ABCD is a square with side AB = 2. A point P moves such that its distance from A equals its distance from the line BD. The locus of P meets the line AC at `T_1` and the line through A parallel to BD at `T_2` and `T_3`. The area of the triangle `T_1 T_2 T_3` is :

Let ABCD be a square of side length 2 units. C_(2) is the circle through vertices A, B, C, D and C_(1) is the circle touching all the sides of the square ABCD. L is a line through A A line M through A is drawn parallel to BD. Point S moves such that its distances from the line BD and the vertex A are equal. If locus of S cuts. M at T_(2) and T_(3) and AC at T_(1) , then area of DeltaT_(1)T_(2)T_(3) is

A body moves in a straight line along x-axis, its distance from the origin is given by the equation x = 8t-3t ^(2). The average velocity in the interval from t =0 to t =4 is

A particle moves in a straight line such that its distance in 't' secodns from a fixed point is (6t-t^(2)) cm. find its velocity at the end of t=2 se c.

A particle is moving on a straight line and its distance x cms from a fixed point O on the line is given by x=sqrt(t^(2)+1) then the velocity of particle at t=1 is

Two planets are at distance R_1 and R_2 from the Sun. Their periods are T_1 and T_2 then (T_1/T_2)^2 is equal to

A point moves in the straight line during the time t=0 to t=3 according to the law s=15t-2t^2 . The average velocity is