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Inverse Trigonometric Functions

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  1. 51.If ^-1(17)+^-1(45)-^-1(7736)=0, 0<<13, then ^-1()+^-1() is equal to
  2. 52.If the sum and product of four positive consecutive terms of a G.P.
  3. 53.Let S be the set of all solutions of the equation ^-1(2x)-2^-1(√1-x^2)=, x[-12,12].
  4. 54.Let S=xR: 0<x<1 and 2^-1(1-x1+x)=^-1(1-x^21+x^2).
  5. 55.If S=xR:^-1x+1(x+1)^2+1-^-1xx^2+1=4, then _x S[(((x^2+x+5))/(2))-((x^2+x+5))] is equal to …
  6. 56.Let x*y=x^2+y^3 and (x*1)*1=x*(1*1).
  7. 57.The value of ^-1((15)/(4)-1()/(4)) is equal to :
  8. 58.If the inverse trigonometric functions take principal values then ^-1(310(^-143)+25(^-143)…
  9. 59.^-1(23)+^-1(76)+^-1(34) is equal to:
  10. 60.The value of (_n=1^50^-111+n+n^2) is
  11. 61.50(3^-112)+2^-11√5+4√2(12^-1(2√2)) is equal to Answer: 29
  12. 62.The set of all values of k for which (^-1x)^3+(^-1x)^3=k^3, xR, has a solution, is the int…
  13. 63.Let x=(2^-1) and y=(12^-143).
  14. 64.[2^-115+^-1√52+2^-118] is equal to :
  15. 65.If 0<x<1√2 and ^-1(x)=^-1(x), then the value of (2+) is
  16. 66.For kR, let the solutions of the equation (^-1(x(^-1((^-1x)))))=k, 0<x<1√2, be and , where…
  17. 67.Considering the principal values of the inverse trigonometric functions, the sum of all th…
  18. 68.If ^-1xa=^-1xb=^-1yc, 0<x<1, then the value of ( ca+b) is
  19. 69.cosec[2^-1(5)+^-145] is equal to
  20. 70.A possible value of [14^-1√638] is
  21. 71.If ^-1()=^-12+^-18+^-118+^-132+ up to 100 terms, then is
  22. 72.The sum of possible values of x for ^-1(x+1)+^-1(1x-1)=^-1831 is
  23. 73.The number of solutions of the equation ^-1[x^2+13]+^-1[x^2-23]=x^2, for x[-1,1], where [x…
  24. 74.Let S_k=_r=1^k^-1(6^r2^2r+1+3^2r+1).
  25. 75.Given that the inverse trigonometric functions take principal values only, the number of r…
  26. 76.The number of real roots of the equation ^-1x(x+1)+^-1x^2+x+1=4 is
  27. 77.The value of [2^-135+^-1513] is equal to
  28. 78.If (^-1x)^2-(^-1x)^2=a, 0<x<1, a0, then the value of 2x^2-1 is
  29. 79.Let M and m respectively be the maximum and minimum values of the function f(x)=^-1( x+ x)…
  30. 80.If y(x)=^-1(√1+ x+√1- x√1+ x-√1- x), x(2,), then dydx at x=56 is
  31. 81.A 10 inch long pencil AB with mid-point C and a small eraser P are placed on the horizonta…
  32. 82.2-[^-145+^-1513+^-11665] is equal to:
  33. 83.If S is the sum of the first 10 terms of the series ^-113+^-117+^-1113+^-1121+, then (S) i…
  34. 84.Considering only the principal values of inverse functions, the set A=x0:^-1(2x)+^-1(3x)=4
  35. 85.All x satisfying the inequality (^-1x)^2-7(^-1x)+10>0, lie in the interval :
  36. 86.The value of (_n=1^19^-1(1+_p=1^n2p)) is:
  37. 87.If x=^-1(10) and y=^-1(10), then y-x is equal to:
  38. 88.If ^-1(23x)+^-1(34x)=2, x>34, then x is equal to:
  39. 89.If =^-135, =^-113, where 0<,<2, then - is equal to:
  40. 90.The value of ^-11213-^-135 is equal to
  41. 91.If ^-1x-^-1y2=, where -1 x1, -2 y2, xy2, then for all x,y, 4x^2-4xy+y^2 is equal to:
  42. 92.A value of x satisfying the equation [^-1(1+x)]=[^-1x], is :
  43. 93.The value of ^-1(√1+x^2+√1-x^2√1+x^2-√1-x^2), |x|<12, x0, is equal to
  44. 94.Let ^-1y=^-1x+^-1(2x1-x^2), where |x|<1√3.
  45. 95.If f(x)=2^-1x+^-1(2x1+x^2), x>1 then f(5) is equal to :
  46. 96.The principal value of ^-1[434] is:
  47. 97.Statement I: The equation (^-1x)^3+(^-1x)^3-a^3=0 has a solution for all a132.
  48. 98.The number of solutions of the equation ^-1x=2^-1x (in principal values) is:
  49. 99.If x,y,z are in A.P.
  50. 100.Let x(0,1).