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Sets, Relations and Functions

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  1. 51.Let A=1,4,7 and B=2,3,8.
  2. 52.Let A = 2, 3, 4, 5, 6.
  3. 53.Let S be the set of the first 11 natural numbers.
  4. 54.The number of relations on the set A=1,2,3, containing at most 6 elements including (1,2),…
  5. 55.For n 2, let S_n denote the set of all subsets of 1,2, ,n with no two consecutive numbers.
  6. 56.Let S=p_1,p_2 ,p_10 be the set of first ten prime numbers.
  7. 57.Let A=1,2,3.
  8. 58.Let [A=2,3,6,7] and [B=4,5,6,8].
  9. 59.In a survey of 220 students of a higher secondary school, it was found that at least 125 a…
  10. 60.Let A=1,2,3, , 20.
  11. 61.Let A=1,2,3, ,100.
  12. 62.Let A=1,2,3,4 and R=(1,2),(2,3),(1,4) be a relation on A.
  13. 63.The number of symmetric relations defined on the set [1,2,3,4] which are not reflexive is …
  14. 64.The number of elements in the set n N:10 n 100 and 3^n-3 is a multiple of 7 is ___________…
  15. 65.Let A=1,2,3,4 and R be a relation on the set A A defined by R=((a,b),(c,d)):2a+3b=4c+5d.
  16. 66.Let A=-4,-3,-2,0,1,3,4 and R=(a,b) A A:b=|a| or b^2=a+1 be a relation on A.
  17. 67.The number of relations, on the set [1,2,3] containing (1,2) and (2,3), which are reflexiv…
  18. 68.The number of elements in the set [ n Z:|n^2 - 10n + 19| < 6 ] is _________.
  19. 69.Let [A=0,3,4,6,7,8,9,10] and R be the relation defined on A such that [R=(x, y) A A: x-y] …
  20. 70.Let A=1,2,3,4, .,10 and B=0,1,2,3,4.
  21. 71.The set of values of k, for which the circle C:4x^2+4y^2-12x+8y+k=0 lies inside the fourth…
  22. 72.Let P and Q be two distinct points on a circle which has centre C(2,3) and which passes th…
  23. 73.Let A=(x,y) R R 2x^2+2y^2-2x-2y=1, B=(x,y) R R 4x^2+4y^2-16y+7=0, C=(x,y) R R x^2+y^2-4x-2…
  24. 74.Let the equation x^2+y^2+px+(1-p)y+5=0 represent circles of varying radius r(0,5].
  25. 75.Let Z be the set of all integers, A=(x,y) Z Z:(x-2)^2+y^24, B=(x,y) Z Z:x^2+y^24 and C=(x,…
  26. 76.If a variable line 3x+4y-=0 is such that the two circles x^2+y^2-2x-2y+1=0 and x^2+y^2-18x…
  27. 77.Two sets A and B are as under: [A=(a,b) R R:|a-5|<1 and |b-5|<1] [B=(a,b) R R:4(a-6)^2+9(b…
  28. 78.Let z C, the set of complex numbers.
  29. 79.The largest value of r for which the region represented by the set C: |-4-i| r is containe…
  30. 80.Let S = x^3 + ax^2 + bx + c : a,b,c N, a,b,c 20 be a set of polynomials.
  31. 81.If the set of all a R, for which the equation 2x^2+(a-5)x+15=3a has no real root, is the i…
  32. 82.Let S be the set of all real roots of the equation 3^x(3^x-1)+2 = |3^x-1|+|3^x-2|.
  33. 83.If A = x R: |x|<2 and B = x R: |x-2|3; then:
  34. 84.Consider the two sets: A = m R: both the roots of x^2-(m+1)x+m+4=0 are real and B = [-3,5)…
  35. 85.Let S be the set of the first 11 natural numbers.
  36. 86.The number of elements in the relation R = (x,y) : 4x^2+y^2<52, x,yZ is:
  37. 87.Let A = 0,1,2,,9.
  38. 88.Let R1,2,3,41,2,3,4 be a relation defined on the set A=1,2,3,4 by [R = ((a,b),(c,d)) : 2a+…
  39. 89.Consider the relation R on the set -2,-1,0,1,2 defined by (a,b) R if and only if 1+ab>0.
  40. 90.The number of relations on the set 1,2,3, containing at most 6 elements including (1,2), w…
  41. 91.The relation R = (x,y) : x,yZ, x+y is even is:
  42. 92.Define a relation R on the interval [0,2) by xRy if and only if ^2x - ^2y = 1.
  43. 93.Let A = 1,2,3,,100 and R be a relation on A such that R = (a,b) : a=2b+1.
  44. 94.Let A = -2,-1,0,1,2,3.
  45. 95.Consider the sets A = (x,y)RR : x^2+y^2=25, B = (x,y)RR : x^2+9y^2=144, C = (x,y)ZZ : x^2+…
  46. 96.Let A = (x,y) : |x-1|4 and |y-5|6 and B = (x,y) : 16(x-2)^2+9(y-6)^2144.
  47. 97.Let R be a relation on ZZ defined by (a,b),R,(c,d) if and only if ad-bc is divisible by 5.
  48. 98.A group of 40 students appeared in an examination of 3 subjects --- Mathematics, Physics &…
  49. 99.The minimum number of elements that must be added to the relation R = (a,b),(b,c),(b,d) on…
  50. 100.In a group of 100 persons, 75 speak English and 40 speak Hindi.