section: target iit mian &adv prog ii dt: 23-04-2020

SECTION: TARGET IIT MIAN &ADV PROG II Dt: 23-04-2020 TIME: 3HRS UTM-03 Max.Marks:100

JEE MAIN Model MATHEMATICS:

Section Question Type +Ve

Marks - Ve

Marks No.of Qs

Total marks

Sec – I (Q.N : 1 – 20) Questions with Single Correct Choice 4 -1 20 80

Sec – II (Q.N : 21 – 25) Questions with Numerical Answer Type

(+ / - Decimal Number) 4 0 5 20

Total 20 100

PHYSICS: Section Question Type

+Ve Marks

- Ve Marks

No.of Qs Total marks




Total 20 100

CHEMISTRY:

Section Question Type +Ve

Marks - Ve

Marks No.of Qs

Total marks




Total 20 100

PAPER SETTER NAMES: VSP-SARASWATHI BHAVAN-N120-BOYS S.NO NAME SUBJECT PHONE NO 1 VV SUBBARAO SIR MATHS 8122020625 2 SRI KRISHNA SIR PHYSICS 8008882938 3 NAVEEN SIR CHEMISTRY 9291577708

Narayana IIT Academy 23-04-2020 PROGRAM- II-UTM-03

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MATHS Max.Marks:100

SECTION – I (SINGLE CORRECT ANSWER TYPE)

This section contains 20 multiple choice questions. Each question has 4 options (1), (2), (3) and (4) for its answer, out of which ONLY ONE option can be correct. Marking scheme: +4 for correct answer, 0 if not attempted and -1 in all other cases.

01. If 1,2,3A and 1,1 , 1,3 , 3,1 , 2,2 , 2,1 , 3,3R ’then the relation R on A, is

1) reflexive 2) symmetric 3) transitive 4) equivalence

02. If the system of linear equations 2 0 , 3 0 & 4 0x ay az x by bz x cy cz has a non-zero solution, then a, b, c 1)are in A. P. 2) are in G. P. 3) are in H. P. 4) satisfy 2 3 0a b c

03. 40

cos tan coslimx

x xx

=

1) 1/ 6 2) 1/ 3 3) 1/ 6 4) 1/ 3 04. The domain of f x is 0,1 therefore the domain of nxy f e f l x is

1) 1 ,1e

2) , 1e 3) 11,e

4) , 1 1,e e

05. If 2 2f x x x and

min : 2 , 2 0,

max : 0 ,0 3

f t t x xg x

f t t x x

then

1) f(x) is everywhere continuous and differentiable 2) f(x) is differentiable {0}x R

3) f(x) is differentiable x R only 4) g x is differentiable 2,3x 06. A value of c for which conclusion of mean value theorem holds for the function

logef x x on the interval 1,3 is

1) 3log e 2) log 3e 3) 32log e 4) 31 log2

e

07. The total number of local maxima and local minima of the function 3

2/3

2 , 3 1( )

, 1 2

x xf x

x x

is

1) 0 2) 1 3) 2 4) 3 08. Let , ,a b c

be three unit vectors such that 1a b c

and a b

. If c

makes angles ,

with ,a b

respectively then cos cos is equal to

1) 32

2) 1 3) –1 4) none of these

09. If the vectors 3 2 , 3 4a i j k b i j k , and 4 2 6c i j k constitute the sides of a ABC , then the length of the median bisecting the vector c is

1) 2 2) 14 3) 74 4) 6


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10. ‘P’ be a point interior to the acute ABC . If 0PA PB PC then with respect to the triangle ABC, P is its

1) circumcentre 2) orthocentre 3) centroid 4) incentre 11. If q is the angle between the line 2 3 2r i j k t i j k and the plane

3 . 3 4r i j k then q sin

1) 814 11

2) 1 63 11

3) 6311

4) 611

12. If ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ, , 2 ,a i j k b i j k c i j k then value of

. . .

. . .

. . .

a a a b a c

b a b b b cc a c b c c

1) 16 2) 24 3) 256 4) 144 13. Let , ,r a b and c be four non zero vectors such that . 0r a , r b r b and

r c r c then a b c 1) a b c 2) a b c 3) 0 4) 1 14. If , ,a b c

are three non coplanar vectors represented by concurrent edges of a

parallelepiped of volume 4 then . . .a b b c b c c a c a a b

is equal to 1) 10 2) 4 3) 12 4) 0 15. Let ABCD be a tetrahedron in which position vectors of A, B, C & D are ,i j k

2 2i j k , 3 2i j k

and 2 3 2i j k . If ABC be the base of tetrahedron, then the

height of tetrahedron is

1) 32

2) 35

3) 2 23

4) None

16. A tetrahedron has vertices at (0,0,0), (1, 2,1), (2,1,3)O A B and ( 1,1,2).C Then the angle

between the faces OAB and ABC will be 1) 1cos (17 / 31) 2) 030 3) 090 4) 1cos (19 / 35) 17. Shortest distance between the z-axis and the line x y 2z 3 0 2x 3y 4z 4 is ___ 1) 7 2) 3 3) 9 4) 2

18. The ratio in which the plane . 2 3 17r i j k

divides the line joining the points

2 4 7i j k

and 3 5 8i j k

is 1) 3:10 ext 2) 3:5 ext 3) 3: 5 int 4) 3:10 int 19. The vector equation of the line passing through (1,2,3) and perpendicular to the plane

. 2 5 9 0r i j k

is

1) 2 3r i j k

⋋ 3 i j k

2) 2 5r i j k

⋋ 2 3i j k

3) 2 3r i j k

⋋ 8k

4) 2 3r i j k

⋋ 2 5i j k


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20. The point of intersection of the two lines 2 3r i j k

⋋ 3 3 9i j k

and

7 4 3r i j k i j

is_____

1) 3 2i j k

2) 2 3i j k

3) 2 3i j k

4) 3 2i j k

SECTION – II

(Numerical Value Answer Type) This section contains 5 questions. The answer to each question is a Numerical values comprising of positive or negative decimal numbers (place value ranging from Thousands Place to Hundredths Place). Eg: 1234.56, 123.45, -123.45, -1234.56, -0.12, 0.12 etc. Marking scheme: +4 for correct answer, 0 in all other cases.

21. If , then value of the expression , is equal to

22. If the equation 2 1x x p has exactly one solution, then the number of integral values of p is

23. Let , ,u v w be such that 1, 2, 3u v w .If the projection of v along u is equal to that of w along u . Also ,v w are perpendicular to each other then 2u v w

24. Let , ,a i j b j k c a b . If the vectors, 2 ,3i 2 j ki j k and c are coplanar

then

25. If length of projection of the line segment joining , ,a b c and 1,1,1 on the plane 2 3 6x y z ⋋ is maximum,then the possible value of 2 3 6a b c is 0, 0, 0a b c

PHYSICS Max Marks: 100


This section contains 20 multiple choice questions. Each question has 4 options (1), (2), (3) and (4) for its answer, out of which ONLY ONE option can be correct. Marking scheme: +4 for correct answer, 0 if not attempted and -1 if not correct.

26. A solid cylinder of mass m length l and area of cross section A is placed as shown in the figure. If Young’s modulus is Y then strain energy stored in the cylinder is

1) 2)

3) 4) 27. A small air bubble of radius r is found to form at a depth of H from the open surface of

the liquid contained in a beaker. If S is the surface tension and , be the density of the liquid and po, be the atmospheric pressure, then the pressure inside the bubble is

1) + gH + po 2) – gH + po 3) – gH + po 4) + gH + po

,2

x

1 1 1sin cos cos cos sin sinx x

2 2

3m g l

AY

2 2

6m g l

AY

2 2

2m g l

AY

2 2m g lAY

4Sr

2Sr

4Sr

2Sr


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28. The water enters in a tapering tube. Its speed at section-1 is 0.25 m/s. The ratio of

diameters of tube at section-1 and outlet is 4. The water falls on a horizontal surface

below H metre at a horizontal distance of 2 m from the outlet. Find H (g = 10 m/s2)

1)1.25 m 2) 1.75 m 3) 2.25 m 4) 2.75 m

29. A spherical ball of density and radius 0.003 m is dropped into a big tube containing a viscous fluid. Viscosity of the fluid 21.260 N.m .s and its density

-3/ 2 1260 kg.mL . Find its terminal speed in cm/s. (g= acceleration due to gravity 210 ms ).

1) 4 2) 6 3) 2 4) 8 30. A block of wood is floating in water at 00 C . The temperature of water is slowly raised

from 00 C to 010 C with the rise in temperature the volume of block V above water level will

1) increase 2) decrease 3) first increase and then decrease 4) first decrease and then increase 31. The root mean square speed of oxygen molecules (O2)at a certain absolute temperature

is V. If the temperature is doubled and the oxygen gas dissociates into atomic oxygen, the rms speed would be

1) V 2) 2V 3) 2V 4) 2 2V 32. An ideal gas has initial volume V and pressure P. In which of the following processes

the work done will be minimum in doubling the volume of the gas. 1) Isobaric process 2) Isothermal process 3) Adiabatic process 4) May be option 1 or 2

33. Two moles of 27O5

at temperature T0 and 3 moles of CO243

at temperature 2T0

are allowed to mix together in a closed adiabatic vessel. The resulting mixture finally comes in thermal equilibrium. Then

1) final temperature of the mixture is

2) final temperature of the mixture is 031T19

3) adiabatic exponent of the mixture formed is 145

4) adiabatic exponent of the mixture formed is 1714


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34. A rod of length and cross section area A has a variable thermal conductivity given by k T , where is a positive constant and T is temperature in kelvin. Two ends of the rod are maintained at temperatures T1 and T2 (T1> T2). Heat current flowing through the rod will be

1) 2 21 2A T T

2) 2 2

1 2A T T

3) 2 2

1 2A T T3

4) 2 2

1 2A T T2

35. Three rods of the same dimensions have thermal conductivities 3k, 2k, and k. They are arranged as shown, with their ends at . The temperature at common junction ‘O’ of three rods is

1) 075 C 2) 0200

3C 3) 400C 4) 0100

3C

36. One end of a uniform rod of length 1 m is placed in boiling water while its other end is placed in melting ice. A point P on the rod is maintained at a constant temperature of

. The mass of steam produced per second is equal to the mass of ice melted per second. If latent heat of steam is 7 times the latent heat of ice, the distance of P from the steam chamber must be

1) 17

m 2) 18

m 3) 19

m 4) 1

10m

37. A rod of length L is fixed between two rigid supports and supplied heat to raise its temperature T. If is the coefficient of volume expansion of the wire and y is young’s modulus of the wire then the elastic potential energy density stored in the wire is

1) 2 2

2T y 2)

2 2 3

3T y 3)

2 2

18Ty

4) 2 2

18T y

38. The 6.0 kg block is at rest while the 2.0 kg block moves at 1.0 m/s towards the 6.0 kg block, from an initial distance of 16 cm from it. The coefficient of kinetic friction between the blocks and the ground is 0.20. The collision between the blocks is perfectly elastic. The separation between the blocks, (in mm), after both the blocks come to rest is ? Take g = 210m / s

1)35mm 2)40mm 3)45mm 4)50mm

100 C

50 C

0 C

3k O k

2k


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39. A ball is dropped freely from a height of 4.9m at instant of time t=0on to a horizontal plane. If the coefficient of restitution is 0.75, then the ball will strike second time with the plane after a time of (take g=9.8ms-2)

1)1/2 sec 2) 1sec 3) 3/2 sec 4) 5/2 sec 40. A cart initially moving on a frictionless track filled with sand has a hole at its bottom

from where sand leaks out Student A says : The velocity of cart remains constant although mass of sand in cart

decrease. Student B says: Since mass is decreasing, the velocity of cart must increase. 1) Student –A is correct, Student –B is wrong 2) Student A is wrong, Student –B is correct 3) Both are correct 4) Both are wrong 41. A block, released from rest from the top of a smooth inclined plane of inclination , has

a speed v when it reaches the bottom. The same block, released from the top of a rough inclined plane of the same inclination , has a speed on reaching the bottom, where n is a number greater than unity. The coefficient of friction is given by

1) 2

11 tann

2) 2

11 cotn

3)

12

211 tann

4)

12

211 cotn

42. A block of mass 2m kg is placed on a plank of mass M=10kg, which is placed on a smooth horizontal plane. The coefficient of friction between the block and the plank is

13

. If a horizontal force F is applied on the plank, then the maximum value of F for

which the block and the plank move together is 210 /g m s

1) 40 N 2) 30 N 3) 120 N 4) 100 N

43. A body is projected on a rough horizontal surface with a initial horizontal velocity 0v . Coefficient of friction varies as kx (k is constant and x is distance from the initial point) .The maximum distance travelled by the body is 1)

2)

3)

4)

44. Which of the following is a correct statement? 1) If the centre of mass of three particles is at rest and it is known that two of them are

moving along different non-collinear lines, then the third particle must also be moving 2) If the centre of mass a system remains at rest, then the net work done by all the

forces acting on the system must be zero


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3) If the velocity of centre of mass of a system remains zero, then the net external force acting on the system must be zero

4) If the speed of the centre of mass of system is changing, then there must be some work being done by the internal forces on the system

45. In the situation shown below, block A, having mass m, and block B, having mass 3m, are held at rest on horizontal, frictionless surface with a massless spring compressed between them. After the blocks are released from rest, what is the ratio of the magnitude of Bs momentum to the magnitude of As momentum ?

SECTION – II

(Numerical Value Answer Type) This section contains 5 questions. The answer to each question is a Numerical values comprising of positive or negative decimal numbers (place value ranging from Thousands Place to Hundredths Place). Eg: 1234.56, 123.45, -123.45, -1234.56, -0.12, 0.12 etc. Marking scheme: +4 for correct answer, 0 in all other cases.

46. A projectile is fired at a speed of 100 m/s at an angle of above the horizontal. At the highest point, the projectile breaks into two parts of mass ratio , the smaller coming to rest. Find the distance from point P when it is 120m from the launching point to the point where the heavier piece lands (in km)

47. The wedge with hemi-spherical cut of radius R has mass 5m. It is placed on friction

less horizontal surface. A small sphere of radius r and mass m is released from rest

from point A as shown. When m reaches B the speed of the wedge is . Find x

48. A block of wood floats in water kept in a vessel with two-third of its volume inside

water. The vessel is placed in a lift having an upward acceleration 21.2 /m s . Now the

fraction of volume inside water is found to be 4n . What is the value of n? 29.8 /g m s

1) 9/1 2) 3/1 3) 1/1 4) 1/3


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49. A liquid flows at the rate of 1/4200 kg/s through a tube and is heated by a heater dissipating 25 W. The inflow and outflow liquid temperatures are 25ºC and 30ºC respectively. When the rate of flow is increased to 1/2100 kg/s and the rate of heating to 30 W, the inflow and outflow temperatures are unaltered. If the rate of loss of heat from the tube is 5z watt, then find z.

50. An ideal diatomic gas under goes a process in which it internal energy changes with volume as given U = cV2/5 where c is constant. Find the ratio of molar heat capacity to universal gas constant R?

CHEMISTRY Max Marks: 100


This section contains 20 multiple choice questions. Each question has 4 options (1), (2), (3) and (4) for its answer, out of which ONLY ONE option can be correct. Marking scheme: +4 for correct answer, 0 if not attempted and -1 if not correct. 51. The pair having similar geometry is 1) 3 3,BF NF 2) 2

3 3,BF CO 3) 2 2,BeF H O 4) 3 3,BCl PCl 52. The IUPAC name of the following compound is

OH

BrCN

1) 4-bromo-3-cyanophenol 2) 2-bromo-5-hydroxybenzonitrile 3) 2-cyano-4-hydroxy bromobenzen 4) 6-bromo-3-hydroybenzonitrile 53. The heats of neutralization of four acids A,B,C and D are –13.7, –9.4, –11.2 and –12.4

kcal respectively when they are neutralized by a common base. The acidic character obeys the order

1) A B C D 2) A D C B 3) D C B A 4) D B C A 54. One litre of 2CO is passed over hot coke. The volume becomes 1.4L. The final

composition of mixture is 1) 0.6 L of CO 2) 20.8 L of CO 3) 20.6 0.8L of CO and L of CO

4) 20.9 0.5L of CO and L of CO 55. Hydrogen gas is not liberated when the following metals added to dil HCl 1) Mg 2) Sn 3) Ag 4) Zn 56. When sodium metal is dissolved in 3,liq NH a blue solution is formed. The blue colour is

due to. 1) solvated Na ions. 2) solvated electrons 3) solvated 2NH ions 4) solvated protons 57. 375 435

3 3k k red heatH BO A B C where A,B and C are respectively

1) 2 3 2 4 7 2,B O H B O and HBO 2) 2 2 3 2 4 7,HBO B O and H B O 3) 2 2 4 7 2 3,HBO H B O and B O 4) 2 4 7 2 2 3,H B O HBO and B O


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58. Which of the following is the incorrect statement? 1) Chlorides of both Be and Al have bridged chloride structure in the solid phase 2) Aluminium form a polymeric hydride of the formula, 3 nAlH , commonly known as alane

3) B Ga Al In (Atomic radius) 4) B Al In Ga Tl (Melting point) 59. The basic structural unit of ortho silicates is 1) 2

3SiO 2) 24SiO 3) SiO 4) 4

4SiO

60. Which of the following is the incorrect statement? 1) 4PbBr does not exist 2) 2 2 2 2SiX GeX SnX PbX (Stability of

dihalides) 3) 4 4 4 4SnH GeH SiH CH (stability) 4) Density of graphite is 3.52 g/Ml

61. In reaction, ,3 ;NaOH NaOH CaO

HeatCH COOH X Y Y is

1) 3CH CHO 2) 4CH 3) 2 6C H 4) 3 3CH COCH

62. The compound X 5 8C H react with ammonical 3AgNO to give a white precipitate and

reacts with excess of 4KMnO to give the acid 3 2CH CHCOOH. Therefore X is

1) 2 3CH CH CH CH CH 2) 3 2 3CH CH C C CH 3) 3 2

CH CHC CH 4) 3 22CH C C CH

63. How is the following transformation best carried out

HC

CH

O

O

1) 4 3/OsO NaHSO 2) 2 4 2/H SO H O 3) 4 2 4/HgSO H SO 4) 4HIO

64.

A3 2 4/HNO H SO

B Major product

3CH

4KMnO

The product B is

1)

COOH

2NO 2)

3CH

2NO 3)

3CH

2NO 4)

COOH

2NO


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65.

2ClA

B3FeCl

h

A and B respectively are 1) hexa chlorocyclohexane and 6 5C H Cl 2) chlorobenzene and hexachlorocyclohexane 3) O- and P- dichlorobenzene and chlorobenzene

4) chlorobenzene and 6 5 6C H Cl

66. Which of the following gases will have density of 11.8gL at 760 torr pressure and 027 C ? 1) 2O 2) 2CO 3) 3NH 4) 2SO 67. Gases X,Y,Z, P and Q have the van der waals constants ‘a’ and ‘b’ as shown bellow

X Y Z P Q a 6 6 20 0.05 30 b 0.025 0.15 0.1 0.02 0.2

The gas with the highest critical temperature TC is 1) P 2) Q 3) Y 4) X 68. Given 2 2 3 13 2 ,g g gN H NH K

2 2 22g g gN O NO K ,

2 2 2 312g g gH O H O K

The equilibrium constant for 3 2 252 2 32 g g ggNH O NO H O will be

1) 1 2 3K K K 2) 1 2

3

K KK

3) 3

1 3

2

K KK

4) 3

2 3

1

K KK

69. 2XY dissociated as 2XY XY Y . Initial pressure of 2 is 600XY mm of Hg. The total pressure at equilibrium is 800 mm of Hg. Assuming volume of system to remains constant, the value of Kp is

1) 50 2) 100 3) 200 4) 400 70. The solubility product spK of AgCl is 101.8 10 precipitation of AgCl will occur only

when equal volumes of solutions of 1) 4 410 10M of Ag and M of Cl are mixed. 2) 7 710 10M of Ag and M Cl are mixed. 3) 5 510 10M of Ag and M Cl are mixed. 4) 10 1010 10M Ag and M Cl are mixed.


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SECTION – II (Numerical Value Answer Type)

This section contains 5 questions. The answer to each question is a Numerical values comprising of positive or negative decimal numbers (place value ranging from Thousands Place to Hundredths Place). Eg: 1234.56, 123.45, -123.45, -1234.56, -0.12, 0.12 etc. Marking scheme: +4 for correct answer, 0 in all other cases. 71. For 3s-orbital of hydrogen atom, the normalized wave function is given by

0

3/ 2 2/ 3

3 20 0 0

1 1 18 22781 3

r as

r r ea a a

the above mentioned orbital (3s) has two nodes at

01.9a and 0X a . The value of x is 72. An open vessel at 270C is heated until three-fifth of the air in it has been expelled.

Assuming that the volume of the vessel remains constant, find the temperature (K) to which the vessel has been heated?

73. A vessel at 1000k contains CO2 with a pressure of 0.5atm. Some of the CO2 is converted to carbon monoxide on addition of graphite. Calculate the value of Kp if total pressure at equilibrium is 0.8 atm.

74. Calculate the pH of an aqueous solution of 1.0 M ammonium formate assuming complete dissociation (pKa of formicacid is 3.8 and pKb of ammonia is 4.8)

75. Calculate the pH of the buffer solution containing 0.15 moles of NH4OH and 0.25 moles of NH4Cl. [Kb for NH4OH is 51 10 , log5 0.7, log3 0.48 ]

section: target iit mian &adv prog ii dt: 23-04-2020

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