Fischer's Esterification Process

Q. S1: The differential equation of parabolas having their vertices at the origin and foci on the x-axis is an equation whose variables are separable
S2: The differential equation of the straight lines which are at a fixed distance p from the origin is an equation of degree 2
S3: The differential equation of all conics whose both axes coincide with the axes of coordinates is an equation of order 2

1. TTT
2. TFT
3. FFT
4. TTF

Q. The differential equation whose general solution is given by, y =
$\left(c_{1}cos\right(x+c_2\left)\right)-\left(c_3{e}^{-x+c_4}\right)+\left(c_{5}sinx\right)$, where $c_1,c_2,c_3,c_4,c_5$ are arbitrary constants, is

1. $\frac{d^{4}y}{d{x}^4}-\frac{d^{2}y}{d{x}^2}+y=0$
2. $\frac{d^{3}y}{d{x}^3}+\frac{d^{2}y}{d{x}^2}+\frac{dy}{dx}+y=0$
3. $\frac{d^{5}y}{d{x}^5}+y=0$
4. $\frac{d^{3}y}{d{x}^3}-\frac{d^{2}y}{d{x}^2}+\frac{dy}{dx}-y=0$

Q. The differential equation formed by eliminating parameters A and B from the family of curves given by$y=A{e}^{2x}+B{e}^{-2x}$ will be of ___ order.

1. First
2. Second
3. Third
4. None of the above

Q. Which one of the following compound gives aspirin on reacting with acetic anhydride in presence of $H_{2}S{O}_4$

1. 
2. 
3. 
4. 

Q.

The differential equation for all the straight lines which are at a unit distance from the origin is

1. ${(y-x\frac{dy}{dx})}^2=1-{\left(\frac{dy}{dx}\right)}^2$

2. ${(y+x\frac{dy}{dx})}^2=1+{\left(\frac{dy}{dx}\right)}^2$

3. ${(y-x\frac{dy}{dx})}^2=1+{\left(\frac{dy}{dx}\right)}^2$

4. ${(y+x\frac{dy}{dx})}^2=1-{\left(\frac{dy}{dx}\right)}^2$

Q. The DE for the family of circles having a given radius 'a' is same as the DE of the family of circles whose center lies at origin.

1. False
2. True

Q. If $y^2=a{x}^2+bx+c$, then $y^3.\frac{d^{2}y}{d{x}^2}$ is

1. A constant
2. A function of x only
3. A function of y only
4. A function of x and y

Q. An equation of the curve in which subnormal varies as the square of the ordinate is (k is constant of proportionality)

1. $y=A{e}^{kx}$
2. $y=e^{kx}$
3. $\frac{y^2}{2}+kx=A$
4. $y^2+k{x}^2=A$

Q.

The differential equation of the family of curves $y=acos(x+b)$ is

[MP PET 1993]

1. $\frac{d^{2}y}{d{x}^2}-y=0$

2. $\frac{d^{2}y}{d{x}^2}+y=0$

3. $\frac{d^{2}y}{d{x}^2}+2y=0$

4. None of these

Q.

Will CCl₄ give white ppt. of AgCl on heating it with silver nitrate? Give reason for your answer.

Q.

The differential equation of the family of curves $v=\frac{A}{r}+B$ where A and B are arbitrary constants, is

1. $\frac{d^{2}v}{d{r}^2}+\frac{1}{r}\frac{dv}{dr}=0$

2. $\frac{d^{2}v}{d{r}^2}-\frac{2}{r}\frac{dv}{dr}=0$

3. $\frac{d^{2}v}{d{r}^2}+\frac{2}{r}\frac{dv}{dr}=0$

4. None of these