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CG PET 2006 Question Paper

Physics

1. In Huygen's wave theory, the locus of all points in the same state of

vibration is called(a) a half period zone (b) oscillator(c) a wavefront (d) a ray

2. Flux coming out from a unit positive charge enclosed in air is

(a) (b)

(c) (d)

3. The end A of a rod AB of length 1 m is maintained at 100C and the endBat 10C. The temperature at a distance of 60 cm from the end B is(a) 64C (b) 36C(c) 46C (d) 72C

4. A drop of oil is placed on the surface of water then it will spread as a thinlayer because

(a)surface tension tends to give the oil a spherical surface(b)surface tension of water is greater than that of oil(c)both oil and water have nearly equal surface tension(d)oil is lighter than water

5. A ray of light is incident at the glass-water interface at an angle i itemerges finally parallel to the surface of water, then the value of p.gwould be

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(a) (4/3) sini (b) 1/sini(c) 4/3 (d) 1

6. The ratio of electric field and potential (E/V)at midpoint of electric dipole, for which

separation Iis(a) 1/L (b) L(c) 2/L (d) None of these

7. A reverse biased diode is

8. In given circuit when switch Shas been closed then charge on capacitor A and B

respectively are 16q

(a) 3q, 6q (b) 6q, 3q(c) 4.5q, 4.5q (d) 5q, 4q

9. When two different materials A and Bhaving atomic number Zi and Z2 are used as thetarget in Coolidge -ray tube at different operating voltage V1 and V2 respectively theirspectrums are found as below.

The correct relations is

(a)VI >V2 andZ1> Z2(b)VI V2 andZ1< Z2

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10. The nuclear fusion reaction is given 1H2 + 1H

2 0He3 + oNl + Q (energy).If 2 mole of

deuterium are fused the total released energy is(a) 2Q (b) 4 Q(c) Q x 6.02 x1023 (d) Q x 2 x 6 x1023

11. In Davisson-Germer experiment maximum intensity is observed at(a) 50 and 54 V (b) 54 and 50 V(c) 500 and 50 V (d) 65 and 50 V

12.The focal length of a simple convex lens used as a magnifier is 10 cm. For the image to beformed at a distance of distinct vision (D = 25 cm), the object must be placed away fromthe lens at a distance of(a) 0.5 cm (b) 7.14 cm

(c) 7.20 cm (d) 16.16 cm

13. Doppler phenomena is related with

(a)Pitch (Frequency)(b)Loudness(c)Quality(d)Reflection

14. Out of following, incorrect statement is

(a)in Melde's experiment "P27'" remain constant. (P=Loop, T=Tension)(b)

In Kundt's experiment distance between two heaps of powder is /2.(c)Quinckeey's tube experiment is related with beats.

(d)Echo phenomena is related with reflection of sound15. The root mean square velocity of gas molecules at 27 C is 1365 m/s. The gas is

(a)O2 (b) He(c) N2 (d) CO2

16. Streamline flow is more likely for liquids with

(a)high density and low viscosity(b)low density and low viscosity(c)high density and high viscosity(d)low density and low viscosity

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17. A radioactive elementA decay in stable elementB, initially a fresh sample ofA isavailable. In this sample variation in number of nuclei ofBwith time is shown by

18 Which types of losses do not occur in the transformer ?(a) Iron losses (b) Copper losses(c) Mechanical losses (d) Flux leakage

19. Charges are placed at corners of a square of side 'a'as shown in the following figure. The

charge A is in equilibrium. The ratio q1 /q2 is

(a) 1 (b)

(c) 1/ (d) 2

20. The Young's double slit experiment is performed with blue and with green light ofwavelength 4360 A and 5460 A respectively. IfX is distance of 4th maximum from thecentral one, then

(a)X(blue) = X(green)(b)

X(blue) > X(green)(c)X(blue) < X(green)

(d) X(blue)/X(green) = 5490/4360

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21. A particle of mass m is tied to one end of a string of length 1 and rotated through theother end along a horizontal circular path with speed v. The work done in half horizontalcircle is

(a) zero (b)

(c) (d)

22. Which of the following statement is correct?(a) Electric field is zero on the surface of current carrying wire.(b) Electric field is non-zero on the axis of hollow current carrying wire.(c) Surface integral of magnetic field for any closed surface is equal to [I 0 times of total

algebraic sum of current which are crossing through the closed surface.

(d) None of the above23. Which one is correct about fission ?

(a) Approx. 0.1% mass converts into energy(b) Most of energy of fission is in the form of heat(c) In a fission ofU235 about 200 eV energy is released(d) On an average, one neutron is released per

fission ofU235

24. Photoelectric effect supports quantum nature of light because

(A) there is minimum frequency of light below which no photoelectrons are emitted.(B) electric charge of photoelectrons is quantized.(C) maximum kinetic energy of photoelectrons depends only on the frequency of light and

not on its intensity.(D) even when metal surface is faintly illuminated the photoelectrons leave the surface

immediately.(a) (A) (B) (C) (b) (A) (B) (D)(c) (B) (C) (D) (d) (A) (C) (D)

25. Select the wrong statement.(a) Radioactivity is a statistical process.(b) Radioactivity is a spontaneous process.(c) Radioactivity is neutral characteristic of few elements.(d) Radioactive elements cannot be produced in the laboratory.

26.The magnetic needle of a tangent galvanometer is deflected at angle of 300 due to a currentin its coil. The, horizontal component of earth's magnetic field is 0.3410 T then magneticfiled at the centre of the coil due to current.(a) 1.96 x10-5 T (b) 1.96 x10-4 T

(c) 1.96 x104 T (d) 1.96 x105 T

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27.When gas in a vessel expands in internal energy decreases. The process involved is(a) Isothermal (b) isobaric(c) Adiabatic (d) isochoric

28.Three identical resistancesA, B and C are connected as shown in figure.

The heat produced will be maximum(a) in B (b) in B and C(c) in A (d) same for A, B and C

29.A 500 F capacitor is charged at a steady rate of 100 C/s. The potential difference acrossthe capacitor will be 10 V after an interval of(a) 5s (b) 25s(c) 20s (d) 50s

30.A photon creates a pair of electron-positron with equal kinetic energy. Let kinetic energyof each particle is 0.29 MeV Then what should be energy of the photon ?(a) 1.60 MeV (b) 1.63 MeV(c) 2.0 MeV (d) 1.90 MeV

31. Ify =5sin(30 t - - 30)Y mm, t s, x m. For given progressive wave equation, phase difference betweentwo vibrating particle having path difference 3.5 m would be(a) /4 (b)

(c) /3 (d) /2

32.Two cells having the internal resistance 0.2 and 0.4 are connected in parallel. Thevoltage across the battery terminal is 1.5 V. The emf of first cell is 1.2 V. The emf ofsecond cell is(a) 2.7V (b) 2.1V(c) 3V (d) 4.2V

33. Two particles A andB execute simple harmonic motion of period Tand 5T/4. They startfrom mean position. The phase difference between them when the particle A complete anoscillation will be

(a) /2 (b) zero

(c) 2 / 5 (d) /4

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34.A particle is projected with velocity vo along x-axis. The deceleration on the particle isproportional to the square of the distance from the origin ie a = a x2 the distance at whichthe particle stops is

(a) (b)

(c) (d)

35. When cathode-rays strike a metal target of high melting point with a very high velocitythen which of the following are produced?

(a) -rays (b) X-rays

(c) Ultraviolet rays (d) -rays

36. Stationary wave is represented byy = A sin (100 t) cos (0.01x) wherey and a are in mm, tin sec. and x in metre. The velocity of stationary wave is

(a) 1 m/s (b) 103m/s(c) 104m/ s (d) Not derivable

37. What will be ratio of radii of Li7 nucleus to Fe56 nucleus ?(a) 1 : 3 (b) 1 : 2

(c) 1 : 8 (d) 2:6

38.What about Gauss theorem is not incorrect ?

(a) It can be derived by using Coulomb's law(b) It is valid for conservative field obeys inverse square root law(c) Gauss theorem is not applicable in gravitation(d) Both (a) and (b)

39.A body of mass m is thrown upwards at an angle 0 with the horizontal with velocity v.White rising up the velocity of the mass after tseconds will be

(a)

(b)

(c)

(d)

40.A particle moves in a circle of radius 30 cm. Its linear speed is given byv=2t where tis insecond and v in m/s. Find out its, radial and tangential acceleration at t =3 s. respectively,

(a) 220 m/s2, 50 m/s2(b) 100 m/s2, 5 m/s2(c) 120 m/s2, 2 m/s2

(d) 110 m/s2, 10 m/s2

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41. On which principle does sonometer works?(a) Hooke's law (b) Elasticity(c) Resonance (d) Newton's law

42. Write copper, steel, glass and rubber in order in increasing coefficient elasticity.

(a)

Steel, rubber, copper, glass(b) Rubber, glass, copper, steel(c) Rubber, glass, steel, copper(d) Rubber, glass, copper, steel

43. Writing on black board with a piece of chalk is possible by the property of(a) adhesive force (b) cohesive force(c) surface tension (d) viscosity

44. Two large metal plates are placed parallel to each other. The inner surfaces of plates arecharged by + and (C / m2). The outer

surfaces are neutral. The electric field in the region between the plates and outside theplates is

(a) (b)

(c) (d)

45. In order to increase the sensitivity of galvanometer(a) the suspension wire should be made stiff(b)area of the coil should be reduced(c) the magnetic field should be increased(d)the number of turns in the coil should be reduced

46. Calculate the value E, for given circuit, when value of 2A current is either flowing inclockwise or anticlockwise direction.

(a) 32V, 8 V (b) 38 V, 2V(c) 32V, 2V (d) 30 V, 8 V

47. If in a resonance tube a oil of density higher than that water is used then at theresonance frequency would be

(a) increased (b) decreased

(c) slightly increased (d) remains the same

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48. A photon and an electron have equal energyE.(a)(b)(c) 1/E(d)Does not depend uponE

49The instantaneous value of current in an AC circuit is / = 2sin(1007ct+ n/3) A. The currentwill be maximum for the first time at,

(a) t = (b) t =

(c) t = (d) t =

50 The escape velocity of a particle of mass m varies as(a) m

2(b) m

(c) m (d) m-1

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Chemistry

1. In which of the following compounds carboxylic group (COOH) is not present?

(a) Acetic acid (b) Lactic acid

(c) Benzoic acid (d) Picric acid

2.When calcium acetate mixed with calcium formate is distilled, which of the following is notobtained?(a) Acetone (b) Formaldehyde

(c) Acetaldehyde (d) Propionaldehyde

3. Glucose response to silver mirror test due to the presence of(a)COOH group (b) an alkaline group (c) a ketonic group (d) an aldehydic group

4.Which of the following compounds is used to obtain polymer teflon?(a) Difluoro ethane

(b) Monofluoro ethane

(c) Tetrafluoro ethene(d) Tetrafluoro ethane

5.Which of the following equations represent de-Broglie relation?

(a) (b)

(c) (d)

6. Which of the following sequences of the energy levels of the subshells related to principalquantum number four (n = 4) ?

(a) s

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9. The shape of water molecule according to VSEPR theory, is(a) octahedral(b) distorted tetrahedral(c) trigonal planar(d) trigonal bipyramidal

10. On dissolving a non-volatile solute in a solvent, The vapour pressure of the solvent isdecreased by 10 mm of mercury. The mole fraction of the solute in this solution is 0.2. Ifthe vapour pressure of the solvent is decreased by 20 mm of mercury by dissolving moresolute, what is the mole fraction of solvent in this solution now?(a) 0.2 (b) 0.4(c) 0.6 (d) 0.8

11.Which of the following statements about ionic crystals is false?(a) Melting and boiling temperature of ionic crystals are very high(b)These are soluble in water and other solvent(c)At low temperature in solid state they are good conductor of electricity(d)They have high cohesive energy

12. 8.0 g of a radioactive substance remains 0.5 g in 1 h. What is its half-life period?(a) 10 min (b) 15 min(c) 30 min (d) None of these

13. In a radioactive change

R X

Y Z

Rand Zare

(a) isotopes (b) isobars(c) isomers (d) isotones

14. The chemical decomposition of XY2 occurs as XY2(g) XY(g) +Y(g)

The initial vapour pressure of XY2 is 600 mm of mercury and at equilibrium it is 800 mm

of mercury. Find out the value of K for this reaction when the volume of the systemremains constant.(a) 50 (b) 100(c) 166.6 (d) 150

15. The degree of ionisation of decinormal solution of CH 3COOH is 1.3%. If the log of 1.3 is0.11, the pH of this solution is(a) 2.89 (b) 3.89(c) 4.89 (d) 0.89

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16.A buffer solution is obtained by mixing 10 rriL of 1.0 M CH 3COOH and 20 mL of 0.5 MCH3COONa and it is diluted to 100 mL using distilled water. pKa of CH3COOH is 4.76.The pH of this buffer solution is(a) 2.76 (b) 3.76(c) 4.76 (d) 0.76

17. To which of the following determinations of heat, Hess's law is used?(a) Heat of chemical reaction(b) Heat of formation(c) Heat of bond formation(d) All of the above18.1.0 L of 1.0 M solution of sodium hydroxide is neutralised by 1.0 L of 1.0 M of methanoic

acid. If the heat of formation of water is X, the neutralisation energy of above reaction is

(a)less than X (b) more than X(c) equal to X (d) None of these

19. 1.0 L of 2.0 M acetic acid is mixed with 1.0 L of 3.0 M ethyl alcohol. The reaction isCH3COOH + C2H5OH CH3C00C2H5 + H20

If both the solutions are diluted by adding 1.0 L of water in each, the initial rate of reactionis slow by

(a) 0.5 times (b) 2.0 times(c) 4.0 times (d) 0.25 times

20.The velocity constant for a reaction is 0.693 x 10-1 min-1 and the initial concentration is 0.2mol/L, the half-life period is

(a) 400 s (b) 600 s

(c) 800 s (d) 100 s

21. For the chem ical reaction,N2 +3H2 2NH3, if

d[NH3]

dt = 2 x10-4 mol L-1 s-1the value of d[H2] is

dt

(a) 1 x 10-4 mol L-1 s-1(b) 3 x 10-4 mol L-1 s-1(c) 4 x 10 -4 mol L-1 s-1(d) 6 x 10-4 mol L-1 s-1

22.Which of the following units of energy, represents maximum amount of energy?

(a) Calorie (b) Joule(c) Erg (d) Electron volt

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23.The reduction potential of three metallic ionsX,Y andZcorrespondingly are +0.52,3.03and1.18 V. The sequence of reducing capacity of these metals will be(a) Y >Z > X (b)X >Y >Z(c)X > Z >Y (d)Z > X >Y

24.E =

0.44 V for the reaction,Fe2+ + 2e- Fe andE =0.76 V for the

Reaction, Zn2+ + 2e- Zn. Which of thefollowing statement is correct?(a) Fe is more electropositive(b) Zn is more electropositive(c)Zn is more electronegative(d) None of the above

25. For the electrolysis of aqua CuSO4 solution using inert Pt electrodes, the reaction on anode

is(a) 2S S2 +2 O2+ 2e-(b)Cu2+ + 2e- Cu(c)2H20 02 +4 H+ + 4 e-(d) 2H++ 2e- H2

26.Which of the following chemical reactions is homogeneous catalytic reaction?

(a) N2(g)+ 3H2(g) 2NH3(g)(b)

2S02(g)+02g) 2S03(g)

(c) CO(g) + 3H2(g) CH4(g) + H20(g)(d) 2502(g) + 02(g) 2S03(g)27. For the reaction,

Mn + C2 + H+ Mn2+ + CO 2 + H20 which of the following is correct?

Mn2+ C2 CO 2 H+

(a)5 2 4 10

(b)2 5 10 16(c)6 8 16 18

(d)10 12 24 12

28.Acidic K2Cr207 reacting with H2S, the oxidation number of chromium is changed(a) from +3 to +6 (b) from +6 to +3(c) from +6 to +2 (d) remains unchanged

29. In which of the following compound the oxidation number of oxygen is +2?

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(a) H202 (b) CO2(c) H20 (d) OF2

30.Which one of the following is maximum electronegative?

(a) Lead (b) Silicon

(c) Carbon (d) Tin

31. Which one of the following elements belongs to s-block?(a) Aluminium (b) Chromium(c) Carbon (d) Potassium

32.Which one is the correct decreasing order of the ionic radii of the ions?(a) N3- > 02- > F- > Na+(b) N3- > Na+> 02- > F-(c) Na+ > 02- > N3-> F-(d) Na+ > F- > 02- > N3-

33. The electronic configuration of an element is1s2, 2s22p6, 3s

23p63d

10, 4s24p3. To which of

the following elements it is similar in properties?(a) Boron (b) Oxygen(c) Nitrogen (d) Chlorine

34. Malachite is the ore of which metal?(a) Fe (b) Cu(c) Zn (d) Hg

35. Blister copper is melted in a furnace then stirred with green wooden logs. The purpose is(a) to expel the soluble gases out of the blister copper(b) to bring the impurities on the surface to oxidize them(c) to increase the carbon in copper(d) to reduce the metallic oxide impurities by the hydrocarbon gases coming out of the

log during the process

36. During smelting of an ore an additional substance is added to make the impurities fusible.The name of it is(a) slag (b) mud(c) gangue (d) flux

37. Which of the following pairs of compounds cannot exist together?(a) NaHCO3 and NaCl(b) NaHCO3 and NaOH(c) NaHCO 3 and Na2C0 3(d) Na2CO3 and NaOH

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38.Which of the following metals has highest melting point?(a) Barium (b) Strontium(c) Calcium (d) Radium

39. Transitional elements are mostly(a) diamagnetic(b) paramagnetic(c) neither diamagnetic nor paramagnetic(d) diamagentic and paramagnetic both

40. In which of the following complex compoundsthe oxidation number of the metal is zero?

(a) [Pt (NH3)2Cl2] (b) [Cr(C0)6](c) [Cr(NH3)3Cl3] (d) [Cr(en)2Cl2]

41. [(C6H5)2Pd (NCS)2] and [(C 6H5 Pd (SCN)2] are(a) bond isomeric(b) coordinated isomeric(c) ionic isOmeric(d) geometrical isomeric

42.The main compound obtained by fusion of sodium with aniline is(a) NaCN (b) NaN3(c) NaSCN (d) NaNO2

43. Combustion of liquid benzene in oxygen occurs as

2C6H6 + 15O2 12C02+ 6H20At STP, what volume (in litre) of oxygen is required for the full combustion of 3.9 gliquid benzene?(a) 11.2 L (b) 22.4 L(c) 8.4L (d) 7.4L

44. What is the IUPAC name of the following compound/OH

\ CH3(a) 3-methyl cyclo-1-butene-2-ol(b) 4-methyl cyclobut-2-ene-1-ol(c) 4-methyl cyclobut-1-ene-3-ol(d) 2-methyl cyclo-3-butene-1-ol

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45.Which of the following compounds does not show optical isomerism?(a) CH3CH(OH)Br(b) CH3CH(OH)CH3

CH3(c) CH3CH2CHBrCH

NCH3

(d) CH3CHOHCHBrCH2OH46. In dehydrolysing reaction,

CH3CONH2 CH3CN + H20

the hybridisation state of carbon is changed from(a) sp3 to sp2 (b) sp to sp2

(c) sp2 to sp (d) sp to sp3

47. Acetylene reacting with HCN in presence of Ba(CN)2 gives

(a) vinyl cyanide (b) 1,1-dicyanoethane(c) 1,2-dicyanoethane (d) None of these

48. In which of the following compounds, the chlorine atom is most easily substituted?(a) Chlorobenzene(b) Vinyl chloride(c) Ally1 chloride(d) p-chlorotoluene

49. The commercial production of methanol is done by(a) the catalytic reduction of CO in presence of ZnO, Cr20 3(b) the reaction of water vapour on CH4 at 900C in presence of nickle catalyst(c) the reaction of formaldehyde with LiA1H4(d) reaction of aqua KOH on HCHO

50. The increasing order of acidic character of phenol, p-cresol, m-nitrophenol and p-nitrophenol is(a) phenol, p-cresol,p-nitrophenol, m-nitrophenol(b) p-cresol, phenol,m-nitrophenol, p-nitrophenol(c) p-cresol, m-nitrophenol,phenol, p-nitrophenol(d) m-nitrophenol, phenol,p-cresol, p-nitrophenol

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Mathematics

1. dxis equal to

(a) (b)

(c)1 (d)0

2.Equation of the tangent to the hyperbola 2x2 - 3y2 = 6. Which is parallel to the liney-3x - 4= 0 is(a) y= 3x + 8 (b) y= 3x - 8(c) y= 3x + 2 (d) None of these

3. If the coefficient of correlation between two variables is 0.32, covariance is 8 and variance ofx is 25, then variance of yis

(a) 36 (b) 25

(c) 64 (d) None of these

4.Ten coins are thrown simultaneously, the probability of getting at least 7 heads is

(a) (b)

(c) (d)

5.When byx = 0.03 and bxy = 0.3, then r is equal to approximately(a) 0.003 (b) 0.095

(c) 0.3 (d) -0.3

6.Use Simpson's rule to find the value of dx given

X 1 2 3 4 5

y 10 50 70 80 100

(a) 140.88 (b) 256.66(c) 160.26 (d) None of these

7. The feasible region represented by x1 + x2 1, -3x1 + x23, (xi, x2 0) is

(a) a polygon(b) a singleton set(c) empty set(d) None of these

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8. The points on the curve x2 = 2y which are closest to the point (0, 5) are

(a) (2, 2), (-2, 2)(b) (2 , 4), (-2 , 4)(c) ( , 3), ( ,3)(d) (2 ,6), (-2 , 6)

9. Solve( tany = sin (x + y) + sin (x- y)

(a) sec x tany = c

(b) log sin (x + y)= c(c) secx + tany = c(d) secy + 2 cosx = c

10. .{ X( )}equals

(a) [ (b) [

(c) 0 (d) 1

11.If y+ +. = 2[x+ ] then value of y is

(a) (b)

(c) (d) None of these 2x

12.If x = ( + i), then x3 is equal to

(a) 1 (b) -1(c) i (d)-i

13. If the complex numbers sinx + i cos2x and cos x -i sin2x are complex conjugate to each

other, then the value of x is

(a) (b)

(c) (d) None of these

14. is equal to

(a) -1 (c) 2

(b) 1 (d) -2

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15. If = 0, then

(a) z = xy (b) z =

(c) z= (d) None of these

16. cos 4 + cos 4 + cos 4 + cos 4 is equal to(a) (b)

(c) (d)

17. In a triangleABC, if tan and tan

then a + cis equal to

(a) b (b) 2b

(c) 3b (d) 4b

18. Number of solutions of the equationtan x + sec x = 2 cos x lying in the interval [0, 2 ] is

(a) 0 (b) 1

(c) 2 (d) 3

19. Equation of the pair of straight lines bisecting the angles between the lines represented byax2 + hxy + by2 = 0 is

(a) =

(b) =

(c) =(d) None of the above

20.The equation of circle which touches the axes and the line + = 1 and whose centre lies in

thefirst quadrant is x2 + y2 - 2 cx - 2 cy + c2 =0. Then, cis equal to

(a) 1 (b) 2(c) 3 (d) 6

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21. Angle between any two diagonals of a cube is

(a) (b) cos-1( )

(c)cos-1( ) (d) None of these

22. Tfa1, a2, a3, , anare in AP. Where ai > 0 for all i. Find the sum of series

(a) (b)

(c) (d)

23. The ratio in which the : xy-plane meets the line joining the points (-3, 4, -8) and (5, -6, 4)

is(a) 2:3 (b) 2:1

(c) 4: 5 (d) None of these24. The unit vector perpendicular to each of the Vectors 3i + j+ 2k and 2i - 2j + 4k is

(a) (b)

(c) (d) None of these

25.Y = tan

-1than is equal to

(a) (b) -

(c) - (d)

26. a, b, c are coplanar vectors, then which of the following is not correct?

(a) a.(bXc)=0 (b) aX(bXc) =0

(c) [a+b, b+c, c+a] =0 (d) a=pb+qc

27. If 0 andA is of order n, then adj (adjA) is equal to

(a) (b)

(c) I (d) .A

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28. dx is equal to

(a) x log (1 + cosx) + c (b) log (1 + cosx) + c

(c) x tan + c (d) x2 tan-1 +c

29. Find the differential equation of curvesy = Aex

+ Be'for different values of A and B(a) (b)

(c) = 4y + 3 (d) +y = 0

30. Solve =

(a) y=c (b) y=c (c) y = cey/x (d) xy = cey/x

31. If lim = -1then

(a) a = 1 (b) a = 0

(c) a = e (d) a =

32. If four digits are taken from the digits 1, 2, 3, 4, 5, 6, 7. The probability that the sum ofdigits is less than 12, is

(a) (b)

(c) (d)

33.The probability of happening exactly one of the two events A and B is(a) P(A)+ P(B) - 2P(AB)(b) P(A)+ P(B)- P(A B)(c)P(A)-P(B)(d) None of the above

34. Solve xcos x + y (xsin x + cos x) = 1

(a)y = xtan x + sin x + c(b) x = ytan x + c(c)

yxsec x = tan x + c(d) xycos x = x + c35. If the equation + + a (a + 1) = 0 has more than two roots,thenvalue of a is

(a) 0 (b) 1(c) -1 (d) None of these

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36.S1, S2 and S3are the sums of n, 2n and 3n terms of an arithmetic progression respectively,then

(a) S2= 3S3 - 2S1 (b) S3 = 4(S1 + S2)(c) S3 = 3(S2S1) (d) S3= 2(S2+Si)

37. Ifn

= 36,n

= 84 andn

= 126, then nis equal to(a) 8 (b) 9

(c) 10 (d) 11

38.The sides AB, BC, CA of triangle ABChave 3, 4 and 5 interior points respectively onthem. Find the number of triangles that can be constructed using these points as vertices

(a) 201 (b) 120(c) 205 (d) 435

39. Coefficient of xn

in the expansion of

1 + + + +.... is

(a) (b)

(c) ) (d)

40. + + + +. is equal to

(a) (b)

(c) (d)

41. The equation of the parabola having the focus at the point (3, -1) and the vertex at (2, -1)

is

(a) y2 - 4x - 2y + 9 = 0(b) y2 + 4x + 2y -- 9 = 0(c) y2 -4x + 2y + 9 =(d) y2 + 4x - 2y + 9 = 0

42. The equation of lines joining the origin to the points of intersection ofy = x + 3 and 4x2.+4y

2= 1 is

(a) 36(x2 + y2) = (x -y)2(b) 12(x2 + y2) = (x + y)2(c) 9(x2 + y2) = 4(x - y)2(d) None of the above

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43. The angle of elevation of a jet fighter from a point A on the ground is 60'. After a flightof 10 s, the angle of elevation changes to 30. If the jet is flying at a speed of 432 km/h.

Find the constant height at which the jet is flying. _

(a) 200 m (b) 400 m

(c) 600 m (d) 800 m

44. Which is incorrect ?

(a) (AB)' =B'A' (b) (AB =

Cc) = (d) (AB)-1

= B-1A-1

45. Find the equation of plane through the line = = and parallel to x-axis.

(a) 2x + 3y + 5z = 1 (b) 2 x -5y = 4(c) 5y3z3= 0 (d) 3y+ 4z=0

46. Find the moment of the force 51 10j + 16k acting at the point 2i7j + 10k, about the

point5i + 6j10k

(a) 41i- 8j + 55k(b)408i12j + 135k(c)36i + 14j35k(d) None of the above

47. Find the equation of tangents to the ellipse 1, which cut off equal intercepts

on the axes.

(a)Y =(b)y =(c) y =(d) None of the above

48.A square matrixA is called an orthogonal matrix, if

(a) A = I (b) AA =I

(c)A = I (d) A2

=I

49. The value of'c'of Rolle's theorem forf (x) =ex sinx in [0, ]is given by

(a) (b)

(c) (d)

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50. dx is equal to

(a) b)

(c) (d) 0

cgpet2006 article 46527

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