Step 1: Recall the electromagnetic spectrum.
The electromagnetic spectrum organizes different types of radiation by wavelength, frequency, and energy. Wavelength and frequency/energy are inversely related (short wavelength = high energy).
Step 2: List the main parts of the spectrum in order of increasing wavelength. The standard order is: Gamma rays \(\rightarrow\) X-rays \(\rightarrow\) Ultraviolet \(\rightarrow\) Visible light \(\rightarrow\) Infrared \(\rightarrow\) Microwaves \(\rightarrow\) Radio waves.
Step 3: Apply this order to the given radiations. 1. gamma radiations (A) - Shortest wavelength 2. X rays (B) 3. UV radiations (C) 4. Infrared radiations (E) 5. microwave (D) - Longest wavelength
Step 4: Form the final sequence. The correct sequence for increasing wavelength is A, B, C, E, D.
If \(f(t)\) is the inverse Laplace transform of \( F(s) = \frac{s+1+s^{-2}}{s^2-1} \), then \(f(t)\) is
Match LIST-I with LIST-II
LIST-I (Differential Equation)
(A) \(\frac{dy}{dx} = 2x(y-x^2+1)\)
(B) \(x\frac{dy}{dx} + 2(x^2+1)y=6\)
(C) \((x^2+1)\frac{dy}{dx} + 2xy = x \sin x\)
(D) \(x^3\frac{dy}{dx} + 2xy = 2x^2e^{x^2}\)
LIST-II (Integrating Factor)
(I) \(x^2\)
(II) \(e^{-x^2}\)
(III) \(x^2e^x\)
(IV) \(1+x^2\)
Choose the correct answer from the options given below: