If `P=(1,1),Q=(3,2)` and `R` is a point on x-axis then the value of `PR+RQ` will be minimum at

Let P be a plane passing through the points (2,1,0),(4,1,1) and (5,0,1) and R be any point (2,1,6). Then the image of R is the plan P is :

If .^n P_r=^n P_(r+1) and .^n C_r=^n C_(r-1,) then the value of n+r is.

Let (p, q, r) be a point on the plane 2x+2y+z=6 , then the least value of p^2+q^2+r^2 is equal ot

let P be the point (1, 0) and Q be a point on the locus y^2= 8x . The locus of the midpoint of PQ is

Consider f(x)=int_1^x(t+1/t)dt and g(x)=f'(x) If P is a point on the curve y=g(x) such that the tangent to this curve at P is parallel to the chord joining the point (1/2,g(1/2)) and (3,g(3)) of the curve then the coordinates of the point P

If Q (0,1) is equidistant from P(5,-3) and R(x,6) , find the values of x. Also find the distances QR and PR.

The corner points of the bounded feasible region are (0, 1), (0, 7), (2, 7), (6, 3) (6, 0) (1, 0). For the objective function Z = 3x - y …….. At which point, Z is minimum ? (ii) At which point, Z is maximum ? (iii) The maximum value of Z is ......... (iv) The minimum value of Z is ..........

Line passess from fixed point (2, 3) intersects axis of points P and Q. If O is origin and OPRQ will be rectangle then locus of point R is ..........

Let P and Q be points on the line joining A(-2, 5) and B(3, 1) such that AP = PQ = QB. If mid-point of PQ is (a, b), then the value of (b)/(a) is

Let P(3,2,6) be a point in space and Q be a point on line vec r=( hat i- hat j+2 hat k)+mu(-3 hat i+ hat j+5 hat k)dot Then the value of mu for which the vector vec P Q is parallel to the plane x-4y+3z=1 is a. 1/4 b. -1/4 c. 1/8 d. -1/8