A line segment of length 10 cm is divided into two parts and a rectangle is formed with these as adjacent sides, then the dimensions of the rectangle in order that its area is maximum is

If the tangent at any point on the curve x⁴+y⁴=a⁴ cuts off intercepts  p and q on the coordinates axes then p^-4/3+q^-4/3=

If the rate of change of the side of a square is 0.05 cm/sec, then the rate of change in the area of the square when the side is 10 cm is

The length of the subnormal to the curve 2x²+3xy-2y²=8 at (2, 3) is

Water is being poured into the inverted conical vessel at the rate of 1.5 cubic meter per minute. Its depth is always equal to twice its radius. The level of water is rising at the rate of 3/8π meter per minute when its depth is

The distances travelled by a particle in time t is given by s=t³-2t²-3t+5. The velocity of the partial when t=2 sec. is

The sum of three numbers is 30. The first plus three times the second plus four times the third add on to 80. The numbers so that the product of all three is as large as possible are

If the tangent at θ=π/4 to the curve x=a cos³θ, y= a sin³θ meets the x and y axis in A and B, then the length of AB is

The approximate value of cos 45⁰, given that 1⁰=0.1745 radian is

Angle between the tangents to the curve y=x²-5x+6 at the points (2, 0) and (3, 0) is