Physics Chemistry Mathematics IITJEE Test

Vidyamandir Classes

I.P. PRACTICE TEST – 2/2010 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.

 MLT 2   

 M 0 L0T 1   

(B)

(C)

 M 0 LT 0   

(D)

None of these

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.

3.



(A)

R2  S 2  2 P2  Q2

(C)

R 2  S 2  P2  Q2







  2 P

 Q 

(B)

R2  S 2  2 P2  Q2

(D)

R2  S 2

2

2

If a particle is moving on an elliptical path given by r  bcos t ˆi  a sin t ˆj , then find its radial acceleration along r (A)

4.

5.

6.

r

(B)

2 r

(C)

 2 r

(D)

None of these

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 2u cos  (A) (B) Q P cos  u u M 2u (C) (D) u cos  cos  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 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

Vidyamandir Classes 7.

In circular motion : (A) Radial acceleration is non-zero (C) Body is in equilibrium

(B) (D)

Radial velocity is zero 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 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) (B) v0  r v0  r

11.

(C) 12.

(D)

v0

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

16

gl 2 gl (D) 5 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) 13.

r

(C)

VMC/ 2010

W1  W3  W2

(D)

None of these

2

I.P. PRACTICE TEST- 2

Vidyamandir Classes 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)

l T  2    g

(B)

  l T  2  2 2  a0  g 

(C)

  l T   2 2  a0  g 

(D)

  l T  2  2 2  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)

18.

4 rad/s

(B)

8 rad/s

(C)

1 rad/s

(D)

2 rad/s

The linear strain in x, y and z-directions are ex , ey and ez respectively. Then the volumetric strain is given by : (A)

19.

ex ey ez

(B)

ex  ey  ez

(C)

ez  ex ey

(D)

ez 

ex  ey

2 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 :

20.

(A)

 radian

(B)

(A)

12 : 6 : 3 : 4

(B)





2 radian radian (D) 2 4 Figures shows the vibrations of four air coloumn. The ratio of frequencies n p :nq : nr : ns is :

VMC/ 2010

radian

(C)

1:2:4:3

(C)

3

4:2:3:1

(D)

4:3:2:1

I.P. PRACTICE TEST- 2

Vidyamandir Classes 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 1 to 30C , then how much time does the clock lose or gain in one week ?  steel  1.2  105  C     (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 2

15 km / s

(B)

1 2

(C)

10 km / s

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) (C)

26.

27.

28.

1

PV 2 2PV

(B)

PV

(D)

4PV

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)

t

(A)

31 g

L

h2

L

(B)

t

(B)

41 g

h2

 Lh 2

(C)

t

(C)

51 g

 Lh 2

(D)

t

(D)

21 g

2 KT KT 3KT 4 KT 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)

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)

VMC/ 2010

nI 0

(B)

n2 I 0

(C)

4

n3 I 0

(D)

I0 / n

I.P. PRACTICE TEST- 2

Vidyamandir Classes 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)

32.

qQ

(B)

4 0 R 2

zero

(C)

q2

(D)

4 0 R

None of these

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)

35.

4 0 r2

(D)

4 0 r1

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

36.

37.

dielectric constant of wax is : (A) 2 (B)

3

What is R ? (A) 42

(B)

62

(C)

(D)

None of these

The dimension of

(A) 38.

40.

1

0  0

E

(B)

4

(D)

8

are same as : B

(C)

E2

 E  B 

(D)

2

B B E 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) 39.

84

(C)

0.25  103 N

(B)

103 N

An atom is paramagnetic if it has : (A) an electric dipole moment (C) a magnetic moment

(C)

10  103 N

(B) (D)

no magnetic moment no electric dipole moment

(D)

None of these

The formula used for calculating induced emf in a rod moving in a uniform magnetic field is : (A)

VMC/ 2010



eB . 1 v



(B)



e B . 1 .v



5

(C)



e B  1 .v



(D)



eB  1 v



I.P. PRACTICE TEST- 2

Vidyamandir Classes 41.

An A.C. source of voltage V = 100 sin100 t is connected to a resistor of resistance 20 .

42.

The rms value of current through resistor is : 10 5 (A) 10 A (B) (C) A A 2 2 An alternating voltage : is V  30 sin 50t  40 cos 50t

(D) applied

None of these to

a

resistor

of

resistance 10 . The rms value of current through resistor is : (A)

5

(B)

10

(C)

7

43.

(D) A 2 2 2 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

A

A

7A

 - particle   all having the same energy of MeV, in the increasing order will follow the

sequence e ,  p , n ,  (B) (A) 45.

1

(B)

v

v

(C)

(D)

mv

 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 Half-life period of a given radioactive sample is  . Its average life would be : (A)

48.

 p , e ,  , n

4 4 4 m 4 The binding energy expressed in MeV is given for the following nuclear reactions 3 2 He

47.

e , n ,  p ,  (D)

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)

46.

 , n ,  p , e (C)

 ln 2

(B)

What does it represent ? (A) OR (B) (C) NAND (D)



(C)

ln 2

1



ln 2



AND 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)

VMC/ 2010

(D)

6

distance from earth

(D)

mass

I.P. PRACTICE TEST- 2

Vidyamandir Classes

I.P. PRACTICE TEST – 2/2010 SECTION : 2 (CHEMISTRY) 1.

2.

3.

The last unpaired electron of chlorine has quantum number values as : n l m s (A)

3

2

1



(C)

3

1

2



2 1

2

1

(B)

3

1

+1



(D)

3

0

0



(D)

Cu(NO3)2

The nitrate which does not give NO2 on heating : (A) NaNO3 (B) Pb(NO3)2 (C)

AgNO3

2 1

2

Volume of gas at NTP is 1.12  107 c.c. Calculate the number of molecules in it : (A)

4.

1

3.01  1020

(B)

3.01  1012

Monoclinic crystal has dimension : (A) a  b  c ;     90,   90 (C)

a  b  c ;       90

(C)

3.01  1023

(B)

a  b  c ;       90

(D)

a  b  c ;       90

(D)

3.01  1024

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

7. 8. 9.

respectively. The heat of formation of CH4 is : (A) (B) 71.8 kJ / mol (C) 70 kJ / mol

244 kJ / mol

The pH of pure water at 80C will be : (A) >7 (B)