If `f^(prime)(x)=|[mx, mx-p, m x+p], [n, n+p, n-p], [mx+2n, m x+2n+p, mx+2n-p]|` , then `y=f(x)` represents a. a straight line parallel to x-axis b. a straight line parallel to y-axis c. parabola d. a straight line with negative slope

If n is a natural number gt 2 , such that z^(n) = (z+1)^(n) , then (a) roots of equation lie on a straight line parallel to the y-axis (b) roots of equaiton lie on a straight line parallel to the x-axis (c) sum of the real parts of the roots is -[(n-1)//2] (d) none of these

The tangent at a point P of a curve meets the y-axis at A, and the line parallel to y-axis at A, and the line parallel to y-axis through P meets the x-axis at B. If area of DeltaOAB is constant (O being the origin), Then the curve is

Find the distance between P(x_1,\ y_1)a n d\ Q(x_2, y_2) when i. P Q is parallel to the y-axis ii. PQ is parallel to the x-axis.

What will be the value of m and c if the straight line y=mx+c passes through the points (3, -4) and (-1, 2) ?

The graph above depicts a straight line having the equation y = mx + n . What can be said about the line given by the equation y = nx + m ?

For positive l, m and n, if the points x=ny+mz, y=lz+nx, z=mx+ly intersect in a straight line, when Q. l, m and n satisfy the equation

The tangent at any point P onthe parabola y^2=4a x intersects the y-axis at Qdot Then tangent to the circumcircle of triangle P Q S(S is the focus) at Q is a line parallel to x-axis y-axis a line parallel to y-axis (d) none of these

If n lt p lt 2n and p is prime and N=.^(2n)C_(n) , then

The line x/a-y/b=1 cuts the x-axis at P. The equation of the line through P and perpendicular to the given line is

Let the line y = mx intersects the curve y^2 = x at P and tangent to y^2 = x at P intersects x-axis at Q. If area ( triangle OPQ) = 4, find m (m gt 0) .