MATH QUESTIONS ASKED IN JEE MAINS 2002:  QUIZ

1. (JEE MAIN 2002 MATH):-

The number of solution of tan x + sec x = 2 cos x in [0, 2π) is

1. (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

2. (JEE MAIN 2002 MATH):-

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

3. (JEE MAIN 2002 MATH):-

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

4. (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

5. (JEE MAIN 2002 MATH):-

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

6. (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

7. (JEE MAIN 2002 MATH):-

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

8. (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

9. (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

10. (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

11. (JEE MAIN 2002 MATH):-

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

12. (JEE MAIN 2002 MATH):-

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

13. (JEE MAIN 2002 MATH):-

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

14. (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

15. (JEE MAIN 2002 MATH):-

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

16. (JEE MAIN 2002 MATH):-

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

17. (JEE MAIN 2002 MATH):-

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

18. (JEE MAIN 2002 MATH):-

Which one is not periodic

19. (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

20. (JEE MAIN 2002 MATH):-

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

21. (JEE MAIN 2002 MATH):-

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

22. (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.”)

23. (JEE MAIN 2002 MATH):-

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

24. (JEE MAIN 2002 MATH):-

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

25. (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

26. (JEE MAIN 2002 MATH):-

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

27. (JEE MAIN 2002 MATH):-

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

28. (JEE MAIN 2002 MATH):-

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

is

29. (JEE MAIN 2002 MATH):-

1³ − 2³ + 3³ − 4³ +…. +9³ =

30. (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

31. (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

32. (JEE MAIN 2002 MATH):-

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

33. (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

34. (JEE MAIN 2002 MATH):-

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

35. (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

36. (JEE MAIN 2002 MATH):-

∫ ^√2₀ [x²] dx is

37. (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

38. (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

39. (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

40. (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

41. (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

42. (JEE MAIN 2002 MATH):-

The period sin2 θ of is

43. (JEE MAIN 2002 MATH):-

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

44. (JEE MAIN 2002 MATH):-

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

45. (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

46. (JEE MAIN 2002 MATH):-

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

47. (JEE MAIN 2002 MATH):-

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

48. (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

49. (JEE MAIN 2002 MATH):-

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

50. (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

51. (JEE MAIN 2002 MATH):-

THE DOMAIN OF  sin⁻¹ [log₃(x/3)] is

52. (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

53. (JEE MAIN 2002 MATH):-

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

54. (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

55. (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

56. (JEE MAIN 2002 MATH):-

∫ ^10π₀ | sin x |dx is

57. (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

58. (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

59. (JEE MAIN 2002 MATH):-

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

60. (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?

61. (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

62. (JEE MAIN 2002 MATH):-

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

63. (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

64. (JEE MAIN 2002 MATH):-

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

65. (JEE MAIN 2002 MATH):-

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

66. (JEE MAIN 2002 MATH):-

THE ORDER AND DEGREE OF THE DIFFERENTIAL EQUATION

(1 + 3 dy/dx )^2/3= 4 d³y/dx³ ARE

67. (JEE MAIN 2002 MATH):-

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

68. (JEE MAIN 2002 MATH):-

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

69. (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

70. (JEE MAIN 2002 MATH):-

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

71. (JEE MAIN 2002 MATH):-

72. (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

73. (JEE MAIN 2002 MATH):-