| List-I EM-Wave | List-II Wavelength Range |
|---|---|
| (A) Infra-red | (III) 1 mm to 700 nm |
| (B) Ultraviolet | (II) 400 nm to 1 nm |
| (C) X-rays | (IV) 1 nm to \(10^{-3}\) nm |
| (D) Gamma rays | (I) \(<10^{-3}\) nm |
The correct matching between the EM waves and their wavelength ranges is as follows:
- (A) Infra-red corresponds to \( 1 \, \text{mm} \) to \( 700 \, \text{nm} \), which is (III).
- (B) Ultraviolet corresponds to \( 400 \, \text{nm} \) to \( 1 \, \text{nm} \), which is (II).
- (C) X-rays correspond to \( 1 \, \text{nm} \) to \( 10^{-3} \, \text{nm} \), which is (IV).
- (D) Gamma rays correspond to wavelengths less than \( 10^{-3} \, \text{nm} \), which is (I).
Thus, the correct matching is:
\[ \text{(A)-(III), (B)-(II), (C)-(IV), (D)-(I)} \]
Infrared radiation has the longest wavelength among the options, while gamma rays have the shortest wavelength, corresponding to their relative energy levels, with gamma rays being the most energetic and infrared the least.
The dimension of $ \sqrt{\frac{\mu_0}{\epsilon_0}} $ is equal to that of: (Where $ \mu_0 $ is the vacuum permeability and $ \epsilon_0 $ is the vacuum permittivity)
If the system of equations \[ (\lambda - 1)x + (\lambda - 4)y + \lambda z = 5 \] \[ \lambda x + (\lambda - 1)y + (\lambda - 4)z = 7 \] \[ (\lambda + 1)x + (\lambda + 2)y - (\lambda + 2)z = 9 \] has infinitely many solutions, then \( \lambda^2 + \lambda \) is equal to:
The output of the circuit is low (zero) for:

(A) \( X = 0, Y = 0 \)
(B) \( X = 0, Y = 1 \)
(C) \( X = 1, Y = 0 \)
(D) \( X = 1, Y = 1 \)
Choose the correct answer from the options given below:
The metal ions that have the calculated spin only magnetic moment value of 4.9 B.M. are
A. $ Cr^{2+} $
B. $ Fe^{2+} $
C. $ Fe^{3+} $
D. $ Co^{2+} $
E. $ Mn^{2+} $
Choose the correct answer from the options given below
Which of the following circuits has the same output as that of the given circuit?
