Which of the following are chiral molecules?
Choose the correct answer from the options given below:
Match List-I with List-II for the index of refraction for yellow light of sodium (589 nm)
LIST-I (Materials) | LIST-II (Refractive Indices) | ||
---|---|---|---|
A. | Ice | I. | 1.309 |
B. | Rock salt (NaCl) | II. | 1.460 |
C. | CCl₄ | III. | 1.544 |
D. | Diamond | IV. | 2.417 |
Choose the correct answer from the options given below:
Match the LIST-I with LIST-II
LIST-I | LIST-II | ||
---|---|---|---|
A. | Compton Effect | IV. | Scattering |
B. | Colors in thin film | II. | Interference |
C. | Double Refraction | III. | Polarization |
D. | Bragg's Equation | I. | Diffraction |
Choose the correct answer from the options given below:
Match List-I with List-II on the basis of two simple harmonic signals of the same frequency and various phase differences interacting with each other:
LIST-I (Lissajous Figure) | LIST-II (Phase Difference) | ||
---|---|---|---|
A. | Right handed elliptically polarized vibrations | I. | Phase difference = \( \frac{\pi}{4} \) |
B. | Left handed elliptically polarized vibrations | II. | Phase difference = \( \frac{3\pi}{4} \) |
C. | Circularly polarized vibrations | III. | No phase difference |
D. | Linearly polarized vibrations | IV. | Phase difference = \( \frac{\pi}{2} \) |
Choose the correct answer from the options given below:
For Particular Integral, Match the LIST-I with LIST-II
LIST-I | LIST-II | ||
---|---|---|---|
A. | \( \frac{1}{(D-1)} x^2 \) | I. | \( xe^x \) |
B. | \( \frac{1}{D^2+D+1} \cos x \) | II. | \( \sin x \) |
C. | \( \frac{1}{(D-1)^2} e^x \) | III. | \( \frac{x^2 e^x}{2} \) |
D. | \( \frac{1}{D^3-3D^2+4D-2} e^x \) | IV. | \( -(x^2 + 2x + 2) \) |
(Note: List-I Item A is assumed to be \( \frac{1}{D-1} x^2 \) based on the options)
If \( x = r\cos\theta, y = r\sin\theta \) then Match the LIST-I with LIST-II
LIST-I | LIST-II | ||
---|---|---|---|
A. | \( \frac{\partial r}{\partial x} \) | I. | \( \frac{1}{r} \) |
B. | \( \frac{\partial r}{\partial y} \) | II. | \( \frac{y}{r} \) |
C. | \( \frac{\partial(x,y)}{\partial(r,\theta)} \) | III. | \( \frac{x}{r} \) |
D. | \( \frac{\partial(r,\theta)}{\partial(x,y)} \) | IV. | \( r \) |
(Note: There is a typo in the question; it should be \( y = r \sin\theta \))