The following post consists of solutions of all exercises in the chapter 10 Quadratic Equations for SSLC Students.
MATH10-TBS10.1
Solution
Quadratic Equations Exercise 10.1
- YourPalNurav
Question 1:
1(i). Check whether the following is a quadratic equation :
(i).$(x + 1)^2 = 2(x – 3)$
(i).$(x + 1)^2 = 2(x – 3)$
Solution:
Given:
$$
\begin{align}
(x + 1)^2 &= 2(x – 3)\\
(x)^2+(1)^2+{2(x)(1)} &= 2x-6\\
x^2+1+2x &= 2x-6\\
\require{cancel}x^2+1+\cancel{2x}-\cancel{2x}+6 &= 0\\
x^2+1+6 &= 0\\
x^2+7 &= 0\\
\text{As the degree of the} &\text{, } \text{polynomial obtained is 2;}\\
\text{Hence the given equation} &\text{, } \text{is quadratic.}
\end{align}
$$
Question 2:
2. What is decomposition reaction? Give one example.
Solution:
A reaction in which a single reactant breaks down to give simpler products.
Example of this reaction is as follows, $$\ce{CaCO3(s) ->[Heat] CaO(s) + CO2(g)}$$
Example of this reaction is as follows, $$\ce{CaCO3(s) ->[Heat] CaO(s) + CO2(g)}$$
Question 3:
3. What is displacement reaction? Give one example.
Solution:
The chemical reaction in which more reactive element displaces less reactive element from its salt solution.
Example of this reaction is as follows, $$\ce{Fe(s) + CuSO4(aq) -> FeSO4(aq) + Cu(s)}$$
Example of this reaction is as follows, $$\ce{Fe(s) + CuSO4(aq) -> FeSO4(aq) + Cu(s)}$$
Question 4:
4. What is double displacement reaction? Give one example.
Solution:
A reaction in which new compounds are formed by mutual exchange of ions between two compounds.
Example of this reaction is as follows, $$\ce{Na2SO4 (aq) + BaCl2 (aq) → BaSO4 (s) + 2NaCl (aq)}$$
Example of this reaction is as follows, $$\ce{Na2SO4 (aq) + BaCl2 (aq) → BaSO4 (s) + 2NaCl (aq)}$$
Question 5:
5. Define Corrosion.
Solution:
Corrosion is the phenomenon by which a metal that is exposed to substances such as moisture, acid etc. for some time, a layer of hydrated oxide is formed which weakens the metal.
- Rusting of iron, black coating on silver and green coating on copper are examples of corrosion.
- Corrosion can be prevented by galvanization, electroplating or painting.
Question 6:
6. What is Rancidity?
Solution:
The oxidation of fats and oils when exposed to air is known as rancidity. It leads to bad smell and bad taste of food.
Methods to Prevent Rancidity:
Methods to Prevent Rancidity:
- By addding antioxidants
- Keeping food in air tight containers
- Replacing air with nitrogen
- Refrigeration
Question 7:
7. At what pH do teeth decay?
Solution:
Tooth decay starts when pH of mouth is lower than 5.5.
Question 8:
8. Write the pH range for,
(i). Stomach Juice
(ii). Saliva
(iii). Pure Water
(iv). Lemon Juice
(v). Blood
(i). Stomach Juice
(ii). Saliva
(iii). Pure Water
(iv). Lemon Juice
(v). Blood
Solution:
The pH ranges are,
(i). Stomach Juice >> 1.5 to 3.5
(ii). Saliva >> 7.4
(iii). Pure Water >> 7
(iv). Lemon Juice >> 2 to 3
(v). Blood >> 7.365
(i). Stomach Juice >> 1.5 to 3.5
(ii). Saliva >> 7.4
(iii). Pure Water >> 7
(iv). Lemon Juice >> 2 to 3
(v). Blood >> 7.365
Question 9:
9. Write the uses of Baking Soda & Washing Soda.
Solution:
Uses of Baking Soda are,
(a) For making baking powder (mixture of baking soda and tartaric acid). When baking powder is heated or mixed with water, CO2 is produced which causes bread and cake to rise making them soft and spongy.
(b) An ingredient in antacid.
(c) Used in soda acids, fire extinguishers.
Uses of Washing soda are,
(a) In glass, soap and paper industry.
(b) Manufacture of borax.
(c) Cleaning agent for domestic purposes.
(d) For removing permanent hardness of water.
(a) For making baking powder (mixture of baking soda and tartaric acid). When baking powder is heated or mixed with water, CO2 is produced which causes bread and cake to rise making them soft and spongy.
(b) An ingredient in antacid.
(c) Used in soda acids, fire extinguishers.
Uses of Washing soda are,
(a) In glass, soap and paper industry.
(b) Manufacture of borax.
(c) Cleaning agent for domestic purposes.
(d) For removing permanent hardness of water.
Question 10:
10. What are ore roasting and calcination?
Solution:
(i). Roasting: The sulphide ores are converted into oxides by heating strongly in the Metals And Non-Metals presence of excess air. This process is called roasting.
$$\ce{2ZnS + 3O2 ->[Heat] 2ZnO + 2SO2}$$ (ii). Calcination: The carbonate ores are changed into oxides by heating strongly in limited air. This process is called calcination.
$$\ce{ZnCO3 ->[Heat] ZnO + CO2}$$
$$\ce{2ZnS + 3O2 ->[Heat] 2ZnO + 2SO2}$$ (ii). Calcination: The carbonate ores are changed into oxides by heating strongly in limited air. This process is called calcination.
$$\ce{ZnCO3 ->[Heat] ZnO + CO2}$$
Question 11:
11. What are isomers? Give two example.
Solution:
Compounds with identical molecular formula but different structures are called isomers.
Example: Pentane & Iso-pentane
Example: Pentane & Iso-pentane
Question 12:
12. What are Functional Groups? Give two example.
Solution:
Functional groups are the atoms or groups of atoms that replace one or more hydrogen atoms in a hydrocarbon molecules and gives the molecule specific character to the original molecule.
Example:
-OH (Alcohol) ~ Propanol
-CHO (Aldehyde) ~ Propanal.
Example:
-OH (Alcohol) ~ Propanol
-CHO (Aldehyde) ~ Propanal.
Question 13:
13. Write any two differents between soaps & detergents.
Solution:
| Soaps | Detergents |
| Soaps are sodium or potassium salts of long chain carboxylic acids. | Detergents are ammonium or solphonate salts of long chain carboxylic acids. |
| Soaps have lesser cleansing action or quality as compared to detergents. | Detergents have better cleansing action as compared to soaps. |
| Soaps are made from animal or plant fats. | Detergents are made from petrochemicals. |
| Soaps are more biodegradable. | Detergents are less biodegradable. |
| Ionic Part of Soap is $\ce{-COO-Na^+}$ | Ionic Part of Soap is $\ce{-OSO_3-Na^-}$ |
| They don't produce lather with hard water and are not able to clean the cloth. | They clean the cloth even in hard water. |
| Lot of water is needed to remove soap from the cloth. | They are removed very easily so less quantity of water is needed. |
| There are cheap. | They are costly. |
Question 14:
14. Practice Diagrams 10.7 & 10.17.
Solution:
Refer textbook
Question 15:
15. What are Fossils?
Solution:
The remains of prehistoric living things in rocks and soil are known as fossils.
Question 16:
16. Define Ohm's Law and write it's mathematical relation.
Solution:
The potential difference, V, across the ends of a given metallic wire in an electric circuit is directly proportional to the current flowing through it, provided its temperature remains the same. This is called Ohm’s law.
$$ \begin{align} V &\propto I\\ \frac{V}{I} &= \text{constant}\\ \frac{V}{I} &= R\\ \therefore V &=IR\\ \end{align} $$
$$ \begin{align} V &\propto I\\ \frac{V}{I} &= \text{constant}\\ \frac{V}{I} &= R\\ \therefore V &=IR\\ \end{align} $$
Question 17:
17. Draw the series & parallel resistors & write their mathematical formula.
Solution:
Series Connection:
$$ R_s = R_1+R_2+R_3+...+R_n $$
Parallel Connection:
$$ \frac{1}{R_p} = \frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+...+\frac{1}{R_n} $$
$$ R_s = R_1+R_2+R_3+...+R_n $$
Parallel Connection:
$$ \frac{1}{R_p} = \frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+...+\frac{1}{R_n} $$
Question 18:
18. List the applications of heating effect of electric current.
Solution:
The principle of heating effect of electric current is used in:
(i). Electric Bulb
(ii). Water Heater
(iii). Hair Dryer
(iv). Electric Cooker
(v). Room Heater
(vi). Electric Fuse
(i). Electric Bulb
(ii). Water Heater
(iii). Hair Dryer
(iv). Electric Cooker
(v). Room Heater
(vi). Electric Fuse
Question 19:
19. Write the functions of Insulin and Thyroxin.
Solution:
Insulin is produced by the pancreas and helps in regulating blood sugar levels.
Thyroxin regulates carbohydrate, protein and fat metabolism in the body so as to provide the best balance for growth.
Thyroxin regulates carbohydrate, protein and fat metabolism in the body so as to provide the best balance for growth.
Question 20:
20. How neuron works?
Solution:
All information from our environment is detected by the specialised tips of some nerve cells. These receptors are usually located in our sense organs, such as the inner ear, the nose, the tongue, and so on. So gustatory receptors will detect taste while olfactory receptors will detect smell.
This information, acquired at the end of the dendritic tip of a nerve cell, sets off a chemical reaction that creates an electrical impulse.
This impulse travels from the dendrite to the cell body, and then along the axon to its end.
At the end of the axon, the electrical impulse sets off the release of some chemicals. These chemicals cross the gap, or synapse, and start a similar electrical impulse in a dendrite of the next neuron.
This is a general scheme of how nervous impulses travel in the body. A similar synapse finally allows delivery of such impulses from neurons to other cells, such as muscles cells or gland.
This information, acquired at the end of the dendritic tip of a nerve cell, sets off a chemical reaction that creates an electrical impulse.
This impulse travels from the dendrite to the cell body, and then along the axon to its end.
At the end of the axon, the electrical impulse sets off the release of some chemicals. These chemicals cross the gap, or synapse, and start a similar electrical impulse in a dendrite of the next neuron.
This is a general scheme of how nervous impulses travel in the body. A similar synapse finally allows delivery of such impulses from neurons to other cells, such as muscles cells or gland.
Question 21:
21. What is Reflex arc and Reflex action?
Solution:
Reflex arc: The pathway through which nerve impulses pass during reflex action is called reflex arc.
Reflex action It is a quick, sudden and immediate response of the body to a stimulus.
E.g., Knee jerk, withdrawal of hand on touching hot object.
Reflex action It is a quick, sudden and immediate response of the body to a stimulus.
E.g., Knee jerk, withdrawal of hand on touching hot object.
Question 22:
22. Explain working of DC Motor & DC Generator
Solution:
Refer Textbook
Question 23:
23. What is Myopia & Hypermetropia
Solution:
Myopia: This is also known as short-sightedness. In this defect, the person affected can see nearby objects clearly but cannot see distant objects clearly. In this defect, image is formed in front of the retina.
Causes:Excessive curvature of eye lens. / Elongation of eye ball.
Correction: By using concave lens of appropriate power.
Hypermetropia: This is also known as far-sightedness. In this defect, the person affected can see far objects clearly but cannot see nearer objects clearly. In this defect, image is formed behind the retina.
Causes:Lesser curvature of eye lens. / Focal length of the eye lens becomes too long. / Eye ball becomes too small.
Correction: By using convex lens of appropriate power.
Causes:Excessive curvature of eye lens. / Elongation of eye ball.
Correction: By using concave lens of appropriate power.
Hypermetropia: This is also known as far-sightedness. In this defect, the person affected can see far objects clearly but cannot see nearer objects clearly. In this defect, image is formed behind the retina.
Causes:Lesser curvature of eye lens. / Focal length of the eye lens becomes too long. / Eye ball becomes too small.
Correction: By using convex lens of appropriate power.
Question 24:
24. Draw a neat labled diagram of neuron.
Solution:
Refer textbook
Question 25:
25. Draw a neat labled diagram of brain.
Solution:
Refer textbook
Question 26:
26. Draw a neat labled diagram of VS of a Heart.
Solution:
Refer textbook
Question 27:
27. Balance the following chemical equations.
(i). $$\ce{HNO3 + Ca(OH)2 -> Ca(NO3)2 + H2O}$$
(ii). $$\ce{BaCl2 + H2SO4 -> BaSO4 + HCl}$$
(ii). $$\ce{BaCl2 + H2SO4 -> BaSO4 + HCl}$$
Solution:
(i). $$\ce{2HNO3 + Ca(OH)2 -> Ca(NO3)2 + 2H2O}$$
(ii). $$\ce{BaCl2 + H2SO4 -> BaSO4 + 2HCl}$$
(ii). $$\ce{BaCl2 + H2SO4 -> BaSO4 + 2HCl}$$
Question 28:
28. Draw a Neat labelled diagram of Human Digestive System.
Solution:
Refer textbook
Question 29:
29. Draw a neat labled diagram of electrolysis of copper.
Solution:
Refer textbook
Question 30:
30. What is electromagnetic induction?
Solution:
When a conductor is placed in a changing magnetic field, some current is induced in it. Such current is called induced current and the phenomenon is called ElectroMagnetic Induction.
Question 31:
31. Write the factors affecting induced e.m.f in electromagnetic induction.
Solution:
Factors affecting induced e.m.f in electromagnetic induction are,
(i). Magnetic strength of the core in the coil of wire. (stronger --> bigger emf)
(ii). Number of turns of wire in the coil (more turns --> bigger emf)
(iii). The cross-sectional area of the coil (bigger area --> bigger emf)
(iv). Relative speed between the magnetic field and the conductor. (Faster --> bigger emf)
(i). Magnetic strength of the core in the coil of wire. (stronger --> bigger emf)
(ii). Number of turns of wire in the coil (more turns --> bigger emf)
(iii). The cross-sectional area of the coil (bigger area --> bigger emf)
(iv). Relative speed between the magnetic field and the conductor. (Faster --> bigger emf)
Question 32:
32. Write the laws of electromagnetic induction.
Solution:
Faraday's First Law:
Whenever a conductor is placed in a varying magnetic field an EMF gets induced across the conductor (called as induced emf), and if the conductor is a closed circuit then induced current flows through it.
Faraday's Second Law:
The magnitude of induced emf is equal to the rate of change of flux linkages with the coil. The flux linkages is the product of number of turns and the flux associated with the coil.
Lenz's Law: When an emf is induced according to Faraday's law, the polarity (direction) of that induced emf is such that it opposes the cause of its production.
Whenever a conductor is placed in a varying magnetic field an EMF gets induced across the conductor (called as induced emf), and if the conductor is a closed circuit then induced current flows through it.
Faraday's Second Law:
The magnitude of induced emf is equal to the rate of change of flux linkages with the coil. The flux linkages is the product of number of turns and the flux associated with the coil.
Lenz's Law: When an emf is induced according to Faraday's law, the polarity (direction) of that induced emf is such that it opposes the cause of its production.
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