The value of Henry’s constant KH
Question: The value of Henrys constant KH is _____________. (i) greater for gases with higher solubility. (ii) greater for gases with lower solubility. (iii) constant for all gases. (iv) not related to the solubility of gases. Solution: Option (ii)greater for gases with lower solubilityis the answer....
Read More →Value of Henry’s constant KH
Question: Value of Henrys constant KH ____________. (i) increases with increase in temperature. (ii) decreases with increase in temperature. (iii) remains constant. (iv) first increases then decrease. Solution: Option (i)increases with increase in temperature is the answer....
Read More →Which of the following statements is false?
Question: Which of the following statements is false? (i) Units of atmospheric pressure and osmotic pressure are the same. (ii) In reverse osmosis, solvent molecules move through a semipermeable membrane from a region of lower concentration of solute to a region of higher concentration. (iii) The value of molal depression constant depends on the nature of the solvent. (iv) Relative lowering of vapour pressure is a dimensionless quantity. Solution: Option (ii)In reverse osmosis, solvent molecules...
Read More →Let A be the set of all points in a plane and let O be the origin.
Question: Let $A$ be the set of all points in a plane and let $O$ be the origin. Show that the relation $R=\{(P, Q): P, Q \in A$ and $O P=O Q$ ) is an equivalence relation. Solution: In order to show $R$ is an equivalence relation, we need to show $R$ is Reflexive, Symmetric and Transitive. Given that, $A$ be the set of all points in a plane and $O$ be the origin. Then, $R=\{(P, Q): P, Q \in A$ and $O P=$ OQ)\} Now, $\underline{R}$ is Reflexive if $(P, P) \in \underline{R} \underline{\forall} \u...
Read More →The values of Van’t Hoff factors for KCl,
Question: The values of Vant Hoff factors for KCl, NaCl and K2SO4 , respectively, are _____________. (i) 2, 2 and 2 (ii) 2, 2 and 3 (iii) 1, 1 and 2 (iv) 1, 1 and 1 Solution: Option (ii)2, 2 and 3is the answer....
Read More →Which of the following statements is false?
Question: Which of the following statements is false? (i) Two different solutions of sucrose of the same molality prepared in different solvents will have the same depression in freezing point. (ii) The osmotic pressure of a solution is given by the equation Π = CRT ( where C is the molarity of the solution). (iii) Decreasing order of osmotic pressure for 0.01 M aqueous solutions of barium chloride, potassium chloride, acetic acid and sucrose is BaCl2 KCl CH3COOH sucrose. (iv) According to Raoul...
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{1}{5+7 \cos x+\sin x} d x$ Solution: Given $I=\int \frac{1}{5+7 \cos x+\sin x} d x$ We know that $\sin x=\frac{2 \tan \frac{x}{2}}{1+\tan ^{2} \frac{x}{2}}$ and $\cos x=\frac{1-\tan ^{2} \frac{x}{2}}{1+\tan ^{2} \frac{x}{2}}$ $\Rightarrow \int \frac{1}{5+\sin x+7 \cos x} d x=\int \frac{1}{5+\left(\frac{2 \tan \frac{x}{2}}{1+\tan \frac{2}{2}}\right)+7\left(\frac{1-\tan ^{2} \frac{x}{2}}{1+\tan ^{2} \frac{x}{2}}\right)} d x$ $=\int \frac{1+\t...
Read More →At a given temperature, osmotic pressure of a concentrated
Question: At a given temperature, osmotic pressure of a concentrated solution of a substance _____________. (i) is higher than that at a dilute solution. (ii) is lower than that of a dilute solution. (iii) is same as that of a dilute solution. (iv) cannot be compared with an osmotic pressure of a dilute solution. Solution: Option (i)is higher than that at a dilute solution is the answer....
Read More →An unripe mango placed in a concentrated
Question: An unripe mango placed in a concentrated salt solution to prepare pickle, shrivels because _____________. (i) it gains water due to osmosis. (ii) it loses water due to reverse osmosis. (iii) it gains water due to reverse osmosis. (iv) it loses water due to osmosis. Solution: Option (iv)it loses water due to osmosisis the answer....
Read More →In comparison to a 0.01 M solution of glucose,
Question: In comparison to a 0.01 M solution of glucose, the depression in freezing point of a 0.01 M MgCl2 solution is _____________. (i) the same (ii) about twice (iii) about three times (iv) about six times Solution: Option (iii)about three timesis the answer....
Read More →The unit of ebulioscopic constant is _______________.
Question: The unit of ebulioscopic constant is _______________. (i) K kg mol1 or K (molality)1 (ii) mol kg K1 or K1(molality) (iii) kg mol1 K1 or K1(molality)1 (iv) K mol kg1 or K (molality) Solution: Option (i)K kg mol1 or K (molality)1is the answer....
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{1}{\sin x-\sqrt{3} \cos x} d x$ Solution: Given $\mathrm{I}=\int \frac{1}{\sin \mathrm{x}-\sqrt{3} \cos \mathrm{x}} \mathrm{dx}$ Let $1=r \cos \theta$ and $\sqrt{3}=r \sin \theta$ $r=\sqrt{3+1}=2$ And $\tan \theta=\sqrt{3} \rightarrow \theta=\pi / 3$ $\Rightarrow \int \frac{1}{\sin x-\sqrt{3} \cos x} d x=\int \frac{1}{r \cos \theta \sin x-r \sin \theta \cos x} d x$ $=\frac{1}{r} \int \frac{1}{\sin (x-\theta)} d x$ $=\frac{1}{r} \int \operat...
Read More →Find the value
Question: Let $S$ be the set of all sets and let $R=\{(A, B): A \subset B)\}, i . e ., A$ is a proper subset of $B$. Show that $R$ is (i) transitive (ii) not reflexive (iii) not symmetric. Solution: Let $R=\{(A, B): A \subset B)\}$, i.e., $A$ is a proper subset of $B$, be a relation defined on $S .$ Now, Any set is a subset of itself, but not a proper subset. $\Rightarrow(A, A) \notin R \forall A \in S$ $\Rightarrow \mathrm{R}$ is not reflexive. Let $(A, B) \in R \forall A, B \in S$ $\Rightarrow...
Read More →Which of the following aqueous solutions
Question: Which of the following aqueous solutions should have the highest boiling point? (i) 1.0 M NaOH (ii) 1.0 M Na2SO4 (iii) 1.0 M NH4NO3 (iv) 1.0 M KNO3 Solution: Option (ii)1.0 M Na2SO4 is the answer....
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{1}{\sqrt{3} \sin x+\cos x} d x$ Solution: Given $I=\int \frac{1}{\sqrt{3} \sin x+\cos x} d x$ Let $\sqrt{3}=r \cos \theta$ and $1=r \sin \theta$ $r=\sqrt{3+1}=2$ And $\tan \theta=1 / \sqrt{3} \rightarrow \theta=\pi / 6$ $\Rightarrow \int \frac{1}{\sqrt{3} \sin x+\cos x} d x=\int \frac{1}{r \cos \theta \sin x+r \sin \theta \cos x} d x$ $=\frac{1}{r} \int \frac{1}{\sin (x+\theta)} d x$ $=\frac{1}{r} \int \operatorname{cosec}(x+\theta) d x$ We...
Read More →Colligative properties depend on ____________.
Question: Colligative properties depend on ____________. (i) the nature of the solute particles dissolved in solution. (ii) the number of solute particles in solution. (iii) the physical properties of the solute particles dissolved in solution. (iv) the nature of solvent particles. Solution: Option (ii)the number of solute particles in solution is the answer....
Read More →Considering the formation,
Question: Considering the formation, breaking and strength of hydrogen bond, predict which of the following mixtures will show a positive deviation from Raoults law? (i) Methanol and acetone. (ii) Chloroform and acetone. (iii) Nitric acid and water. (iv) Phenol and aniline. Solution: Option (i)Methanol and acetone is the answer....
Read More →Low concentration of oxygen in the blood
Question: Low concentration of oxygen in the blood and tissues of people living at high altitude is due to ____________. (i) low temperature (ii) low atmospheric pressure (iii) high atmospheric pressure (iv) both low temperature and high atmospheric pressure Solution: Option (ii)low atmospheric pressure is the answer....
Read More →Solve this
Question: Let $R=\{(a, b): a, b \in N$ and $b=a+5, a4\} .$ Find the domain and range of $R$. Solution: $\operatorname{dom}(R)=\{1,2,3\}$ and range $(R)=\{6,7,8\}$...
Read More →The maximum amount of a solid solute
Question: The maximum amount of a solid solute that can be dissolved in a specified amount of a given liquid solvent does not depend upon ____________. (i) Temperature (ii) Nature of solute (iii) Pressure (iv) Nature of solvent Solution: Option (iii) Pressureis the answer....
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{1}{\sin x+\sqrt{3} \cos x} d x$ Solution: Given $I=\int \frac{1}{\sin x+\sqrt{3} \cos x} d x$ We know that $\sin \mathrm{X}=\frac{2 \tan \frac{\mathrm{x}}{2}}{1+\tan \frac{2}{2}}$ and $\cos \mathrm{X}=\frac{1-\tan ^{2} \frac{\mathrm{X}}{2}}{1+\tan ^{2} \frac{2}{2}}$ $\Rightarrow \int \frac{1}{\sin x+\sqrt{3} \cos x} d x=\int \frac{1}{\frac{2 \tan \frac{x}{2}}{1+\tan ^{2} \frac{x}{2}}+\sqrt{3}\left(\frac{1-\tan 2 \frac{x}{2}}{1+\tan \frac{2}...
Read More →Solve this
Question: Let $R=\left\{\left(a, \frac{1}{a}\right): a \in N\right.$ and $\left.1a5\right\}$ Find the domain and range of $R$. Solution: $\operatorname{dom}(R)=\{2,3,4\}$ and range $(R)=\left\{\frac{1}{2}, \frac{1}{3}, \frac{1}{4}\right\}$...
Read More →A beaker contains a solution of a substance ‘A’.
Question: A beaker contains a solution of a substance A. Precipitation of substance A takes place when a small amount of A is added to the solution. The solution is _________. (i) saturated (ii) supersaturated (iii) unsaturated (iv) concentrated Solution: Option (ii)supersaturatedis the answer....
Read More →At equilibrium the rate of dissolution of a solid
Question: At equilibrium the rate of dissolution of a solid solute in a volatile liquid solvent is __________. (i) less than the rate of crystallisation (ii) greater than the rate of crystallisation (iii) equal to the rate of crystallisation (iv) zero Solution: Option (iii)equal to the rate of crystallisationis the answer....
Read More →Solve this
Question: Let $R=\{(a, b): b=|a-1|, a \in Z$ and $|a|3\}$ Find the domain and range of $R$. Solution: dom $(R)=\{-2,-1,0,1,2\}$ and range $(R)=\{3,2,1,0\}$...
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