For a point Pin the plane, let d1(P)andd2(P)be the distances of the point Pfrom the lines x−y=0andx+y=0respectively. The area of the region Rconsisting of all points Plying in the first quadrant of the plane and satisfying 2≤d1(P)+d2(P)≤4,is
Let PR=3i^+j^−2k^andSQ=i^−3j^−4k^determine diagonals of a parallelogram PQRS,andPT=i^+2j^+3k^be another vector. Then the volume of the parallelepiped determine by the vectors PT, PQand PSis5b. 20c. 10d. 30
In R', consider the planes P1,y=0 and P2:x+z=1. Let P3, be a plane, different from P1, and P2, which passes through the intersection of P1, and P2. If the distance of the point (0,1,0) from P3, is 1 and the distance of a point (α,β,γ) from P3 is 2, then which of the following relation is (are) true ?
Let f:R→(0,∞) and g:R→R be twice differentiable functions such that f" and g" are continuous functions on R. suppose fprime(2)=g(2)=0,f(2)=0 and g′(2)=0, If x→2limf′(x)g′(x)f(x)g(x)=1 then
A rectangular sheet of fixed perimeter with sides having their lengths in the ratio 8:15is converted into anopen rectangular box by folding after removing squares of equal area from all four corners. If the total area of removed squares is 100, the resulting box has maximum volume. Then the length of the sides of the rectangular sheet are24 (b) 32 (c) 45 (d) 60
A circle C of radius 1 is inscribed in an equilateral triangle PQR. The points of contact of C with the sides PQ, QR, RP are D, E, F, respectively. The line PQ is given by the equation 3x+y−6=0 and the point D is (3 sqrt3/2, 3/2). Further, it is given that the origin and the centre of C are on the same side of the line PQ. (1)The equation of circle C is (2)Points E and F are given by (3)Equation of the sides QR, RP are