JEE Main B.E. B.Tech Paper 1

1. Molar mass of the hydrocarbon (X) which on ozonolysis consumes one mole  of  O₃  per  mole of (X) and gives one mole each of ethanal and propanone is g mol–1 (Molar mass of C

: 12 g mol–1, H : 1 gmol–1)

2. The area of the region {(x, y): x2 £ y £ 8 – x2, y £ 7}

3.

4. The momentum of a body is increased by 50%. The percentage increase in the kinetic energy of the body is %

5.

6. The magnetic intensity at the center of a long current carrying solenoid is found to be
1.6 × 103 Am–1. If the number of turns is 8 per cm, then the current flowing through the solenoid is A.

7.

8. The number of arrangements of the letters of the word “INDEPENDENCE” in which all the vowels always occur together is

9.  XeF4 reacts with SbF5 to form [XeFm]n+[SbFy]z–

m + n + y + z =

10. The titration curve of a weak acid vs. strong base with phenolphthalein as indictor is shown below. The Kphenolphthalein = 4 × 10–10    Given: log 2 = 0.3

The number of following statement/s which is/are correct about phenolphthalein is               

11.

12. The number of ways, in which 5 girls and 7 boys can be seated at a round table so that no two girls sit together, is

13. In a reflecting telescope, a secondary mirror is used to:

14. The engine of a train moving with speed 10 ms^–1 towards a platform sounds a whistle at frequency

400 Hz. The frequency heard by a passenger inside the train is : (neglect air speed. Speed of Sound in air = 330 ms^–1)

15.

16. A  TV  transmitting  antenna  is  98  m  high  and the receiving antenna is at the ground level. If the radius of the earth is 6400 km, the surface area covered by the transmitting antenna is approximately:

Graphical variation of electric field due to a uniformly charged insulating solid sphere of radius R, with distance r from the centre O is represented by:

19. Which of the following represent the Freundlich adsorption isotherms?

20. Let R be the focus of the parabola y2 = 20x and the line y = mx + c intersect the parabola at two points P and Q.

Let the point G(10, 10) be the centroid of the triangle PQR. If c – m = 6, then (PQ)2 is

21. A current of 2 A through a wire of cross-sectional area 25.0 mm2. The number of free electrons in a cubic meter are 2.0 × 1028. The drift velocity of the electrons is    × 10–6 ms–1

(given, charge on electron = 1.6 × 10–19 C).

22. Which of the following metals can be extracted through alkali leaching technique?

23. equal to  .

24. In a bolt factory, machines A, B and C manufacture respectively 20%, 30% and 50% of the total bolts. Of their output 3, 4 and 2 percent are respectively defective bolts. A bolt is drawn at random form the product. If the bolt drawn is found the defective, then the probability that it is manufactured by the machine C is.

25. In this figure the resistance of the coil of galvanometer G is 2 W. The emf of the cell is 4 V. The ratio of potential difference across C₁ and C₂ is:

26.

Sulphur (S) containing amino acids from the following are:

27.  

(a)  isoleucine

(b)  cysteine

27.  

(c)  lysine

27.  

(d)  methionine

27.  

(e)  glutamic acid

28.  

Let C(a, b) be the circumcenter of the triangle formed by the lines

4x + 3y = 69,

4y – 3x = 17 and

x + 7y = 61.

Then (a – b)2 + a + b is equal to

28.  

29. where R is the radius and M is the mass of the semicircular ring. The value of x will be .

30. An organ pipe 40 cm long is open at both ends. The speed of sound in air is 360 ms^–1. The frequency of the second harmonic is  Hz.

31. Let the mean and variance of 8 numbers x, y, 10, 12, 6, 12, 4, 8 be 9 and 9.25 respectively. If x > y, then 3x – 2y is equal to   .

32. Two projectiles A and B are thrown with initial velocities of 40 m/s and 60 m/s at angles 30° and 60° with the horizontal respectively. The ratio of their ranges respectively is (g = 10 m/s²)

33.

34. The number of  following  factors  which  affect the percent covalent character of the ionic bond is           

35.

36. 0.5 g of an organic compound (X) with 60% carbon will produce × 10–1 g of CO2 on complete combustion.

37. is a, then [a] is equal to .

38. An air bubble of volume 1 cm³ rises from the bottom of a lake 40 m deep to the surface at a temperature of 12°C. The atmospheric pressure is 1 × 10⁵ Pa, the density of water is 1000 kg/m³ and g = 10 m/s². There is no difference of the temperature of water at the depth of 40 m and on the surface. The volume of air bubble when it reaches the surface will be:

40. Let a, b, g, be the three roots of the equation x3 +bx + c = 0. If bg = 1 = –a, then b3 + 2c3 – 3a3 – 6b3  – 8g3 is equal to

41. At any instant the velocity of a particle of mass 500 g is  (2tˆi + 3t2ˆj)  ms^–1. If the force acting on the

particle at t = 1s is  (ˆi + xˆj) N . Then the value of x

will be:

42.

43.

44. When a 60 W electric heater is immersed in a gas for 100s in a constant volume container with adiabatic walls, the temperature of the gas rises by 5°C. The heat capacity of the given gas is J K–1(Nearest integer).

45. The correct order of electronegativity for given elements is:

46. Choose the halogen which is most reactive towards SN1 reaction in the given compounds (A, B, C, & D)

47. A charge  particle  moving  in  magnetic  field  B, has the components of velocity along B as well as perpendicular to B. The path of the charge particle will be

48.

50. Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R. Assertion A: Butan-1-ol has higher boiling point than ethoxyethane.
Reason R: Extensive hydrogen bonding leads to stronger association of molecules.
In the light of the above statements, choose the correct answer from the options given below:

51. An air bubble of diameter 6 mm rises steadily through a solution of density 1750 kg/m3 at the rate of 0.35 cm/s. TGe co-efficient of viscosity of the solution (neglect density of air) is    poise (given, g = 10 ms–2).

52. Given below are two statements: Statement I: Lithium and Magnesium do not form superoxide Statement II: The ionic radius of Li+ is larger than ionic radius of Mg2+ In the light of the above statements, choose the most appropriate answer from the options given below:

53.  

If the coefficients of three consecutive terms in the expansion of (1 + x)n are in the ratio 1 : 5 : 20, then the coefficient of the fourth term is

54. What is the purpose of adding gypsum to cement?

55. An oscillating LC circuit consists of a 75 mH inductor and a 1.2 mF capacitor. If the maximum charge to the capacitor is 2.7 mC. The maximum current in the circuit will be mA.

56. Consider a circle C1 : x² + y² – 4x –2y = a – 5. Let its mirror image in the line y = 2x +1 be another circle C2 : 5x² + 5y² –10fx – 10gy + 36 = 0. Let r be the radius of C₂. Then a + r is equal to .

57. Which of the following complex is octahedral, diamagnetic and the most stable?

Two vertical parallel mirrors A and B are separated by 10 cm. A point object O is placed at a distance of 2 cm from mirror A. The distance of the second nearest image behind mirror A from the mirror A is   cm

58.  

59. Let A = {0, 3, 4, 6, 7, 8, 9, 10} and R be the relation defined on A such that R =(x, y) Î A × A: x – y is odd positive integer or x – y = 2}. The minimum number of elements that must be added to the relation R, so that it is a symmetric relation, is equal to .

60. A nucleus with mass number 242 and binding energy per nucleon as  7.6  MeV  breaks  into two fragment each with mass number 121. If each fragment nucleus has binding energy per nucleon as 8.1 MeV, the total gain in binding energy is MeV.

61.

62. The weight of a body on the earth is 400 N. Then weight of the body when taken to a depth half of the radius of the earth will be:

63. An  aluminium   rod   with   Young’s   modulus Y = 7.0 × 10¹⁰ N/m² undergoes elastic strain of 0.04%. The energy per unit volume stored in the rod in SI unit is:

64. Negation of (p ® q) ® (q ® p) is

65.

C.  The volume energy bv = a₃A

D. Decrease in the binding energy is proportional to surface area.

E.   While estimating the surface energy, it is assumed that each nucleon interacts with 12 nucleons. (a1, a2 and a3 are constants)

Choose the most appropriate answer from the

options given below:

66. The largest natural number n such that 3n divides 66! is .

67.

69. The correct order of spin only magnetic moments for the following complex ions is

70.  The number of given statement/s which is/are correct is                  

71. Certain galvanometers have a fixed core made of non magnetic metallic material. The function of this metallic material is

72. The water gas on reacting with cobalt as a catalyst forms

73. be atm. (Nearest integer)

74. The vapour pressure vs. temperature curve for a solution solvent system is shown below:

The boiling point of the solvent is °C

75. Let the number of elements in sets A and B be five and two respectively. Then the number of subsets of A × B each having at least 3 and at most 6 elements is:

76.

77.

78.

79.

80.  Which halogen is known to cause the reaction given below:

2Cu2++4X– ® Cu2X2(s)+X2

81. Given below are two statements:

Statement I: If heat is added to a system, its temperature must increase.

Statement II: If positive work is done by a system in a thermodynamic process, its volume must increase.

In the light of the above statements, choose the correct answer from the options given below

82. The number of following statements which is/are incorrect is_________

For the logic circuit shown, the output waveform at Y is:

84. In chromyl chloride, the number of d-electrons present on chromium is same as in (Given at no. of Ti: 22, V : 23, Cr : 24, Mn : 25, Fe : 26)

85. Proton (P) and electron (e) will have same de- Broglie wavelength when the ratio of their momentum is (assume, mp = 1849 me):

86. A cylindrical wire of mass (0.4 ± 0.01)g has length (8 ± 0.04) cm and radius (6 ± 0.03) mm. The maximum error in its density will be:

87.  

If the eqation of the plane containing the line x + 2y + 3z – 4 = 0 = 2x + y –z + 5 and perpendicular to the plane  r→ = (ˆi - ˆj) + l(ˆi + ˆj + kˆ) + m(ˆi - 2ˆj + 3kˆ) is ax + by + cz = 4, then (a – b + c) is equal to

88. An electric dipole of dipole moment 6.0 × 10^–6 Cm placed in a uniform electric field of 1.5 × 10³ NC^–1 in such a way that dipole moment is along electric field. The work done in rotating dipole by 180° in this field will be mJ.

89.

90.