Step 1: Analyze each structure.
- (A) Truss → Members mainly carry axial force → Structural behavior: Shortening (III).
- (B) Beam → Designed to resist bending → Structural behavior: Bending (I).
- (C) Column → Prone to buckling → Structural behavior: Buckling (IV).
- (D) Shaft → Transmits torque → Structural behavior: Twisting (II).
Step 2: Matching.
\[
A - III, B - I, C - IV, D - II
\]
Step 3: Conclusion.
The correct match corresponds to option (4).
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:
For the frame shown in the figure below, the maximum moment in the left column shall be (Assuming Moment of Inertia (I) of all the members is same):
