16-04-20 TARGET JEE MAIN & ADVANCED 2020 PROGRAMME-II …

Sec: TARGET JEE MAIN & ADVANCED 2020 PROGRAMME-II UTM _ 2 Date: 16-04-20 Time: 3 Hrs Max. Marks: 300 Name of the Student: ___________________ H.T. NO:

16-04-20_ TARGET JEE MAIN & ADVANCED 2020 PROGRAMME-II _ UTM _ 2

SUBJECT MISTAKES

JEE SYLLABUS Q'S

JEE EXTRA SYLLABUS Q'S

TOTAL Q'S

MATHS

PHYISCS

CHEMISTRY

Narayana IIT Academy 12-04-20_ TARGET JEE MAIN&ADVANCED 2020 PROGRAMME-II UTM _2

Page. No. 2

PHYSICS MAX.MARKS: 100

SECTION – I (SINGLE CORRECT ANSWER TYPE)

This section contains 20 multiple choice questions. Each question has 4 options (A), (B), (C) and (D) 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.

1. A block of mass ‘m’ is pushed towards a movable wedge of mass 2m and height ‘h’ with a velocity ‘u’. All surfaces are smooth. The minimum value of ‘u’ for which the block will reach the top of the wedge is

h

2mu

m

1) 2 gh 2) 3gh 3) 6gh 4) 3/ 2 gh

2. A wooden block of mass 10gm is dropped from the top of a tower 100m high. Simultaneously, a bullet of mass 10gm is fired from the foot of the towers vertically up wards with a velocity of 100 m/s. If the bullet is embedded in it, how high will it rise above the tower before it starts falling? 2g 10m / s

L 100m

u 100m/s

1) 80 m 2) 85 m 3) 75 m 4) L/5 3. A ring of radius R rolls down an inclined plane and reaches the bottom with speed V. If the radius of the

ring is doubled keeping its moment of inertia constant. The speed of the bottom of the inclined plane will be

1) 2V 2) 2v 3) v / 2 4) v


Page. No. 3

4. A thin disc of mass 9m and radius R from which a disc of radius R/3 is cut is shown. Then moment of inertia of the remaining disc about O, perpendicular to the plane of disc is

R2R / 3

O

1) 24MR 2) 29MR 3) 237 MR9

4) 240 MR9

5. Two particles A and B are moving as shown in the figure. At this moment of time, the angular speed of B with respect to A is

a b

A B

bVaV

r

1) b a1 V Vr

2) b a1 V Vr

3) b b a a1 V sin V sinr

in anti clockwise direction

4) a a b b1 V sin V sinr

in clockwise direction

6. A uniform rod AB of mass ‘m’ and length 2a is falling freely without rotation under gravity with AB horizontal suddenly. The end A is fixed when the speed of the rod is V. The angular speed with which the rod begins to rotate is

1) V2a

2) 4V3a

3) V3a

4) 3V4a

7. A shell fired from a cannon with a velocity V at an angle with the horizontal. At the highest point if explodes into two pieces of equal masses. One of the pieces retraces its path to the cannon. The speed of the other piece immediately after the explosion is

1) 3V cos 2) 2V cos 3) 3/ 2V cos 4) V cos


Page. No. 4

8. Two particles of equal mass are projected simultaneously with speeds 20 m/s and 10 3 m / s as shown find the maximum height reached by the centre of mass of particles

y

x

060030

20m/s

10 3 m /s

1) 25 m4

2) 75 m16

3) 125 m16

4) 125 m4

9. Two blocks of equal mass are tied with light strong which passes over a massless pulley as shown. The magnitude of acceleration of centre of mass of both blocks is (neglect friction every where)

030060

1) 3 1g4 2 2) 3 1 g 3) g

2 4) 3 1 g

2

10. A projectile of mass 3m explodes at highest point of its path. It breaks into three equal parts. One part retraces its path, The second one comes to rest. The range of the projectile was 100m. The third part from the point of projection when it finally lands on the ground is

1) 100 m 2) 150 m 3) 250 m 4) 300 m

11. The centre of mass of non-uniform rod of length L whose mass per unit length 2Kx

L , where K is a

constant and R is the distance from the end is

1) 3L4

2) L8

3) KL

4) 3KL

12. A solid ball of radius ‘r’ rolls inside a hemispherical shell of radius R, it is released from rest from point A as shown. The angular velocity of centre of the ball in position B about the centre of the shell is

A

B

1)

g25 R r

2) 10g

7 R r 3)

2g

5 R r 4)

5g

2 R r


Page. No. 5

13. A cylinder is rolling without slipping on a plank. Which is also moving with speed 10 m/s on a horizontal surface as shown. The speed of centre of the cylinder is 20 m/s. The mass of cylinder is 2kg. The kinetic energy of the cylinder when observed from ground is

20m/s

10m/s 1) 450 J 2) 500 J 3) 600 J 40 800 J 14. Suppose speed of light (C), Force (F) and kinetic energy (K) are taken as the fundamental units, Then the

dimensional formula of mass will be

1) 2KC 2) 2KF 3) 2CK 4) 2FC

15. A projectile is given an initial velocity of i 2j . The Cartesian equation of its path is 2g 10m / s

1) 2y 2x 5x 2) 2y x 5x 3) 24y 2x 5x 4) 2y 2x 2x

16. In figures a body of mass ‘m’ is tied at one end of a light string and this string is wrapped around the solid cylinder of mass M and radius R. At the moment t = 0. The system starts moving. If the friction is negligible, angular velocity at time would be

M

m

1) mgRTM m

2)

2MgtM 2m

3) 2Mgt

R M 2m 4)

2Mgt

R M 2m

17. A ball of mass 1kg moving with a velocity of 0.4 m/s collidies with another stationary ball. After the collision. The first ball moves with a velocity of 0.3 m/s in a direction making an of 900 with its initial direction. The momentum of second ball after collision will be (in Kg-m/s)

1) 0.1 2) 0.3 3) 0.5 4) 0.7


Page. No. 6

18. A bullet of mass ‘m’ moving with a velocity ‘v’ strikes a suspended wooden block of mass M as shown and sticks to it, If the block rises to a height h, the initial velocity of the bullet is

m M

hM

m V

1) m M 2ghm 2) 2gh 3) m M 2gh

M 4) m 2gh

M m

19. The moment of inertia of a rod of length L about an axis passing through its centre of mass and perpendicular to rod is I. the moment of inertia of hexagonal shape formed by six such rods about an axis passing through its centre of mass and perpendicular to its plane will be

1) 16 I 2) 40 I 3) 60 I 4) 80 I 20. A thin circular ring of mass M and radius R is rotating about its axis with a constant angular velocity four

objects each of mass m are kept gently to the opposite ends of wo perpendicular diameters of the ring. The angular velocity of the ring will be

1) MM 4m

2) M 2mM

3) M 4mM 4m

4) M4m

SECTION-II

(Numerical Value Answer Type)

This section contains 5 questions. The answer to each question is a Numerical value. If the numerical value has

more than two decimal places, round-off the value of Two decimal places. Answer to each question will be

evaluated according to the following marking scheme:

Marking scheme: +4 for correct answer, 0 in all other cases.

21. A piece of wire is bent in the shape of parabola 2y kx (y – axis vertical) with a bead of mass ‘m’ on it. The bead can slide on the wire without friction. It stays at the lowest point, on the parabola when the wire is at rest. The wire is now accelerated parallel to the x-axis with a constant acceleration ‘a’. The distance of the new equilibrium position of the bead, where the bead can stay at rest with respect to the wire, from

the y-axis is aNgK

. The value of ‘N’ is


Page. No. 7

22. A block of mass 0.18 Kg is attached to a spring of force constant 2 N/m. The coefficient of friction between the block and the floor is 0.1. Initially the block is at rest and the spring is unstretched. An impulse is given to the block. The block slides a distance of 0.06 m and comes the rest for the first time. The initial velocity of the block in m/s is 2take g 10ms

23. Four solid spheres each of diameter 5cm and mass 0.5 kg are placed with their centres at the corners of

a square of a side 4 cm. The moment of inertia of the system about the diagnol of the square is 4 2N 10 Kgm , then N is

24. A bob of mass ‘m’ suspended by a string of length L1, is given a minimum velocity required to complete a full circle in the vertical plane. At the height point it collides elastically with another bob of mass ‘m’ suspended by a string of length L2. Which is initially at rest. Both the strings ae massless and inextensible. If the second bob after collision acquires the minimum speed required to complete a full

circle in the vertical plane, the ratio 1

2

LL

is

25. Figure shows a small wheel fixed coaxially on a bigger one of double the radius. The system rotates about the common axis. The strings supporting A and B do not slip on the wheels. If x and y be the distance travelled by A and B is the same interval then y = Nx the value of N is

A

B


Page. No. 8

CHEMISTRY MAX.MARKS: 100


This section contains 20 multiple choice questions. Each question has 4 options (A), (B), (C) and (D) 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. The basic character of the oxides, 2 2, , , ,MgO SrO K O NiO Cs O increases in the order 1) 2 2MgO SrO K O NiO Cs O 2) 2 2Cs O K O MgO SrO NiO 3) 2 2NiO MgO SrO K O Cs O 4) 2 2K O NiO MgO SrO Cs O 27. 2KO (Potassium superoxide) is used in oxygen cylinders in space and submarines because it 1) Absorbs 2CO and increases 2O concentration 2) Eliminates moisture 3) Absorbs 2CO 4) Produces ozone 28. A mixture of FeO and 3 4Fe O when heated in air to constant weight gains 5% in its weight. The % of

FeO in the sample is 1) 79.75 2) 20.25 3) 30.25 4) 10.25 29. Dissolving 120g of urea (mol. Wt. 60) in 1000g of water gave a solution of density 1.15 g/mL. The

molarity of the solution is 1) 1. 78M 2) 2.00M 3) 2.05M 4) 2.22M 30. The volume of 0.1M 2

M Ca OH needed for the neutralization of 40 ml of 0.05M oxalic acid is 1) 10ml 2) 20ml 3) 30 ml 4) 40 ml 31. A sample of 3 2 3NaHCO Na CO required 20ml of HCl using phenolphthalein as indicator and 35ml

more required if methyl orange is used as indicator. Then molar ratio of 3NaHCO to 2 3Na CO is

1) 12

2) 23

3) 34

4) 13

32. Molecular shapes of 3 3,CIF I and 3XeO respectively are 1) T-shape, Linear, Pyramidal 2) Planar, Linear, Tetrahedral 3) T-shape, Planar, Pyramidal 4) Trigonal bipyramidal, Linear, Tetrahedral 33. To a 25 ml 2 2H O solution, excess of acidified solution of potassium iodide was added. The iodine

liberated required 20ml of 0.3N sodium thiosulphate solution. Calculate the volume strength of 2 2H O solution.

1) 1.34 2) 1.84 3) 2.50 4) 3.18 34. Which are the compounds, which can be oxidized and reduced by 2 2H O in acidic and basic medium

respectively? 1) 2 2,K O NaAIO 2) 4 2 4,KMnO K MnO

3) 4 36 6,K Fe CN K Fe CN 4) 3 46 6

,K Fe CN K Fe CN

35. Which among the following elements has the highest value for third ionization energy ? 1) Mg 2) Al 3) Na 4) Ar


Page. No. 9

36. The correct decreasing order for acid strength is : 1) 2 2 2 2 2NO CH COOH FCH COOH CNCH COOH ClCH COOH 2) 2 2 2 2 2CNCH COOH NO CH COOH FCH COOH ClCH COOH 3) 2 2 2 2 2FCH COOH NCCH COOH NO CH COOH ClCH COOH 4) 2 2 2 2 2NO CH COOH NCCH COOH FCH COOH ClCH COOH 37. What is the IUPAC name of the following compound ?

1) 4 – Bromo – 3 – mythylpent – 2 – ene 2) 3 – Bromo 1, 2 – dimethylbut – 1 - ene 3) 3 – Bromo – 3 – mythyl – 1, 2 – dimethylprop -1 - ene 4) 2 – Bromo – 3 methylpent – 3 – ene 38. Which hydrogen in compound (E) is easily replaceable during bromination reaction in presence of

light? 3 2 2CH CH CH CH

(E)

1) hydrogen 2) -hydrogen 3) -hydrogen 4) -hydrogen 39. The major pro9duct of the following reaction is

40. Given: i) C(graphite) 0 1

2 2 ;O g CO g rH xkJ mol

ii) C(graphite) 0 12 2

1 ;2

O g CO g rH ykJ mol

iii) 0 12 2

1 ;2

CO g O g CO g rH zkJmol

Based on the above thermochemical equations, find out which one of the following algebraic relationships is correct?

1) z = x + y 2) x = y – z 3) x = y + z 4) y = 2z – x 41. An orange coloured solution of 2 2 7K Cr O acidified with 2 4H SO and treated with a substance X gives a

blue coloured solution of 5CrO . The substance X is 1) 2H O 2) .dil HCl 3) 2 2H O 4) .conc HCl 42. Potassium acetate on Koble’s electrolysis process the following 1) 2 4C H 2) 4CH 3) 2 6C H 4) 3 8C H


Page. No. 10

43. The temporary hardness of water is due to 1) 2 4Na SO 2) 2CaCl 3) NaCl 4) 3 2

Ca HCO 44. Select the incorrect statement 1) ortho and para hydrogen are different due to difference in their nuclear spins 2) Ortho and para hydrogena re different due to difference in their electron spins 3) Para hydrogen has a lower internal energy than that of ortho hydrogen 4) Para hydrogen is mores stable at lower temperature 45. 2Be C on hydrolysis yields 1) 3BeCO 2) 2 2C H 3) 4CH 4) 2 6C H

SECTION-II (Numerical Value Answer Type)

This section contains 5 questions. The answer to each question is a Numerical value. If the numerical value has more than two decimal places, round-off the value of Two decimal places. Answer to each question will be evaluated according to the following marking scheme: Marking scheme: +4 for correct answer, 0 in all other cases.

46. 1.82g of a metal requires 32.5 ml of 1N HCl to dissolve it. What is the equivalent weight of metal?

47. The maximum number of H-bonds in water molecule can form are

48. A process has 1200H Jmol and 1 140S JK mol . Out of the values given below, choose the

minimum temperature (K) above which the process will be spontaneous

49. A fuel has the same knocking property as a mixture of 70% isooctane (2,2,4-trimethylpentane) and

30%n-heptane by volume. The octane number of the fuel is

50. Maximum electron in 3rd shell having 1 2m will be

MATHEMATICS 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. If 2 1g x x x and 24 10 5g f x x x then 54

f

1) 12

2) -12

3) -13

4) 13

52. Domain of the function 2 1 1log 10.3 9 1 cos 1x xf x x is

1) 0,1 2) 1,2 3) 0, 2 4) 0,1


Page. No. 11

53. The smallest natural number K for which 2

5 10log 1 sin xf x x x xk

in an odd function

2 , 2x , is denotes G.I.F xx 1) 38 2) 39 3) 40 4) 41

54. The maximum value of the function 4 2

6 32 1x xf x

x x

, where x >1 =

1) 1/3 2) 1/6 3) 1/18 4) 1/2

55. 3 22 3 cos sin6 1 6 1x

x xLt xx x

1) 612 2) 6

12 3) 6

24 4) 6

24

56. 2 2 2 2

3 3 3

1 2 1 3 2 .... .11 2 ....n

n n n nLt

n

1) 1/3 2) 2/3 3) ½ 4) 1/6

57. If f x y f x f y for all ,x y R , and 1 1f , then

tan sin

20

2 2sin

f x f x

xLt

x f x

1) log 2 2) log 4 3) log 2 4) log8

58. If 2 1 4,

1x

x xLt ax bx

then

1) 1, 4a b 2) 1, 4a b 3) 2, 3a b 4) 2, 3a b

59. Let

0

1 1 , 2

5 7 , 2,

x

f x t dt if x

x if x then

1) f is not continuous at x=2 2) f is continuous but not differentiable at x = 2 3) f in differentiable every where 4) ' 2f does not exist

60. If 32

sin 2 cos 2x

f x x a xa

, (where [.] denotes G.I.F) in continous and differentiable

in (4,6), then 1) 8,64a 2) 0,8a 3) 64,a 4) 4,8a

61. Let f be continuous function on R such that 22

2

1 sin4 1

n n nf e en n

, then the value f(0)=

1) 1 2) 1/2 3) 0 4) 2

62. Let 2, , 2

8 2 , 2 4

max x x xf x

x x

Let S be the set of points in 4,4 at which f is not

differentiable the S is 1) 2, 1,1, 2 2) 2, 1,0,1,2 3) 2, 2 4) empty set


Page. No. 12

63. The angle between the tangent Lines to the graph of the function 2

2 5x

f x t dt at the points

where the graph cuts x - axis is

1) 6

2) 4

3) 3

4) 2

64. Let :[0, )f R be continuous, strictly increasing function such that 3 2

0

x

f x t f t dt . If normal

is drawn the curve y f x , with gradient -1/2, then intercept made by it on y-axis is 1) 4 2) 5 3) 8 4) 9

65. For 2

log7

xf xx

. Rolle’s theorem is applicable on [3,4] Then the value of ''f C

1) 1/12 2) -1/12 3) 1/6 4) -1/6 66. A spherical balloon is filled with 4500 cu m of helium gas If a leak in balloon causes the gas to

escape rate of 72 cu m/min then the rate (in m/min) at which the radius of the balloon decreases 49 min after the leakage began is

1) 9/7 2) 7/9 3) 2/9 4) 9/2

67. For 0

50, , sin2

x

x f x t t dt , then f has

1) local minimum at and 2 2) local minimum at and local maximum at 2 3) Local minimum at 2 and local maximum at 4) local maximum at & 2

68. Let f x be a polynomial of degree 4 having extreme value at x = 1, x = 2. If 20

1 3x

f xLt

x

then

1f 1) 9/2 2) 5/2 3) 3/2 4) 1/2

69. The least value of R , for which 2 14 1xx

, for all x > 0, is

1) 1

64 2)

132

3) 127

4) 125

70. The values of a for which the function 2 3 2 cos 1 ,2xf x a a a x

posses critical points

1) ( ,0] [4, )a 2) ( ,1) (1, ) 3) ( , 1) (1, 2)a 4) ( ,0) (0,1)a


Page. No. 13

SECTION-II

(Numerical Value Answer Type)

This section contains 5 questions. The answer to each question is a Numerical value. If the numerical value has

more than two decimal places, round-off the value of Two decimal places.

Answer to each question will be evaluated according to the following marking scheme:

Marking scheme: +4 for correct answer, 0 in all other cases.

71. Let , , are the roots of the equation 3 2 0x ax bx c , , , 0a b c R a . If the system of equations 0x y z

0x y z

0x y z has non-trivial solutions, they the value of 2a

b

72. Number of solutions of the equation 2

3 1 3cos sin 12 4

x x

in , is

73. Suppose 1 2 30, ....A A A are 30 sets each having five elements and 1 2, .... nB B B are n sets each with 3

elements such that 30

1 1

n

i ji jU A U B S

.if each element of S belongs the exactly 10 of 'iA s and exactly 9

of 'jB s , then value of n =

74. If 1cot ,6

n n N

then maximum value of n is

75. Let 1 0 03 1 0 ,9 3 1

ijP Q q

be two 3 x 3 matrices such that 53Q P I then 21 31

32

q qq

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16-04-20 TARGET JEE MAIN & ADVANCED 2020 PROGRAMME-II …