CUET Mathematics 2026 30th May Shift 2 PYQs

If a person rides his motorbike $x$ km at 30 km per hour, he has to spend ₹ 3 per kilometer on petrol. If he rides $y$ km at a faster speed of 40 km per hour, the petrol cost increases to ₹ 4 per kilometer. If he has ₹ 100 to spend on petrol and wishes to find the maximum distance he can travel within one hour, then linear programming problem (LPP) formulation is:

The maximum value of $z = 5x + 7y$ subjected to constraints $x + y \leq 5$, $x \geq 0$, $y \geq 0$ is:

A LPP $max\,z = ax+by$ having bounded feasible region with vertices on $(2,1), (3,2), (5,6)$ and $(1,7)$. Then which of following are TRUE?

A. $max\,z$ occurs at $(1,7)$ and $(5,6)$ if $b = 4a$

B. $max\,z$ occurs at $(1,7)$ and $(5,6)$ if $b = -4a$

C. $max\,z$ does not exist

D. if $max\,z$ occurs at $(1,7)$ and $(5,6)$, then $max\,z$ occurs for infinite number of value of $x$ and $y$

Choose the correct answer from the options given below: