eSaral - JEE | NEET | Class 8-10 Exam Prep App

A reaction, A + B → C + D + q is found to have a positive entropy change. The reaction will be

Question: A reaction, A + B C + D +qis found to have a positive entropy change. The reaction will be (i) possible at high temperature (ii) possible only at low temperature (iii) not possible at any temperature (iv) possible at any temperature Solution: For a reaction to be spontaneous, ΔGshould be negative. ΔG= ΔHTΔS According to the question, for the given reaction, ΔS= positive ΔH= negative (since heat is evolved) ⇒ ΔG= negative Therefore, the reaction is spontaneous at any temperature. Hence,...

An umbrella has 8 ribs which are equally spaced.

Question: An umbrella has 8 ribs which are equally spaced. Assuming umbrella to be a flat circle of radius 45 cm, find the area between the two consecutive ribs of the umbrella. Solution: Here, radius (r) = 45 cm Since circle is divided in 8 equal parts, $\therefore$ Sector angle corresponding to each part $\theta=\frac{\mathbf{3 B 0}^{\circ}}{\mathbf{8}}=45^{\circ}$ $\Rightarrow$ Area of a sector (part) $=\frac{\theta}{\mathbf{3 6 0}^{\circ}} \times \pi \mathbf{r}^{\mathbf{2}}=\frac{\mathbf{4 5...

The Cartesian product A × A has 9 elements among which are found

Question: The Cartesian product $A \times A$ has 9 elements among which are found $(-1,0)$ and $(0,1)$. Find the set $A$ and the remaining elements of $A \times A$. Solution: We know that if $n(A)=p$ and $n(B)=q$, then $n(A \times B)=p q$. $\therefore n(A \times A)=n(A) \times n(A)$ It is given that $n(A \times A)=9$ $\therefore n(A) \times n(A)=9$ $\Rightarrow n(\mathrm{~A})=3$ The ordered pairs $(-1,0)$ and $(0,1)$ are two of the nine elements of $A \times A$. We know that $A \times A=\{(a, a)...

The enthalpy of combustion of methane, graphite and dihydrogen at 298

Question: The enthalpy of combustion of methane, graphite and dihydrogen at $298 \mathrm{~K}$ are, $-890.3 \mathrm{~kJ} \mathrm{~mol}^{-1}-393.5 \mathrm{~kJ} \mathrm{~mol}^{-1}$, and $-285.8 \mathrm{~kJ} \mathrm{~mol}^{-1}$ respectively. Enthalpy of formation of $\mathrm{CH}_{4(g)}$ will be (i) $-74.8 \mathrm{~kJ} \mathrm{~mol}^{-1}$ (ii) $-52.27 \mathrm{~kJ} \mathrm{~mol}^{-1}$ (iii) $+74.8 \mathrm{~kJ} \mathrm{~mol}^{-1}$ (iv) $+52.26 \mathrm{~kJ} \mathrm{~mol}^{-1}$ Solution: According tothe ...

A brooch is made with silver wire in the form of a circle with diameter 35 mm.

Question: A brooch is made with silver wire in the form of a circle with diameter 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors as shown in fig. Find: (i) the total length of the silver wire required. (ii) the area of each sector of the brooch. Solution: Diameter of the circle = 35 mm $\therefore \operatorname{Radius}(\mathrm{r})=\frac{\mathbf{3 5}}{\mathbf{2}} \mathrm{mm}$ (i) Circumference $=2 \pi \mathrm{r}$ $=2 \times \frac{22}{7} \times \fr...

Let A and B be two sets such that n(A) = 3 and n (B) = 2.

Question: Let $A$ and $B$ be two sets such that $n(A)=3$ and $n(B)=2$. If $(x, 1),(y, 2),(z, 1)$ are in $A \times B$, find $A$ and $B$, where $x, y$ and $z$ are distinct elements. Solution: It is given that $n(A)=3$ and $n(B)=2 ;$ and $(x, 1),(y, 2),(z, 1)$ are in $A \times B$. We know that A = Set of first elements of the ordered pair elements of A B B = Set of second elements of the ordered pair elements of A B. x,y, andzare the elements of A; and 1 and 2 are the elements of B. Since $n(A)=3$ ...

Let A = {1, 2} and B = {3, 4}. Write A × B.

Question: Let $A=\{1,2\}$ and $B=\{3,4\}$. Write $A \times B$. How many subsets will $A \times B$ have? List them. Solution: $A=\{1,2\}$ and $B=\{3,4\}$ $\therefore A \times B=\{(1,3),(1,4),(2,3),(2,4)\}$ $\Rightarrow n(A \times B)=4$ We know that if $C$ is a set with $n(C)=m$, then $n[P(C)]=2^{m}$. Therefore, the set $A \times B$ has $2^{4}=16$ subsets. These are $\Phi,\{(1,3)\},\{(1,4)\},\{(2,3)\},\{(2,4)\},\{(1,3),(1,4)\},\{(1,3),(2,3)\}$ $\{(1,3),(2,4)\},\{(1,4),(2,3)\},\{(1,4),(2,4)\},\{(2,...

ΔUθof combustion of methane is – X kJ mol–1. The value of ΔHθ is

Question: $\Delta U^{\theta}$ of combustion of methane is $-X \mathrm{~kJ} \mathrm{~mol}^{-1}$. The value of $\Delta H^{\theta}$ is (i) $=\Delta U^{\theta}$ (ii) $\Delta U^{\theta}$ (iii) $\Delta U^{\theta}$ (iv) $=0$ Solution: Since $\Delta H^{\theta}=\Delta U^{\theta}+\Delta n_{g} R T$ and $\Delta U^{\theta}=-X \mathrm{~kJ} \mathrm{~mol}^{-1}$, $\Delta H^{\theta}=(-X)+\Delta n_{g} R T$ $\Rightarrow \Delta H^{\theta}\Delta U^{\theta}$ Therefore, alternative (iii) is correct....

A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 5 m long rope.

Question: A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 5 m long rope. Find (i) the area of that part of the field in which the horse can graze. (ii) the increase in the grazing area if the rope were $10 \mathrm{~m}$ long instead of $5 \mathrm{~m}$. (Use $\pi=3.14$ ) Solution: (i) $r=5 \mathrm{~m}, \theta=90^{\circ}$ The required area (Grazing area for horse) $=$ The sector area of the sector $\mathrm{OAB}$ $=\frac{90}{360} \times \pi r^{2}=\fra...

Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that

Question: Let $A=\{1,2\}, B=\{1,2,3,4\}, C=\{5,6\}$ and $D=\{5,6,7,8\}$. Verify that (i) $A \times(B \cap C)=(A \times B) \cap(A \times C)$ (ii) $A \times C$ is a subset of $B \times D$ Solution: (i) To verify: $A \times(B \cap C)=(A \times B) \cap(A \times C)$ We have $B \cap C=\{1,2,3,4\} \cap\{5,6\}=\Phi$ $\therefore$ L.H.S. $=A \times(B \cap C)=A \times \Phi=\Phi$ $A \times B=\{(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(2,4)\}$ $A \times C=\{(1,5),(1,6),(2,5),(2,6)\}$ $\therefore$ R.H.S. $=(...

The enthalpies of all elements in their standard states are:

Question: The enthalpies of all elements in their standard states are: (i) unity (ii) zero (iii) 0 (iv) different for each element Solution: Theenthalpy of all elements in their standard state is zero. Therefore, alternative (ii) is correct....

If A × B = {(a, x), (a, y), (b, x), (b, y)}. Find A and B.

Question: If $A \times B=\{(a, x),(a, y),(b, x),(b, y)\}$. Find $A$ and $B$. Solution: It is given that $\mathrm{A} \times \mathrm{B}=\{(a, x),(a, y),(b, x),(b, y)\}$ We know that the Cartesian product of two non-empty sets $P$ and $Q$ is defined as $P \times Q=\{(p, q): p \in P, q \in Q\}$ $\therefore \mathrm{A}$ is the set of all first elements and $\mathrm{B}$ is the set of all second elements. Thus, $A=\{a, b\}$ and $B=\{x, y\}$...

For the process to occur under adiabatic conditions, the correct condition is:

Question: For the process to occur under adiabatic conditions, the correct condition is: (i) $\Delta T=0$ (ii) $\Delta p=0$ (iii) $q=0$ (iv) $w=0$ Solution: A system is said to beunder adiabatic conditions if there is no exchange of heat between the system and its surroundings. Hence, under adiabatic conditions,q= 0. Therefore, alternative (iii) is correct....

A chord of a circle of radius 12 cm subtends an angle of 120° at the centre.

Question: A chord of a circle of radius $12 \mathrm{~cm}$ subtends an angle of $120^{\circ}$ at the centre. Find the area of the corresponding segment of the circle. (Use $\pi=3.14$ and $\sqrt{\mathbf{3}}=1.73$ ) Solution: Here $\theta=120^{\circ}$ and $\mathrm{r}=12 \mathrm{~cm}$ $\therefore \quad$ Area of the sector $=\frac{\theta}{\mathbf{3 6 0}^{\circ}} \times \pi \mathrm{r}^{2}$ $=\frac{120}{360} \times \frac{314}{100} \times 12 \times 12 \mathrm{~cm}^{2}$ $=\frac{314 \times 4 \times 12}{10...

If A = {–1, 1}, find A × A × A.

Question: If $A=\{-1,1\}$, find $A \times A \times A$. Solution: It is known that for any non-empty set A, A A A is defined as $\mathrm{A} \times \mathrm{A} \times \mathrm{A}=\{(\mathrm{a}, b, c): a, b, c \in \mathrm{A}\}$ It is given that $A=\{-1,1\}$ $\therefore A \times A \times A=\{(-1,-1,-1),(-1,-1,1),(-1,1,-1),(-1,1,1)$ $(1,-1,-1),(1,-1,1),(1,1,-1),(1,1,1)\}$...

Choose the correct answer. A thermodynamic state function is a quantity

Question: Choose the correct answer. A thermodynamic state function is a quantity (i) used to determine heat changes (ii) whose value is independent of path (iii) used to determine pressure volume work (iv) whose value depends on temperature only. Solution: A thermodynamic state function is a quantity whose value is independent ofa path. Functions likep,V,Tetc. depend only on the state of a system and not on the path. Hence, alternative (ii) is correct....

State whether each of the following statement are true or false.

Question: State whether each of the following statement are true or false. If the statement is false, rewrite the given statement correctly. (i) If $\mathrm{P}=\{m, n\}$ and $\mathrm{Q}=\{n, m\}$, then $\mathrm{P} \times \mathrm{Q}=\{(m, n),(n, m)\}$. (ii) If $A$ and $B$ are non-empty sets, then $A \times B$ is a non-empty set of ordered pairs $(x, y)$ such that $x \in A$ and $y \in B$. (iii) If $A=\{1,2\}, B=\{3,4\}$, then $A \times(B \cap \Phi)=\Phi$. Solution: (i) False If $\mathrm{P}=\{m, n\...

If G = {7, 8} and H = {5, 4, 2}, find G × H and H × G.

Question: If $\mathrm{G}=\{7,8\}$ and $\mathrm{H}=\{5,4,2\}$, find $\mathrm{G} \times \mathrm{H}$ and $\mathrm{H} \times \mathrm{G}$. Solution: $\mathrm{G}=\{7,8\}$ and $\mathrm{H}=\{5,4,2\}$ We know that the Cartesian product P Q of two non-empty sets P and Q is defined as $\mathrm{P} \times \mathrm{Q}=\{(p, q): p \in \mathrm{P}, q \in \mathrm{Q}\}$ $\therefore G \times H=\{(7,5),(7,4),(7,2),(8,5),(8,4),(8,2)\}$ $H \times G=\{(5,7),(5,8),(4,7),(4,8),(2,7),(2,8)\}$...

A chord of a circle of radius 15 cm subtends an angle of 60° at the centre.

Question: A chord of a circle of radius $15 \mathrm{~cm}$ subtends an angle of $60^{\circ}$ at the centre. Find the areas of the corresponding minor and major segments of the circle. (Use $\pi=3.14$ and $\sqrt{\mathbf{3}}=1.73$ ) Solution: Here, radius (r) = 15 cm and Sector angle $(\theta)=60^{\circ}$ $\therefore \quad$ Area of the sector $=\frac{\theta}{\mathbf{3 6 0}^{\circ}} \times \pi \mathbf{r}^{\mathbf{2}}=\frac{\mathbf{6 0}^{\circ}}{\mathbf{3 B 0}^{\circ}} \times \frac{\mathbf{3 1 4}}{\m...

If the set A has 3 elements and the set B = {3, 4, 5},

Question: If the set $A$ has 3 elements and the set $B=\{3,4,5\}$, then find the number of elements in $(A \times B)$ ? Solution: It is given that set A has 3 elements and the elements of set B are 3, 4, and 5. ⇒Number of elements in set B = 3 Number of elements in (A B) = (Number of elements in A) (Number of elements in B) = 3 3 = 9 Thus, the number of elements in (A B) is 9....

Explain the physical significance of Van der Waals parameters.

Question: Explain the physical significance of Van der Waals parameters. Solution: Physical significance of a: a is a measure of the magnitude of intermolecular attractive forces within a gas. Physical significance of b: b is a measure of the volume of a gas molecule....

Critical temperature for carbon dioxide and methane are 31.1 °C and –81.9 °C respectively.

Question: Critical temperature for carbon dioxide and methane are 31.1 C and 81.9 C respectively. Which of these has stronger intermolecular forces and why? Solution: Higher is the critical temperature of a gas, easier is its liquefaction. This means that the intermolecular forces of attraction between the molecules of a gas are directly proportional to its critical temperature. Hence, intermolecular forces of attraction are stronger in the case of CO2....

In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre.

Question: In a circle of radius 21 cm, an arc subtends an angle of 60 at the centre. Find: (i) the length of the arc (ii) area of the sector formed by the arc (iii) area of the segment formed by the corresponding chor Solution: Here, radius $=21 \mathrm{~cm}$ and $\theta=60^{\circ}$ (i) Circumference of the circle $=2 \pi \mathrm{r}$ $=2 \times \frac{22}{7} \times 21 \mathrm{~cm}=2 \times 22 \times 3 \mathrm{~cm}=132 \mathrm{~cm}$ $\therefore \quad$ Length of $\operatorname{arc}$ APB $=\frac{\th...

In terms of Charles’ law explain why –273°C is the lowest possible temperature.

Question: In terms of Charles law explain why 273C is the lowest possible temperature. Solution: Charles law states that at constant pressure, the volume of a fixed mass of gas is directly proportional to its absolute temperature. It was found that for all gases (at any given pressure), the plots of volume vs. temperature (in C) is a straight line. If this line is extended to zero volume, then it intersects the temperature-axis at 273C. In other words, the volume of any gas at 273C is zero. This...

What would be the SI unit for the quantity pV2T 2/n?

Question: What would be the SI unit for the quantity $\rho V^{2} T^{2} / n ?$ Solution: The SI unit for pressure,pis Nm2. The SI unit for volume,Vis m3. The SI unit for temperature,Tis K. The SI unit for the number of moles,nis mol. Therefore, the SI unit for quantity $\frac{p V^{2} T^{2}}{n}$ is given by, $=\frac{\left(\mathrm{Nm}^{-2}\right)\left(m^{3}\right)^{2}(\mathrm{~K})^{2}}{\mathrm{~mol}}$ $=\mathrm{Nm}^{4} \mathrm{~K}^{2} \mathrm{~mol}^{-1}$...

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