1. JEE MAIN 2002 CHEMISTRY):-

What is the product when acetylene reacts with hypochlorous acid ?

(1) CH₃COCl

(2) ClCH₂CHO

(3) Cl₂CHCHO

(4) ClCHCOOH

1. JEE MAIN 2002 CHEMISTRY):-

When H₂ S is passed through Hg₂ S we get

(1) HgS

(2) HgS + Hg₂ S

(3) Hg₂ S

(4) Hg₂ S₂

2. JEE MAIN 2002 CHEMISTRY):-

Units of rate constant of first and zero order reactions in terms of molarity M unit are respectively

(1) sec⁻¹, Msec⁻¹

(2) sec⁻¹, M

(3) Msec^-1, sec⁻¹

(4) M, sec⁻¹

3. (JEE MAIN 2002 CHEMISTRY):-

At a specific instant emission of radioactive compound is deflected in a magnetic field. The compound can emit (i) electrons (ii) protons (iii) He²⁺ (iv) neutrons The emission at instant can be

4. JEE MAIN 2002 CHEMISTRY):-

The integrated rate equation is Rt = logC₀ − logC_t. The straight line graph is obtained by plotting

(1) time vs log C_t

(2) 1/time vs C_t

(3) time vs C_t

(4) 1/time vs 1/C_t

5. JEE MAIN 2002 CHEMISTRY):-

Arrange Ce⁺³, La⁺³, Pm⁺³ and Yb⁺³ in increasing order of their ionic radii

(1) Yb⁺³ < Pm⁺³ < Ce⁺³ < La⁺³

(2) Ce⁺³ < Yb⁺³ < Pm⁺³ < La⁺³

(3) Yb⁺³ < Pm⁺³ < La⁺³ < Ce⁺³

(4) Pm⁺³ < La⁺³ < Ce⁺³ < Yb⁺³

6. JEE MAIN 2002 CHEMISTRY):-

Polymer formation from monomers starts by

7. JEE MAIN 2002 CHEMISTRY):-

The metal extracted by leaching with a cyanide is

8. JEE MAIN 2002 CHEMISTRY):-

Species acting as both Bronsted acid and base is

(1) (HSO4)⁻¹

(2) Na₂CO₃

(3) NH₃

(4) OH⁻¹

9. JEE MAIN 2002 CHEMISTRY):-

In a compound C, H and N atoms are present in 9 : 1 : 35 by weight. Molecular weight of compound is 108. Molecular formula of compound is

10. JEE MAIN 2002 CHEMISTRY):-

Cyanide process is used for the extraction of

11. JEE MAIN 2002 CHEMISTRY):-

Most common oxidation states of Ce (cerium) are

12. JEE MAIN 2002 CHEMISTRY):-

Which of the following reaction is possible at anode?

(1) 2Cr³⁺ + 7H₂O → Cr₂O²⁻₇ + 14H⁺

(2) F₂ → 2 F⁻

(3) (1/2)O₂ + 2H⁺ → H₂O

(4) none of these

13. JEE MAIN 2002 CHEMISTRY):-

With increase of temperature, which of these changes?

14. (JEE MAIN 2002 CHEMISTRY):-

If 13.6eV energy is required to ionize the hydrogen atom, then the energy required to remove an electron from n = 2 is

15. JEE MAIN 2002 CHEMISTRY):-

The part of a transistor which is most heavily doped to produce large number of majority carriers is

16. JEE MAIN 2002 CHEMISTRY):-

Which of the following does not show geometrical isomerism?

17. JEE MAIN 2002 CHEMISTRY):-

When the sample of copper with zinc impurity is to be purified by electrolysis, the appropriate electrodes are

18. JEE MAIN 2002 CHEMISTRY):-

Which of these will not react with acetylene ?

(1) NaOH

(2) ammonical AgNO₃

(3) Na

(4) HCl

19. JEE MAIN 2002 CHEMISTRY):-

If ϕ denotes reduction potential, then which is true ?

(1) E⁰_cell = ϕ_right − ϕ_left

(2) E⁰_cell = ϕ_{left +} ϕ_right

(3) E⁰_cell = ϕ_{left -} ϕ_right

(4) E⁰_cell = -(ϕ_{left +} ϕ_right )

20. JEE MAIN 2002 CHEMISTRY):-

β - particle is emitted in radioactivity by

21. JEE MAIN 2002 CHEMISTRY):-

KO₂ (potassium super oxide) is used in oxygen cylinders in space and submarines because it

(1) absorbs CO₂ and increases O₂ content

(2) eliminates moisture

(3) absorbs CO₂

(4) produces ozone.

22. JEE MAIN 2002 CHEMISTRY):-

If an endothermic reaction is non- spantaneous at freezing point of water and becomes feasible at its boiling point, then

23. JEE MAIN 2002 CHEMISTRY):-

At absolute zero, Si acts as

24. JEE MAIN 2002 CHEMISTRY):-

Arrangement of (CH₃)₃ − C−, (CH₃)₂ − CH−,CH₃ − CH₂ - when attached to benzyl or an unsaturated group in increasing order of inductive effect is

(1) (CH₃)₃ − C− < (CH₃)₂ − CH− < CH₃ − CH₂

(2) CH₃ − CH₂− < (CH₃)₂− < CH− < (CH₃)₃ − C−

(3) (CH₃)₂ − CH− < (CH₃)₃ − C− < CH₃,−CH₂

(4) (CH₃)₃ − C− < CH₃ − CH₂ − (CH₃)₂ − CH−

25. JEE MAIN 2002 CHEMISTRY):-

Aluminium is extracted by the electrolysis of

26. JEE MAIN 2002 CHEMISTRY):-

If N₀ is the original mass of the substance of half- life period t_1/2 = 5 years, then the amount of substance left after 15 years is

27. JEE MAIN 2002 CHEMISTRY):-

If half-life of a substance is 5 yrs, then the total amount of substance left after 15 years, when initial amount is 64 grams is

28. JEE MAIN 2002 CHEMISTRY):-

The heat required to raise the temperature of body by 1 K is called

29. JEE MAIN 2002 CHEMISTRY):-

The differential rate law for the reaction H₂ + I₂ → 2HI is

(1) − d[H₂]/dt = − d[I₂]/dt = − d[HI]/dt

(2) d[H₂]dt = d[I₂]/dt = ½ 1d[Hl]/dt

(3) ½ d[H₂]/dt = ½ 2d[I₂]/dt = − d[HI]/dt

(4) −2 d[H₂]/dt = −2 d[I₂]/dt = d[HI]/dt

30. JEE MAIN 2002 CHEMISTRY):-

H₂O

The reaction: (CH₃)₃ C – Br      ⟶       (CH₃)₃ − C − OH

31. JEE MAIN 2002 CHEMISTRY):-

What will be the emf for the given cell Pt |H2 (P1)|H+(aq)||H2 (P2) ∣ Pt

(1) RT/f  log P1/P2

(2) RT/2f  log P1/P2

(3) RT/f  log P2/P1

(4) none of these

32. JEE MAIN 2002 CHEMISTRY):-

Change in volume of the system does not alter the number of moles in which of the following equilibria ?

(1) N2( g) + O2( g) ⇌ 2NO(g)

(2) PCl5( g) ⇌ PCl3( g) + Cl2( g)

(3) N2( g) + 3H2( g) ⇌ 2NH3( g)

(4) SO2Cl2( g) ⇌ SO2( g) + Cl2( g)

33. JEE MAIN 2002 CHEMISTRY):-

How do we differentiate between Fe³⁺ and Cr³⁺ in group III?

(1) by taking excess of NH₄OH solution

(2) by increasing NH₄ ⁺ ion concentration

(3) by decreasing OH⁻ ion concentration

(4) both (b) and (c)

34. JEE MAIN 2002 CHEMISTRY):-

Which is the correct order of ionic sizes ? (Atomic Number : Ce = 58, Sn = 50, Yb = 70 and Lu = 71)

35. JEE MAIN 2002 CHEMISTRY):-

Which of the following compounds has wrong IUPAC name ?

(1) CH3​–CH2​–CH2​–COO–CH2​CH3 -ethyl butanoate

(2) CH₃​–CH- CH₂- CH ​–CHO - 3-methyl butanal

(3) CH₃​–CH-(OH)–CH-(CH₃​)–CH₃​- 2-methyl-3-butanol

(4) CH₃​–CH-(CH₃​)–C=O–CH₂​–CH₃​- 2-methyl-3-pentanone

36. JEE MAIN 2002 CHEMISTRY):-

If mass-energy equivalence is taken into account, when water is cooled to form ice, the mass of water should

37. JEE MAIN 2002 CHEMISTRY):-

Let the solubility of an aqueous solution of Mg(OH)₂ be x then its k_sp is

(1) 4 x³

(2) 108 x⁵

(3) 27 x⁴

(4) 9x

38. JEE MAIN 2002 CHEMISTRY):-

In a hydrogen atom, if energy of an electron in ground state is 13.6 eV, then that in the 2nd excited state is

39. JEE MAIN 2002 CHEMISTRY):-

Conductivity (unit Siemen’s S) is directly proportional to area of the vessel and the concentration of the solution in it and is inversely proportional to the length of the vessel then the unit of the constant of proportionality is

(1) Sm mol⁻¹

(2) Sm² mol⁻¹

(3) S⁻² m² mol

(4) S² m² mol⁻²

40. JEE MAIN 2002 CHEMISTRY):-

In which of the following species is the underlined carbon having sp³ hybridization ?

(1) CH₃​COOH.

(2) CH₃​CH₂​OH.

(3) CH₃​COCH₃

(4) CH₂​=CH−CH₃

41. JEE MAIN 2002 CHEMISTRY):-

In which of the following reactions, increase in the volume at constant temperature does not affect the number of moles at equilibrium

(1)2NH₃ → N₂ + 3H₂

(2) C(g) + (1/2)O₂( g) → CO(g)

(3) H₂( g) + O₂( g) → H₂O₂( g)

(4) none of these

42. JEE MAIN 2002 CHEMISTRY):-

For the reaction CO(g) + (1/2)O₂( g) = CO₂( g),K_p/K_c is

43. JEE MAIN 2002 CHEMISTRY):-

Na and Mg crystallize in BCC and FCC type crystals respectively, then the number of atoms of Na and Mg present in the unit cell of their respective crystal is

44. JEE MAIN 2002 CHEMISTRY):-

When primary amine reacts with chloroform in ethanoic KOH then the product is

45. JEE MAIN 2002 CHEMISTRY):-

Which of the following are arranged in an increasing order of their bond strengths ?

(1) O⁻₂ < O₂ < O⁺₂ < O²₋

(2) O²⁻₂ < O⁻₂ < O² < O⁺₂

(3) O⁻₂ < O²⁻₂ < O² < O⁺₂

(4) O⁺₂ < O² < O⁻₂ < O²₋

46. JEE MAIN 2002 CHEMISTRY):-

RNA is different from DNA because RNA contains

47. JEE MAIN 2002 CHEMISTRY):-

In XeF₂, XeF₄, XeF₆ the numebr of lone pairs of Xe are respectively

48. JEE MAIN 2002 CHEMISTRY):-

Number of sigma bonds in P₄O₁₀ is

49. JEE MAIN 2002 CHEMISTRY):-

In case of nitrogen, NCl₃ is possible but not NCl₅ while in case of phosphorous, PCl₃ as well as

PCl₅ are possible. It is due to

50. JEE MAIN 2002 CHEMISTRY):-

The type of isomerism present in nitropentamine chromium (III) chloride is

51. JEE MAIN 2002 CHEMISTRY):-

Cl_{2             alc. KOH}

CH₃CH₂COOH   ⟶     A     ⟶        B. What is B ?

red P

(1) CH₃CH₂COCl

(2) CH₃CH₂CHO

(3) CH₂ = CHCOOH

(4) ClCH₂CH₂COOH

52. JEE MAIN 2002 CHEMISTRY):-

The most stable ion is

(1) [Fe(OH)₃]³⁻

(2) [Fe(Cl)₆]³⁻

(3) [Fe(CN)₆]³⁻

(4) [Fe(H₂O)₆]³⁺

53. JEE MAIN 2002 CHEMISTRY):-

The compound is used as

54. JEE MAIN 2002 CHEMISTRY):-

A square planar complex is formed by hybridisation of which atomic orbitals ?

(1) s, p_x, p_y, d_yz

(2) s, p_x, p_y, d_x2−y2

(3) s, p_x, p_y, d_z²

(4) s, p_y, p_z, d_xy

55. JEE MAIN 2002 CHEMISTRY):-

Which of the following statements is true ?

56. JEE MAIN 2002 CHEMISTRY):-

The formation of gas at the surface of tungsten due to adsorption is the reaction of order

57. JEE MAIN 2002 CHEMISTRY):-

Value of gas constant R is

(1) 0.082 litre atm

(2) 0.987cal mol⁻¹ K⁻¹

(3) 8.3 J mol⁻¹ K⁻¹

(4) 83 erg mol⁻¹ K⁻¹

58. JEE MAIN 2002 CHEMISTRY):-

Alum helps in purifying water by

59. JEE MAIN 2002 CHEMISTRY):-

On vigorous oxidation by permanganate solution

(CH₃)₂C = CH − CH₂ − CHO gives

60. JEE MAIN 2002 CHEMISTRY):-

The energy band gap is maximum in

61. JEE MAIN 2002 CHEMISTRY):-

The functional group, which is found in amino acid is

(1) COOH GROUP

(2) NH_{2 GROUP}

(3) CH_{3 GROUP}

(4) both (a) and (b)

62. JEE MAIN 2002 CHEMISTRY):-

Racemic mixture is formed by mixing two

63. JEE MAIN 2002 CHEMISTRY):-

In which of the following species the interatomic bond angle is 109∘28′?

64. JEE MAIN 2002 CHEMISTRY):-

When KMnO⁴ acts as an oxidising agent and ultimately forms [MnO4]⁻¹, MnO₂, Mn₂O₃,Mn⁺²

then the number of electrons transferred in each case respectively is

65. JEE MAIN 2002 CHEMISTRY):-

A similarity between optical and geometrical isomerism is that

66. JEE MAIN 2002 CHEMISTRY):-

For the reactions, C + O₂⟶CO₂; ΔH = −393 J 2Zn + O₂⟶2ZnO; ΔH = −412 J

67. JEE MAIN 2002 CHEMISTRY):-

The solubility of Mg(OH)₂ is S moles/litre. The solubility product under the same condition is

(1) 4 S³

(2) 3S⁴

(3) 4 S²

(4) S³

68. (JEE MAIN 2002 CHEMISTRY):-

Formation of covalent bonds in compounds exhibits

69. JEE MAIN 2002 CHEMISTRY):-

A metal M readily forms its sulphate MSO₄ which is water - soluble. It forms its oxide MO which becomes inert on heating. It forms an insoluble hydroxide M(OH)₂ which is soluble in NaOH solution. Then M is

70. JEE MAIN 2002 CHEMISTRY):-

Number of atoms in 558.5 gram Fe (at.wt. of = 55.85 g mol⁻¹

) is

71. JEE MAIN 2002 CHEMISTRY):-

A heat engine absorbs heat Q1 at temperature T1 and heat Q2 at temperature T2 . Work done by the engine is J (Q1 + Q2). This data

72. JEE MAIN 2002 CHEMISTRY):-

CH₃ −Mg − Br is an organo metallic compound due to

73. JEE MAIN 2002 CHEMISTRY):-

Un certainty in position of a minute particle of mass 25 g in space 10⁻⁵ is . What is the uncertainity in its velocity (in ms−1) ? (h = 6.6 × 10⁻³⁴Js)

74. JEE MAIN 2002 CHEMISTRY):-

1 M NaCl and 1 M HCl are present in an aqueous solution. The solution is

75. JEE MAIN 2002 CHEMISTRY):-

Kinetic theory of gases proves

76. JEE MAIN 2002 CHEMISTRY):-

Which of the following ions has the maximum magnetic moment ?

(1) Mn⁺²

(2) Fe⁺²

(3) Ti⁺²

(4) Cr⁺²

77. JEE MAIN 2002 CHEMISTRY):-

In mixture A and B component show -ve deviation as

78. JEE MAIN 2002 CHEMISTRY):-

For the reaction A + 2B → C , rate is given by R = [A][B]²  then the order of the reaction is

79. JEE MAIN 2002 CHEMISTRY):-

For an ideal gas, number of moles per liter in terms of its pressure P, gas constant R and temperature T is

80. JEE MAIN 2002 CHEMISTRY):-

Freezing point of an aqueous solution is (−0.186)∘C. Elevation of boiling point of the same solution is Kb = 0.512∘C,Kf = 1.86∘C , find the increase in boiling point.

(1) 0.186∘C

(2) 0.0512∘C

(3) 0.092∘C

(4) 0.2372∘C

81. JEE MAIN 2002 CHEMISTRY):-

Which of the following is a redox reaction ?

(1) NaCl + KNO₃ → NaNO₃ + KCl

(2) CaC₂O₄ + 2HCl → CaCl₂ + H₂C₂O₄

(3) Mg(OH)₂ + 2NH₄Cl → MgCl₂ + 2NH₄OH

(4) Zn + 2AgCN → 2Ag + Zn(CN)₂

82. JEE MAIN 2002 CHEMISTRY):-

EMF of a cell in terms of reduction potential of its left and right electrodes is

(1) E = E_left − E_right

(2) E = E_left + E_right

(3) E = E_right − _Eleft

(4) E = −(E_right + E_left )

1. (JEE MAIN 2002 MATH):-

In a triangle with sides a, b, c, r1 > r2 > r3 (which are the ex-radii) then

2. (JEE MAIN 2002 MATH):-

Sum of infinite number of terms of GP is 20 and sum of their square is 100. The common ratio of GP is

3. (JEE MAIN 2002 MATH):-

The centre of the circle passing through (0, 0 ) and (1, 0) and touching the circle x2 + y2 = 9 is

4. (JEE MAIN 2002 MATH):-

∫ ^10π₀ | sin x |dx is

5. (JEE MAIN 2002 MATH):-

If a > 0 discriminant of ax2 + 2bx + c is -ve, then

is

6. (JEE MAIN 2002 MATH):-

The sides of a triangle are 3x + 4y, 4x+37 and 5x + 57 where x, y > 0 then the triangle is

7. (JEE MAIN 2002 MATH):-

The sum of integers from 1 to 100 that are divisible by 2 or 5 is

8. (JEE MAIN 2002 MATH):-

l, m, n are the p^th , q^th and r^th term of a G.P. all positive, then

equals

9. (JEE MAIN 2002 MATH):-

Total number of four digit odd numbers that can be formed using 0, 1, 2, 3, 5, 7 (using repetition allowed) are

10. (JEE MAIN 2002 MATH):-

The value of 2^1/4, 4^1/8, 8^1/6 +……∞ is

11. (JEE MAIN 2002 MATH):-

Fifth term of a GP is 2, then the product of its 9 terms is

12. (JEE MAIN 2002 MATH):-

If the sum of the coefficients in the expansion of (a + b) power n is 4096 , then the greatest coefficient in the expansion is

13. (JEE MAIN 2002 MATH):-

A problem in mathematics is given to three students A, B,C and their respective probability of solving the problem is 1/2, 1/3 and 1/4. Probability that the problem is solved is

14. (JEE MAIN 2002 MATH):-

The d.r. of normal to the plane through (1, 0, 0), (0, 1, 0) which makes an angle π/4 with plane x + y = 3 are

15. (JEE MAIN 2002 MATH):-

IF →a ×→b = →b × →c = →c × →a THEN  →a +→b + →c =

16. (JEE MAIN 2002 MATH):-

A die is tossed 5 times. Getting an odd number is considered a success. Then the variance of distribution of success is

17. (JEE MAIN 2002 MATH):-

If |→a| = 4, |→ b| = 2 and the angle between vector →a and  vector →b is π/6 then (→a ×→ b)2 = 2 is equal to

18. (JEE MAIN 2002 MATH):-

1³ − 2³ + 3³ − 4³ +…. +9³ =

19. (JEE MAIN 2002 MATH):-

I_n = ∫ ^π/4₀ tanⁿ xdx then Lim _n→∞n [I_n + I_n−2] equals

20. (JEE MAIN 2002 MATH):-

If f(1) = 1, f ′(1) = 2 , then  Lim _x→1(√f(x)−1)/√x-1 is

21. (JEE MAIN 2002 MATH):-

The locus of the centre of a circle which touches the circle |z − z1| = a  and |z − z2| = b externally (z, z1 and z2 are complex numbers) will be

22. (JEE MAIN 2002 MATH):-

Two common tangents to the circle x2 + y2 = 2a2 and parabola y2 = 8ax  are

23. (JEE MAIN 2002 MATH):-

Number greater than 1000 but less than 4000 is formed using the digits 0, 1, 2, 3, 4 (repetition allowed) is

24. (JEE MAIN 2002 MATH):-

If the chord y = mx + 1 of the circle x2 + y2 = 1 subtends an angle of measure at 45 degree the major segment of the circle then value of m is

25. (JEE MAIN 2002 MATH):-

A plane which passes through the point (3, 2, 0) and the line  (x−4)/
1 = (y−7)/5 = (z−4)/4 is

26. (JEE MAIN 2002 MATH):-

If |z − 4| < |z − 2|, its solution is given by

27. (JEE MAIN 2002 MATH):-

In a class of 100 students there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class is 72, then what is the average of the girls?

28. (JEE MAIN 2002 MATH):-

If →a,→ b, → C (VECTOR A, VECTOR B, VECTOR C) are vectors such that →a +→b + →c = 0 and |→a| = 7, |→ b| = 5, |→c| = 3 then angle between vector →b and  →c is

29. (JEE MAIN 2002 MATH):-

cot⁻¹(√cos α) = tan⁻¹(√cos α) = x then sin x =

30. (JEE MAIN 2002 MATH):-

If  an = √7 +√7 + √7 +…having radical signs then by methods of mathematical induction which is true

31. (JEE MAIN 2002 MATH):-

f(x) and g(x) are two differentiable functions on [0, 2] such that  f ′′(x) − g′′(x) = 0

f ′(1) = 2g′(1) = 4f(2) = 3g(2) = 9 then  f(x) − g(x) x = 3/2 is

32. (JEE MAIN 2002 MATH):-

33. (JEE MAIN 2002 MATH):-

If →a,→ b, → are vectors such |→a→b→c| = 4 that then [a×bb×cc×a] =

34. (JEE MAIN 2002 MATH):-

Locus of mid point of the portion between the axes of x cos α + y sin α = p where p is constant is

35. (JEE MAIN 2002 MATH):-

If the pair of lines ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 intersect on the y - axis then

36. (JEE MAIN 2002 MATH):-

z and w are two non zero complex no such |z| = |w| that and Arg z + Argw = π then z equals

37. (JEE MAIN 2002 MATH):-

If 2a + 3b + 6c = 0(a, b, c ∈ R) then the quadratic equation ax²+ bx + c = 0 has

38. (JEE MAIN 2002 MATH):-

If  an = √7 +√7 + √7 +…having radical signs then by methods of mathematical induction which is true

39. (JEE MAIN 2002 MATH):-

The positive integer just greater than (1 + 0.0001)power 10000 is

40. (JEE MAIN 2002 MATH):-

THE ORDER AND DEGREE OF THE DIFFERENTIAL EQUATION

(1 + 3 dy/dx )^2/3= 4 d³y/dx³ ARE

41. (JEE MAIN 2002 MATH):-

r and n are positive integers  r > 1, n > 2 and coefficient of (r + 2)th term 3rth  and term in the expansion of (1 + x)2n are equal, then n equals

42. (JEE MAIN 2002 MATH):-

If y = [x +( √(1 + x²)]ⁿ then (1 + x²) d²y/dx² + x dy /dx is 

43. (JEE MAIN 2002 MATH):-

A triangle with vertices (4, 0), (-1, -1), (3, 5) is

44. (JEE MAIN 2002 MATH):-

∫ ^π_−π 2x (1+sin x) / (1+cos²x) dx is

45. (JEE MAIN 2002 MATH):-

3λ→c + 2μ(→a ×→ b) = 0 THEN

(“Three lambda times vector c plus two mu times the cross product of vector a with vector b equals zero.”)

46. (JEE MAIN 2002 MATH):-

If y = f(x) makes +ve intercept of 2 and 0 unit on x and y axes and encloses an area 3/ 4 of square unit with the axes then ∫²₀ xf ′(x)dx is

47. (JEE MAIN 2002 MATH):-

The point of lines represented by 3ax2 + 5xy + (a2 − 2)y2 = 0 and perpendicular to each other for

48. (JEE MAIN 2002 MATH):-

Five digit number divisible by 3 is formed using 0, 1, 2, 3, 4, 6 and 7 without repetition. Total number of such numbers are

49. (JEE MAIN 2002 MATH):-

The coefficients of x power p and x power q in the expansion of  (1 + x) power p+q are

50. (JEE MAIN 2002 MATH):-

If  p and q are the roots of the equation x² + px + q = 0, then

51. (JEE MAIN 2002 MATH):-

If the sum of the coefficients in the expansion of (a + b) power n is 4096 , then the greatest coefficient in the expansion is

52. (JEE MAIN 2002 MATH):-

53. (JEE MAIN 2002 MATH):-

If  f(x + y) = f(x) ⋅ f(y)∀x ⋅ y and f(5) = 2, f ′(0) = 3 then f ′(5) is

54. (JEE MAIN 2002 MATH):-

Product of real roots of the equation t²x² + |x| + 9 = 0

55. (JEE MAIN 2002 MATH):-

Lim_n→∞ (1^p + 2^p + 3^p +…+ n^p) / n^p+1 is

56. (JEE MAIN 2002 MATH):-

The area bounded by the curves y = ln x, y = ln |x|, y = | ln x| and y = | ln ||x| is

57. (JEE MAIN 2002 MATH):-

The maximum distance from origin of a point on the curve x =α sin t - b sin (αt/b) y =α cos t - b cos (αt/b),  both a, b > 0  is

58. (JEE MAIN 2002 MATH):-

f is defined in [-5, 5] as f(x) = x if x is rational and = -x is irrational. Then

59. (JEE MAIN 2002 MATH):-

Let f(x) = 4 and f ′(x) = 4 . Then Lim_x→2 (xf(2)−2f(x)) / ( x−2) is given by

60. (JEE MAIN 2002 MATH):-

THE SOLUTION OF THE EQUATION d²y/dx²=e^-2x

61. (JEE MAIN 2002 MATH):-

∫ ^√2₀ [x²] dx is

62. (JEE MAIN 2002 MATH):-

If a, b, c are distinct +ve real numbers and a² + b² + c² = 1 then ab + bc + ca is

63. (JEE MAIN 2002 MATH):-

Lim_x→0 (log xⁿ−[x])/[x] , n ∈ N([x] denotes greatest integer less than or equal to x)

64. (JEE MAIN 2002 MATH):-

If 1, log₉ (3^1−x + 2), log₃ (4.3^x − 1) are in A.P. then x equals

65. (JEE MAIN 2002 MATH):-

A and B are events such that P(A ∪ B) = 3/4, P(A ∩ B) = 1/4, P(A¯) = 2/3 then P(A¯ ∩ B) is

66. (JEE MAIN 2002 MATH):-

If α ≠ β but α² = 5α − 3 and β² = 5β − 3 then the equation having α/β and β/α as its roots is

67. (JEE MAIN 2002 MATH):-

Which one is not periodic

68. (JEE MAIN 2002 MATH):-

The equation of a circle with origin as a centre and passing through equilateral triangle whose median is of length 3a is

69. (JEE MAIN 2002 MATH):-

The period sin2 θ of is

70. (JEE MAIN 2002 MATH):-

The centres of a set of circles, each of radius 3 , lie on the circle x2 + y2 = 25 . The locus of any point in the set is

71. (JEE MAIN 2002 MATH):-

Difference between the corresponding roots of x² + ax + b = 0 and x² + bx + a = 0

is same and a ≠ b, then

72. (JEE MAIN 2002 MATH):-

If |a| = 5, |b| = 4, |c| = 3 thus what will be the value of |a ⋅ b + b. c + c. a|, given that →a +→b + →c = 0

73. (JEE MAIN 2002 MATH):-

THE DOMAIN OF  sin⁻¹ [log₃(x/3)] is

1. (JEE MAIN 2002 PHYSICS):

The minimum velocity (in ms-) with which a car driver must traverse a flat curve of radius and
coefficient of friction 0.6 to avoid skidding is

2. (JEE MAIN 2002 PHYSICS):

A bead of weight can slide on smooth circular wire in a vertical plane. The bead is attached by a light thread to the highest point of the wire and in equilibrium, the thread is taut and make an angle with the vertical then tension of the thread and reaction of the wire on the bead are

3. (JEE MAIN 2002 PHYSICS):

A solid sphere, a hallow sphere and a ring are released from top of an inclined plane (frictionless) so that they slide down the plane. Then maximum acceleration down the plane is for (no rolling)

4. (JEE MAIN 2002 PHYSICS):-

Which of the following is more closed to a black body?

5. (JEE MAIN 2002 PHYSICS):-

If there are n capacitors in parallel connected to V volt source, then the energy stored is equal to

6. (JEE MAIN 2002 PHYSICS):-

Length of a string tied to two rigid supports is 40 cm. Maximum length (wave length in cm) of a stationary
wave produced on it is

7. (JEE MAIN 2002 PHYSICS):

A ball whose kinetic energy is E, is projected at an angle of 45 degree to the horizontal. The kinetic energy of the ball at the highest point of its flight will be

8. (JEE MAIN 2002 PHYSICS):-

If a current is passed through a spring then the spring will

9. (JEE MAIN 2002 PHYSICS):-

Sodium and copper have work functions 2.3eV and 4.5eV respectively. Then the ratio of the wave lengths is nearest to

10. (JEE MAIN 2002 PHYSICS):

A light string passing over a smooth light pulley connects two blocks of masses m1 and m2 (vertically). If the acceleration of the system is g/8, then the ratio of the masses is

11. (JEE MAIN 2002 PHYSICS):

Heat given to a body which raises its temperature by 1 degree c is

12. (JEE MAIN 2002 PHYSICS):-

Tube A has both ends open while tube B has one end closed, otherwise they are identical. The ratio of fundamental frequency of tube and is

13. At what temperature is the r.m.s. velocity of a hydrogen molecule equal to that of an oxygen molecule at 47 degree C