1.

The resultant of two vectors \( \vec{A} \) and \( \vec{B} \) is perpendicular to \( \vec{A} \) and its magnitude is half that of \( \vec{B} \). The angle between vectors \( \vec{A} \) and \( \vec{B} \) is ________ .

2.

A 1 kg mass is suspended from the ceiling by a rope of length 4m. A horizontal force 'F' is applied at the mid point of the rope so that the rope makes an angle of 45° with respect to the vertical axis as shown in figure. The magnitude of F is

• \( \frac{10}{\sqrt{2}} \, \text{N} \)
• \( 1 \, \text{N} \)
• \( \frac{1}{10 \times \sqrt{2}} \, \text{N} \)
• \( 10 \, \text{N} \)

3.

UV light of 4.13 eV is incident on a photosensitive metal surface having work function 3.13 eV. The maximum kinetic energy of ejected photoelectrons will be

• 4.13 eV
• 1 eV
• 3.13 eV
• 7.26 eV

4.

The energy released in the fusion of 2 kg of hydrogen deep in the sun is $E_H$ and the energy released in the fission of 2 kg of $^{235}U$ is $E_U$. The ratio $\frac{E_H}{E_U}$ is approximately:

• 9.13
• 15.04
• 7.62
• 25.6

5.

A circular disc reaches from top to bottom of an inclined plane of length \( l \). When it slips down the plane, it takes \( t \) s. When it rolls down the plane, then it takes \[ \left( \frac{\alpha}{2} \right)^{1/2} t \, \text{s}, \] where \( \alpha \) is __________ .

6.

In the truth table of the above circuit the value of X and Y are

• 1,1
• 1,0
• 0,1
• 0,0