Which of the following statements (with respect to compass traversing) are correct?
A. True meridian at a station is constant.
B. True meridian passing through different points on the earth surface converges towards the pole.
C. The angle between the true meridian and the line is known as declination.
D. The angle between the magnetic meridian and the line is known as azimuth.
Choose the most appropriate answer from the options given below:
Step 1: Check statement A.
The true meridian at a station is fixed and does not change. Hence, (A) is correct.
Step 2: Check statement B.
True meridians from different locations converge towards the geographic North Pole. Hence, (B) is correct.
Step 3: Check statement C.
The angle between the true meridian and magnetic meridian is known as declination, not between true meridian and the line. So, (C) is incorrect.
Step 4: Check statement D.
The angle between a line and true meridian is called azimuth, not with magnetic meridian. So, (D) is incorrect.
Step 5: Conclusion.
Correct statements are A and B only.
The solution(s) of the ordinary differential equation $y'' + y = 0$, is:
(A) $\cos x$
(B) $\sin x$
(C) $1 + \cos x$
(D) $1 + \sin x$
Choose the most appropriate answer from the options given below:
For the matrix, $A = \begin{bmatrix} -4 & 0 \\ -1.6 & 4 \end{bmatrix}$, the eigenvalues ($\lambda$) and eigenvectors ($X$) respectively are:
The value of $\iint_S \vec{F} \cdot \vec{N} \, ds$ where $\vec{F} = 2x^2y \hat{i} - y^2 \hat{j} + 4xz^2 \hat{k}$ and $S$ is the closed surface of the region in the first octant bounded by the cylinder $y^2 + z^2 = 9$ and the planes $x = 0, x = 2, y = 0, z = 0$, is:
The value of the integral $\displaystyle \oint_C \frac{z^3 - 6}{2z - i} \, dz$, where $C: |z| \leq 1$, is: