List-I (Function) | List-II (Derivative w.r.t. x) | |
---|---|---|
(A) \( \frac{5^x}{\ln 5} \) | (I) \(5^x (\ln 5)^2\) | |
(B) \(\ln 5\) | (II) \(5^x \ln 5\) | |
(C) \(5^x \ln 5\) | (III) \(5^x\) | |
(D) \(5^x\) | (IV) 0 |
The value of current \( I \) in the electrical circuit as given below, when the potential at \( A \) is equal to the potential at \( B \), will be _____ A.
Two light beams fall on a transparent material block at point 1 and 2 with angle \( \theta_1 \) and \( \theta_2 \), respectively, as shown in the figure. After refraction, the beams intersect at point 3 which is exactly on the interface at the other end of the block. Given: the distance between 1 and 2, \( d = \frac{4}{3} \) cm and \( \theta_1 = \theta_2 = \cos^{-1} \left( \frac{n_2}{2n_1} \right) \), where \( n_2 \) is the refractive index of the block and \( n_1 \) is the refractive index of the outside medium, then the thickness of the block is …….. cm.