Two stars of masses 3 $$ \times $$ 10³¹ kg each, and at distance 2 $$ \times $$ 10¹¹ m rotate in a plane about their common centre of mass O. A meteorite passes through O moving perpendicular to the star’s rotation plane. In order to escape from the gravitational field of this double star, the minimum speed that meteorite should have at O is - (Take Gravitational constant; G = 6.67 $$ \times $$ 10^–11 Nm² kg^–2)

The diameter and height of a cylinder are measured by a meter scale to be 12.6 $$ \pm $$ 0.1 cm and 34.2 $$ \pm $$ 0.1 cm, respectively. What will be the value of its volume in appropriate significant figures ?

Two vectors $$\overrightarrow A $$ and $$\overrightarrow B $$ have equal magnitudes. The magnitude of $$\left( {\overrightarrow A + \overrightarrow B } \right)$$ is 'n' times the magnitude of $$\left( {\overrightarrow A - \overrightarrow B } \right)$$ . The angle between $${\overrightarrow A }$$ and $${\overrightarrow B }$$ is -

Consider the nuclear fission

Ne²⁰ $$ \to $$ 2He⁴ + C¹²

Given that the binding energy/ nucleon of Ne²⁰, He⁴ and C¹² are, respectively, 8.03 MeV, 7.07 MeV and 7.86 MeV, identify the correct statement -