Let `A-=(3,-4),B-=(1,2)dot` Let `P-=(2k-1,2k+1)` be a variable point such that `P A+P B` is the minimum. Then `k` is (a)7/9 (b) 0 (c) 7/8 (d) none of these

If A(1,p^2),B(0,1) and C(p ,0) are the coordinates of three points, then the value of p for which the area of triangle A B C is the minimum is 1/(sqrt(3)) (b) -1/(sqrt(3)) 1/(sqrt(2)) (d) none of these

Let f(x)=x+2|x+1|+2|x-1|dot If f(x)=k has exactly one real solution, then the value of k is (a) 3 (b) 0 (c) 1 (d) 2

If a ,b ,c are in A.P., the a/(b c),1/c ,1/b will be in a. A.P b. G.P. c. H.P. d. none of these

Let A(2,3) and B(2,-4) be two points. If P lie on the x - axis , such that AP = (3)/(7)AB , Find the coordinate of P.

If A and B are two events such that P(A) =(1)/(4), P(B) = (1)/(2) and P(A cap B) = (1)/(8) , find P (not A and not B).

The value of k such that (x-4)/1=(y-2)/1=(z-k)/2 lies in the plane 2x-4y+z=7 is (A) 7 (B) -7 (C) no real value (D) 4

Consider the points A(0,1)a n dB(2,0),a n dP be a point on the line 4x+3y+9=0 . The coordinates of P such that |P A-P B| is maximum are (-(12)/5,(17)/5) (b) (-(84)/5,(13)/5) ((31)/7,(31)/7) (d) (,0)

Let A ,B ,C ,D be independent events such that P(A)=1//2,P(B)=1//3, P(C)=1//5, a n dP(D)=1//6. Then theprobability that none of A ,B ,C ,a n dD occurs a. 1//180 b. 1//45 c. 1//18 d. none of these

Let A and B be two events such that P(A)=0.3 and P(AuuB)= 0.8 . If A and B are independent events, then P(B)=

Let A B C D be a rectangle and P be any point in its plane. Show that A P^2+P C^2=P B^2+P D^2dot