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Trigonometric Ratios and Identities

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  1. 201.The number of solutions of the equation (x+3)(3-x) = 14^22x, x[-3,3] is:
  2. 202.The value of 2(12^) - (72^) is:
  3. 203.The value of 27+47+67 is equal to:
  4. 204.=36^ is a root of which of the following equations?
  5. 205.If =1 and = -53, where <<32 and 2<<, then the value of (+) and the quadrant in which + lie…
  6. 206.cosec,18^ is a root of the equation:
  7. 207.The value of 282838586878 is:
  8. 208.If + = 12, then 16(2+4+6) is equal to:
  9. 209.The value of 24 is:
  10. 210.If 15^4+10^4 = 6 for some R, then the value of 27^6+8^6 is equal to:
  11. 211.If for x(0,2), _10 x+_10 x = -1 and _10( x+ x) = 12(_10n-1), n>0, then the value of n is e…
  12. 212.If 0<a,b<1 and ^-1a+^-1b = 4, then the value of (a+b)-a^2+b^22+a^3+b^33-a^4+b^44+ is:
  13. 213.All possible values of [0,2] for which 2+2>0 lie in:
  14. 214.If 0<x,y< and x+ y-(x+y) = 32, then x+ y is equal to:
  15. 215.If n is the number of solutions of the equation 2 x[4(4+x)(4-x)-1]=1, x[0,], and S is the …
  16. 216.The number of solutions of the equation 3^2^2x+3^2^2x=81, 0 x4 is:
  17. 217.Let S be the sum of all solutions (in radians) of the equation ^4+^4 - = 0 in [0,4].
  18. 218.The sum of solutions of the equation x1+ x = |2x|, x(-2,2)4 is:
  19. 219.The number of solutions of ^7x+^7x=1, x[0,4] is equal to:
  20. 220.Let = _xR8^23x4^43x and = _xR8^23x4^43x.
  21. 221.The number of solutions of the equation | x| = x+1 x in the interval [0,2] is ___________ …
  22. 222.The number of solutions of the equation x+2 x = 2 in the interval [0,2] is:
  23. 223.The number of roots of the equation (81)^^2x+(81)^^2x=30 in the interval [0,] is equal to:
  24. 224.If √3^2x = (√3-1) x+1, the number of solutions of the given equation when x[0,2] is ______…
  25. 225.The number of integral values of k for which the equation 3 x+4 x = k+1 has a solution, kR…
  26. 226.The value of ^3838+^3838 is:
  27. 227.If L = ^216-^28 and M = ^216-^28, then:
  28. 228.If √2√1+2 = 17 and 1-22 = 1√10, ,(0,2), then (+2) is equal to ___________ Answer: 1
  29. 229.The set of all possible values of in the interval (0,) for which the points (1,2) and (,) …
  30. 230.If the equation ^4+^4+=0 has real solutions for , then lies in the interval:
  31. 231.The number of distinct solutions of the equation _1/2| x| = 2-_1/2| x| in the interval [0,…
  32. 232.For any (4,2), the expression 3(-)^4+6(+)^2+4^6 equals:
  33. 233.The angle of elevation of the top of a vertical tower standing on a horizontal plane is ob…
  34. 234.The value of ^210^ - 10^50^+^250^ is:
  35. 235.Two poles standing on a horizontal ground are of heights 5,m and 10,m respectively.
  36. 236.The value of 10^30^50^70^ is:
  37. 237.If (+)=35, (-)=513, and 0<,<4, then (2) is equal to:
  38. 238.If ^4+4^4+2 = 4√2, ,[0,], then (+)-(-) is equal to:
  39. 239.Let f_k(x) = 1k(^kx+^kx) for k=1,2,3,.
  40. 240.The value of 2^22^32^102^10:
  41. 241.The number of solutions of the equation 1+^4x=^23x, x[-52,52] is:
  42. 242.Let S be the set of all R such that the equation 2x+ x = 2-7 has a solution.
  43. 243.If [x] denotes the greatest integer x, then the system of linear equations []x+[-]y=0, []x…
  44. 244.Let S = [-2,2] : 2^2+3=0.
  45. 245.If 0 x<2, then the number of values of x for which x-2x+3x=0 is:
  46. 246.The number of solutions of 3x=2x in the interval (2,) is:
  47. 247.If the sum of all solutions of the equation 8 x(6+x)(6-x) - 12 = 1 in [0,] is k, then k is…
  48. 248.If 5(^2x-^2x) = 22x+9, then the value of 4x is:
  49. 249.If m and M are the minimum and the maximum values of 4+12^22x-2^4x, xR, then M-m is equal …
  50. 250.If 0 x<2, then the number of real values of x which satisfy the equation x+2x+3x+4x=0 is: