A chord of a circle of radius 10 cm subtends a right angle at the centre.

Question: A chord of a circle of radius $10 \mathrm{~cm}$ subtends a right angle at the centre. Find the area of the corresponding: (i) minor segment (ii) major sector. (Use $\pi=3.14$ ) Solution: Here, the radius of the circle is r = 10 cm. Sector angle of the minor sector made corresponding to the chord AB is 90 Now, the area of the minor sector $=\frac{\mathbf{9 0}}{\mathbf{3 6 0}} \times \pi \mathrm{r}^{2}$ $=\frac{1}{4} \times \pi \times(10)^{2} \mathrm{~cm}^{2}=\frac{1}{4} \times 3.14 \tim...

A mixture of dihydrogen and dioxygen at one bar pressure contains 20% by weight of dihydrogen.

Question: A mixture of dihydrogen and dioxygen at one bar pressure contains 20% by weight of dihydrogen. Calculate the partial pressure of dihydrogen. Solution: Let the weight of dihydrogen be 20 g and the weight of dioxygen be 80 g. Then, the number of moles of dihydrogen, $n_{\mathrm{H}_{2}}=\frac{20}{2}=10$ moles and the number of moles of dioxygen, $n_{\mathrm{O}_{2}}=\frac{80}{32}=2.5$ moles. Given, Total pressure of the mixture,ptotal= 1 bar Then, partial pressure of dihydrogen, $p_{\mathr...

The length of the minute hand of a clock is 14 cm.

Question: The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes. Solution: We know that in 1 hour (i.e., 60 minutes), the minute hand rotates 360. In 5 minutes, minute hand will rotate $=\frac{\mathbf{3 6 0}^{\circ}}{\mathbf{6 0}} \times 5=30^{\circ}$ Therefore, the area swept by the minute hand in 5 minutes will be the area of a sector of 30 in a circle of 14 cm radius. Area of sector of angle $\theta=\frac{\theta}{\mathbf{3 6 0}^{\circ}} \times ...

If $left(rac{x}{3}+1, y-rac{2}{3}ight)=left(rac{5}{3}, rac{1}{3}ight)$, find the values of $x$ and $y$.

Question: If $\left(\frac{x}{3}+1, y-\frac{2}{3}\right)=\left(\frac{5}{3}, \frac{1}{3}\right)$, find the values of $x$ and $y$. Solution: It is given that $\left(\frac{x}{3}+1, y-\frac{2}{3}\right)=\left(\frac{5}{3}, \frac{1}{3}\right)$. Since the ordered pairs are equal, the corresponding elements will also be equal. Therefore, $\frac{x}{3}+1=\frac{5}{3}$ and $y-\frac{2}{3}=\frac{1}{3}$ $\frac{x}{3}+1=\frac{5}{3}$ $\Rightarrow \frac{x}{3}=\frac{5}{3}-1 \quad \Rightarrow y-\frac{2}{3}=\frac{1}{3...

Find the area of a quadrant of a circle whose circumference is 22 cm.

Question: Find the area of a quadrant of a circle whose circumference is 22 cm. Solution: Let radius of the circle = r $\therefore \quad 2 \pi \mathrm{r}=22$ $\Rightarrow 2 \times \frac{22}{7} \times r=22$ $\Rightarrow \mathrm{r}=22 \times \frac{\mathbf{7}}{\mathbf{2 2}} \times \frac{\mathbf{1}}{\mathbf{2}}=\frac{\mathbf{7}}{\mathbf{2}} \mathrm{cm}$ Here, $\theta=90^{\circ}$ $\therefore$ Area of the $\left(\frac{\mathbf{1}}{\mathbf{4}}\right)^{\text {th }}$ quadrant of the circle, $=\frac{\theta...

Find the area of a sector of a circle with radius 6 cm if angle of the sector is 60°.

Question: Find the area of a sector of a circle with radius 6 cm if angle of the sector is 60. Solution: Radius, $r=6 \mathrm{~cm}$; sector angle, $\theta=60$ degrees Area of the sector $=\frac{\theta}{360} \times \pi r^{2}=\frac{60}{360} \times \frac{22}{7} \times(6)^{2} \mathrm{~cm}^{2}$ $=\frac{1}{6} \times \frac{22}{7} \times(6)^{2} \mathrm{~cm}^{2}=\frac{132}{7} \mathrm{~cm}^{2}$...

Tick the correct answer in the following and justify your choice.

Question: Tick the correct answer in the following and justify your choice. If the perimeter and area of a circle are numerically equal, then the radius of the circle is (A) 2 units (B) $\pi$ units (C) 4 units (D) 7 units Solution: (A) We have [Numerical area of the circle] $\Rightarrow \pi \mathrm{r}^{2}=2 \pi \mathrm{r}$ $\Rightarrow \pi r^{2}-2 \pi r=0$ $\Rightarrow r^{2}-2 r=0$ $\Rightarrow \mathrm{r}(\mathrm{r}-2)=0$ $\Rightarrow \mathrm{r}=0$ or $\mathrm{r}=2$ But r cannot be zero $\theref...

In a survey it was found that 21 people liked product A, 26 liked product B and 29 liked product C.

Question: In a survey it was found that 21 people liked product A, 26 liked product B and 29 liked product C. If 14 people liked products A and B, 12 people liked products C and A, 14 people liked products B and C and 8 liked all the three products. Find how many liked product C only. Solution: Let A, B, and C be the set of people who like product A, product B, and product C respectively. Accordingly, $n(\mathrm{~A})=21, n(\mathrm{~B})=26, n(\mathrm{C})=29, n(\mathrm{~A} \cap \mathrm{B})=14, n(\...

Match the following:

Question: Match the following: Solution:...

2.9 g of a gas at 95 °C occupied the same volume as 0.184 g of dihydrogen at 17 °C, at the same pressure

Question: 2.9 g of a gas at 95 C occupied the same volume as 0.184 g of dihydrogen at 17 C, at the same pressure. What is the molar mass of the gas? Solution: Volume (V) occupied by dihydrogen is given by, $V=\frac{m}{M} \frac{\mathrm{R} T}{p}$ $=\frac{0.184}{2} \times \frac{\mathrm{R} \times 290}{p}$ Let M be the molar mass of the unknown gas. Volume (V) occupied by the unknown gas can be calculated as: $V=\frac{m}{M} \frac{\mathrm{R} T}{p}$ $=\frac{2.9}{M} \times \frac{\mathrm{R} \times 368}{p...

The wheels of a car are of diameter 80 cm each.

Question: The wheels of a car are of diameter 80 cm each. How many complete revolutions does each wheel make in 10 minutes when the car is travelling at a speed of 66 km per hour? Solution: Diameter of the wheel of the car = 80 cm Then, the radius of the wheel of the car = 40 cm = 0.4 cm Distance travelled by the car when the wheel of the car completes one revolution $=2 \pi \times(0.4) \mathrm{m}=\frac{\mathbf{4} \pi}{\mathbf{5}} \mathbf{m}$ Let us suppose the wheel of the car completes n revol...

Briefly mention the mechanism of action of FSH.

Question: Briefly mention the mechanism of action of FSH. Solution: Follicle stimulating hormone (FSH) is secreted by the pars distalis region of the anterior pituitary. It regulates the development, growth, and reproductive processes of the human body. In the ovary, FSH stimulates the growth and maturation of ovarian follicle. As the follicle grows and matures, it releases an inhibitory hormone known as inhibin that ends the process of FSH production. Action of FSH: Follicle stimulating hormone...

In a survey of 60 people, it was found that 25 people read newspaper H,

Question: In a survey of 60 people, it was found that 25 people read newspaper H, 26 read newspaper T, 26 read newspaper I, 9 read both H and I,11 read both H and T, 8 read both T and I, 3 read all three newspapers. Find: (i) the number of people who read at least one of the newspapers. (ii) the number of people who read exactly one newspaper. Solution: Let A be the set of people who read newspaper H. Let B be the set of people who read newspaper T. Let C be the set of people who read newspaper ...

Which hormone deficiency is responsible for the following?

Question: Which hormone deficiency is responsible for the following? (a) Diabetes mellitus (b) Goitre (c) Cretinism Solution: (a) Diabetes mellitus is characterized by abnormally high glucose levels in the blood due to the deficiency of hormone, called insulin. (b) Goitre is characterised by an abnormal enlargement of the thyroid gland due to the deficiency of thyroxin hormone in the body. (c) Cretinism is characterized by stunted growth in the baby due to the deficiency of thyroid hormone in th...

Give example(s) of:

Question: Give example(s) of: (a)Hyperglycemic hormone and hypoglycemic hormone (b)Hypercalcemic hormone (c)Gonadotrophic hormones (d)Progestational hormone (e)Blood pressure lowering hormone (f)Androgens and estrogens Solution: (a)Hyperglycemic hormone and hypoglycemic hormone: Hyperglycemic hormone is glucagon, while hypoglycemic hormone is insulin. (b)Hypercalcemic hormone: Parathyroid hormone (PTH) is hypercalcemic hormone. (c)Gonadotrophic hormones: Luteinizing hormone and follicle stimulat...

The fig. depicts an archery target marked with its five scoring regions from the centre outwards as Gold,

Question: The fig. depicts an archery target marked with its five scoring regions from the centre outwards as Gold, Red, Blue, Black and White. The diameter of the region representing Gold score is 21 cm and each of the other bands is 10.5 cm wide. Find the area of each of the five scoring regions. Solution: Radius of the Gold scoring region $=\frac{21}{2} \mathrm{~cm}=10.5 \mathrm{~cm}(\because$ Diameter $=21 \mathrm{~cm})$ Therefore, the area of the Gold scoring region (circle) $=\pi \times\le...

In a group of students 100 students know Hindi, 50 know English and 25 know both.

Question: In a group of students 100 students know Hindi, 50 know English and 25 know both. Each of the students knows either Hindi or English. How many students are there in the group? Solution: Let U be the set of all students in the group. Let E be the set of all students who know English. Let H be the set of all students who know Hindi. $\therefore H \cup E=U$ Accordingly, $n(\mathrm{H})=100$ and $n(\mathrm{E})=50$ $n(\mathrm{H} \cap \mathrm{E})=25$ $n(\mathrm{U})=n(\mathrm{H})+n(\mathrm{E})...

Write short notes on the functions of the following hormones,

Question: Write short notes on the functions of the following hormones, (a)Parathyroid hormone (PTH) (b)Thyroid hormones (c)Thymosins (d)Androgens (e)Estrogens (f)Insulin and Glucagon Solution: (a)Parathyroid hormone (PTH) The parathyroid hormone is secreted by the parathyroid gland. Its main function is to increase the level of calcium in blood. It promotes the reabsorption of calcium from nephrons and also, promotes the absorption of calcium from digested food. Hence, it plays an important rol...

In a survey of 600 students in a school,

Question: In a survey of 600 students in a school, 150 students were found to be taking tea and 225 taking coffee, 100 were taking both tea and coffee. Find how many students were taking neither tea nor coffee? Solution: Let U be the set of all students who took part in the survey. Let T be the set of students taking tea. Let C be the set of students taking coffee. Accordingly, $n(\mathrm{U})=600, n(\mathrm{~T})=150, n(\mathrm{C})=225, n(\mathrm{~T} \cap \mathrm{C})=100$ To find: Number of stude...

Fill in the blanks:

Question: Fill in the blanks: HormonesTarget gland (a)Hypothalamic hormones __________________ (b)Thyrotrophin (TSH) __________________ (c)Corticotrophin (ACTH) __________________ (d)Gonadotrophins (LH, FSH) __________________ (e)Melanotrophin (MSH) __________________ Solution: HormonesTarget gland (a)Hypothalamic hormones (b)Thyrotrophin (TSH) (c)Corticotrophin (ACTH) (d)Gonadotrophins (LH, FSH) (e)Melanotrophin (MSH)...

Question: List the hormones secreted by the following: (a)Hypothalamus (b)Pituitary (c)Thyroid (d)Parathyroid (e)Adrenal (f)Pancreas (g)Testis (h)Ovary (i)Thymus (j)Atrium (k)Kidney (l)G-I Tract Solution: (a)Hypothalamus: Hormones secreted by the hypothalamus include: (1) Releasing hormones: These hormones stimulate the secretions of the pituitary hormone. Examples of these hormones are: (i) Gonadotrophin-releasing hormone (ii) Thyrotrophin-releasing hormone (iii) Somatotropin-releasing hormone ...

Find sets A, B and C such that A ∩ B, B ∩ C and A ∩ C are non-empty sets and A ∩ B ∩ C = Φ.

Question: Find sets $A, B$ and $C$ such that $A \cap B, B \cap C$ and $A \cap C$ are non-empty sets and $A \cap B \cap C=\Phi$. Solution: Let $A=\{0,1\}, B=\{1,2\}$, and $C=\{2,0\}$. Accordingly, $A \cap B=\{1\}, B \cap C=\{2\}$, and $A \cap C=\{0\} .$ $\therefore A \cap B, B \cap C$, and $A \cap C$ are non-empty. However, $A \cap B \cap C=\Phi$...

The radii of two circles are 8 cm and 6 cm respectively.

Question: The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having area equal to the sum of the areas of the two circles. Solution: We have, Radius of circle- $\mathrm{I}, \mathrm{r}_{1}=8 \mathrm{~cm}$ Radius of circle-II, $r_{2}=6 \mathrm{~cm}$ $\therefore \quad$ Area of circle- $\mathrm{I}=\pi \mathrm{r}_{1}^{2}=\pi(8)^{2} \mathrm{~cm}^{2}$ Area of circle- $\mathrm{II}=\pi \mathrm{r}_{2}^{2}=\pi(6)^{2} \mathrm{~cm}^{2}$ Let the radius of the circle-III be ...

Calculate the volume occupied by 8.8 g of CO2 at 31.1°C and 1 bar pressure.

Question: Calculate the volume occupied by 8.8 g of CO2at 31.1C and 1 bar pressure. $\mathrm{R}=0.083$ bar $\mathrm{LK}^{-1} \mathrm{~mol}^{-1}$ Solution: It is known that, $p V=\frac{m}{M} \mathrm{RT}$ $\Rightarrow V=\frac{m \mathrm{R} T}{M p}$ Here, m= 8.8 g R = 0.083 bar LK1mol1 T= 31.1C = 304.1 K M= 44 g p= 1 bar Thus, volume $(V)=\frac{8.8 \times 0.083 \times 304.1}{44 \times 1}$ $=5.04806 \mathrm{~L}$ $=5.05 \mathrm{~L}$ Hence, the volume occupied is 5.05 L....

Let A and B be sets. If A ∩ X = B ∩ X = Φ and A ∪ X = B ∪ X for some set X, show that A = B.

Question: Let $A$ and $B$ be sets. If $A \cap X=B \cap X=\Phi$ and $A \cup X=B \cup X$ for some set $X$, show that $A=B$. (Hints $A=A \cap(A \cup X), B=B \cap(B \cup X)$ and use distributive law) Solution: Let $A$ and $B$ be two sets such that $A \cap X=B \cap X=f$ and $A \cup X=B \cup X$ for some set $X$. To show: $A=B$ It can be seen that $A=A \cap(A \cup X)=A \cap(B \cup X)[A \cup X=B \cup X]$ $=(A \cap B) \cup(A \cap X)[$ Distributive law $]$ $=(A \cap B) \cup \Phi[A \cap X=\Phi]$ $=A \cap B...