An artificial satellite of mass $m$ is moving along an elliptical path around the Earth. The areal velocity of the satellite is proportional to

The solution set contained in $R$ of the inequation $3^x+3^{1-x}-4 < 0$ is:

$A$ whistle of frequency $540 \ Hz$ rotates in a horizontal circle of radius $2 \ m$ at an angular speed of $15 \ rad/s$. What is the highest frequency heard by a listener at rest with respect to the centre of the circle (in $Hz$)? (Velocity of sound in air $= 330 \ m/s$)

The equation of the line joining the centres of the circles belonging to the coaxial system of circles $4x^2 + 4y^2 - 12x + 6y - 3 + \lambda(x + 2y - 6) = 0$ is

The area (in square units) of the region bounded by the curves $x=y^2$ and $x=3-2y^2$ is

$A$ liquid of mass $m$ and specific heat $c$ is heated to a temperature of $2T$. Another liquid of mass $m/2$ and specific heat $2c$ is heated to a temperature of $T$. If these two liquids are mixed,what will be the final temperature of the mixture?