The asymptote of the hyperbola `x^2/a^2+y^2/b^2=1` form with ans tangen to the hyperbola triangle whose area is `a^2 tan lambda` in magnitude then its eccentricity is: (a) `sec lambda` (b) `cosec lambda` (c) `sec^2 lambda` (d) `cosec^2 lambda`

Portion of asymptote of hyperbola x^2/a^2-y^2/b^2 = 1 (between centre and the tangent at vertex) in the first quadrant is cut by the line y + lambda(x-a)=0 (lambda is a parameter) then (A) lambda in R (B) lambda in (0,oo) (C) lambda in (-oo,0) (D) lambda in R-{0}

If A satisfies the equation x^3-5x^2+4x+lambda=0 , then A^(-1) exists if (a) lambda!=1 (b) lambda!=2 (c) lambda!=-1 (d) lambda!=0

The area of the triangle formed by any tangent to the hyperbola x^(2) //a^(2) -y^(2) //b^(2) =1 with its asymptotes is

If the sum of the slopes of the normal from a point P to the hyperbola x y=c^2 is equal to lambda(lambda in R^+) , then the locus of point P is (a) x^2=lambdac^2 (b) y^2=lambdac^2 (c) x y=lambdac^2 (d) none of these

If the sum of the slopes of the normal from a point P to the hyperbola x y=c^2 is equal to lambda(lambda in R^+) , then the locus of point P is (a) x^2=lambdac^2 (b) y^2=lambdac^2 (c) x y=lambdac^2 (d) none of these

If the line y=2x+lambda be a tangent to the hyperbola 36x^(2)-25y^(2)=3600 , then lambda is equal to

P is any point on the hyperbola x^(2)-y^(2)=a^(2) . If F_1 and F_2 are the foci of the hyperbola and PF_1*PF_2=lambda(OP)^(2) . Where O is the origin, then lambda is equal to

If vec a is a nonzero vector of magnitude a and lambda a nonzero scalar, then lambda vec a is unit vector if (A) lambda = 1 (B) lambda= -1 (C) a = |lambda| (D) a = 1/(|lambda|)

Function f(x)=cosx-2\ lambda\ x is monotonic decreasing when (a) lambda>1//2 (b) lambda 2

If the line y=3x+lambda touches the hyperbola 9x^(2)-5y^(2)=45 , then the value of lambda is