vriti iit part test 2_paper i test paper

7/28/2019 Vriti IIT Part Test 2_Paper I Test Paper

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DEXL | IIT-JEE PARTTEST 2 (PAPERI)

CHEMISTRY

SECTION ISingle Correct Choice Type

This section contains 8 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer,

out of which ONLY ONE is correct.

1. Find the molality of a solution containing a nonvolatile if the vapour pressure is 2% below the vapour

pressure of pure water:

(A) 1.1326 (B) 2.492 (C) 3.562 (D) 4.090

2. The ratio of activities of two radio nuclides X and Y in a mixture at time t = 0 was found to be 4 : 1. After two

hours, the ratio of activities become 1 : 1. If the t 1/2 of radio nuclide X is 20 min then t1/2 [in minutes] of radio

nuclide Y is

(A) 10 (B) 20 (C) 30 (D) 40

3. To make the crystal lattice structure MO2; metal ions are arranged as face centred cubic lattice. The oxide ions

are arranged in all tetrahedral voids. The total number of ions present in unit cell are :

(A) 3 (B) 6 (C) 12 (D) 10

4. The acidic hydrolysis of thioacetamide takes place as

||

3 2 2 2 3 2

S

CH C NH H O H S CH CONH + +Its rate law is; rate = k[H+] [CH3CSNH2]. If some amount of solid NaOH is added to the 0.1 M thioacetamide

and H+ ion solution at 298 K, then

(A) the reaction rate and rate constant remains constant.

(B) the reaction rate and rate constant both increases.

(C) the reaction rate decreases, and rate constant remains constant.

(D) the reaction rate increases and rate constant remains constant.

Space for Rough Work

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IIT-JEE PARTTEST 2 (PAPERI) | DEXL

5. 1 gm of radium is known to emit 3.7 1010 particles/ sec. The half life of radium is:[given: atomic weight of Ra = 226]

(A) 3 1010 sec (B) 5 1010 sec (C) 4.9 1011 sec (D) 3.9 1010 sec.

6. A sample of 16 g charcoal was brought into contact with a CH4 gas contained in a vessel of 1 litre at 27C. The

pressure of gas was found to fall from 760 to 608 torr. The density of charcoal sample is 1.6 g/cm3

. What is thevolume of the CH4 gas adsorbed per gram of the adsorbent at 608 torr and 27C?

(A) 125 mL/g (B) 16.25 mL/g (C) 26 mL/g (D) 30.75 mL/g

7. A body centered cubic lattice is made up of hollow spheres of B. Spheres of solid A are present in hollow

spheres of B. Radius A is half of radius of B. What is the ratio of total volume of spheres of B unoccupied by

A in a unit cell and volume of unit cell

(A)7 3

64

(B)

7 3

128(C)

7

24

(d) none of these

8. One gram of activates carbon has a surface area of 1000 m2. Considering complete coverage as well as

monomolecular adsorption, how much ammonia at STP would be adsorbed on the surface of 447

g carbon if

radius of ammonia molecules is 108 cm. [NA = 6 1023]

(A) 7.46 L (B) 0.33 L (C) 44.8 L (D) 23.5 L

SECTION II

Multiple Correct Choice Type


out of which ONE OR MORE is/are correct.

9. Select the correctstatement :(A) Law of mass action and rate law expression are same for elementary process.

(B) Order of a complex reaction is determined by the slowest elementary process of the mechanism.

(C) Order of reaction 2H2O2 2H2O + O2; is two(D) The factor /aE RTe

refers to the effective collisions.



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10. Which of the following is/are correctfor CsCl type crystal:

(A) It is ideal BCC structure.

(B) Cs+ and Clboth ions forms a simple cubic lattice which inter penetrate each other.

(C) Cs+ ions are at the body centre of Cl unit cell

(D) Cl ions are at the body centre of Cs+ unit cell.

11. The capacity of an ion to flocculate the colloidal solution depends upon:

(A) amount of its charge (B) type of its charge (C) its shape (D) None of these

12. The correct starting material and end product of different disintegration series are

(A)232 208Th, Pb (B) 235 206U, Pb (C) 38 207U, Pb2 (D) 237 209Np, Bi

SECTION III

Comprehension Type

This section contains 2 groups of questions. Each group has 3 multiple choice questions based on a paragraph.Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONLY ONE is correct.

Paragraph for Questions Nos. 13 to 15A vessel contains gaseous dimethylether at initial pressure p 0 atm. Dimethyl ether decomposes on heating as per

the reaction by first order kinetics.

CH3 O CH3(g) CH4(g) + CO(g) + H2(g)

It is observed that the halflife period for this reaction is 0.2 hour. After a very long time, pressure in the vessel is

observed to be 1.2 atm. Assume ideal behaviour of all gases with constant VT conditions.

13. What would be the approximate pressure in the vessel at 0.6 hour? [log108 0.9](A) 0.05 atm (B) 1.5 atm (C) 2.303 atm (D) 1.1 atm

14. The initial rate of formation of CH4 gas is

(A) 1.386 atm h1 (B) 0 (C) 2.07 atm h1 (D) 1.4 atm h1

15. The approximate molar ratio of gases at 0.6 hour and at zero hour is :

(A) 11: 4 (B) 4 : 11 (C) 7 : 8 (D) 8 : 7



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Paragraph for Questions Nos. 16 to 18Two completely miscible liquid makes a homogeneous solution of single phase. When such solution is kept in a

closed evacuated vessel, the total pressure exerted by vapour is the sum of partial pressure of constituents. If solution

is ideal it will follow Raoults law and partial pressure of each component is given bypi =

o

i ip x , xi = mole fraction of constituent,o

ip = vapour pressure of pure constituent.

Change in thermodynamic function when ideal solution is formed by mixing pure components is

ln lnmix i i total i ii i

G n RT X n RT X X = = lnmix total i i

i

S n R X X = ln ln = mix total i i total i i

i i

H n RT X X n R X X = a

Umix = 0As both the components are making ideal solution Raoults law is applicable over entire range of solution and partial

pressure exerted by vapours can be calculated and also the composition of vapours can be determined by DaltonsLaw.

16. Two liquids A and B makes an ideal solution at T K. When the total vapour pressure above the solution is 600 torr,

XA in vapour phase is 0.35. Calculate &o o

A Bp p . Given : XA in liquid is 0.70.

(A) 800 torr, 300 torr (B) 300 torr, 1300 torr (C) 1300 torr, 300 torr (D) 300 torr, 800 torr

17. One mole of pure nC6H14 and two moles of nC7H16 are mixed at 27oC to form an ideal binary solution.

&mix mixG S are(A) 2065 J. and 6.88 J K1 (B) 1585.38 J & 5.28 J K1 (C) 1585 J & 5.28 J K1 (D) 2065 J & 6.88 J K1

18. A and B makes ideal solution. At what mole fraction of A and B, Gibbs free energy of mixing is minimum(A) XA = XB = 0.5 (B) XA = XB = 1 (C) XA = XB = 0.75 (D) XA = XB = 0.66



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SECTION IVMatrix-Match Type

This section contains 2 questions. Each question contains statements given in two columns, which have to be

matched. The statements in Column I are labelled A, B, C and D, while the statements in Column II are labelled p,

q, r, s and t. Any given statement in Column I can have correct matching with ONE OR MORE statement(s) inColumn II. The appropriate bubbles corresponding to the answers to these questions have to be darkened as

illustrated in the following example: If the correct matches are A p, s and t; B q and r; C p and q; and D s

and t; then the correct darkening of bubbles will look like the following.

19. Match the questions in Column I with their answers in Column II.

Column I Column II

(A) The edge length of unit cell of NaCl (in pm); If the distance

between Na+ and Cl is 265 pm

75

(B) A certain compound A tetramerises in water to the extent

80%. Its 2.5 gm in 100 gm H2O lowers the freezing point by

0.3 oC. Its molar mass is [kf(H2O) = 1.86 K kg mol1].

(q) 530

(C) A and B are two identical vessels. A contains 15g of ethane at

298 K and 1 atm. The vessel B contains 75 g gas X 2 at the

same temperature and pressure. The vapour density of X2 is

20

(D) Two liquids A and B have vapour pressure in the ratio

: 1: 2=o oA B

p p at a certain temperature. Suppose that we have

an ideal solution of A and B in the mole fraction ratio A : B =

1 : 2, the mole % of A in the vapour in equilibrium with the

solution at the given temperature is

62



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20. Match the questions in Column I with their answers in Column II

Column I Column II

(A) Thermal decomposition of a compound is of first

order. If 50% of a sample of the compound isdecomposed in 120 minute show long will it take

for 90% of the compound to decompose in minutes

(p) 363.5

(B) Two organic liquids A and B have vapour pressure

1 2&o op p at 80oC in their pure states. A mixture of

the two boils at 80oC and shows ideal behaviour. It

has mole fraction of A = 0.16. If 2 1o op p = 472

mm; than 1op will be

(q) 2736

(C) What mass of sugar (Mo = 342) must be dissolved

in 4.0 Kg of H2O to yield a solution that will freeze

at 3.72C (Take kf= 1.86/m)

(r) 254

(D) At 45C the vapour pressures in torr, of methyl

alcoholethyl alcohol solutions is represented by

the equation. P = 119 XA + 135; where XA is

molefraction of methyl alcohol in solution phase,

then the value of the value of3

o

CH OHp is

(s) 399



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MATHEMATICS




21. If m and n are positive integers and f(x) = ( ) ( )x

2n 2m 1

1

t a t b dt+ , a b, then

(A) x = b is a point of local minimum (B) x = b is a point of local maximum

(C) x = a is a point of local minimum (D) x =a is a point of local maximum

22. The solution of x2dy y2dx + xy2 (x y)dy = 0 is

(A)

2

x y yln cxy 2 = + (B)

2

xy xln cx y 2

= +

(C)

2

x y xln cxy 2 = + (D) x yln y c

xy = +

23. The value of

1/ 2

x 1

2 3 /2

0

xe sin x dx

(1 x )

is

(A)e 2

6 3 3

(B)

2e 1

6 3

+

(C)e 4

6 3 3

(D) 0

24. F : R R, f(x) = sin x + x, then the value of 1

0

(f (x))dx

is equal to

(A)2

22

+ (B)

2

22

(C) 2 (D) cant be evaluated



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25. The area bounded by y = x2 + 2 and y = 2|x| cos x is equal to

(A)1

3

(B)2

3

(C)4

3

(D)8

326. If the straight lines a1x + b1y + c1 = 0, a1x + b1y + c2 = 0, a2x + b2y + d1 = 0, a2x + b2y + d2 = 0 are the sides of

rhombus then :

(A)2 2 2 2 2 2

2 2 1 2 1 1 1 2(a b )(c c ) (a b )(d d )+ = + (B) 2 2 2 21 1 1 2 2 2 1 2(a b ) | d d | (a b ) | c c |+ = +

(C)2 2 2 2

2 2 1 2 1 1 1 2(a b )(d d ) (a b )(c c )+ = + (D) 2 2 2 21 1 1 2 2 2 1 2(a b ) | c c | (a b ) | d d |+ = +

27. A point P moves inside a triangle formed by A(0, 0), B(1, 3) , C(2, 0) such that

min{PA, PB, PC} = 1, then the area bounded by the curve traced by P is

(A)

3

3 3 2

(B) 3 2

(C)3

3 3 2

+ (D) 3 2

+28. The range of values of for which the line 2y = gx + is a normal to the circle x2 + y2 + 2gx +2g y 2 = 0 for

all values of g is

(A) [1, ) (B) [1, ) (C) (0, 1) (D) ( , 1]

SECTION IIMultiple Correct Choice Type



29. Let f(x) =

x

0

| 2t 3 | dt . Then f is



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(A) Continuous at3

x2

= (B) Continuous at x = 3

(C) Differentiable at3

x2

= (D) Differentiable at x = 0

30. The equation(s) of the tangent at the point (0, 0) to the circle, making intercepts of length 2a and 2b units on

the coordinate axes, is/are

(A) ax + by = 0 (B) ax by = 0 (C) x = y (D) None of these

31. Let ax + by + c = 0 be a variable straight line, where a, b and c are 1st, 3rd and 7th term of some increasing A.P.

Then the variable straight line always passes through a fixed point which lies on

(A) x2 + y2 = 13 (B) x2 + y2 = 5 (C)2 9

y x2

= (D) 3x + 4y=9

32. For the differential equation y = edy/dx

(A) Order is not defined (B) Order is 1 (C) Degree is undefined (D) Degree is 1

SECTION III

Comprehension Type

This section contains 2 groups of questions. Each group has 3 multiple choice questions based on a paragraph.

Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONLY ONE is correct.

Paragraph for Questions Nos. 33 to 35

Equation of the circumcircle of a triangle formed by the lines L 1 = 0, L2 = 0 and L3 = 0 can be written as L1L2 +

L2L3 + L3L1 = 0, where and are such that coefficient of x2 = coefficient of y2 and coefficient of xy = 0.

33.2 2 2

1 2 2 3 3 1L L L L L L 0+ + = represent(A) a curve passing through point of intersection of L1L2 and L3

(B) a circle if coefficient x2 = coefficient y2 and coefficient of xy = 0

(C) a parabola (D) pair of straight lines



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34. L1 = 0, L2 = 0 be the distinct parallel lines L3 = 0 and L4= 0 be two other distinct parallel lines which are not

parallel to L1 = 0. The equation of a circle passing through the vertices of the parallelogram formed must be of

the form

(A) L1L4 + L2L3 = 0 (B) L1L3 + L2L4 = 0 (C) L1L2 + L3L4 = 0 (D) L12 L3 + L22L4 = 0

35. If L1L2 + L2L3 + L3L1 = 0 is such that = 0 and is nonzero, then it represents(A) a parabola (B) a pair of straight lines(C) a circle (D) an ellipse

Paragraph for Questions Nos. 36 to 38Let C1 : x

2 + y2 = r2 is a fixed circle and C2 is a circle from which two perpendicular tangents are drawn from the

circumference of any point on the circle C2 on C1. A third circle C3 passes through the centre of C1 and intersects C2at P and Q and C1 at A and B such that the line PQ is a tangent to C1 at R.

36. Locus of the centre of variable circle C3 is

(A) C1 (B) C2 (C) C3 (D) none of these

37. RatioAB

PQequals

(A) 3 (B)1

3(C)

2

3(D)

3

2

38.Area ( OARB)

Area ( APQB)

W

Wequals where (O : origin)

(A) 4 3 + 6 (B) 4 3 6 (C) 2 3 3+ (D) 2 3 3



matched. The statements in Column I are labelled A, B, C and D, while the statements in Column II are labelled p,q, r, s and t. Any given statement in Column I can have correct matching with ONE OR MORE statement(s) in

Column II. The appropriate bubbles corresponding to the answers to these questions have to be darkened as





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39. Match the following :

Column I Column II

(A)

If

1 6

0 6 3

cos x cos x / 3dx A and dx A

1 x 6 3 x

= = + + then is (p) 1

(B) The area bounded by the curve y = x + sin x and its inverse

function between the ordinates x = 0 and

x = 2 is 4A then the value of A is

(q) 2

(C)The area bounded by y = xe |x| and the lines |x| = 1,

y = 0 is(r) 3

(D) If

20

0

20k 21 cos xdx , =

then k is (s) 4

40. Match the following :

Column I Column II

(A)dy 2y

0,dx x

+ = y(1) = 1, then y(2) = (p)1

2

(B)If y(x) is solution of

dy(x 1) xy 1,

dx+ =

y(0) = 1, then y(1) =(q) 15



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(C)(x2 + y2) dy = xydx and y(1) = 1 and y() = e,then is equal to

(r)1

4

(D)x dy = y(dx + ydy), y > 0, y(1) = 1 and y() = 3,then is equal to

(s) 3e



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PHYSICS




41. A rod is kept making an angle with the vertical as shown, there is a smallbead of mass m at a distance r from end A. End A of rod is hinged. The

rod starts rotating about end A making an angle with the vertical with anangular acceleration and makes a cone. If the coefficient of staticfriction between the ring and rod is , find the time after which ring willstart slipping on the rod. (consider the system is placed in gravity free

space)

r

A

(A) 12 2 2 2(sin cos )

(B) 12 2(sin cos )

(C) 2 2 2(sin cos )

(D) 2 2 2

2

(sin cos )

42. AB is smooth rod and CD is the rod of length L whose one end D

is fixed at distance R/2 from centre of disc of mass M and radius

R, other end C is free to move over rod AB. Velocity of C.O.M of

disc is V0. At the instant rod CD makes angle with AB, the

angular velocity of rod CD is : (Assuming disc is pure rollingover the horizontal surface):

(A) 03V

2Lcos(B) 0

3V

Lcos



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(C) 03V

Lcos(D) 0

3V

2Lcos

43. A stone of mass 1 kg is attached to one end of a 1m long aluminium wire of 1mm diameter. Stone is now

rotated in horizontal plane at a rate such that wire makes an angle of 60 o with vertical. The increase in length

of wire makes an angle of 60o with vertical. The increase in length of wire is (Youngs modulus of alumimum

= 7 1010 N/m2, neglect the mass of wire)

(A) 0.72 mm (B) 1.6 mm (C) 0.36 mm (D) 0.18 mm

44. A wide vessel with a small hole in the bottom is filled with water and kerosene of density 1 & 2 respectively.The velocity of water flow if the thickness of water layer is t 1 and that of kerosene is t2 (neglecting the

viscosity)

(A) ( )1 2 2 12 /g t t + (B) ( )2 1 2 12 /g t t +

(C) ( )1 2 1 2

2 /g t t +

(D) ( )2 1 1 2

2 /g t t +

45. A solid cylinder of radius R is attached to a uniform sphere. This

combination is floating in a liquid as shown in the figure. The total volume

of the solid immersed in the liquid is V. The force exerted by liquid on the

solid is (P0 = Atmospheric pressure, = density)

(A) Vg (B) Vg P0R2

(C) Vg + P0R2 (D) P0R2

R

atmosphericpressure

46. A string is wrapped around a cylinder of mass m and radius R the string is pulled vertically upward to preventcentre of mass from falling as the cylinder unwinds the string. Length of string unwound when the cylinder

has reached a speed will be

(A)

2 2

4

R

g

(B)

2 23

8

R

g

(C)

2 23

4

R

g

(D)

2 2

8

R

g



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47. A uniform rod of mass m = 2 kg and length l= 1 m rests on a smooth horizontal surface. One of the ends of

rod is struck with impulse J = 2N sec in horizontal direction perpendicular to the rod. As a result, the rod

obtains the momentum P = 2Ns. The force exerted by one half of the rod on other in the process of motion

(A) 6N (B) 9N (C) 12N (D) 15N

48. A steel ring of radius r and cross-sectional area A is fitted on to a wooden disc of radius R(R > r). If Youngs

modulus be Y, then the force with which the steel ring is expanded is:

(A)r

RAY (B)

r

rRAY (C)

r

)rR(

A

Y (D)

AR

Yr

SECTION IIMultiple Correct Choice Type



49. The mathematical statement cv v v '= + , where cv is the velocity of centre of mass, v ' is the velocity of thepoint with respect to the centre of mass and v is the total velocity of the point with respect to ground(A) is true for a rolling sphere

(B) is true for a block moving on frictionless horizontal surface

(C) is true for a rolling cylinder

(D) none of these

50. A particle of mass m and charge q is projected vertically upwards. A uniform electric field E is applied

vertically downwards. If the total potential energy is U (gravitational plus electrostatic) and height is h (


16/19


(A) Pressure at point D = pressure at point E = pressure at point A

(B) Pressure at point D is greater than pressure at point A

(C) Pressure at point D is greater than pressure at point B

(D) Pressure at point A = pressure at point B

52. From figure, select the correct alternative (s)

(A) In escaping condition total energy of particle (P) of mass m is

zero

(B) Escape velocity of particle P is ( )e e m4G

v M Mr

= +

(C) Escape velocity is e e p2G

v (M M )r

= +

(D) In escaping condition T.E. (Total energy) of particle is negative

Re P ( m )

Mm

Me

E a r t hM o o n

Rm

r

SECTION III

Comprehension TypeThis section contains 2 groups of questions. Each group has 3 multiple choice questions based on a paragraph.

Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONLY ONE is correct.


AB is horizontal diameter of a ball of mass m = 0.4 kg and radius R = 0.2 m. At time

t = 0, a sharp impulse is applied at an angle of 45 with horizontal as shown in figure,

so that the ball immediately starts to move with velocity v0 = 20 m/s. If the coefficient

of kinetic friction between the floor and the ball is m = 0.2 (take g = 10 m/s 2, Neglect

the frictional impulse at t = 0)

AB

4 5

53. Initial angular velocity of ball

(A) 250 rad/sec Anticlockwise (B) 4000 rad/sec Clockwise

(C) 125 rad/sec Anticlockwise (D) 1600 rad/sec Clockwise

54. The time taken by ball to achieve pure rolling



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(A) 5.2 sec (B) 10 sec (C) 11.9 sec (D) 12.8 sec

55. Work done by kinetic friction to achieve pure rolling

(A) 70 J (B) 140 J (C) 280 J (D) 560 J


A cylindrical tank having crosssectional area A = 0.5 m 2 is filled with two liquids

of density 1 = 900 kg m3 and 2 = 600 kg m3, to a height h = 60 cm each asshown in figure. A small hole having area a = 5 cm2 is made in right vertical wall at

a height y = 20 cm from the bottom. A horizontal force F is applied on the tank to

keep it in static equilibrium. The tank is lying on a horizontal surface. Neglect mass

of cylindrical tank comparison to mass of liquids. (take g = 10 ms -2)

2

1

h

hF y

56. The velocity of efflux

(A) 10 ms1 (B) 20 ms1 (C) 4 ms1 (D) 35 ms1

57. Horizontal force F to keep the cylinder in static equilibrium, if it is placed on a smooth horizontal plane

(A) 7.2 N (B) 10 N (C) 15.5 N (D) 20.4 N

58. Minimum and maximum values of F to keep the cylinder in static equilibrium just after the water starts to spill

through the hole. If the co-efficient of static friction between contact surfaces is 0.01.

(A) 0, 40 N (B) 5.4 N, 52.2 N (C) 0, 70 N (D) 0, 52.2 N



matched. The statements in Column I are labelled A, B, C and D, while the statements in Column II are labelled p,q, r, s and t. Any given statement in Column I can have correct matching with ONE OR MORE statement(s) in

Column II. The appropriate bubbles corresponding to the answers to these questions have to be darkened as





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59. With regard to dependence of quantities given in Column A on the quantities mentioned in Column B, match

Columns A and Column B

Column I Column II

(A) Youngs modulus of a substance (p) Depends on area of cross-section

(B) Bulk modulus of a substance (q) Depends on the nature of material

(C) Modulus of rigidity of a substance (r) Depends on temperature

(D) Volume of a substance (s) Depends on length

60. Match the following :Column I Column II

(A) Bernoullis theorem (p) Elasticity

(B) Yield point is related to (q) Venturimeter

(C) Hookes law (r) Aspirator pump

(D) Viscous liquid (s) Terminal velocity



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vriti iit part test 2_paper i test paper

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