Consider a situation in which reserve biased current of a particular P-N junction increases when it is exposed to a light of wavelength $$\le$$ 621 nm. During this process, enhancement in carrier concentration takes place due to generation of hole-electron pairs. The value of band gap is nearly.

A ray of light passing through a prism ($$\mu$$ = $$\sqrt 3 $$) suffers minimum deviation. It is found that the angle of incidence is double the angle of refraction within the prism. Then, the angle of prism is _____________ (in degrees).

Three students S₁, S₂ and S₃ perform an experiment for determining the acceleration due to gravity (g) using a simple pendulum. They use different lengths of pendulum and record time for different number of oscillations. The observations are as shown in the table.

Student No.	Length of Pendulum (cm)	No. of oscillations (n)	Total time for n oscillations	Time period (s)
1	64.0	8	128.0	16.0
2	64.0	4	64.0	16.0
3	20.0	4	36.0	9.0

(Least count of length = 0.1 cm and Least count for time = 0.1 s)

If E₁, E₂ and E₃ are the percentage errors in 'g' for students 1, 2 and 3 respectively, then the minimum percentage error is obtained by student no. ______________.

Three particles P, Q and R are moving along the vectors $$\overrightarrow A = \widehat i + \widehat j$$, $$\overrightarrow B = \widehat j + \widehat k$$ and $$\overrightarrow C = - \widehat i + \widehat j$$ respectively. They strike on a point and start to move in different directions. Now particle P is moving normal to the plane which contains vector $$\overrightarrow A $$ and $$\overrightarrow B $$. Similarly particle Q is moving normal to the plane which contains vector $$\overrightarrow A $$ and $$\overrightarrow C $$. The angle between the direction of motion of P and Q is $${\cos ^{ - 1}}\left( {{1 \over {\sqrt x }}} \right)$$. Then the value of x is _______________.