An engine has an efficiency of $1/6$. When the temperature of the sink is reduced by $62^{\circ}C$,its efficiency is doubled. The temperature of the source is $.........^{\circ}C$.

Which one of the following statements is wrong?

If $f(x) = x^2 + 2bx + 2c^2$ and $g(x) = -x^2 - 2cx + b^2$ such that $\min f(x) > \max g(x)$,then the relation between $b$ and $c$ is:

The horizontal and vertical displacements $x$ and $y$ of a projectile at a given time $t$ are given by $x = 6t \text{ m}$ and $y = 8t - 5t^2 \text{ m}$. The range of the projectile in metres is

$A$ ball rests upon a flat piece of paper on a table top. The paper is pulled horizontally but quickly towards the right as shown. Relative to its initial position with respect to the table,the ball :-
$(A)$ Remains stationary if there is no friction between the paper and the ball.
$(B)$ Moves to the left and starts rolling backwards,i.e.,to the left if there is friction between the paper and the ball.
$(C)$ Moves forward,i.e.,in the direction in which the paper is pulled if there is friction between the paper and the ball.
Here,the correct statement$(s)$ is/are :-

$A$ ring of radius $4a$ is rigidly fixed in a vertical position on a table. $A$ small disc of mass $m$ and radius $a$ is released as shown in the figure. When the disc rolls down,without slipping,to the lowest point of the ring,then its speed will be