Let \( (X, Y)^T \) follow a bivariate normal distribution with
\[ E(X) = 3, \quad E(Y) = 4, \quad \text{Var}(X) = 25, \quad \text{Var}(Y) = 100, \quad \text{Cov}(X, Y) = 50 \rho, \]
An electricity utility company charges ₹7 per kWh. If a 40-watt desk light is left on for 10 hours each night for 180 days, what would be the cost of energy consumption? If the desk light is on for 2 more hours each night for the 180 days, what would be the percentage-increase in the cost of energy consumption?
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.
For the clock shown in the figure, if
O = O Q S Z P R T, and
X = X Z P W Y O Q,
then which one among the given options is most appropriate for P?