Let `f(x)=-x^2 sin^2 theta-2x cos theta + 1, theta !=npi, nepsilonZ` The parabola `y=f(x)` cuts x-axis at : (A) no point (B) at exactly one point (C) at two points (D) None of these

Let f(x)=-x^2 sin^2 theta-2x cos theta + 1, theta !=npi , .Then locus of vertex of parabola y=f(x) is : (A) x^2/y^2 - 1/y = 1 (B) x^2/y^2 + 1/y = 1 (C) y^2/x^2 + 1/y = 1 (D) none of these

Let f(x)=-x^2 sin^2 theta-2x cos theta + 1, theta !=npi, nepsilonZ . If (1, 0) lies between the point where parabola cuts x-axis, then theta belongs to: (A) [-pi/2, pi/2] (B) [pi/2, pi] (C) [-pi, - pi/2] (D) none of these

Find (dy)/(dx) if x= 3 cos theta - cos 2theta and y= sin theta - sin 2theta.

Let f(x)={x^2-4x+3,x<3 and x-4,xgeq3 }a n d g(x)={1,x<1 and x^2-x,1lt=x<4 and x-3,xgeq4 then function f(x)dotg(x) is discontinuous at (a)exactly 1 point (b) exactly 2 points (c)exactly 3 points (d) None of these

Find (dy)/(dx) if x=cos theta - cos 2 theta and" "y = sin theta - sin 2theta

Let (a,b) be a point on the parabola y=4x-x^(2) and is the point nearest to the point A(-1,4) Find (a+b).

The function f(x) : (x-1)/(x( x^(2) -1)) is discontinuous at (a) exactly one point (b) exactly two points (c) exactly three points (d) no point

If f(x)=int_0^(pi/2)ln(1+xsin^2theta)/(sin^2theta) d theta, x >= 0 then :

If x= a sin 2theta (1+ cos 2theta) , y= b cos 2theta(1- cos 2theta) , then (dy)/(dx) =

if x = "cos" theta - "cos" 2 theta, y = "sin" theta - "sin" 2 theta , then dy/dx is