A) 2 (B) 3 (C) 4 (D) 5

47. The dissociation constant of n-butyric acid is 1.6 × 10–5 and the molar conductivity at infinite dilutionis 380 × 10–4 Sm2mol–1. The specific conductance of the 0.01 M acid solution is(A) 1.52 × 10–5 Sm–1 (B) 1.52 × 10–2 Sm–1

(C) 1.52 × 10–3 Sm–1 (D) None

48. 1.0 molal aqueous solution of an electrolyte A2B3 is 60% ionised. The boiling point of the solution at

1 atm is ( 1)OH(b molkgK52.0K

2

)

(A) 274.76 K (B) 377 K (C) 376.4 K (D) 374.76 K

49. N2O5 and H2O can react to form HNO3, according to given reactionN2O5 + H2O 2HNO3

the concentration of a mixture of HNO3 and N2O5 (g) can be expressed similar to oleum. Then answerthe following question.Find the percentage labelling of a mixture containing 23 gm HNO3 and 27 gm N2O5.(A) 104.5% (B) 109% (C) 113.5% (D) 118%

50. When excess of AgNO3 is treated with KI solution, AgI forms(A) +ve charged sol (B) –vely charged sol (C) neutral sol (D) true solution

51. The IE values of Al(g) Al(g)+ +e is 577.5 kJ mol–1 and H for Al(g) AlAl(g)

3+ +3e is 5140 kJmol–1. If second and third IE values are in the ratio 2 : 3. Calculate IE2 and IE3.(A) 1825, 2737.5 (B) 912.5, 1825 (C) 2038, 2504.5 (D) 1930, 2432.5




52 Match the followingList – I List - IIA) Replication 1) Formation of RNA from DNAB) Transcription 2) Synthesis of copy of DNAC) Translation 3) Synthesis of proteins by RNA

(A) 1, 2, 3A B C (B) 3, 2, 1A B C

(C) 2, 1, 3A B C (D) 2, 3, 1A B C

53 3 2

3

1. / .2 2.

Ca OHCH MgCl D E DrydistillationH O

CO A B C . In the sequence ‘C’ is ……….

(A) Chloroform (B) Acetaldehyde (C) Acetone (D) Acetic acid

54 Let us consider the following compounds :I) Phenol, II) 4 – Methylphenol, III) 3 - Nitrophenol, IV) 4 – Nitrophenol .What is the correct order of acidic strength?

(A) III IV I II (B) I IV III II (C) II I III IV (D) IV III I II

55 Arrange the following in decreasing order of reactivity towards EAS(Electrophilic Aromatic Substitution)

A)

CH3

B)

CD3

C)

CT3

(A) A > B > C (B) C > B > A (C) A > C > B (D) C > A > B

56 The correct statement(s) is among the following is (are)IUPAC name of terylene is poly (ethylene terephthalate) and its monomers are terephalic acid andethylene glycol. It is referred to or by Brand name Dacron in Britain or terylene in Russia.I. Terylene is a condensation polymer of ethylene glycol and terephthalic acidII. Dacron is an example of polyesterIII. Dacron is a linear polymer.

(A) I and II only (B) II and III only (C) I and III only (D) I, II and III only




57 2 2 7 3 2

2 4

/3 2 2

K cr o NH Br KOHHONOH SOCH CH NH A B C D E identify the

final product in the series E(A) Ethyl amine (B) Methyl amine

(C) Ethylbromide (D) Methylbromide

58 Compounds X and Y give effervescence with 3NaHCO solution, X gives a silver mirror with ammonical

3AgNO , while Y gives a sweet smelling compound on heating with alcohol in the presence of 2 4H SO ;X and Y are(A) 3HCOOH and CH COOH (B) 3 3CH CHO and CH COOH

(C) 3 3 3CH COOH and CH COCH (D) 3 3CH COCH and HCOOH

59 a) 3 2 2 3 3 2 2 3.Conc HICH CH CH O CH CH CH CH OH CH I

OC2H5

+ HBr + C2H5Br

OH

b)

OC2H5conc. H2SO4

O2N

+

OC2H5

NO2

conc. HNO3

OC2H5

c)

d) 3 2 5 3 2 53 3.Conc HICH C O C H CH C OH C H I

Which of the above equations indicate incorrect product?(A) a (B) b (C) d (D) c

60. If the anions (A) form hexagonal closest packing and cations (C) occupy only 2/3 octahedral voids init, then the general formula of the compound is(A) CA (B) CA2 (C) C2A3 (D) C3A2




PART-C: MATHEMATICS[Single Answer Choice Type]

This Section contains 30 multiple choice questions. Each question has 4 choices (A),(B),(C) and (D) out of which ONLY ONE is correct.= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =61. 0,2 and 1 2 3, ,z z z are three complex numbers such that they are collinear and

1 2 31 sin cos 1 2z z z =0 .If at least one of the complex numbers 1 2 3, ,z z z is non- zerothen number of possible values of is(A) Infinite (B) 4 (C) 2 (D) 8

62. The value of the integral 5

1

1 2 3 4 5x x x x x dx =

(A) 0 (B) 5 (C) 1 (D) 4

63 The differential equation whose solution is 2 2 1Ax By where A and B are arbitrary constants, is of(A) first order and second order (B) first order and first degree(C) second order and first degree (D) second order and second degree

64. The area of the smaller region bounded by the circle 2 2 1x y and the lines | | 1y x is

(A) 2

4

sq.units (B) 2

2

sq.units (C) 2

2

sq.units (D) 2 1 sq.units

65. A circle touches both the axes and its centre lies in the third quadrant and lies on the line 2 3x y .

Then the distance of the centre from the point 5,1 is

(A) 2 5 (B) 4 5 (C) 5 (D) 2 2

66. If the vertex of a triangle is (1,1) and the mid points of two sides through this vertex are ( –1,2) and

( 3, 2) then centroid of the triangle is

(A) 71,3

(B) 1 7,

3 3

(C) 71,3

(D) 1 7,3 3

67. The plane 2 3 6 11 0x y z makes an angle 1sin with X-axis. Then the value of ' ' is

(A) 3

2(B)

23

(C) 27

(D) 37




68. Let the vectors , , ,a b c d such that 0a b c d

. Let 1 2P and P be planes determined by the

pairs of vectors , ,a b and c d respectively . Then angle between 1 2P and P is _________

(A) 0 (B) 4

(C) 3

(D) 2

69. Maximum no. of parallel tangents of curves y = x3 – x2 – 2x + 5 and y = x2 – x + 3 is

(A) 2 (B) 3 (C) 4 (D) infinite

70. Statement – I : The sum of the series 1 1 2 4 4 6 9 9 12 16 .... 361 380 400

is 8000

Statement – II : 33 3

11

n

kk k n

,for any natural number n

(A) (I) is false but (II) is true(B) Both (I) and (II) are true and (II) is correct explanation of (I)(C) Both (I) and (II) are true and (II) is not correct explanation of (I)(D) (I) is true but (II) is false

71. Joint equation of the diagonals of the square formed by the pair of lines 4 3 12 0xy x y and3 4 12 0xy x y is

(A) 2 2 0x y x y (B) 2 2 0x y x y

(C) 2 22 0x xy y x y (D) 2 22 0x xy y x y

72. If the function 3 2 22 9 12 1f x x ax a x where 0a attains its local maximum and local minimum

values at p and q respectively such that 2p q then a =

(A) 3 (B) 1 (C) 2 (D) 1/ 2

73. The locus of a point, which moves in such a way that the sum of the squares of its distances from the

four sides of a square is constant 22c is (A) a straight line (B) a circle (C) an ellipse (D) a parabola




74. PQ is a double ordinate of a parabola 2 4y ax . If the locus of its points of trisection is anotherparabola of whose latusrectum is K times the length of the latus rectum of the given parabola, then K =

(A) 19 (B)

13 (C)

23 (D)

29

75. If 0

2

tan30

2 | | 2 | | 3log 2| | 1

z zz

, then

(A) 3| |2

z (B) 3| |2

z (C) | | 2z (D) | | 2z

76. The anti derivative of 1 2 .log 2xf x is g x and the curve y g x passes through 1,1/ 2 ,

then the curve y g x meets the y-axis at

(A) 0, 2 (B) 0, 1 (C) 0,1 (D) 0, 2

77.3 / 2

/ 2[2sin x]dx

(A) (B) 0 (C) / 2 (D) / 2

78. The first term of an A.P. of consecutive integers is 2 1p . The sum of 2 1p terms of this series canbe expressed as

(A) 21p (B) 22 1 1p p (C) 31p (D) 33 1p p

79. If 0a b c then the quadratic equation 23 2 0ax bx c has atleast one root in (A) 0,1 (B) 1, 2 (C) 2,3 (D) 1,0

80. If the angle between the line 1 1 21 2 2

x y z and the plane 2 4 0x y z is such that

2 2cos3

then the value of is

(A) 53 (B)

35

(C) 34 (D)

43

81. All the values of m for which both roots of the equation 2 22 1 0x mx m are greater than –2 butless than 4, lie in the interval

(A) 1 3m (B) 1 4m (C) 2 0m (D) 3m




82. The exponent of 7 in 10050C is

(A) 0 (B) 2 (C) 4 (D) 8

83. If , ,a b c are , ,th th thp q r term respectively of a G.P., then

log 1log 1log 1

a pb qc r

(A) 0 (B) 1 (C) abc (D) pqr

84. If 1 1a and 14 33 2n

n

n

aaa

, 1n and if nn

Lt a a

then the value of a is

(A) 2 (B) 3 (C) 2 (D) 8

85. If . . , ,f x y z f x f y f z x y z R and '2 4, 0 3f f then , '(2)f

(A) 12 (B) 9 (C) 16 (D) 6

86. If 1 1tan 2, tan 3 are two angles of a triangle then the third angle is

(A) 030 (B) 045 (C) 060 (D) 075

87. If 2sin sinA B and 2 22cos 3cosA B then the triangle ABC is (A) right angled (B) obtuse angled (C) isosceles (D) equilateral

88. For nonzero vectors a,b,c ; | . | | || || |a b c a b c holds if and only if

(A) . . . 0a b b c c a (B) . . . 0a b b c c a

(C) 0a b c (D) 0a b c

89. If 2y p x is a polynomial of degree 3 then, 2

322 .d d yy

dx dx

=

(A) ''' 'p x p x (B) '' . '''p x p x (C) . '''p x p x (D) '''p x p x

90. If the system of equations x cy bz , y az cx , z bx ay has a non zero solution then2 2 2 2a b c abc

(A) 0 (B) 1 (C) 2 (D) 5

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qp sr 15 main test 7

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