A five-member truss system is shown in the figure. The maximum vertical force \(P\) in kN that can be applied so that loads on the member CD and BC do NOT exceed 50 kN and 30 kN, respectively, is:
A truss structure is loaded as shown in the figure below. Among the options given, which member in the truss is a zero-force member?
\[ {Given: } F = 1000\,{N} \]
A regular dodecagon (12-sided regular polygon) is inscribed in a circle of radius \( r \) cm as shown in the figure. The side of the dodecagon is \( d \) cm. All the triangles (numbered 1 to 12 in the figure) are used to form squares of side \( r \) cm, and each numbered triangle is used only once to form a square. The number of squares that can be formed and the number of triangles required to form each square, respectively, are:
In the given figure, the numbers associated with the rectangle, triangle, and ellipse are 1, 2, and 3, respectively. Which one among the given options is the most appropriate combination of \( P \), \( Q \), and \( R \)?
The table shows the data of running a machine for five years. The original machine cost is Rupees 70,000. In order to minimize the average total cost per year for running the machine, the machine should be replaced after ............. years. (Answer in integer)