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Trigonometric Ratios and Identities

Showing 50 of 298 · 298 total
  1. 151.Let P(3,2) and Q(3,2), where +=2, be two distinct points on the hyperbola x^29-y^24=1.
  2. 152.Given a circle 2x^2+2y^2=5 and a parabola y^2=4√5x.
  3. 153.Statement 1: The line x-2y=2 meets the parabola y^2+2x=0 only at the point (-2,-2).
  4. 154.Equation of the line passing through the points of intersection of the parabola x^2=8y and…
  5. 155.A common tangent to the conics x^2=6y and 2x^2-4y^2=9 is:
  6. 156.A tangent to the hyperbola x^24-y^22=1 meets the x-axis at P and the y-axis at Q.
  7. 157.The number of common tangents to the circles given by x^2+y^2-8x-2y+1=0 and x^2+y^2+6x+8y=…
  8. 158.If the line y=mx+1 meets the circle x^2+y^2+3x=0 in two points equidistant from and on opp…
  9. 159.If three distinct points A,B,C are given in the 2-dimensional coordinate plane such that t…
  10. 160.The equation of the circle passing through the point (1,2) and through the points of inter…
  11. 161.Statement 1: y=mx-1m is always a tangent to the parabola y^2=-4x for all non-zero values o…
  12. 162.If P_1 and P_2 are two points on the ellipse x^24+y^2=1 at which the tangents are parallel…
  13. 163.The equation of the circle passing through the points (1,0) and (0,1) and having the small…
  14. 164.Three distinct points A,B,C are given in the 2-dimensional coordinate plane such that the …
  15. 165.The ellipse x^2+4y^2=4 is inscribed in a rectangle aligned with the coordinate axes, which…
  16. 166.If the pair of lines ax^2+2(a+b)xy+by^2=0 lie along diameters of a circle and divide the c…
  17. 167.The equation of a circle with origin as centre and passing through the vertices of an equi…
  18. 168.Two common tangents to the circle x^2+y^2=2a^2 and the parabola y^2=8ax are:
  19. 169.Let _, _ be the roots of 2x^2 + ()x - 1 = 0, (0,2).
  20. 170.Let the equation x(x+2)(12-k) = 2 have equal roots.
  21. 171.All the pairs (x,y) that satisfy the inequality [2^^2x-2 x+5 14^^2 y 1] also satisfy the e…
  22. 172.If ^2 48^ - ^2 12^^2 24^ - ^2 6^ = + √52, where , N, then + is equal to ___________ Answer…
  23. 173.Let (+) = -110 and (-) = 38, where 0 < < 3 and 0 < < 4.
  24. 174.Let a_k = (_k) i + j and b_k = i - (_k) j, where _k = 2^k-12n+1, for some n N, n>5.
  25. 175.The value of √3,cosec,10^ - 10^ is equal to:
  26. 176.Let 2 < < and = -12√2.
  27. 177.The value of √3,cosec,20^-20^20^40^60^80^ is equal to:
  28. 178.If (A-B) A + ^2C^2A = 1, where A,B,C (0,2), then:
  29. 179.If (18)(518)(718) = K(10K3)
  30. 180.If x+^2x=1, x(0,2), then [(^12x+^12x) + 3(^10x+^10x+^8x+^8x) + (^6x+^6x)] is equal to:
  31. 181.Let the set of all a R such that the equation 2x + a x = 2a - 7 has a solution be [p,q].
  32. 182.If 23x+2x x+4 x-4=0 has exactly 3 solutions in the interval [0,n2], nN, then the roots of …
  33. 183.If m and n respectively are the numbers of positive and negative values of in the interval…
  34. 184.Let S = [0,2) : () + () = 0.
  35. 185.Let f() = 3^4(32-) + ^4(3+) - 2(1-^22) and S = [0,] : f'() = -√32.
  36. 186.The set of all values of for which the equation ^22x - 2^4x - 2^2x = has a solution:
  37. 187.If 15^+175^+1105^+195^ = 2a, then the value of a+1a is:
  38. 188.If the solution of the equation _ x x + 4_ x x = 1, x (0,2), is ^-1(+2), where , are integ…
  39. 189.The value of 36(4^29^-1)(4^227^-1)(4^281^-1)(4^2243^-1) is:
  40. 190.Let S = x (-2,2) : 9^1-^2x+9^^2x=10 and b = _x S^2( x3).
  41. 191.The number of solutions of | x| = x, such that -4 x 4 is:
  42. 192.Let S = [0,2] : 8^2^2 + 8^2^2 = 16.
  43. 193.If the sum of solutions of the system of equations 22 - 2 = 0 and 22+3=0 in the interval […
  44. 194.Let S = (0,2) : 7^2 - 3^2 - 2^22 = 2.
  45. 195.2(22)(322)(522)(722)(922) is equal to:
  46. 196.Let S = [-, 2] (excluding the points where the expression below is undefined), and =√5.
  47. 197.Let S = [-,]2 : + = 2.
  48. 198.The number of elements in the set S = [-4,4] : 3^22+62-10^2+5=0 is: Answer: 32
  49. 199.The number of solutions of the equation 2 - ^2+√2=0 in R is equal to: Answer: 1
  50. 200.The number of solutions of the equation x = ^2x in the interval (0,10) is ___________ Answ…