Physics Chemistry Mathematics IITJEE Test

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VMC/ 2010 1 I.P. PRACTICE TEST- 2

I.P. PRACTICE TEST – 2/2010

SECTION : 1 (PHYSICS)

1. The radius of nucleus is rr A₀ 1 3/ , where A is mass number. The dimensions of r0 is :

(A) _MLT2_ (B) _M L T0 0 1_ (C) _M LT0 0_ (D) None of these 2. The resultant of two vectors P andQ is R . If the vectors Q is reversed, then the resultant

becomes S , then choose the correct option.

(A) R2 S22



P2Q2



(B) R2 S22



P2Q2



(C) R2S2



P2Q2



(D) R2 S22



P2Q2



3. If a particle is moving on an elliptical path given by r bcos t i ˆa sin t j ˆ, then find its radial acceleration along r

(A) r (B) 2r (C) 2r (D) None of these

4. In the arrangement shown in figure, the ends P and Q of an inextensible string move downwards with uniform speed u. Pulleys A and B are fixed. The mass m moves upwards with a speed

(A) 2u cos (B) u

cos (C) 2u

cos (D) u cos

5. Observer O1 is in a lift going upwards and O2 is on the ground. Both apply Newton’s law, and

measure normal reaction on the body (A) the both measure the same value (B) the both measure zero

(C) the both measure different value (D) no sufficient data

6. Two blocks of masses M = 3 kg and m = 2 kg are in contact on a horizontal table. A constant horizontal force F = 5 N is applied to block M as shown. There is a constant frictional force on 2N between the table and the block m but no frictional force between the table and the first block M, then acceleration of the two blocks is :

(A) 0 4. ms2 (B) 0 6. ms2 (C) 0 8. ms2 (D) 1 ms2 u  u  B A Q P M

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VMC/ 2010 2 I.P. PRACTICE TEST- 2 7. In circular motion :

(A) Radial acceleration is non-zero (B) Radial velocity is zero

(C) Body is in equilibrium (D) All of these

8. A small sphere of mass m is suspended by a thread of length l. It is raised upto the height of suspension with thread fully stretched and released. Then the maximum tension in thread will be :

(A) mg (B) 2 mg

(C) 3 mg (D) 6 mg

9. A wind powered generator converts wind energy into electrical energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy for wind speed v, the electrical power output will be proportional to :

(A) v (B) v2 (C) v3 (D) v4

10. Centre of mass of a semicircular plate of radius R, the density of which linearly varies with distance, d at centre to a value 2d at circumference is :

(A) 3R  from centre (B) 4 2 R  from centre (C) 5R  from centre (D) 7 5 R  from centre

11. In the given figure, the sphere rolls without slipping on the plank which is moving with constant velocity v0. The radius and

angular velocity of the sphere is r and  respectively. The velocity of centre of mass of the sphere is :

(A) v₀r (B) v₀r (C) r (D) v ₀

12. A weightless rod of length l carries two equal masses m one fixed at the end and other in the middle of the rod. The rod can revolve in a vertical plane about A. Then horizontal velocity which must be imparted to end C of rod to deflect it to horizontal position is :

(A) 12

5 gl (B) 3 gl (C) 16

5 gl (D) 2 gl

13. A gravitational field is present in a region. A point mass is shifted from A to B, from different paths shown in the figure. If

W1, W2 and W3 represent work done by gravitational force for

respective paths. Then :

(A) W₁W₂W₃ (B) W₁W₂W₃ (C) W₁W₃W₂ (D) None of these

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VMC/ 2010 3 I.P. PRACTICE TEST- 2 14. Two point masses of 3 kg and 1 kg are attached to opposite ends of a horizontal spring whose

spring constant is 300 N/m as shown in figure. The natural vibration frequency of the system is of order :

(A) 4 Hz (B) 3 Hz

(C) 2 Hz (D) 1 Hz

15. From the ceiling of a train a pendulum of length ‘l’ is suspended. The train is moving with an acceleration a0 on horizontal surface. What must be the period of oscillation of pendulum ?

(A) T 2 l g     _{ }   (B) 2 2 0 2 l T a g     _ _    (C) 2 2 0 l T a g     _ _    (D) 2 2 0 2 l T a g     _ _   

16. The excess pressure inside a soap bubble of radius 4 cm is 30 dyne/cm2. The surface tension is :

(A) 30 dyne/cm (B) 20 dyne/cm (C) 40 dyne/cm (D) 80 dyne/cm

17. A body of mass m = 10 kg is attached to a wire of length 0.3m. Calculate the maximum angular velocity with which it can be rotated in a horizontal circle (Breaking stress of wire = 4 8. 107N / m2 and area of cross-section of a wire =106m2)

(A) 4 rad/s (B) 8 rad/s (C) 1 rad/s (D) 2 rad/s

18. The linear strain in x, y and z-directions are e , e_x _y and e respectively. Then the volumetric strain _z

is given by : (A) e e e x y z (B) ex ey ez (C) eze ex y (D) 2 x y z e e e  

19. Wave of frequency 500 Hz has a phase velocity 360 m/s. The phase difference between two displacement at a certain point at time 10 s3 apart will be :

(A)  radian (B) 2  radian (C) 4  radian (D) 2 radian 20. Figures shows the vibrations of four air coloumn. The ratio of frequencies n n_p: _q:n_r:n is : _s

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VMC/ 2010 4 I.P. PRACTICE TEST- 2 21. There is a road between two parallel rows of building and distance between the rows of building is

106 m. Find the velocity of car if a car blows a horn whose echo is heard by the driver after 1s. (Given : Speed of sound = 340 m/s)

(A) 180 m/s (B) 165 m/s (C) 323 m/s (D) 150 m/s

22. A second’s pendulum clock having steel wire is calibrated at 20 C . When temperature is increased to 30 C , then how much time does the clock lose or gain in one week ?__steel 1 2. 105

 

C 1_

(A) 0.3628 s (B) 3.626 s (C) 362.8 s (D) 36.23 s

23. Four molecules of a gas have speeds 1, 2, 3 and 4 km/s. The value of the root-mean square speed of the gas molecules is :

(A) 1 15 2 km / s (B) 1 10 2 km / s (C) 2.5 km/s (D) 15 2 km / s      

24. If the temperature of 3 moles of helium gas is increased by 2 K., then the change in the internal energy of helium gas is :

(A) 70.0 J (B) 68.2 J (C) 74.8 J (D) 78.2 J

25. An ideal monoatomic gas is taken around the cycle

ABCDA as shown in the P-V diagram. The work done

during cycle is given by : (A) 1

2PV (B) PV (C) 2PV (D) 4PV

26. Find the time in which a layer of ice of thickness h will grow on the surface of the pond of surface area A, when the surrounding temperature falls to T C  .

(Assume K = thermal conductivity of ice  = density of water, L = latent heat of fusion)

(A) 2 2 L t h KT   (B) t Lh2 KT   (C) 2 3 Lh t KT   (D) 2 4 Lh t KT  

27. What amount of ice at  14 C, required to cool 200 g of water from 25 C to 10 C ? (Given : C_ice0 5. cal / g C , Lf for ice = 80 cal/g)

(A) 31 g (B) 41 g (C) 51 g (D) 21 g

28. Calculate the time taken by the light to travel a distance of 500 metre in water of refractive index of 4/3 (Given : velocity of light in vacuum =310 cm / s10 )

(A) 3 10 10sec (B) 2 22. 106sec (C) 4 3. 105sec (D) 3106sec 29. How many image are formed by the lens shown if an object is

kept on its axis ?

(A) one (B) two

(C) three (D) four

30. If n coherent source of intensity I0 are super imposed at a point, the intensity of the point is :

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VMC/ 2010 5 I.P. PRACTICE TEST- 2 31. A point charge Q is placed at the centre of a circular wire of

radius R having charge q. The force of electrostatic interaction between point charge and the wire is :

(A) ₂ 0 4 qQ R  (B) zero (C) 2 0 4 q R  (D) None of these

32. What is the electric field intensity at a point at a distance 20 cm on a line making an angle of 45 with the axis of the dipole of moment 10 C-m is ?

(A) 1 77. 1013V / m (B) 0 177. 1013V / m (C) 17 7. 1013V / m (D) 17710 V / m13

33. In a region electric field is parallel to x-axis. The equation of equipotential surface is :

(A) y = C (B) x = C (C) z = C (D) None of these 34. Two spherical conductors A1 and A2 of radii r1 and r2 are placed

concentrically in air. The two are connected by a copper wire as shown in figure. Then the equivalent capacitance of the system is :

(A) 0 1 2 2 1 4 Kr r r r   (B) 40



r2 r1



(C) 4_{0 2}r (D) 4_{0 1}r

35. An air filled parallel plate capacitor has a capacitance of 1012F. The separation of the plates is doubled and wax is inserted between them, which increases the capacitance to 21012F. The dielectric constant of wax is :

(A) 2 (B) 3 (C) 4 (D) 8 36. What is R ? (A) 42 (B) 62 (C) 84 (D) None of these 37. The dimension of 0 0 1   are same as : (A) E B (B) B E (C) 2 2 E B (D) E B      

38. Three similar magnetic south poles each of strength 10 Am are placed at the corners of an equilibrium triangle of 20 cm. Find the magnetic force on one of the pole :

(A) 0 25. 103N (B) 10 N3 (C) 1010 N3 (D) None of these 39. An atom is paramagnetic if it has :

(A) an electric dipole moment (B) no magnetic moment

(C) a magnetic moment (D) no electric dipole moment

40. The formula used for calculating induced emf in a rod moving in a uniform magnetic field is : (A) eB .



1v



(B) eB .

 

1 . v (C) eB 

 

1. v (D) eB 



1v



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VMC/ 2010 6 I.P. PRACTICE TEST- 2 41. An A.C. source of voltage V = 100 sin100t is connected to a resistor of resistance 20.

The rms value of current through resistor is :

(A) 10 A (B) 10

2 A (C) 5

2 A (D) None of these 42. An alternating voltage : V30sin50t40cos50t is applied to a resistor of

resistance 10. The rms value of current through resistor is : (A) 5 2 A (B) 10 2 A (C) 7 2 A (D) 7A 43. If the velocity of an electron is doubled, its de-Broglie frequency will be :

(A) half (B) remain same

(C) doubled (D) become four times

44. The magnetic of the de Broglie wavelength

 

 of an electron (e), proton (p), neutron (n) and

- particle

 

 all having the same energy of MeV, in the increasing order will follow the sequence

(A)    e, p, n,  (B)    , n, p, e (C)    e, n, p,  (D)    p, e, , n

45. If the uncertainity in the position of a particle is equal to its de-Broglie wavelength, the minimum uncertainity in its velocity should be :

(A) 1 4 (B) 4 v  (C) 4 v m  (D) 4 mv 

46. The binding energy expressed in MeV is given for the following nuclear reactions

3 1 4

2He  0n  2He 20MeV

4 1 5

2He  0n 2He 0 9. MeV

Which of the following conclusion is correct ? (A) 2He

4

is less stable than both 2He 3 and 2He 5 (B) 2He 4

is less stable than both 2He 3

but more stable than 2He 5

(C) 2He

4

is less stable than 2He 5

but more stable than 2He 3

(D) 2He 4

is more stable than both 2He 3

and 2He 5

47. Half-life period of a given radioactive sample is . Its average life would be : (A) ln2 (B) 2 ln  (C) 1  (D) 2 ln 

48. What does it represent ?

(A) OR (B) AND

(C) NAND (D) NOR

49. The universe is :

(A) expanding (B) contracting (C) constant in size (D) increases northwards and decreases southwards

50. The spectrum of stars is most closely related to :

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I.P. PRACTICE TEST – 2/2010

SECTION : 2 (CHEMISTRY)

1. The last unpaired electron of chlorine has quantum number values as :

n l m s (A) 3 2 1 1 2  (B) 3 1 +1 1 2  (C) 3 1 2 1 2  (D) 3 0 0 1 2 

2. The nitrate which does not give NO2 on heating :

(A) NaNO3 (B) Pb(NO3)2 (C) AgNO3 (D) Cu(NO3)2

3. Volume of gas at NTP is 1 12. 107c.c. Calculate the number of molecules in it :

(A) 3 01 10.  20 (B) 3 01 10.  12 (C) 3 01 10.  23 (D) 3 01 10.  24 4. Monoclinic crystal has dimension :

(A) a b c ;       90 , 90 (B) a b c ;      90 (C) a b c ;       90 (D) a b c ;       90 5. An isolated system is that system in which :

(A) there is no exchange of energy with the surroundings (B) there is exchange of mass and energy with the surroundings (C) there is no exchange of mass and energy with the surroundings (D) there is exchange of mass with surroundings

6. Given that H_comb. of C(s) H2 (g) and CH4(g) are 394kJ / mol, 284 kJ / mol and 892kJ / mol

respectively. The heat of formation of CH4 is :

(A) 70 kJ / mol (B) 71.8 kJ / mol (C) 244 kJ / mol (D) 782 kJ / mol 7. The pH of pure water at 80 C will be :

(A) > 7 (B) < 7 (C) = 7 (D) cannot be predicted 8. The half-life period of a first order process is 1.6 minutes. It will be 90% complete in :

(A) 0.8 min (B) 3.2 min (C) 5.3 min (D) 1.6 min

9. The rate of certain reaction at different times are as follows : Time Rate (Moles L sec ) 1 1

0 2.8102

10 2.78102

20 2.81 10 2

30 2.79102

The reaction is of :

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VMC/ 2010 8 I.P. PRACTICE TEST- 2 10. The molal freezing point constant for water is 1.86 C/ mole . If 342 g. of cane sugar is dissolved in

1000 g of water, the solution will freeze is :

(A) 1.86 C (B) 1.86 C (C) 3.92 C (D) 2.42 C

11. The curve showing the variation of adsorption with pressure at constant temperature, is called :

(A) adsorption isobar (B) an isostere

(C) adsorption isotherm (D) all of these

12. Blood may be purified by :

(A) dialysis (B) electro-osmosis (C) coagulation (D) filteration 13. In which of the following, the oxidation number of oxygen has been arranged in increasing order :

(A) BaO2 < O3 < OF2 < KO2 (B) BaO2 < KO2 < O3 < OF2

(C) OF2 < KO2 < BaO2 < O3 (D) KO2 < OF2 < O3 < BaO2

14. On passing 3 ampere of electricity for 50 minutes, 1.9 grams of metal deposits. The equivalent mass of metal is :

(A) 20.5 (B) 25.8 (C) 19.3 (D) 30.7

15. In an electrochemical cell :

(A) Kinetic energy changes into potential energy (B) Chemical energy changes into electrical energy (C) Potential energy changes into kinetic energy (D) Kinetic energy changes into chemical energy 16. One fermi is equal to :

(A) 1015cm (B) 2 10 15cm (C) 1013cm (D) 1012cm 17. Molecular O2 contains two unpaired electrons, they are in :

(A) *and (B) *and (C) *and* (D) *and* 18. The largest bond-angle is in :

(A) AsH3 (B) NH3 (C) H2O (D) PH3

19. Which of the following ionic species has largest size ?

(A) Rb (aq) (B) Li (g) (C) Na (aq) (D) Li (aq)

20. Sodium salt gives bunsen flame the colour :

(A) dull red (B) golden yellow (C) green (D) pink

21. Which one of the following mixed sulphates is not an alum ?

(A) K SO .Cr (SO ) .24H O ₂ ₄ ₂ _{4 3} ₂ (B) Na SO .Al (SO ) .24H O ₂ ₄ ₂ _{4 3} ₂ (C) CuSO .Al (SO ) .24H O 4 2 4 3 2 (D) K SO .Al (SO ) .24H O 2 4 2 4 3 2

22. When silver ore is dissolved in dilute solution of NaCN in the presence of air, which of the following is formed ?

(A) Complex sodium argenticyanide (B) Silver cyanide

(C) Silver oxide (D) Complex sodium argentocyanide

23. IUPAC name of Li[AlH4] is :

(A) lithium aluminium hydride (B) lithium tetrahydro aluminium (III) (C) lithium tetrahydridoaluminate (III) (D) aluminium (III) lithiumhydride

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VMC/ 2010 9 I.P. PRACTICE TEST- 2 24. Which of the following has highest conductivity in water ?

(A) Fe [Fe(CN) ] (B) 3 6 2 K [Fe(CN) ] (C) 3 6 [Ag(NH ) ]Cl (D) 3 2 [Cr(NH ) ]Cl 3 6 6 25. Hydrogen cannot reduce :

(A) hot CuO (B) Fe2O3 (C) hot SnO2 (D) hot Al2O3

26. Which of the following is pseudo halide ?

(A) CN (B) IF5 (C) ICl (D) I3



27. The metaborate which is blue is :

(A) Ni(BO ) _{2 2} (B) Co(BO ) _{2 2} (C) Cr(BO ) _{2 3} (D) NaBO2

28. An ore of tin containing FeCrO4 is concentrated by :

(A) froth-floatation (B) electrostatic method

(C) gravity separation (D) magnetic separation

29. Acidified K2Cr2O7 is turned green by :

(A) SiO2 (B) SO2 (C) CO2 (D) HCl

30. A brick red colour in flame test is given by :

(A) Ca2 (B) Sr2 (C) Ba2 (D) Na 31. The compound (A) and (B) are :

(A) conformational isomers (B) enantiomers

(C) geometric isomers (D) identical molecules

32. During Lassaigne’s test, N and S present in an organic compound, changes into :

(A) Na2S and NaCN (B) Na2SO4 and NaCN

(C) NaSCN (D) Na2S and NaCNO

33. Which FeCl3 is added to a (FeSO4 + sodium extract) solution of compound, blood red colour

appears. It shows the presence of :

(A) N and S in the compound (B) S in the compound

(C) N and P in the compound (D) Br in the compound

34. The reaction,

6 5 3 6 5 3

C H Br2 NaBrCH C H .CH 2NaBr is knows as :

(A) Wurtz reaction (B) Wurtz-Fittig reaction

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35. 3

NaOBr

(A)CHBr

Here (A) is :

(A) isopropyl alcohol (B) n-butyl alcohol

(C) methanol (D) ethanoic acid

36. (CH ) C_{3 3} ClOH (CH ) C_{3 3} OHCl The true statement about the above process is :

(A) The rate becomes four times if the [halide] becomes twice (B) The rate does not change by reducing [OH ] to half (C) The rate does not change by doubling [halide] (D) The rate becomes twice on doubling the [OH ]

37. When phenol is reacted with CHCl3 and NaOH followed by acidification, salicylaldehyde is

obtained. Which of the following species are involved in the above mentioned reaction as intermediate ?

(A) (B) (C) (D) All of these

38. CH₃CHCHCHO [O] CH₃CHCHCOOH The above reaction is completed by the reagent :

(A) alkaline KMnO4 (B) Tollen’s reagent

(C) selenium dioxide (D) osmium tetraoxide

39. The appropriate reagent for the following transformation :

(A) Zn(Hg), HCl (B) NH2NH2, OH (C) H2/Ni (D) NaBH4

40. The product of which of the following reaction is capable of changing orange colour of Cr O₂ ₇2 to green colour of Cr3 : (A) CH (COOH)₂ ₂  (B) CH CN₃ H3O   (C) HCN H3O   (D) 3 2 2 O H CH CONH 

41. Towards electrophilic substitution, the most reactive species will be :

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VMC/ 2010 11 I.P. PRACTICE TEST- 2 42. The reaction: 2 3 2 RNH CHCl 3KOH R N C 3KCl 3H O          (Ethanolic) is called :

(A) Cope reaction (B) Curtius reaction

(C) Hofmann-bromamide reaction (D) Carbylamine reaction 43. Artificial sweetener used in soft drinks, is:

(A) aspartame (B) cellulose (C) fructose (D) glucose

44. The chemical name of aspirin is:

(A) methyl salicylate (B) acetylsalicyclic acid

(C) sodium salicylate (D) salicylic acid

45. Which one of the following compounds is different from the rest?

(A) Sucrose (B) Maltose (C) Lactose (D) Glucose

46. Most reactive carbonyl compound is :

(A) CH COCH ₃ ₃ (B) CH COC H (C) ₃ ₂ ₅ CH CHO 3 (D) C H COC H 2 5 2 5 47. Ketones giving yellow precipitate with 2, 4-dinitrophenyl hydrazine as well as with alkaline iodine

solution are :

I. propanone II. 2-butanone

III. 3-pentanone IV. 2, 2-dimethyl-3-pentanone The correct code is :

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

48. If 2.303RT 0.059

F  and activity of solids are constant, then EMF of the cell

2 2 (aq) 1 2 Zn(s) | Zn  (a ) || Cu (a ) | Cu(s) is : (A) 2 1 a E E 0.059 log a    (B) 1 2 a E E 0.059 log a    (C) 1 2 0.059 a E E log 2 a    (D) 2 1 0.059 a E E log 2 a   

49. The type of isomerism shown by [Co(en) (NCS) ]Cl and ₂ ₂ [Co(en) (NCS)Cl]NCS is : ₂ (A) co-ordination (B) ionisation (C) linkage (D) all of these 50. Calgon used as water softner is :

(A) Na [Na (PO ) ] ₂ ₄ _{3 6} (B) Na₄_Na₂



PO_{3 6}



_ (C) Na [Na (PO ) ] ₂ ₄ _{4 5} (D) Na [Na (PO ) ] ₄ ₂ _{4 6}

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I.P. PRACTICE TEST – 2/2010

SECTION : 3 (MATHEMATICS)

1. Let f :RR g R, : R be two functions given by : 3

( ) 2 3, ( ) 5

f x  x g x  x  Then



fog



1( )x is equal to : (A) 1 3 7 2 / x        (B) 1 3 7 2 / x  _      (C) 1 3 2 7 / x        (D) 1 3 7 2 / x       

2. Suppose f x

  

 x1



2 for x 1.If g(x) is function whose graph is reflection of the graph of

f (x) with respect to the line y = x then g (x) equals : (A)  x 1 ,x0(B)





2 1 1 1 x x     (C) x1,x 1(D) x 1,x0

3. Which of the following is correct :

(A) 1  i 2 i (B) 2  i 1 i (C) 2  i 1 i (D) None of these 4. If ,  , are the roots of x3 3x2 3x 7 0 (where is the cube root of unity), then

1 1 1 1 1 1               is : (A) 3  (B) 2  (C) 22 (D) 32

5. The number of real roots of the equation

2 2 3 6 6 1 1 1 x x x x x        is :

(A) zero (B) 1 (C) 2 (D) None of these

6. If a, b, and c are real numbers such that a2 b2 c2 1 then abbcca lies in the interval : (A) 1 , 2 2       (B)



1, 2



(C) 1 , 1 2 _      (D) 1 1, 2 _     

7. The value of 2 357. is equal to : (A) 2355 1001 (B) 2355 999 (C) 2355 1111 (D) None of these

8. If log2,log(2x 1) and log(2x 3) are in A.P., then value of x is given by : (A) 5

2 (B) log 5 2 (C) log35 (D) log53

9. A question paper is divided into two parts A and B. Each part contains 5 questions. The number of ways in which a candidate can answer 6 questions selecting at least two questions from each part is

(A) 50 (B) 100 (C) 200 (D) None of these

10. The total number of seven digit numbers then sum of whose digits is even is :

(A) 9 10 6 (B) 45 10 5 (C) 81 10 5 (D) 9 10 5

11. The coefficient x6 in the expansion of



1x2 x3



8 is equal to :

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VMC/ 2010 13 I.P. PRACTICE TEST- 2 12. If the absolute term in the expansion of

10 2 5x x   _   

  is 405, then the value of  is :

(A) 1 (B) 2 (C) 3 (D) None of these

13. If l, m, n are pth, qth, rth terms of a G.P., then

1 1 1 log l p log m q log n r is equal to :

(A) pqr (B) lmn (C) 0 (D) None of these

14. The value of the determinant

1 2 3 1 2 3 1 2 3 x x x y y y z z z C C C C C C C C C is equal to: (A) 1



 





10 xyz y z zx x y (B)



 





1 12 x y yz zx (C) 1

 

 



12 xyz x y yz (D)



 





1 12 xyz y z zx x y 15. The number log2 7 is :

(A) an integer (B) a rational (C) an irrational (D) a prime number

16. If 2 3 1 1! 2! 3! x x x y    ... and 2 3 2 3 y y z _y   ...._

  then the value of x is :

(A) log 1



ez



(B) log 1 1 ez      _    (C) log 1





z e  (D) log 1 1 ez      _    17. If 0 1 1 0 A  _  , then A 4 is equal to : (A) 1 0 0 1       (B) 1 1 0 0       (C) 0 0 1 1       (D) 0 1 1 0       18. The matrix 0 1 1 0    

  is the matrix of reflection in the line :

(A) x = 1 (B) y = 1 (C) x + y = 1 (D) x = y

19. The value of the function

 

2 2 3 16 f x sin  x          

lies in the interval :

(A) , 4 4   _      (B) 3 0, 2       (C)



3 3,



(D) None of these 20. 3 5 0 6 x x sin x x lim x                equal to : (A) 0 (B) 1 (C) 1 60 (D) 1 120

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VMC/ 2010 14 I.P. PRACTICE TEST- 2 21. Let g(x) be the inverse of the function f (x) and

 

1 ₃

1 f x x    , then g x

 

is equal to : (A) 1 ₃ 1 ( ( )) g x (B) 3 1 1 ( ( )) f x (C) 3 1 ( ( )) g x (D) 1 ( ( ) ) f x3 22. If ycos1(4x3 3 )x , then dy dx is equal to : (A) 2 3 1x (B) 2 3 1 x   (C) 2 1 x (D) None of these

23. The angle of intersection of the curves x2  y2 2a2and x2  y2 a2 is :

(A) 30 (B) 45 (C) 60 (D) 90

24. Let f x

 

 



1 b2



x2 2bx1and let m(b) be the minimum value of f(x) and b varies, the range of m(b) is : (A) (0, 1) (B) 0 1 2 ,       (C) 1 1 2,       (D) (0,1) 25. 5 55 5 x _x x . . dx  



is equal to : (A) 5 3 5 (log 5) x c  (B) 555 (log 5)3 x c  (C) 5 5 3 5 (log 5) x c  (D) None of these

26.



esec x.sec x3



sin x2 cos xsin x sin x cos x dx



is equal to :

(A) esec x



sec x2 sec x tan x c



(B) esec x c

(C) esec x



sec x tan x



c (D) None of these

27. If

 

4

0

x

g x 



cos t dt, theng x







equals :

(A) g x

 

 g

 

 (B) g x

 

g

 

 (C) f x g

   

 (D)

 

g x g  28. 2 2 2 1 1 n n r r lim n _n _r 



_ _ equal to : (A) 1 5 (B)  1 5 (C)  1 2 (D) 1 2 29. The solution of the differential equation



2x 10y3



dx y 0

dy

   is :

(A) x + y = ce2x (B) y2 = 2x3 + c (C) xy2 = 2y5+c (D) x(y2 + xy) = 0 30. If y = f(x) passing through (1, 2) satisfies the differential equation y



1xy dx



 x dy0, then :

(A) ( ) 2 ₂ 2 x f x x   (B) 2 1 ( ) 1 x f x x    (C) 2 1 ( ) 4 x f x x    (D) 2 4 ( ) 1 x f x x  

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VMC/ 2010 15 I.P. PRACTICE TEST- 2 31. Angle between the lines x2  y2 2y 1 0 is:

(A) 2  (B) 3  (C) 5 12  (D) 5 

32. If t1, t2 and t3 are distinct, the points



t , at1 2 1at13

 

, t22at2 at23



and





3 3 2 3 3 t , at at are collinear if : (A) t1t2t3 = 1 (B) t1 + t2 + t3 = t1t2t3 (C) t1 + t2 + t3 = 0 (D) t1 + t2 + t3 = 1

33. The length of the tangents from any point on the circle 15x2 15y2 48x64y0 to the two circles 5x25y2 24x32y75 0 5x2 5y2 48x64y3000 are in the ratio :

(A) 1 : 2 (B) 2 : 3 (C) 3 : 4 (D) None of these

34. To which of the following circles, the line y  x 3 0is normal at the point 3 3 3 2 , 2        is given by : (A) 2 3 3 3 9 2 2 x y                  (B) 2 2 3 3 9 2 2 x y                 (C) x2 



y3



2 9 (D)



x3



2  y2 9 35. If



a2



x2 9y2 4 represents a rectangular hyperbola ‘a’ equal to :

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

36. The eccentricity of the ellipse 9x2 5y230y0 is equal to :

(A) 1/3 (B) 2 / 3 (C) 3 / 4 (D) None of these

37. The number of values of x in the interval



0 5, 



satisfying the equation

2

3sin x7sin x 2 0is :

(A) 0 (B) 5 (C) 6 (D) 10

38. If



2 12



1 14

2 3

xsin tan , y sin_ tan _

 then :

(A) xyandy2  1 x (B) x y (C) x yand y2 x (D) y2  1 x

39. Volume of the parallelopiped whose sides are OA 2i 3j, OB  i j k , OC3ik is: (A) 4 13 (B) 4 (C) 2 7 (D) 3 7 40. a . a

 

b is equal to : (A) 0 (B) a2 ab (C) a b2 (D) a . b

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VMC/ 2010 16 I.P. PRACTICE TEST- 2 41. The length of the perpendicular from the point with position vector i2j3k to the line



3 4 3

 

2 3 6



r i j k  i j k equal to :

(A) 6 (B) 2 6 (C) 6 2 (D) None of these 42. The equation of the sphere described on the join of (1,2,3) and (3, 4, 5) as a diameter is :

(A) x2y2 z2 4x6y8z260 (B) x2  y2 z2 4x6y8z260 (C) x2  y2 z2 4x6y8z260 (D) x2  y2 z2 4x6y8z260 43. The number 0.0009845 when rounded off to three significant digits yields :

(A) 0.001 (B) 0.000987 (C) 0.000985 (D) None of these

44. The solution of the following system of equations using elimination is :

4 5 x y  z x y 6z 12 3x  y z 4 (A) x = 1, y = 1, z = 10 (B) x = 3, y = 1, z = 12 (C) 117 81 148 71 71 71 x , y   , z (D) None of these

45. Which of the following is not a convex region ?

(A)



 

x y, :x2  y2 1



(B)



 

x y, :x2  y2 1



(C)



 

x y, : 4x2 9y2 36



(D)



 

x y, :y1 and y4



46. A furniture dealer deals in only two items namely tables and chairs. He has Rs. 5,000 to invest and space to store at the most 60 pieces. A table costs him Rs. 250 and a chair Rs. 60. He can steel a table at a profit of Rs. 50 and a chair at a profit of Rs. 15 Assume that he can sell all the items that he produces. The number of constraints in the problem are :

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

47. The maximum and minimum values of z5x2y, subject to the constraints 2x3y6;

2 2 x y ; 6x4y24; 3 x2y3 ; x, y0 are respectively : (A) 18 2 7 ,7 (B) 63 19 13 , (C) 19, 63 (D) 19, 13

48. The mean age of a combined group of mean and women is 30 years. If the mean of the age of men and women are respectively 32 and 27, then the percentage of women in the group is :

(A) 30 (B) 40 (C) 50 (D) 60

49. A probability that a leap year selected at random contains either 53 Sundays or 53 Mondays, is (A) 2 7 (B) 4 7 (C) 3 7 (D) 1 7

50. If a 



20 0,



, then the probability that the graph of the function y16x2 8



a5



x7a5 is strictly above the x-axis is :

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VMC/ 2010 17 I.P. PRACTICE TEST- 2 ANSWERS FOR I.P. PRACTICE TEST – 2

PHYSICS 1 2 3 4 5 6 7 8 9 10 C B C B C B D C C D 11 12 13 14 15 16 17 18 19 20 A A A B B A A B A B 21 22 23 24 25 26 27 28 29 30 C D D C B A A B A B 31 32 33 34 35 36 37 38 39 40 B A A C C A A A A A 41 42 43 44 45 46 47 48 49 50 C A C C B D B B A A CHEMISTRY 1 2 3 4 5 6 7 8 9 10 A A B A C A B C B A 11 12 13 14 15 16 17 18 19 20 C A B C B C D B D B 21 22 23 24 25 26 27 28 29 30 C D C D D A B D B A 31 32 33 34 35 36 37 38 39 40 B C A B A C B B B C 41 42 43 44 45 46 47 48 49 50 B D A B D C D C B A MATHEMATICS 1 2 3 4 5 6 7 8 9 10 D D D D D C B B C B 11 12 13 14 15 16 17 18 19 20 B C C D C B A D B D 21 22 23 24 25 26 27 28 29 30 C B C A C C A B C A 31 32 33 34 35 36 37 38 39 40 A C A D C B C A B A 41 42 43 44 45 46 47 48 49 50 C D C C B C B B C D