CUET Mathematics 2026 30th May Shift 2 PYQs

The differential equation representing family of curves $y = ae^{mx} + be^{nx}$, where $a$ and $b$ are arbitrary constants, is

If curve represented by differential equation $x \frac{dy}{dx} + y = e^x$ passes through (1, 1), then $y(-1)$ is :

Curd is at 80° F, five minutes later it came down at 60°F. After another 5 minutes, its temperature became 50° F. Given that the rate of change of temperature is proportional to (T - S), where S is temperature of the surroundings and T is temperature of the curd at any time t. Then the temperature of the surroundings is :