If the lines $3x - 4y - 7 = 0$ and $2x - 3y - 5 = 0$ are two diameters of a circle with an area of $49\pi$ square units,then the equation of the circle is:

Two rotating bodies $A$ and $B$ of masses $m$ and $2m$ with moments of inertia $I_A$ and $I_B$ $(I_B > I_A)$ have equal kinetic energy of rotation. If $L_A$ and $L_B$ are their angular momenta respectively,then:

$1\, g$ of hydrogen is converted into $0.993\, g$ of helium in a thermonuclear reaction. The energy released is

Let $\alpha$ and $\beta$ be the roots of the equation $x^2 - x - 1 = 0$. If $p_k = (\alpha)^k + (\beta)^k$ for $k \geq 1$,then which one of the following statements is not true?

Two workers $A$ and $B$ are engaged to do a piece of work. Working alone,$A$ takes $8 \text{ h}$ more to complete the work than if both worked together. On the other hand,working alone,$B$ would need $4 \frac{1}{2} \text{ h}$ more to complete the work than if both worked together. How much time would they take to complete the job working together (in $\text{ h}$)?

Which of the following statements is correct?