Ip entrance test paper 1

I.P. PRACTICE TEST
SECTION : 1 (PHYSICS)
1. The radius of nucleus is r  r0 A1 / 3 , where A is mass number. The dimensions of r0 is :
(A)  2 
(B)  M 0 L0T 1  (C)  M 0 LT 0  (D) None of these
 MLT     
2. The resultant of two vectors P and Q is R . If the vectors Q is reversed, then the resultant
becomes S , then choose the correct option.
(A) 
R2  S 2  2 P2  Q2  (B) 
R2  S 2  2 P2  Q2 
(C) 
R2  S 2  P2  Q2  (D) R2  S 2  2 P 2
Q  2

3. If a particle is moving on an elliptical path given by r  bcos t ˆ  a sin t ˆ , then find its radial
i j
acceleration along r
(A) r (B) 2 r (C)  2 r (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.
A B
Pulleys A and B are fixed. The mass m moves upwards with a
speed
 
u
(A) 2u cos  (B)
cos  P Q
u M u
2u
(C) (D) u cos 
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

VMC/ 2010 1 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 :
3R 4R
(A) from centre (B) from centre
 2
5R 7R
(C) from centre (D) from centre
 5
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) v0

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 :
12
(A) gl (B) 3 gl
5
16
(C) gl (D) 2 gl
5
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


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 ?
l  l 
(A) T  2   (B) T  2  2 2
 g  a0  g 

 l   l 
(C) T   2 2
(D) T  2  2 2
 a0  g   a0  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  107 N / m2 and area of cross-section of a wire = 106 m2 )
(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 ex , ey and ez respectively. Then the volumetric strain
is given by :
ex  ey
(A) ex ey ez (B) ex  ey  ez (C) ez  ex ey (D) ez 
2
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3 s apart will be :
 
(A)  radian (B) radian (C) radian (D) 2 radian
2 4
20. Figures shows the vibrations of four air coloumn. The ratio of frequencies n p :nq : nr : ns is :

(A) 12 : 6 : 3 : 4 (B) 1:2:4:3 (C) 4:2:3:1 (D) 4:3:2:1


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 :
1 1  15 
(A) 15 km / s (B) 10 km / s (C) 2.5 km/s (D)  2  km / s
2 2  
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 :
1
(A) PV (B) PV
2
(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)
L L  Lh 2  Lh 2
(A) t h2 (B) t h2 (C) t (D) t
2 KT KT 3KT 4 KT
27. What amount of ice at 14C , required to cool 200 g of water from 25C to 10C ?
(Given : Cice  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  1010 cm / s )
(A) 3  1010 sec (B) 2.22  106 sec (C) 4.3  105 sec (D) 3  106 sec
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 :
(A) nI 0 (B) n2 I 0 (C) n3 I 0 (D) I0 / n


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 :
qQ q2
(A) (B) zero (C) (D) None of these
4 0 R 2 4 0 R
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  1013 V / m (B) 0.177  1013 V / m
(C) 17.7  1013 V / m (D) 177  1013 V / m
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 :
4 0 Kr1 r2
(A) (B) 4 0  r2  r1 
r2  r1
(C) 4 0 r2 (D) 40 r1
35. An air filled parallel plate capacitor has a capacitance of 1012 F . The separation of the plates is
doubled and wax is inserted between them, which increases the capacitance to 2  1012 F . 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
1
37. The dimension of are same as :
0  0
E B E2  E
(A) (B) (C) (D)  B
B E B 2
 
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3 N (B) 103 N (C) 10  103 N (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  


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 :
10 5
(A) 10 A (B) A (C) A (D) None of these
2 2
42. An alternating voltage : V  30 sin 50t  40 cos 50t is applied to a resistor of
resistance 10 . The rms value of current through resistor is :
5 10 7
(A) A (B) A (C) A (D) 7A
2 2 2
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 :
1 v v mv
(A) (B) (C) (D)
4 4 4 m 4
46. The binding energy expressed in MeV is given for the following nuclear reactions

2 He
3
 0 n1  2 He4  20MeV
 2 He
4
 0 n1  2 He5  0.9MeV

Which of the following conclusion is correct ?
4 3 5
(A) 2He is less stable than both 2He and 2He
4 3 5
(B) 2He is less stable than both 2He but more stable than 2He
4 5 3
(C) 2He is less stable than 2He but more stable than 2He
4 3 5
(D) 2He is more stable than both 2He and 2He

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

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 :
(A) colour (B) pressure (C) distance from earth (D) mass


I.P. PRACTICE TEST
SECTION : 2 (CHEMISTRY)

1. The last unpaired electron of chlorine has quantum number values as :
n l m s
1 1
(A) 3 2 1  (B) 3 1 +1 
2 2
1 1
(C) 3 1 2  (D) 3 0 0 
2 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7 c.c. Calculate the number of molecules in it :
(A) 3.01  1020 (B) 3.01  1012 (C) 3.01  1023 (D) 3.01  1024
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 Hcomb. 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1 sec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 :
(A) first order (B) zero order (C) second order (D) third order


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15 cm (B) 2  1015 cm (C) 1013 cm (D) 1012 cm
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) K2SO4 .Cr2 (SO4 )3 .24H2O (B) Na 2SO4 .Al2 (SO4 )3 .24H2O
(C) CuSO4 .Al2 (SO4 )3 .24H2O (D) K2SO4 .Al2 (SO4 )3 .24H2O
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


24. Which of the following has highest conductivity in water ?
(A) Fe3[Fe(CN)6 ]2 (B) K3[Fe(CN)6 ] (C) [Ag(NH3 )2 ]Cl (D) [Cr(NH3 )6 ]Cl6

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(BO2 )2 (B) Co(BO2 )2 (C) Cr(BO2 )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) Ca 2 (B) Sr 2 (C) Ba 2 (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,
C6 H5Br  2 Na  BrCH3  C6 H5 .CH3  2NaBr

is knows as :
(A) Wurtz reaction (B) Wurtz-Fittig reaction
(C) Friedal-Craft reaction (D) Berthelot synthesis


NaOBr
35. (A)  CHBr3

Here (A) is :
(A) isopropyl alcohol (B) n-butyl alcohol
(C) methanol (D) ethanoic acid
36. (CH3 )3 C  Cl  OH  (CH3 )3 C  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

[O]
38. CH3  CH  CH  CHO  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 Cr2 O7 2 to
green colour of Cr 3 :
 H O
(A) CH2 (COOH)2 
 (B) CH3CN 
3

H O H O
(C) HCN 
3
 (D) CH3CONH2 
2


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

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


42. The reaction:
 
RNH 2  CHCl3  3KOH  R  N  C 3KCl  3H 2O

(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) CH3COCH3 (B) CH3COC2 H5 (C) CH3CHO (D) C2 H5COC2 H5

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

2.303RT
48. If  0.059 and activity of solids are constant, then EMF of the cell
F
Zn(s) | Zn (aq) (a1 ) || Cu 2 (a 2 ) | Cu(s) is :
2

a2 a1
(A) E  E  0.059 log (B) E  E  0.059 log
a1 a2
0.059 a1 0.059 a2
(C) E  E  log (D) E  E  log
2 a2 2 a1
49. The type of isomerism shown by [Co(en)2 (NCS)2 ]Cl and [Co(en)2 (NCS)Cl]NCS is :
(A) co-ordination (B) ionisation (C) linkage (D) all of these

50. Calgon used as water softner is :
(A) Na 2 [Na 4 (PO3 )6 ] (B) Na 4  Na 2  PO3 6 
 
(C) Na 2 [Na 4 (PO4 )5 ] (D) Na 4 [Na 2 (PO4 )6 ]


I.P. PRACTICE TEST
SECTION : 3 (MATHEMATICS)
1. Let f : R  R, g : R  R be two functions given by :
f ( x)  2 x  3, g ( x)  x3  5 Then  fog  ( x) is equal to :
1

1/ 3 1/ 3 1/ 3 1/ 3
 x  7  7  x  2  x  7
(A)  2  (B) x  2 (C)  7  (D)  2 
       
Suppose f  x    x 1 for x   1. If g(x) is function whose graph is reflection of the graph of
2
2.
f (x) with respect to the line y = x then g (x) equals :
1
(A)  x  1 , x  0 (B) 
x   1 (C) x  1, x   1 (D) x  1, x  0
 x  12
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
  is :
 1  1  1
3
(A) (B) 2 (C) 2 2 (D) 3 2

2x  3 6 x2  x  6
5. The number of real roots of the equation 1 is :
x 1 x 1
(A) zero (B) 1 (C) 2 (D) None of these

6. If a, b, and c are real numbers such that a 2  b2  c2  1 then ab  bc  ca lies in the interval :
1   1   1
(A)  2 , 2 (B) 1, 2 (C)   2 , 1 (D)  1, 2 
     
7. The value of 2.357 is equal to :
2355 2355 2355
(A) (B) (C) (D) None of these
1001 999 1111
8. If log2,log(2x  1) and log(2 x  3) are in A.P., then value of x is given by :
5
(A) (B) log 2 5 (C) log35 (D) log53
2
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  106 (B) 45  105 (C) 81  105 (D) 9  105

 
8
11. The coefficient x6 in the expansion of 1 x 2  x3 is equal to :
(A) 80 (B) 84 (C) 88 (D) 92


 
10

12. If the absolute term in the expansion of  5x  2  is 405, then the value of  is :
 x 
(A) 1 (B) 2 (C) 3 (D) None of these
log l p 1
13. If l, m, n are pth, qth, rth terms of a G.P., then log m q 1 is equal to :
log n r 1
(A) pqr (B) lmn (C) 0 (D) None of these
x x x
C1 C2 C3
y y y
14. The value of the determinant C1 C2 C3 is equal to:
z z z
C1 C2 C3
1 1
(A) xyz  y  z   z  x  x  y  (B)  x  y   y  z  z  x 
10 12
1 1
(C)  xyz  x  y   y  z  (D) xyz  y  z   z  x  x  y 
12 12
15. The number log2 7 is :
(A) an integer (B) a rational (C) an irrational (D) a prime number

x x 2 x3  y2 y3 
16. If y  1     ... and z    y 
   .... then the value of x is :

1! 2! 3!  2 3 
 1   1 
(A) 
log 1  e z  (B) log 
 1  ez 
 (C) 
log 1  e z  (D) log 
 1  ez 

   
0 1 
If A   , then A4 is equal to :
1 0
17.
 
1 0  1 1  0 0 0 1 
(A) 0 1  (B) 0 0 (C) 1 1  (D) 1 0 
       
0 1 
18. The matrix   is the matrix of reflection in the line :
1 0 
(A) x=1 (B) y=1 (C) x+y=1 (D) x=y

 2 
19. The value of the function f  x   3 sin   x 2  lies in the interval :
 16 
 
    3 
(A)  4 , 4  (B) 0,  (C)  3 , 3 (D) None of these
   2
 x3 
 sin x  x  
20. lim  6  equal to :
x 0  x5 
 
 
1 1
(A) 0 (B) 1 (C) (D)
60 120


1
21. Let g(x) be the inverse of the function f (x) and f   x   , then g   x  is equal to :
1  x3
1 1
(A) (B) (C) 1 ( g ( x))3 (D) 1  ( f ( x)3 )
1 ( g ( x))3 1 ( f ( x))3
dy
22. If y  cos 1 (4 x3  3x) , then is equal to :
dx
3 3
(A) (B)  (C) 1 x 2 (D) None of these
1 x 2
1  x2
23. The angle of intersection of the curves x2  y 2  2a2 and x2  y 2  a2 is :
(A) 30 (B) 45 (C) 60 (D) 90
24. Let f  x   1 b  2
x 2
 2bx  1 and let m(b) be the minimum value of f(x) and b varies, the range
of m(b) is :
 1 1 
(A) (0, 1) (B)  0,  (C)  ,1 (D) (0,1)
 2 2 
x

x
25. 5 .55 .5x dx is equal to :
x 5x
55 55
x
55
(A) c (B) 5 (log5)3  c (C) c (D) None of these
(log 5)3 (log 5)3
26. e
sec x

.sec3 x sin2 x  cos x  sin x  sin x cos x dx is equal to : 
(A) esec x  sec 2
x  sec x tan x c  (B) esec x  c

(C) esec x  sec x  tan x   c (D) None of these
x
27. If g  x   cos 4 t dt , then g  x    equals :

0

g  x
(A) g  x   g   (B) g  x   g   (C) f  x  g   (D)
g  
1 2n

r
28. lim equal to :
n n r  1 n2  r 2

(A) 1 5 (B) 1  5 (C) 1  2 (D) 1 2

29. The solution of the differential equation 2 x  10 y 3   dy  y  0 is :
dx

(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 :
2x x 1 x 1 4x
(A) f ( x)  (B) f ( x)  (C) f ( x)  (D) f ( x) 
2  x2 x2  1 4  x2 1  x2


31. Angle between the lines x2  y 2  2 y  1  0 is:
  5 
(A) (B) (C) (D)
2 3 12 5
32.     
If t1, t2 and t3 are distinct, the points t1 , 2at1  at1 , t2 2at2  at2 and t3 ,2at3  at3 are
3 3 3

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  15 y 2  48x  64 y  0 to the two
circles 5x2 5 y 2  24 x  32 y  75  0 5x2  5 y 2  48x  64 y  300  0 are in
the ratio :
(A) 1:2 (B) 2:3 (C) 3:4 (D) None of these
 3 3 
34. To which of the following circles, the line y  x  3  0 is normal at the point  3  ,  is
 2 2
given by :
2 2 2
 3   3   3   3 
(A) x  3   y   9 (B) x   y   9
 2  2  2  2
x 2   y  3  9  x  3 2  y 2  9
2
(C) (D)
35. If  a  2  x2  9 y 2  4 represents a rectangular hyperbola ‘a’ equal to :
(A) 0 (B) 2 (C) 1 (D) 3

36. The eccentricity of the ellipse 9 x2  5 y 2  30 y  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
3 sin2 x  7 sin x  2  0 is :
(A) 0 (B) 5 (C) 6 (D) 10

38.   1 4
If x  sin 2 tan 1 2 , y  sin  tan 1  then :
2 3
(A) x  y and y 2  1  x (B) x y
(C) x  y and y 2  x (D) y2  1  x

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

(A) 0 (B) a 2  ab (C) a 2b (D) a .b


41. The length of the perpendicular from the point with position vector i  2 j  3k to the line

   
r  3i  4 j  3k   2i  3 j  6k 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  y 2  z 2  4 x  6 y  8z  26  0 (B) x2  y 2  z 2  4 x  6 y  8z  26  0
(C) x2  y 2  z 2  4 x  6 y  8z  26  0 (D) x2  y 2  z 2  4 x  6 y  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 :
x  4y  z   5 x  y  6 z   12 3x  y  z  4
(A) x = 1, y = 1, z = 10 (B) x = 3, y = 1, z = 12
117 81 148
(C) x , y   , z (D) None of these
71 71 71
45. Which of the following is not a convex region ?
(A)  x, y  : x  y  1
2 2
(B)  x, y  : x 2
 y2  1 
(C)  x, y  : 4x  9 y  36
2 2
(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  2 y , subject to the constraints 2 x  3 y  6 ;
x  2 y  2 ; 6 x  4 y  24 ; 3x  2 y  3 ; x, y  0 are respectively :
18 2 63
(A) , (B) 19, (C) 19, 63 (D) 19, 13
7 7 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
2 4 3 1
(A) (B) (C) (D)
7 7 7 7
50. If a   20 , 0 , then the probability that the graph of the function y  16 x  8  a  5 x  7a  5
2

is strictly above the x-axis is :
(A) 1/2 (B) 1 / 17 (C) 17 / 20 (D) None of these


ANSWERS FOR I.P. PRACTICE TEST

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


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Ip entrance test paper 1