If cosθ = \(\frac{-3}{5}\)- and π < θ < \(\frac{3π}{2}\), then tan \(\frac{ θ}{2}\) + sin \(\frac{ θ}{2}\)+ 2cos \(\frac{ θ}{2}\) =
The period of function f(x) = \(e^{log(sinx)}+(tanx)^3 - cosec(3x - 5)\)is
If sin 2θ and cos 2θ are solutions of x2 + ax - c = 0, then
If \(\frac{3x+2}{(x+1)(2x^2+3)} = \frac{A}{x+1}+ \frac{Bx+C}{2x^2+3}\), then A - B + C=
lim n→∞ \(\frac{1}{n^3} \)
In a triangle BC, if the mid points of sides AB, BC, CA are (3,0,0), (0,4,0),(0,0,5) respectively, then AB2 + BC2 + CA2 =
If the points of intersection of the parabola y2 = 5x and x2 = 5y lie on the line L, then the area of the triangle formed by the directrix of one parabola, latus rectum of another parabola and the line L is
A tangent PT is drawn to the circle x2 + y2 = 4 at the point P(√3, 1). If a straight line L which is perpendicular to PT is a tangent to the circle (x- 3)2 + y2 = 1, then a possible equation of L is
The radius of a circle touching all the four circles (x ± λ)2 + (y ± λ)2 = λ2 is
If the radical center of the given three circles x2 + y2 = 1, x2 + y2 -2x - 3 =0 and x2 + y2 -2y - 3 = 0 is C(α,β) and r is the sum of the radii of the given circles, then the circle with C(α,β) as center and r as radius is
If x - 2y + k = 0 is a tangent to the parabola y2 - 4x - 4y + 8 = 0, then the value of k is
If the line x cos α + y sin α = 2√3 is tangent to the ellipse \(\frac{x^2}{16} + \frac{y^2}{8} = 1\) and α is an acute angle then α =
If the angle between the asymptotes of a hyperbola is 30° then its eccentricity is
If l,m,n and a,b,c are direction cosines of two lines then
On differentiation if we get f (x,y)dy - g(x,y)dx = 0 from 2x2-3xy+y2+x+2y-8 = 0 then g(2,2)/f(1,1) =
If x+√3y = 3 is the tangent to the ellipse 2x2 + 3y2 = k at a point P then the equation of the normal to this ellipse at P is
The quadratic equation whose roots are
\(l = \lim_{\theta\to0} \frac{3sin\theta - 4sin^3\theta}{\theta}\)
m = \(\lim_{\theta\to0} \frac{2tan\theta}{\theta(1-tan^2\theta)}\) is
If (2,-1,3) is the foot of the perpendicular drawn from the origin to a plane, then the equation of that plane is