A rod of fixed length `k` slides along the coordinates axes, If it meets the axes at `A(a ,0)a n dB(0,b)` , then the minimum value of `(a+1/a)^2+(b+1/b)^2` (a)`0` (b)`8` (c)`k^2+4+4/(k^2)` (d)`k^2+2+4/(k^2)`

If the focus of the parabola x^2-k y+3=0 is (0,2), then a values of k is (are) 4 (b) 6 (c) 3 (d) 2

If a circle of constant radius 3k passes through the origin O and meets the coordinate axes at Aa n dB , then the locus of the centroud of triangle O A B is (a) x^2+y^2=(2k)^2 (b) x^2+y^2=(3k)^2 (c) x^2+y^2=(4k)^2 (d) x^2+y^2=(6k)^2

If a , b , c are consecutive positive integers and (log(1+a c)=2K , then the value of K is logb (b) loga (c) 2 (d) 1

If the line x-1=0 is the directrix of the parabola y^2-k x+8=0 , then one of the values of k is 1/8 (b) 8 (c) 4 (d) 1/4

The tangent to the curve y=e^(k x) at a point (0,1) meets the x-axis at (a,0), where a in [-2,-1] . Then k in [-1/2,0] (b) [-1,-1/2] [0,1] (d) [1/2,1]

The tangent to the curve y=e^(k x) at a point (0,1) meets the x-axis at (a,0), where a in [-2,-1] . Then k in [-1/2,0] (b) [-1,-1/2] [0,1] (d) [1/2,1]

Find the values of k for which the points (2k ,3k),(1,0),(0,1),a n d(0,0) lie on a circle.

If a and b are the roots of the equation x^2 - kx + 16 =0 satisfy a^2 + b^2 =32 , then the value of k is …………… .

If a and b are the roots of the equation x^(2)- kx + 9 = 0 and satisfy a^(2) + b^(2) = 18 then the value of k is