If one root `x^2-x-k=0` is square of the other, then `k=` a.`2+-sqrt(5)` b. `2+-sqrt(3)` c. `3+-sqrt(2)` d. `5+-sqrt(2)`

sqrt(3)x^(2) - sqrt(2)x + 3sqrt(3)=0

The length of the chord of the parabola y^2=x which is bisected at the point (2, 1) is 2sqrt(3) (b) 4sqrt(3) (c) 3sqrt(2) (d) 2sqrt(5)

If the area enclosed between the curves y=kx^2 and x=ky^2 , where kgt0 , is 1 square unit. Then k is: (a) 1/sqrt(3) (b) sqrt(3)/2 (c) 2/sqrt(3) (d) sqrt(3)

Find the value of p, when a/sqrt2 = b/sqrt3 = c/sqrt5 = (sqrt(2a) - sqrt(3b) + sqrt(5c))/p .

Solve sqrt(5)x^(2) + x + sqrt(5)=0

A beam of light is sent along the line x-y=1 , which after refracting from the x-axis enters the opposite side by turning through 30^0 towards the normal at the point of incidence on the x-axis. Then the equation of the refracted ray is (a) (2-sqrt(3))x-y=2+sqrt(3) (b) (2+sqrt(3))x-y=2+sqrt(3) (c) (2-sqrt(3))x+y=(2+sqrt(3)) (d) y=(2-sqrt(3))(x-1)

If center of a regular hexagon is at the origin and one of the vertices on the Argand diagram is 1+2i , then its perimeter is 2sqrt(5) b. 6sqrt(2) c. 4sqrt(5) d. 6sqrt(5)

Find square root of x + y + z + 2 sqrt(yz) + 2sqrt(zx) + 2sqrt(xy)

A non-zero vector vec a is such that its projections along vectors ( hat i+ hat j)/(sqrt(2)),(- hat i+ hat j)/(sqrt(2)) and hat k are equal, then unit vector along vec a is a. (sqrt(2) hat j- hat k)/(sqrt(3)) b. ( hat j-sqrt(2) hat k)/(sqrt(3)) c. (sqrt(2))/(sqrt(3)) hat j+( hat k)/(sqrt(3)) d. ( hat j- hat k)/(sqrt(2))

If x ,y in R satify the equation x^2+y^2-4x-2y+5=0, then the value of the expression [(sqrt(x)-sqrt(y))^2+4sqrt(x y)]//(x+sqrt(x y)) is a. sqrt(2)+1 b. (sqrt(2)+1)/2 c. (sqrt(2)-1)/2 d. (sqrt(2)+1)/(sqrt(2))