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 \( y = r \sin\theta \))
Match the LIST-I with LIST-II
LIST-I (Expressions) | LIST-II (Values) | ||
---|---|---|---|
A. | \( i^{49} \) | I. | 1 |
B. | \( i^{38} \) | II. | \(-i\) |
C. | \( i^{103} \) | III. | \(i\) |
D. | \( i^{92} \) | IV. | \(-1\) |
Choose the correct answer from the options given below:
Match the LIST-I with LIST-II
LIST-I (Energy of a particle in a box of length L) | LIST-II (Degeneracy of the states) | ||
---|---|---|---|
A. | \( \frac{14h^2}{8mL^2} \) | I. | 1 |
B. | \( \frac{11h^2}{8mL^2} \) | II. | 3 |
C. | \( \frac{3h^2}{8mL^2} \) | III. | 6 |
Choose the correct answer from the options given below:
Match the LIST-I with LIST-II
LIST-I (Type of decay in Radioactivity) | LIST-II (Reason for stability) | ||
---|---|---|---|
A. | Alpha decay | III. | Nucleus is mostly heavier than Pb (Z=82) |
B. | Beta negative decay | IV. | Nucleus has too many neutrons relative to the number of protons |
C. | Gamma decay | I. | Nucleus has excess energy in an excited state |
D. | Positron Emission | II. | Nucleus has too many protons relative to the number of neutrons |
Choose the correct answer from the options given below:
Match the LIST-I with LIST-II
LIST-I (Configuration of Bipolar Transistors) | LIST-II (Characteristics) | ||
---|---|---|---|
A. | Common Base | I. | Current Gain but no Voltage Gain |
B. | Common Emitter | III. | Both Current and Voltage Gain |
C. | Common Collector | II. | Voltage Gain but no Current Gain |
Choose the correct answer from the options given below: