Formation of DE

Q. A body originally at ${60}^{\circ }$ C cools down to ${40}^{\circ }$ C in 15 min when kept in air at a temperature of ${25}^{\circ }$ C. What will be the temperature of the body at the end of 30 min?

1. 35.2${}^{\circ }$ C
2. 31.5${}^{\circ }$ C
3. 28.7${}^{\circ }$ C
4. 15${}^{\circ }$ C

Q. A spherical naphthalene ball exposed to the atmosphere loses volume at a rate propotional to its instantaneous surface area due to evaporation. If the initial diameter of the ball is 2 cm and the diameter reduces to 1 cm after 3 months, the ball completely evaporates in

1. 6 months
2. 9 months
3. 12 months
4. Infinite time

Q.

The general solution of the differential equation $\frac{d^{2}y}{d{x}^2}+8\left(\frac{dy}{dx}\right)+16y=0$ is

1. $(A+Bx)e^{5x}$

2. $(A+Bx)e^{-4x}$

3. $(A+B{x}^2)e^{4x}$

4. $(A+B{x}^4)e^{4x}$

Q. Which one of the following differential equations has a solution given by the function y = 5 sin $(3x+\frac{\pi }{3})$

1. $\frac{dy}{dx}-\frac{5}{3}cos\left(3x\right)=0$
2. $\frac{dy}{dx}+\frac{5}{3}cos\left(3x\right)=0$
3. $\frac{d^{2}y}{d^{2}x}+9y=0$
4. $\frac{d^{2}y}{d^{2}x}-9y=0$

Q. The figure shows the plot of y as a function of x. The function shown is the solution of the differential equation (assuming all initial condition to be zero) is

1. $\frac{d^{2}y}{d{x}^2}=1$
2. $\frac{dy}{dx}=-x$
3. $\frac{dy}{dx}=-x$
4. $\frac{dy}{dx}=\left|x\right|$