If the entries in each column of a square matrix $$M$$ add up to $$1$$, then an eigenvalue of $$M$$ is

The magnitudes of vectors P, Q and R are 100 kN, 250 kN and 150 kN, respectively as shown in the figure. The respective values of the magnitude (in kN) and the direction (with respect to the x-axis) of the resultant vector are

A rigid member ACB is shown in the figure. The member is supported at A and B by pinned and guided roller supports, respectively. A force P acts at C as shown. Let R_Ah and R_Bh be the horizontal reactions at supports A and B, respectively, and R_Av be the vertical reaction at support A. Self- weight of the member may be ignored. Which one of the following sets gives the correct magnitudes of R_Av, R_Bh and R_Ah ?

Effluent from an industry 'A' has a pH of 4.2. The effluent from another industry 'B' has double the hydroxyl (OH^-) ion concentration than the effluent from industry 'A'. pH of effluent from the industry 'B' will be _______.