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JEE MAIN PART TEST-4 PHYSICS

1. A gas bubble from an explosion under water oscillates with a time period T, depends upon static

pressure P, density of water and the total energy of explosion E. Find the expression for the time

period T. (where, K is a dimensionless constant.)

(A) T = KP– 5/6 1/2E1/3 (B) T = KP– 4/71/2E1/3

(C) T = KP– 5/6 1/2E1/2 (D) T = KP– 4/71/3E1/2

2. The relation gives the value of x as 3 3a bx

c d the percentage error in x, if the percentage error in a, b,

c, d are 2%, 1%, 3% and 4% respectively , is :

(A) 8% (B) 10% (C) 12% (D) 14%

3. Two particles 1 and 2 are projected with same speed v as shown in figure. Particle 2 is on the ground

and particle 1 is at a height h from the ground and at a horizontal distance s from particle 2. If a graph

is plotted between v and s for the condition of collision of the two then (v on y-axis and s on x-axis)

(A) it will be a parabola passing through the origin

(B) it will be a straight line passing through the origin and having

a slope of g8g

(C) it will be straight line passing through the origin and having a slope of g4g

(D) it will be straight line not passing through the origin

4. AB is an inclined roof and a body is projected from origin towards the roof as shown in figure. The

value of h for which body will just touch the roof is:

[Given : = = 45o and u = 10 m/s, g = 10 m/s2]

(A) 12 m

(B) 15 m

(C) 10 m

(D) 5 m

5. A house directs a horizontal jet of water moving with a velocity of 20 m/s on to a vertical wall. The

cross –sectional area of the jet is 5 10–4 m2 . If the density of water is 1000 kg/m3, the force on the

wall assuming that the water comes to rest after striking the wall, is

(A) 200 N (B) 100 N (C) 75 N (D) 50 N

6. A solid rubber ball of density d and radius R falls vertically through air. Assume that the air resistance

acting on the ball is F = k R V, where k is constant and V its velocity. Because of this air resistance,

the ball attains a constant velocity called terminal velocity Vt after some time. Then Vt is

(A) 24 R dg

3k (B)

24 Rd g3k

(C) 24 Rdg

3k (D) 4 Rdg

3k


7. A body of mass m was slowly halved upon the hill by a force which at each point was directed along a

tangent to the path. The work done by the applied force:

(A) does not depend upon path followed by the body (B) depends upon path

(C) does not depend upon positions of A and B

(D) both a and c are correct

8. A long spring, when stretched by x cm has a potential energy U. On increasing the length of spring by

stretching to nx cm, the potential energy stored in the spring will be:

(A) Un

(B) nU (C) n2U (D) 2Un

9. A 2.0 kg block is dropped from a height of 40 cm onto a spring of spring constant k = 1960 N/m. Find

the maximum distance the spring is compressed .

(A) 0.080 m

(B) 0.20 m

(C) 0.40 m

(D) 0.10 m

10. A mass 2m rests on a horizontal table. It is attached to a light inextensible string which passes over a

smooth pulley and carries a mass m at the other end. If the mass m at the other end. If the mass m is

raised vertically through a distance h and is then dropped, what is the speed with which the mass 2m

begins to rise?

(A) 2gh5

(B) 2gh3

(C) gh3

(D) 2gh

11. Two blocks m1 and m2 (m2 > m1) are connected with a spring of force constant k and are inclined at

an angle with horizontal. If the system is released from rest, which one of the following statements

is/are correct?

(A) Maximum compression in the spring is 1 2(m m )gsink

if there is no

friction any where

(B) There will be no compression or elongation in the spring if there is no friction any where.

(C) If m1 is smooth and m2 is rough there will be compression in the spring .

(D) Maximum elongation in the spring is 1 2(m m )gsink

if all the surfaces are smooth


12. A light rod carries three equal masses A, B and C as shown in figure. The velocity of B in vertical

position of rod if it is released from horizontal position as shown in figure is :

(A) 2gl (B) 18gl7

(C) 4gl3

(D) 8gl7

13. Four holes of radius R are cut from a thin square plate of side 4R and mass M. The moment of inertia

of the remaining portion about z-axis is :

(A) 2MR12 (B) 24 MR

3 3

(C) 28 10 MR3 16

(D) 24 MR3 6

14. A force F is applied on the top of a cube as shown in figure. The coefficient of friction between the cube and the ground is μ. If F is gradually increased, the cube will topple before sliding if:

(A) μ > 1 (B) μ < 21

(C) μ > 21

(D) μ < 1

15. A straight rod of length L extends from x = a to x = L + a. The gravitational force exerted by it on a

point mass m at x = 0 if the linear density of rod is = A + Bx2, is :

(A) AGm BLa

(B) 1 1Gm A BL

a a L

(C) AGm BLa L

(D) AGm BL

a

16. A satellite of mass ms revolving in a circular orbit of radius rs around the earth of mass M has a total energy E. Then its angular momentum will be :

(A) 2s s

Em r

(B) 2s s

E2m r

(C) 2s s2Em r (D) s s2Em r

17. In figure, the spring has a force constant k. The pulley is light and smooth, the spring and the string

are light. The suspended block has a mass m. If the block is slightly displaced from its equilibrium

position and then released, the period of its vertical oscillation is :

(A) m2k

(B) m4k

(C) k2m

(D) k4m


18. Starting from the origin a body oscillates simple harmonically with a period of 2 s. After what time will

its kinetic energy be 75% of the total energy?

(A) 1s6

(B) 1 s4

(C) 1 s3

(D) 1 s12

19. A cyclic process for 1 mole of an ideal gas is shown in the V-T diagram. The work done in AB, BC

and CA respectively are :

(A) 11 1 2

2

V0,RT ln ,R(T T )V

(B) 11 2 1 1

2

VR(T T ),R,RT T lnV

(C) 2 12 1 2

1 1

V RT0,RT ln , (V V )V V

(D) 12 2 1

2

V0,RT ln ,R(T T )V

20. For a positively charged particle moving in X-Y plane initially along the X-axis,

there is a sudden change in its path due to the presence of electric and /or

magnetic fields beyond P. as shown in fig. The curved path is shown in X-Y

plane and is found to be non-circular. Which one of the following combinations

is possible ?

(A) E = 0; B = b j + c k (B) E = a i; B = c k + b i

(C) E = 0; B = c j + b k (D) E = a i; B = c k + b j

21. Two circular coils X and Y having equal number of turns and carry equal currents in the same sense and subtend same solid angle at point O. If the

smaller coil X is midway between O and Y, then it we represent the magnetic

induction due to the bigger coil Y at O as By and that due to smaller coil x at O

as Bx, then

(A) y

x

B 1B 4

(B) y

x

B 1B 2

(C) y

x

B1

B (D) y

x

B2

B

22. Two long parallel wires are at a distance 2d apart. They carry steady equal currents flowing out of the

plane of the paper, as shown. The variation of the magnetic field B along the line X X’ is given by

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

23. Two charges, each equal to 1 C, are placed at the vertices A and B of a triangle ABC. The product

of AC and BC is 30 cm2. The sum of the sides AC and BC is 10 cm. The potential at C is

(A) 3 x 105 V (B) 6 x 105 V (C) 9 x 105 V (D) 18 mV


24. The two metallic plates of radius r are placed at a distance d apart and its capacity is C. If a plate of

radius r/2 and thickness d of dielectric constant 6 is placed between the plates of the condenser, then

its capacity will be

(A) 7C /2 (B) 3C /7 (C) 7C /3 (D) 9C /4

25. Four metallic plates each with a surface area A of one side are placed at a

distance ‘d’ from each other. The plates are connected as shown in fig. Then the

capacitance of the system between ‘a’ and ‘b’ is

(A) 03 Ad

(B) 02 Ad

(C) 02 A3d

(D) 03 A2d

26. In the circuit shown in fig. the total current supplied by the battery is

(A) 2 A (B) 4 A

(C) 1 A (D) 6 A

27. AB is a potentiometer wire of length 100 cm and its resistance is 10 . It is connected in series with a

resistance R = 40 and a battery of emf 2 V and negligible internal resistance. If source of unknown

emf E is balanced by 40 cm length of the potentiometer wire, then the value of E is

(A) 0.8 V

(B) 1.6 V

(C) 0.08 V

(D) 0.16 V

28. A torch bulb rated at 4.5 W, 1.5 V is connected as shown in fig. The emf of the cell needed to make

the bulb glow at full intensity is

(A) 4.5 V

(B) 1.5 V

(C) 2.67 V

(D) 13.5 V

29. Name the Gate represented by the following circuit.

(A) OR gate

(B) XOR gate

(D) AND gate

(D) NAND gate


30. A full wave rectifier along with the output is shown in fig. The contribution(s) from the diode 1 are

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


JEE MAIN PART TEST-4 CHEMISTRY

31. Hydrogenation of benzoyl chloride in the presence of Pd on BaSO4 gives

(A) Benzyl alcohol (B) Benzaldehyde (C) Benzoic acid (D) Phenol

32. Under Wolff Kishner reduction conditions, the conversion which may be through about is -

(A) Benzaldehyde into Benzyl alcohol (B) Cyclohexanol into Cyclohexane

(C) Cyclohexanol into Cyclohexanol (D) Benzophenone into Diphenylmethane

33. Among the given compounds, the most succeptible to nucleophilic attack at the carbonyl group is -

(A) MeCOCl (B) MeCHO (C) MeCOOMe (D) MeCOOCOMe

34. Which of the following will react with water to form a stable hydrate -

(A) CHCl3 (B) Cl3CCHO (C) CCl4 (D) ClCH2CH2Cl

35. + Phenol, P & Q are -

(A) and (B) and

(C) and (D) and

36. The reaction products of, C6H5OCH3 + HI are :

(A) C6H5OH + CH3I (B) C6H5I + CH3OH (C) C6H5CH3 + HOI (D) C6H6 + CH3 OI

37. The order of reactivity of the following alcohols -

(I) (II) (III) (IV)

towards conc. HCl is -

(A) I > II > III > IV (B) I > III > II > IV (C) IV > III > II > I (D) IV > III > I > II

38. 3(excess)

CH MgBr + Ethyl ester which can be formed as product :

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

CH–CH–CH–Cl3 2 2

AlCl3P Q

(i) O/2

(ii) HO3

CH– C–H3 CH–2

O

CH–C–3 CH3

O

CH–C–3 CH3

O

CH– C–H3 CH–2

O

F

CH3

OH FCH3

OH

CH3

OH

CH3

Ph OH

HO

CHCH2 3

CHCH2 3

CHCH2 3

HO

CH3

CH CH2 3CH2

CHCH2 3

HO

CH3

CHCH2 3

CHCH2 3

HO

CH3

CH3

CH3


39.

NO2

OH

SO H3

NaHCO 3 NaHCO 3(I) (II)

NO2O N2

Gases released in reaction (I) and (II) are :

(A) CO2, CO2 (B) SO2,NO2 (C) SO2, CO2 (D) SO2, no

40. Identify the correct order of reactivity in electrophilic substitution reaction of the following compounds

(A) 1 > 2 > 3 > 4 (B) 4 > 3 > 2 > 1 (C) 2 > 1 > 3 > 4 (D) 2 > 3 > 1 > 4

41. In conversion of lime-stone to lime, CaCO3(s) CaO(s) + CO2(g) the values of H° and S° are

+179.1 kJ mol–1 and 160.2 J/K respectively at 298 K and 1 bar. Assuming that H° and S° do not

change with temperature, temperature above which conversion of limestone to lime will be spontaneous is :-

(1) 1008 K (B) 1200 K (C) 845 K (D) 1118 K

42. The entropy change involved in the isothermal reversible expansion of 2 moles of an ideal gas from a volume of 10 dm3 to a volume of 100 dm3 at 27°C is :-

(A) 32.3 J mol–1 K–1 (B) 42.3 J mol–1 K–1 (C) 38.3 J mol–1 K–1 (D) 35.8 J mol–1 K–1

43. The incorrect expression among the following is :-

(A) K = e–G°/RT (B)

system

total

GS

= – T

(C) In isothermal process, Wreversible = – nRT ln f

i

VV

(D) lnK = H T SRT

44. One mole of an ideal gas is expanded isothermally and reversibly to half its initial pressure. S for

the process in J K–1 mol–1 is [ln 2 = 0.693 and R = 8.314, J/(mol/K)] :

(A) 10.76 (B) 6.76 (C) 8.03 (D) 5.76

45. A piston filled with 0.04 mol of an ideal gas expands reversibly from 50.0 mL to 375 mL at a constant temperature of 37.0°C. As it does so, it absorbs 208J of heat. The values of q and w for the process will be :-

(R = 8.314 J/mol K) (ln 7.5 = 2.01)

(A) q = + 208 J, w = – 208 J (B) q = – 208 J, w = – 208 J

(C) q = – 208 J, w = + 208 J (D) q = + 208 J, w = + 208 J

46. For sparingly soluble salt ApBq, the relationship of its solubility product (Ls) with its solubility (S) is

(A) Ls = Sp+q, pp.qq (B) Ls = Sp+q, pp.qp (C) Ls = Spq, pp.qq (D) Ls = Spq, (p.q)p+q

1 2 3 4

CH3 Cl NO2


47. A solution which is 10–3 M each in Mn2+, Fe2+, Zn2+ and Hg2+ is treated with 10–16M sulphide ion. If

Ksp, MnS, FeS, ZnS and HgS are 10–15, 10–23, 10–20 and 10–54 respectively, which one will precipitate

first ?

(A) FeS (B) MnS (C) HgS (D) ZnS

48. HX is a weak acid (Ka = 10–5). It forms a salt NaX (0.1 M) on reacting with caustic soda. The degree

of hydrolysis of NaX is

(A) 0.01% (B) 0.0001% (C) 0.1% (D) 0.5%

49. CH3NH2 (0.1 mole, Kb = 5 × 10–4) is added to 0.08 moles of HCl and the solution is diluted to one

litre, resulting hydrogen ion concentration is

(A) 1.6 × 10–11 (B) 8 × 10–11 (C) 5 × 10–5 (D) 2 × 10–2

50. The average kinetic energy of an ideal gas, per molecule at 25°C is :

(A) 6.1 x 10-21 J (B) 6.1 x 10-23 J (C) 6.1 x 10-25 J (D) 6.1 x 10-26 J

51. Root mean square velocity of a molecule is 1000 m/s. The average velocity of the molecule is:

(A) 455.55 m/s (B) 675.55 m/s (C) 921.58 m/s (D) 1221.58 m/s

52. Van der Waals equation for one mol of CO2 gas at low pressure will

(A) P(V - b) = RT - 2a

V (B) P = 2

RT aV b V

(C) P =

RT

V b (D) 2

aPV

V = RT

53. Which of the following volume versus temperature (celsius) plots represents the behavior of 1 mol of

an ideal gas at a pressure of 1 atm?

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

54. The correct set of four quantum numbers for the valence electron of rubidium atom (Z = 37) is:-

(A) 5, 0, 0, + ½ (B) 5, 1, 0, + ½ (C) 5, 1, 1, + ½ (D) 6, 0, 0 + ½

55. The orbital angular momentum of a p-electron is given as :-

(A) 32

h (B) 6 .2h (C)

2 h (D) 3

2h

(22.4L,273.15 K)

tºC

(38.8L,373.15 K)V(L)

(22.4L,273.15 K)

tºC

(28.6L,373.15 K)V(L)

(22.4L,273.15 K)

tºC

(30.6L,373.15 K)V(L)

(22.4L,273.15 K)

tºC

(14.2L,373.15 K)

V(L)


56. The uncertainity in position of an electron & helium atom are same. If the uncertainity in momentum

for the electron is 32 × 105 , then the uncertainity in momentum of helium atom will be

(A) 32 × 105 (B) 16 × 105 (C) 8 × 105 (D) None

57. What is the ratio of the De-Broglie wave lengths for electrons accelerated through 200 volts and

50 volts :-

(A) 1 : 2 (B) 2 : 1 (C) 3 : 10 (D) 10 : 3

58. Which represents the correct pattern of electron filling in Cr :-

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

59. For H atom, the energy required for the removal of electron from various sub-shells is given as

under:-

The order of the energies would be :-

(A) E1 > E2 > E3 (B) E3 > E2 > E1 (C) E1 = E2 = E3 (D) None of these

60. Radius of H-atom in its ground state is 5.3 × 10–11 m. After collision with an electron it is found to

have a radius of 21.2 × 10–11m. What is the principal quantum no. 'n' of the final state of the atom:-

(A) n = 2 (B) n = 3 (C) n = 4 (D) n = 16

3s 3p 3dE1

E2

E3

000

n=


JEE MAIN PART TEST-4 MATHEMATICS

61. The domain of the real valued function 1 3x 1f x 1 2x 2sin2

is :

(A) 1, 13

(B) 1 , 1

2

(C) 1 1,2 3

(D) 1 1,

3 2

62. The domain of the function 23 xf x log x 1 is :

(A) 3, 1 1, (B) 3, 1 1,

(C) 3, 2 2, 1 1, (D) 3, 1 2, 1 1,

63. The range of the function 221f x x

x 1

is :

(A) 1, (B) 2, (C) 3 ,2

(D) None of these

64. If 4 2f x 2x 13x ax b is divisible by 2x 3x 2 , then (a, b) is equal to :

(A) 9, 2 (B) (6, 4) (C) (9, 2) (D) (2, 9)

65. The function f (x) which satisfies f xf x f x

x

and f (0) = 1, is given by :

(A) 2xf x e (B) 2xf x e (C) 2x 2f x e / (D) 2x 2f x e /

66. If f : R R and g : R R are defined by f x x 3 and 2g x x 1 , then the values of x for

which g f x 10 are :

(A) 0, 6 (B) 2, 2 (C) 1, 1 (D) 0, 6

67. Which one of the following is not bounded on the intervals as indicated ?

(A) 1

x 1f x 2 on (0, 1) (B) 1g x x cosx

on ,

(C) xh x xe on 0, (D) 1 xl x tan 2 on ,

68. If f 3 6 and f 3 2 , then x 3

xf 3 f xlim

x 3

is given by :

(A) 6 (B) 4 (C) 0 (D) None of these

69. If for a continuous function f, f 0 f 1 0, f 1 2 and f xxg x f e e , then g 0 is equal to:



70. If f(x) = eg(x) and g(x) = x

42

t dt1 t then f (2)

(A) equals 2/17 (B) equals 0

(C) equals 1 (D) cannot be determined

71. The area of the quadrilateral with its vertices at the foci of the conics

9x2 – 16y2 – 18x + 32y – 23 = 0 and 25x2 + 9y2 – 50x – 18y + 33 = 0, is

(A) 5/6 (B) 8/9 (C) 5/3 (D) 16/9

72. Given f (x) = x

2e cos2x x

x for x R {0} , g (x) = f ({x}) for n < x < n + 1

2 = f (1 – {x}) for

n + 12

< x < n + 1 , n I where {x}denotesfractionalpartfunction

= 5/2 otherwise then g (x) is

(A) discontinuous at all integral values of x only

(B) continuous everywhere except for x = 0

(C) discontinuous at x = n + 1/2 ; n I and at some n I

(D) continuous everywhere

73. Total number of integral value of ‘K’ so that the graphs of the functions y = 2 Kx + 1 and

y = ( K – 6 ) x2 – 2 do not intersect, are

(A) 9 (B) 11 (C) 13 (D) none of these

74. If and be the roots of the equation x2 + 3x + 1 = 0 then the value of 2 2

1 1

is equal to

(A) 15 (B) 18 (C) 21 (D) none

75 A man starts from point. P(– 3, 4) and reaches Q(0, 1) touching x-axis at R such that PR + RQ is

minimum then R is

(A) 3 , 05

(B) 3 , 05

(C) 2 , 05

(D) 2, 0

76. A variable line x my 1 ( , m are parameters) intersect a circle 2 2x y 4x 3 0 at points P and

Q. The chord PQ subtends a right angle at origin. If the locus of foot of perpendicular drawn from

(0, 0) on the given variable line is 2 2x y 4x 3 0 then find .

(A) 4 (B) 3 (C) 2 (D) 1

77. Let R be the region containing the point (x, y) on the plane satisfying 2 | x 3y | | x y | 4 then

area of R is

(A) 8 (B) 10 (C) 6 (D) 12


78. Let d(P, L) represents the perpendicular distance of the p from the line L. If A(0, 0), B(5, 0), C(5, 3),

D(0, 3) are the vertices of a rectangle ABCD. If P is a variable point lying inside the rectangle ABCD

such that d(P, AB) max {d(p, BC), d(P, CD), d(P, AD)}, then the area of the region in which P lies is

(A) 1 (B) 1/2 (C) 1/4 (D) 3/4

79. Give the number of common tangents to circle 2 2x y 2x 8y 23 0 and 2 2x y 4x 10y 9 0


80. A line x my n 0 meets the circle 2 2 2x y a at the points P and Q. The tangents drawn at the

points P and Q meet at R, then the coordinates of R is

(A) 2 2a a m,n n

(B)

2 2a a m,n m

(C)

2 2a n a n,m

(D) None of these

81. A line through (0,0) cuts the circle 2 2x y 2ax 0 at A and B, then locus of the centre of the circle

drawn on AB as a diameter is

(A) 2 2x y 2ay 0 (B) 2 2x y ay 0 (C) 2 2x y ax 0 (D) 2 2x y ax 0

82. The number of all possible 5-triplets 1 2 3 4 5(a ,a ,a ,a ,a ) such that

1 2 3 4 5a a sin x a cos x a sin 2x a cos 2x 0 holds for all x is :

(A) 0 (B) 1 (C) 2 (D) infinite

83. The number of pairs (x, y) satisfying the equations sinx siny sin(x y) and | x | | y | 1, is

(A) 2 (B) 4 (C) 6 (D) infinite

84. Total number of roots of the equation cos x3 | sin x |, belonging to [ 2 , 2 ] are :

(A) 6 (B) 8 (C) 10 (D) 12

85. Let f(x) max {1 x, 1 x}, then number of solutions in the interval [0, 2 ] satisfying f(x) = tanx is


86. If the length of the latus rectum of the parabola 2 2 2169 {(x 1) (y 3) } (5x 12y 17) is L then the

value of 13 L4

is

(A) 7 (B) 5 (C) 14 (D) 21


87. If 2x 2x

x 0

ae bcos2x ce x sinxlim 1x sinx

and 2f(t) (a b) t (a b) t c, then

(A) 1a4

(B) 1c2

(C) 3f(1)2

(D) f(1) 1

88. Let 1 1 1a sin (sin3) sin (sin4) sin (sin5), 2x |x|f(x) e , domain of f(x) be [a, ), range of f(x) be

[b, ), 4 7 1/ 71g(x) (4cos x 2cos2x cos 4x x ) ,2

domain and range of g(x) is set of real numbers.

Which of the following are correct ?

(A) a 3 (B) b a 1

(C) 3f(gog (b)) e (D) both f(x), g(x) are non-invertible functions

89. Let f(x) be a differentiable function on [0, 8]. Such that f(1) 3, f(2) 1/ 2, f(3) 4, f(4) 2, f(5) 6,

f(6) 1/ 3, f(7) 1/ 4 . Then the minimum number of points of intersection of the curves

2y f '(x) and y f '(x) (f(x)) is

(A) 7 (B) 10 (C) 11 (D) 8

90. If f :R R is a function defined by 2x 1f(x) [x]cos2

where [x] denotes the greatest integer

function, then f is

(A) continuous for every real x (B) discontinuous only at x = 0

(C) discontinuous only at non-zero integral values of x

(D) continuous only at x = 0

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