If water contains dissolved calcium hydrogen carbonate,
Question: If water contains dissolved calcium hydrogen carbonate, out of soaps and synthetic detergents which one will you use for cleaning clothes? Solution: Synthetic detergentsare preferred for cleaning clothes. When soaps are dissolved in water containing calcium ions, these ions form insoluble salts that are of no further use. However,when synthetic detergents are dissolved in water containing calcium ions, these ions form soluble salts that act as cleansing agents....
Read More →Explain the cleansing action of soaps.
Question: Explain the cleansing action of soaps. Solution: Soap molecules form micelles around an oil droplet (dirt) in such a way that the hydrophobic parts of the stearate ions attach themselves to the oil droplet and the hydrophilic parts project outside the oil droplet. Due to the polar nature of the hydrophilic parts, the stearate ions (along with the dirt) are pulled into water, thereby removing the dirt from the cloth....
Read More →In the given figure, PQ is a chord of a circle with centre O and PT is a tangent.
Question: In the given figure, PQ is a chord of a circle with centre O and PT is a tangent. If QPT = 60∘, find PRQ Solution: We know that the radius and tangent are perperpendular at their point of contact.OPT = 90∘Now, OPQ = OPT QPT = 90∘ 60∘= 30∘Since, OP = OQ as both are radiusOPQ = OQP = 30∘ (Angles opposite to equal sides are equal)Now, In isosceles △POQPOQ + OPQ + OQP = 180∘ (Angle sum property of a triangle)⇒ POQ = 180∘ 30∘ 30∘= 120∘Now, POQ + reflex POQ = 360∘ (Complete angle)⇒ reflex PO...
Read More →The workdone by a gas molecule in an isolated system is given by,
Question: The workdone by a gas molecule in an isolated system is given by, $\mathrm{W}=\alpha \beta^{2} \mathrm{e}^{-\frac{x^{2}}{a k \mathrm{~T}}}$, where $\mathrm{x}$ is the displacement, $\mathrm{k}$ is the Boltzmann constant and $\mathrm{T}$ is the temperature. $\alpha$ and $\beta$ are constants. Then the dimensions of $\beta$ will be -$\left[\mathrm{M}^{0} \mathrm{LT}^{0}\right]$$\mathrm{M}^{2} \mathrm{LT}^{2}$$\left[\mathrm{MLT}^{-2}\right]$$\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}\right]$C...
Read More →Can you use soaps and synthetic detergents to check the hardness of water?
Question: Can you use soaps and synthetic detergents to check the hardness of water? Solution: Soaps get precipitated in hard water, but not in soft water. Therefore, soaps can be used for checking the hardness of water. However,synthetic detergents do not get precipitated either in hard water or in soft water. Therefore, synthetic detergents cannot be used for checking the hardness of water....
Read More →The radii of two cylinders are in the ratio 3 : 5
Question: The radii of two cylinders are in the ratio 3 : 5 and their heights are in the ratio 2 : 3. What is the ratio of their curved surface areas? Solution: Given that, $r_{1}: r_{2}=3: 5$ and $h_{1}: h_{2}=2: 3$ Now, the ratio of their curved surface area $s_{1}: s_{2}=2 \pi r_{1} h_{1}: 2 \pi r_{2} h_{2}$ $s_{1}: s_{2}=2 \pi r_{1} h_{1}: 2 \pi r_{2} h_{2}$ $=\left(\frac{r_{1}}{r_{2}}\right)\left(\frac{h_{1}}{h_{2}}\right)$ $\frac{s_{1}}{s_{2}}=\frac{3}{5} \times \frac{2}{3}=\frac{2}{5}$ He...
Read More →Why do soaps not work in hard water?
Question: Why do soaps not work in hard water? Solution: Soaps are sodium or potassiumsalts of long-chain fatty acids. Hard water contains calcium and magnesium ions. When soaps are dissolved in hard water, these ions displace sodium or potassium from their salts and form insoluble calcium or magnesium salts of fatty acids. These insoluble salts separate as scum. This is the reason why soaps do not work in hard water....
Read More →In two concentric circles, a chord of length 8 cm of the larger circle touches the smaller circle.
Question: In two concentric circles, a chord of length 8 cm of the larger circle touches the smaller circle. If the radius of the larger circle is 5 cm then Find the radius of the smaller circle. Solution: We know that the radius and tangent are perperpendular at their point of contactSince, the perpendicular drawn from the centre bisect the chord. $\therefore \mathrm{AP}=\mathrm{PB}=\frac{\mathrm{AB}}{2}=4 \mathrm{~cm}$ In right triangle AOPAO2= OP2+ PA2⇒ 52= OP2+ 42⇒ OP2= 9⇒ OP = 3 cmHence, th...
Read More →What are biodegradable and non-biodegradable detergents?
Question: What are biodegradable and non-biodegradable detergents? Give one example of each. Solution: Detergents that can be degraded by bacteria are called biodegradable detergents. Such detergents have straight hydrocarbon chains. For example: sodium lauryl sulphate Detergents thatcannot be degraded by bacteria are called non-biodegradable detergents. Such detergents have highly-branched hydrocarbon chains. For example: sodium -4- (1, 3, 5, 7- tetra methyl octyl) benzene sulphonate...
Read More →A cone, a hemisphere and a cylinder stand
Question: A cone, a hemisphere and a cylinder stand on equal bases and have the same height. What is the ratio of their volumes? Solution: Letrbe the radius of the base. Andhis the height. Here,h = r. Now, The ratio of their volumes will be Volume of cone: volume of hemisphere: volume of a cylinder $\frac{1}{3} \pi r^{2} h: \frac{2}{3} \pi r^{3}: \pi r^{2} h$ $V_{1}: V_{2}: V_{3}=\frac{1}{3} \pi r^{3}: \frac{2}{3} \pi r^{3}: \pi r^{3}$ Hence, $V_{1}: V_{2}: V_{3}=1: 2: 3$...
Read More →Explain the following terms with suitable examples
Question: Explain the following terms with suitable examples (i)Cationic detergents (ii)Anionic detergents and (iii)Non-ionic detergents Solution: (i) Cationic detergent Cationic detergents are quaternary ammonium salts of acetates, chlorides, or bromides. These are called cationic detergents because the cationic part of these detergents contains a long hydrocarbon chain and a positive charge on the N atom. For example: cetyltrimethylammonium bromide (ii) Anionic detergents Anionic detergents ar...
Read More →How are synthetic detergents better than soap?
Question: How are synthetic detergents better than soap? Solution: Soaps work in soft water. However, they are not effective in hard water. In contrast, synthetic detergents work both in soft water and hard water. Therefore, synthetic detergents are better than soaps....
Read More →In the given figure, O is the centre of the circle. PA and PB are tangents.
Question: In the given figure, O is the centre of the circle.PAandPBare tangents. Show thatAOBPis a cyclic quadrilateral Solution: We know that the radius and tangent are perpendicular at their point of contact∵OBP = OAP = 90∘Now, In quadrilateral AOBPAPB + AOB + OBP + OAP = 360∘ [Angle sum property of a quadrilateral]⇒ APB + AOB + 90∘+ 90∘= 360∘⇒ APB + AOB = 180∘Also, OBP + OAP = 180∘Since, the sum of the opposite angles of the quadrilateral is 180∘Hence, AOBP is a cyclic quadrilateral....
Read More →What problem arises in using alitame as artificial sweetener?
Question: What problem arises in using alitame as artificial sweetener? Solution: Alitame is a high potency sweetener. It is difficult to controlthe sweetness of food while using alitame as an artificial sweetener....
Read More →Name a sweetening agent used in the preparation of sweets for a diabetic patient.
Question: Namea sweetening agent used in the preparation of sweets for a diabetic patient. Solution: Artificial sweetening agents such as saccharin, alitame, and aspartame can be used in preparing sweets for diabetic patients....
Read More →If a cone and a sphere have equal radii and equal volumes.
Question: If a cone and a sphere have equal radii and equal volumes. What is the ratio of the diameter of the sphere to the height of the cone? Solution: Given that, A cone and a sphere have equal radii and equal volume i.e.,volume of cone = volume of sphere $r^{2} h=4 r^{3}$ $h=4 r$ $h=(2 r) \times 2$ $\frac{h}{2 r}=\frac{2}{1}$ $\frac{h}{2}=\frac{2}{1} \quad($ diameterd $=2 r)$ $h: d=2: 1$ or $d: h=1: 2$...
Read More →In the given figure, a circle inscribed in a triangle ABC, touches the sides AB, BC and AC at point D,
Question: In the given figure, a circle inscribed in a triangle ABC, touches the sides AB, BC and AC at point D, E and F respectively. If AB = 14 cm, BC = 8 cm and AC = 12 cm. Find the lengths of AD, BE and CF Solution: We know that tangent segments to a circle from the same external point are congruent.Now, we haveAD = AF, BD = BE and CE = CFNow, AD + BD = 14 cm .....(1)AF + FC = 12 cm⇒ AD + FC = 12 cm .....(2)BE + EC = 8 cm⇒ BD + FC = 8 cm .....(3)Adding all these we getAD + BD + AD + FC + BD ...
Read More →What are artificial sweetening agents?
Question: What are artificial sweetening agents? Give two examples. Solution: Artificial sweetening agents are chemicalsthat sweeten food. However, unlike natural sweeteners, they do not add calories to our body. They do not harm the human body. Some artificial sweeteners are aspartame, saccharin, sucrolose, and alitame....
Read More →Why is use of aspartame limited to cold foods and drinks?
Question: Why is use of aspartame limited to cold foods and drinks? Solution: Aspartame becomes unstable at cooking temperature.This is the reason why its use is limited to cold foods and drinks....
Read More →What are food preservatives?
Question: What are food preservatives? Solution: Food preservatives are chemicalsthat prevent food from spoilage due to microbial growth. Table salt, sugar, vegetable oil, sodium benzoate (C6H3COONa), and salts of propanoic acid are some examples of food preservatives....
Read More →A solid cylinder of diameter 12 cm and height 15 cm
Question: A solid cylinder of diameter 12 cm and height 15 cm is melted and recast into toys with the shape of a right circular cone mounted on a hemisphere of radius 3 cm.If the height of the toy is 12 cm, find the number of toys so formed. Solution: Diameter of cylinder = 12 cm Therefore r= 6 cm Height = 15 cm Therefore, Volume of cylinder $=\pi r^{2} h$ $=36 \times 15 \times \pi \mathrm{cm}^{3}$ Therefore, Volume of toy = volume of cone + volume of hemisphere $=\frac{1}{3} \pi r^{2} h+\frac{2...
Read More →In the given figure, two tangents RQ and RP are drawn from an external point R to the circle with centre O.
Question: In the given figure, two tangents RQ and RP are drawn from an external point R to the circle with centre O. If PRQ = 120∘then prove that OR = PR + RQ Solution: Construction: Join PO and OQIn △POR and △QOROP = OQ (Radii)RP = RQ (Tangents from the external point are congruent)OR = OR (Common)By SSS congruency, △POR △QORPRO =QRO (C.P.C.T)Now, PRO + QRO = PRQ⇒ 2PRO = 120∘⇒ PRO = 60∘Now, In △POR $\cos 60^{\circ}=\frac{\mathrm{PR}}{\mathrm{OR}}$ $\Rightarrow \frac{1}{2}=\frac{\mathrm{PR}}{\m...
Read More →What is tincture of iodine?
Question: What is tincture of iodine? What is its use? Solution: Tincture of iodine is a 2 3 percent solution of iodine in alcohol water mixture. It is applied to wounds as an antiseptic....
Read More →What is tincture of iodine?
Question: What is tincture of iodine? What is its use? Solution: Tincture of iodine is a 2 3 percent solution of iodine in alcohol water mixture. It is applied to wounds as an antiseptic....
Read More →What are the main constituents of dettol?
Question: What are the main constituents of dettol? Solution: The main constituents of dettol are chloroxylenol and-terpineol....
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