CUET Mathematics 2026 29th May Shift 2 PYQs

For a given differential equation $e^{dy/dx} = x + 1; x \in (-1,\infty)$, then which of the following statements are TRUE?

(A) Its general solution is $y = x\log_e(x+1) - x + \log_e(x+1) + C$; C is an arbitrary constant.

(B) Its particular solution is $y = (x+1)\log_e(x+1) - x + 5; y(0) = 5$

(C) Its general solution is $y = (x-1)\log(x+1) - x + C$; C is an arbitrary constant

(D) Its particular solution is $y = (x-1)\log(x+1) - x + 5; y(0) = 5$

Choose the correct answer from the options given below:

The solution of the differential equation $e^{\frac{dy}{dx}} = x+1$; $y(0)=5$ 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 :