Structure of Carboxylic Acids

Q.

2. Find minimum no. of carbon required in ester that can show metamerism

Q. Which of the following compounds is most reactive towards nucleophilic addition reactions?

1. 
   
2. 
   
3. 
   
4. 
   

Q.

Are esters more acidic than amides?

Q.

Which of the following is a measure of degree of unsaturation in oils and fats?

1. Iodine value

2. Saponification value

3. Acid value

4. Acetyl value

Q. The solution of the given differential equation $\frac{dy}{dx}+2xy=y$ is

1. $y=c{e}^{x-x^2}$
   
2. $y=c{e}^{x^2-x}$
   
3. $y=c{e}^x$
   
4. $y=c{e}^{-x^2}$

Q. Which of the following acids does not exhibit optical isomerism?

1. Lactic acid
2. Tartaric acid
3. Maleic acid
4. $\alpha -$ amino acid

Q. 48. Give reason for the higher boiling point of ethanol in comparison to metgoxymethane.

Q.

An organic compound 'X' gives brisk effervescence with NaHCO₃ and also reduces Tollen's reagent. 'X' is

1. CH₃COOH

2. CH₃CHO

3. CH₃COCH₃

4. HCOOH

Q. If a curve passes through the point $(1,-2)$ and has slope of the tangent at any point $(x,y)$ on it as $\frac{x^2-2y}{x}$, then the curve also passes through the point :

1. $(3,0)$
2. $(-1,2)$
3. $(-\sqrt{2},1)$
4. $(\sqrt{3},0)$

Q.

Carboxylic acids are more acidic than phenols, because

1. The resonance structures of acid are equivalent while those of phenols are non equivalent

2. In resonance structures of phenols negative charge is on more electro positive carbon while in those of acid it is more electro negative oxygen

3. None

4. (a) and (b) above.

Q. determine the solubilities of silverchromate(Ksp=1.1×10∧-12), barium chromate(1.2×10∧-10), ferric hydroxide(1×10∧-38) , lead chloride(1.6×10∧-5) and mercurous iodide(4.5×10∧-29) at 298K. also determine molarity of individual ion

Q. The solution of $\frac{dv}{dt}+\frac{k}{m}v=-g$ is

1. $v=c{e}^{-\frac{k}{m}t}-\frac{mg}{k}$
2. $v=c-\frac{mg}{k}e-\frac{k}{m}t$
3. $ve-\frac{k}{m}t=c-\frac{mg}{k}$
4. $ve\frac{k}{m}t=c-\frac{mg}{k}$

Q. 29. What is the order of thermal stability and Cl-O bond order of oxy acids of Chlorine?

Q. The equation $(x-a{)}^2+(y-b{)}^2=k(px+qy+r{)}^2,$ where $(pa+qb+r)\ne 0$ represents

1. a parabola for $k<\frac{1}{p^2+q^2}$
2. an ellipse for $0<k<\frac{1}{p^2+q^2}$
3. a hyperbola for $k>\frac{1}{p^2+q^2}$
4. a point circle for $k=0$

Q. Consider the differential equation
$y^{2}dx+(x-\frac{1}{y})dy=0$.
$\text{If}y\left(1\right)=1$, then $x$ is given by :

1. $4-\frac{2}{y}-\frac{e^{\frac{1}{y}}}{e}$
   
2. $3-\frac{1}{y}-\frac{e^{\frac{1}{y}}}{e}$
3. $1+\frac{1}{y}-\frac{e^{\frac{1}{y}}}{e}$
4. $1-\frac{1}{y}-\frac{e^{\frac{1}{y}}}{e}$

Q.

The solution of the differential equation $\frac{dy}{dx}+\frac{3x^2}{1+x^3}y=\frac{si{n}^{2}x}{1+x^3}$ is

1. $y(1+x^3)=x+\frac{1}{2}sin2x+c$

2. $2ta{n}^{-1}\left(\frac{x}{y}\right)+logx+c=0$

3. $log(y+\sqrt{x^2+y^2})+logy+c=0$

4. $sin{h}^{-1}\left(\frac{x}{y}\right)+logy+c=0$

Q. Let the population of rabbits surviving at a time $t$ be governed by the differential equation $\frac{dp\left(t\right)}{dt}=\frac{1}{2}p\left(t\right)-200$. If $p\left(0\right)=100$, then $p\left(t\right)$ equals:

1. $400-300e^{t/2}$
2. $300-200e^{-t/2}$
3. $600-500e^{t/2}$
4. $400-300e^{-t/2}$

Q. Compound (A) produces $C{O}_2$ gas with $NaHC{O}_3$. Compound (A) also produces $H_2$ gas with metallic Na. Further, compound (A) gives a positive iodoform test. Structure of (A) is:

1. 
2. 
3. 
4. 

Q. If the solution of differential equation $x\ln x\frac{dy}{dx}+y=2\ln x$ is $y\left(\ln x\right)=(\ln x{)}^n+C$ then $n=$ ___

Q. Let $y=y\left(x\right)$ be the solution curve of the differential equation, $(y^2-x)\frac{dy}{dx}=1$, satisfying $y\left(0\right)=1$. This curve intersects the $x$-axis at a point whose abscissa is :

1. $2+e$
2. $2$
3. $2-e$
4. $-e$

Q. 12 Give the conformers of cyclohexane.

Q.

Maximum enol content is in:

1. 

2. 

3. 

4. 

Q. If $y_1\left(x\right)$ is a solution of the differential equation $\frac{dy}{dx}-f\left(x\right)y=0$, then a solution of the differential equation $\frac{dy}{dx}+f\left(x\right)y=r\left(x\right)$

1. $\frac{1}{y_1\left(x\right)}\int r\left(x\right)y_1\left(x\right)dx$
2. $y_1\left(x\right)\int \frac{r\left(x\right)}{y_1\left(x\right)}dx$
3. $\int r\left(x\right)y_1\left(x\right)dx$
4. $Noneofthese$

Q. If $y_1\left(x\right)$ is a solution of the differential equation $\frac{dy}{dx}-f\left(x\right)y=0$, then a solution of the differential equation $\frac{dy}{dx}-f\left(x\right)y=r\left(x\right)$ is

1. $\frac{1}{y_1\left(x\right)}\int r\left(x\right)y_1\left(x\right)dx$
2. $y_1\left(x\right)\int \frac{r\left(x\right)}{y_1\left(x\right)}dx$
3. $\int r\left(x\right)y_1\left(x\right)dx$
4. $noneofthese$

Q. The function $y=f\left(x\right)$ is the solution of the differential equation $\frac{dy}{dx}+\frac{xy}{x^2-1}=\frac{x^4+2x}{\sqrt{1-x^2}}$ in (-1, 1) satisfying f(0) =0. Then ${\int }_{\frac{-\sqrt{3}}{2}}^{\frac{\sqrt{3}}{2}}f\left(x\right)d\left(x\right)$ is

1. $\frac{\pi }{3}-\frac{\sqrt{3}}{2}$
2. $\frac{\pi }{3}-\frac{\sqrt{3}}{4}$
3. $\frac{\pi }{6}-\frac{\sqrt{3}}{4}$
4. $\frac{\pi }{6}-\frac{\sqrt{3}}{2}$