Question:medium
Match the LIST-I with LIST-II
Match the LIST-I with LIST-II
Show Hint
For composite functions $f(u) = H(x,y)$ where $H$ is homogeneous of degree $n$, use $x u_x + y u_y = n \frac{f(u)}{f'(u)}$.
Updated On: Jul 29, 2026
- A-IV, B-I, C-III, D-II
- A-III, B-II, C-IV, D-I
- A-IV, B-III, C-I, D-II
- A-IV, B-I, C-II, D-III
Show Solution
The Correct Option is D
Solution and Explanation
Was this answer helpful?
0
Top Questions on Complex Analysis
Match List-I with List-II and choose the correct option:
LIST-I (Function) LIST-II (Value) (A) \( \int_{\gamma} \frac{1}{z-a} \, dz \), where \( \gamma: |z-a|=r, r > 0 \) (III) \( 2i\pi \) (B) \( \int_{\gamma} \frac{z+2}{z} \, dz \), where \( \gamma: z = 2e^{it}, 0 \le t \le \pi \) (IV) \( i\pi \) (C) \( \int_{\gamma} \frac{e^{2z}}{(z-1)(z-2)} \, dz \), where \( \gamma: |z|=3 \) (II) \( 2i\pi(e^4 - e^2) \) (D) \( \int_{\gamma} \frac{z^2 - z + 1}{2(z-1)} \, dz \), where \( \gamma: |z|=2 \) (I) \( -4 + 2i\pi \)
Choose the correct answer from the options given below:- CUET (PG) - 2025
- Mathematics
- Complex Analysis
- Consider the following: Let f(z) be a complex valued function defined on a subset \( S \subset \mathbb{C} \) of complex numbers. Then which of the following are correct?
A. The order of a zero of a polynomial equals to the order of its first non-vanishing derivative at that zero of the polynomial
B. Zeros of non-zero analytic function are isolated
C. Zeros of f(z) are obtained by equating the numerator to zero if there is no common factor in the numerator and the denominator of f(z)
D. Limit points of zeros of an analytic function is an isolated essential singularity- CUET (PG) - 2025
- Mathematics
- Complex Analysis
- The function \( f(z) = |z|^2 \) is differentiable, at
- CUET (PG) - 2025
- Mathematics
- Complex Analysis
- If C is the positively oriented circle represented by \( |z|=2 \), then \( \int_C \frac{e^{2z}}{z-4} dz \) is:
- CUET (PG) - 2025
- Mathematics
- Complex Analysis
- Want to practice more? Try solving extra ecology questions todayView All Questions