For the matrix [A] given below, the transpose is __________.
\[ A = \begin{bmatrix} 2 & 3 & 4 \\ 1 & 4 & 5 \\ 4 & 3 & 2 \end{bmatrix} \]
Consider the following statements (P) and (Q):
(P): Fly ash and ground granulated blast furnace slag can be used as mineral admixtures in concrete.
(Q): As per IS 456:2000, the minimum moist curing period becomes higher when a mineral admixture is added to concrete.
Identify the CORRECT option from choices given below.
Integration of \(\ln(x)\) with \(x\), i.e. \(\int \ln(x)dx =\) __________.
Three villages P, Q, and R are located in such a way that the distance PQ = 13 km, QR = 14 km, and RP = 15 km, as shown in the figure. A straight road joins Q and R. It is proposed to connect P to this road QR by constructing another road. What is the minimum possible length (in km) of this connecting road?
{Note: The figure shown is representative.}
A business person buys potatoes of two different varieties P and Q, mixes them in a certain ratio, and sells them at ₹192 per kg.
The cost of variety P is ₹800 for 5 kg.
The cost of variety Q is ₹800 for 4 kg.
If the person gets an 8% profit, what is the P : Q ratio (by weight)?