12th CBSE Math Guide - Relations and Functions, NCERT Solutions of Exercise 1.2

CBSE Guide NCERT Solutions for Class 12 Mathematics   

Chapter 1, relations and functions
Cbse Ncert Solution of XII Math Textbook Exercise 1.2
(Solutions of CBSE Class 12  NCERT Maths Exercise 1.2, Relations and Functions)
Scroll down and click on the Link in between & at the end of Questions to open Solutions (pdf)
Question 1: Show that the function f: R* → R* defined by f(x) = 1/x is one-one and onto, where R* is the set of all non-zero real numbers. Is the result true, if the domain R* is replaced by N with co-domain being same as R*?
Question 2: Check the injectivity and surjectivity of the following functions:
(i) f: N → N given by f(x) = x2
(ii) f: Z → Z given by f(x) = x2
(iii) f: R → R given by f(x) = x2
(iv) f: N → N given by f(x) = x3
(v) f: Z → Z given by f(x) = x3
Question 3: Prove that the Greatest Integer Function f: R R given by f(x) = [x], is neither one - one nor onto, where [x] denotes the greatest integer less than or equal to x.
Class XII CBSE Maths - NCERT Solutions of Relations and Functions Ex 1.2
Question 4: Show that the Modulus Function f: R → R given by, is neither one-one nor onto, where |x| is x, if x is positive or 0 and |x| is − x, if x is negative.
Question 5: Show that the Signum Function f: R → R, given by
is neither one-one nor onto.
Question 6: Let A = {1, 2, 3}, B = {4, 5, 6, 7} and let f = {(1, 4), (2, 5), (3, 6)} be a function from A to B. Show that f is one-one.
Question 7: In each of the following cases, state whether the function is one-one, onto or bijective.
Justify your answer.
(i) f: R → R defined by f(x) = 3 − 4x
(ii) f: R → R defined by f(x) = 1 + x2
Question 8: Let A and B be sets. Show that f: A × B B × A such that (a, b) = (b, a) is bijective function.
Relations and Functions - Class 12 Mathematics CBSE Guide NCERT Solutions
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Question 9:

Question 10: Let A = R − {3} and B = R − {1}. Consider the function f: A → B defined by

Is f one-one and onto? Justify your answer.
Question 11: Let f: R → R be defined as f(x) = x4. Choose the correct answer.
(A) f is one-one onto
(B) f is many-one onto
(C) f is one-one but not onto
(D) f is neither one-one nor onto
Question 12: Let f: R → R be defined as f(x) = 3x. Choose the correct answer.
(A) f is one-one onto
(B) f is many-one onto
(C) f is one-one but not onto
(D) f is neither one-one nor onto

CBSE Guide and CBSE Notes: Class 10 Control and Coordination - Important Definitions and Study Materials

Class X Science: Chapter 7, Control and Coordination
CBSE Notes | CBSE Guide | Important Terms & Definitions
The upward and downward growth of shoots and roots, respectively in response to the gravity of the earth is termed as Geotropism. Example - roots are positively geotropic while shoots are negatively geotropic.

The tendency of plants to grow towards water or moisture is called hydrotropism. Example - roots are positively hydrotropism.

Phototropism is the growth movement of plants in response to light. The shoots of a plant show positive phototropism and the roots of a plant show negative phototropism. Example - the flower head of sunflower is positively phototropic as it moves from east to west along with sun.

It is the tendency of growth towards some chemical, e.g., growth of pollen tubes towards ovules and some organic substances.

(i) It is a system of conducting tissues that receives stimulus and transmit it to other parts of the body forming network.
(ii) It is the most important for regulation, control and coordination of body functions.
(iii) Comprises of neurons, nerves and nervous organs.
(iv) Vertebrate nervous system consists of two parts:
(A) Central Nervous System (CNS) including brain and spinal cord.
(B) Peripheral Nervous System (PNS) including cranial, spinal and visceral nerves

(i) Regulates involuntary actions.
(ii) Controls and coordinates voluntary muscular activities.
(iii) Keeps us inform about the outside world through the sense organs.
(iv) Enables us to think, reason and remember.
(v) Controls all the reflex actions.

It is a cell or group of cells specialised to detect a particular stimulus and to initiate the transmission of impulses via the sensory nerves. There are five receptors or sense organs through which the animals receive stimuli. These receptors are:
1. Photoreceptors for light (eyes),
2. Photoreceptors for sounds (ears),
3. Gustatory receptors for taste (tongue),
4. Olfactoreceptors for smell (nose),
5. Thigmo receptors for touch (skin).
The receptors pass information to the brain through neurons.

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Reflex action involves the following steps:
(i) Receptor organ like skin perceive the stimulus and activates a sensory nerve impulse.
(ii) Sensory organ carries message in the form of sensory impulse to the spinal cord.
(iii) The spinal cord acts as modulator. The neurons of spinal cord transmit the sensory nerve impulse to motor neuron.
(iv) Motor nerve conducts these impulses to the effectors like leg muscles etc.

(A) It enables the body to give prompt and appropriate responses to harmful stimuli and thus, protects our body.
(B) It minimises overloading of brain.

It is the pathway taken by the nerves impulses and responses in a reflex action. For example, impulses from receptor organs like skin to the spinal cord and from the spinal cord to the effector organs like muscles.
The reflex arc pathway can be shown in a flow chart (Diagram) as below:
https://www.cbsencertsolution.com - flow diagram for Reflex Arc
It is the highest coordinating centre in the body. It is a part of the central nervous system and receives information from various parts of the body and interprets them. There are 12 pairs of cranial nerves which arise from the brain and spread throughout the head. The brain is broadly divided into three regions: Fore-brain, Mid-brain and Hind-brain.
CBSE Guide NCERT Solution - Diagram of Human Brain

(A) Fore-brain
1. It is the main thinking part and the largest region of the brain.
2. Includes prominent regions such as - olfactory lobes, thalamus and hypothalamus.
3. Cerebrum is the dome - shaped roof of the brain. Different areas of cerebrum have different functions, such as, sensory areas and motor areas. There are specific regions of cerebrum for each kind of stimulus and response. For example,
(a) Occipital lobe - region for site ie., visual reception.
(b) Temporal lobe - region for hearing ie., auditory reception.
(c) Frontal lobe - region for speech, facial muscle and higher mental activities.
(d) Parietal lobe - region for taste, smell, touch and consciousness.
(e) Olfactory lobes - contain Olfactoreceptors which are the organs of smell.
4. Thalamus is the major coordinating center for sensory and motor signals, while Hypothalamus controls body temperature, hunger, thirst etc.

(B) Mid-brain
1. Connects the fore-brain to hind-brain.
2. It controls reflex movements of the head, neck and trunk.

(C) Hind-brain
1. Consists of three centres: Cerebellum, Pons and Medulla Oblongeta.
2. Cerebellum lies at the roof of the hind-brain. It controls the coordination of the body movements and posture.
3. Pons lie just above the Medulla and take part in regulating respiration.
4. Medulla Oblongeta lies at the floor of the hind - brain and continues into the spinal cord. It regulates swallowing, coughing, sneezing and vomiting.

1. Receives information carrying impulses from all the sensory organs of the body.
2. Responds to the impulses by sending instructions to the muscles and glands causing then to function accordingly.
3. Correlates various stimuli from different sense organs and produces the most appropriate response.
4. Controls and coordinates all body activities.
5. Stores information so that behaviour can be modified according to the past experience.

1. It is the cylindrical structure and a part of the CNS.
2. It begins in continuation with Medulla oblongeta and extended downwards.
3. It is enclosed in a bony cage called Vertebral Column. Coccyx is the last bone of the Vertebral Column.
4. Thirty one pairs of Spinal Nerves arise from the spinal cord and spread throughout the body.
5. It acts as a modular of reflex action.

Also Read: Class 10 Cbse Ncert Solution for all major subjects (Chapter Exercises plus CBSE Notes and extra CBSE Hots for 10th NCERT textbooks)

1. Auxins, 2. Gibberellins, 3. Cytokinins, and 4. Abscisic Acid (ABA).
(a) Synthesised at the shoot-tip of the plant body.
(b) Promotes cell elongation, root formation, cell division, respiration and physiological processes like protein synthesis, water uptake and proto-plasmic permeability.
(c) Play an important role in development of seedless fruits.

(a) Stimulate stem elongation, seed germination and flowering.
(b) Maximum concentration of Gibberellins is found in fruits and seeds.

(a) Are produced in dividing cells throughout the plant.
(b) In mature plants, Cytokinins are produced in the root tips and are transported to shoot tip.
(c) Promote cell division, breaking of seeds, buds and regulates flowing transport.
(d) Promote opening of stomata.

Abscisic Acid (ABA)
(a) It is a growth inhibitor which reverses the growth.
(b) It causes dormancy of seeds, tubers and bulbs.
(c) Promotes closing of stomata and is responsible for the loss of RNA, proteins and chlorophyll.
 Class 10 NCERT Science Chapter 7, Control and Coordination - Related Posts

Class 10 Science Cbse Ncert Solutions of Control and Coordination - InText Questions

Control and Coordination

Class 10 Science NCERT Solutions of Chapter 7 InText Questions

Control and Coordination - NCERT Solutions of Intext Questions (Page 119)

Question 1: What is the difference between a reflex action and walking?
Answer: Reflex action is a process by which we do something without thinking about it or without being in control of our reactions. It is an automatic response to a stimulus which is done by only the spinal cord without the help of brain.
While walking is a process which is done by thinking, or it is performed by the brain under conscious control unlike reflex action.
Question 2: What happens at the synapse between two neurons?
Answer:  A very small gap that occurs between the last portion of axon of one neuron and the dendron of another neuron is known as synapse. Synapse acts as one way valve to transmit impulses in one direction only. The uni-directional transfer of impulses occur due to the release of some chemicals in only one side of the neuron, ie, the axon's side. These chemicals cross the synapse and start a simple impulse in the dendrite of next neuron.
Question 3: Which part of the brain maintains posture and equilibrium of the body?
Answer: Cerebellum, a part of hind brain is responsible for maintaining the posture and equilibrium of the body.
Question 4: How do we detect the smell of an agarbatti (incense sick)?
Answer:  The smell of an agarbatti is detected by the forebrain. There are separate areas in our forebrain which are specialised for hearing, smelling, sight, taste, touch etc. Our forebrain has also regions that collect information or impulses from the various receptors. When the smell of an agarbatti reaches us, our forebrain interprets it by putting it together with the information received from other receptors and also with the information already stored in the brain.
Question 5: What is the role of the brain in reflex action?
Answer:  Reflex actions are sudden responses to a change in the environment which we do without thinking about it. The nerves from all over the body meet in a bundle in the spinal cord. Thus, reflex arcs are formed in the spinal cord and the information input also goes on to reach the brain. In reflex arc instant and automatic responses possible. The brain is only aware of the signal and the response that has taken place. Here, the brain has no role to play in the creation of the response done by reflex action.

Control and Coordination - NCERT Answers of Intext Questions (Page 122)

Question 1: What are plant hormones?
Answer:  Plant hormones are the chemicals released by stimulated cells. This chemical compounds help to coordinate growth, development and responses to the environment. These are synthesised at places away from where they act. The five different types of plant hormones (phytohormones) are Auxins, Gibberellins, Cytokinins, Abscisic acid, and Ethylene.
Question 2: How is the movement of leaves of the sensitive plant different from the movement of a shoot towards light?
Answer: The movement of leaves of the sensitive plant like Mimosa pudica or "touch-me-not" is either towards nor away from stimulus like touch. While movement of shoot is towards stimulus like light. The movement of leaves of sensitive plants is not directional while the movement of shoot is directional.
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Question 3: Give an example of a plant hormone that promotes growth.
Answer: (i) Auxins help to increase the length of plants.
(ii) Gibberellins help in the growth of stem.
Question 4: How do Auxins promote the growth of a tendril around a support?
Answer: Auxin is synthesised at the shoot tip. The tendrils are sensitive to touch. As these tendrils come in the contact with the support, the auxin diffuses towards the other side away from the support. As it stimulates faster growth of the cells, so, this part grows more rapidly than the other. This causes the tendril to circle around the support and thus climb upwards.
Question 5: Design an experiment to demonstrate hydrotropism.
Answer: Positive hydrotropism can be demonstrated with germinated seedlings, which are allowed to grow on ground (Fig. 7.2). The soil below the roots is separated by a polythene partition. The left side is kept moist but the right side is kept dry. The radicals at first grow in a downward direction due to the effect of gravity (positive geotropism), but after sometime, the roots bend toward the moist soil (positive hydrotropism). This is evidently due to the closeness of the germinating roots to water.

Control and Coordination - NCERT Solutions of Intext Questions (Page 125)

Question 1: How does chemical coordination take place in animals?
Answer: Chemical coordination takes place in animals with the help of some chemical substances called hormones. Hormones are secreted by endocrine glands. The timing and amount of hormone released are regulated by feedback mechanisms.
Question 2: Why is the use of iodised salt advisable?
Answer: The use of iodised salt is advisable because iodine is necessary for the thyroid gland to produce thyroxine hormone. Thyroxine relates carbohydrates, protein and fat metabolism in the body so as to provide the best balance for growth. Iodine is essential for the synthesis of thyroxine. Deficiency of this hormone results in the enlargement of the thyroid gland. This can lead to goitre. Therefore, iodised salt is advised for normal functioning of the thyroid gland.
Question 3: How does our body respond when adrenaline is secreted into the blood?
Answer: Adrenaline is a hormone secreted by the adrenal glands in case of any danger, emergency or any kinds of stress. It is secreted directly into the blood and is carried to different parts of the body. It acts on heart also. As a result, the heart beats faster in order to supply more oxygen to the muscles. This also increases the blood pressure. All these responses enable our body to deal with the situation.
Question 4: Why are some patients of diabetes treated by injections of insulin?
Answer: Insulin is a hormone which is produced by the pancreas and helps in regulating blood sugar levels. If insulin is not secreted in proper amounts, the sugar level in the blood increases causing diabetes which has many harmful effects. Therefore, the patients of diabetes are treated by giving injections of insulin.
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Class 10 Metals and Non-Metals: CBSE Notes, Important Definitions, Chemical Reactions and Equations

CBSE Class X Chemistry - Chapter 3, Metals and Non-metals

1. There are 115 elements known to now.
2. Brass and bronze are highly sonorous and so used in making bells.
3. Silver is the best conductor of electricity followed by Cu, Au, Al, and W (Tungsten). Mercury and lead have low electrical conductivity due to high resistance.
4. Amphoteric oxides being acidic as well as basic, turn red litmus blue as well as blue litmus red.
5. Alkalis turn phenolphthalein pink and turn red litmus blue.
6. Metal oxides react with acids to form salt and water.
7. At room temperature metals like - Al, Zn, Cu, Mg, Sn, Pb form oxide on their surface and became dull. Mercury forms red coloured oxide, HgO.
8. Non-metals gain electrons to form negative ions in order to compete their octet ie., 8 electrons in their outermost orbit.
9. Metals tend to loose electrons to acquire nearest noble gas configuration.
10. Iodine is a non-metal but has metallic lustre.
11. Gallium (Ga) is a metal which becomes liquid if kept on palm. It has very low melting point while its boiling point is very high. Because of this property it is useful for high temperature thermometers.
12. Tungsten (W) has the highest melting point.
13. Graphite is the only non-metal which is good conductor of heat and electricity.
14. Non-metals have generally low density except diamond which has high density.
15. Non-metals generally not firm alloys. Only exception is carbon which is alloyed with iron to form steel.
16. Cinnabar is a bright red naturally occurring form of Mercury sulphide, HgS. It is the chief Ore of Mercury.
17. Blister copper is a kind of impure copper having spots or blisters due to evolution of Sulphur dioxide.
18. Sodium Chloride (NaCl) does not exist as molecules but as aggregates of oppositely charged ions.
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Class 10 NCERT Science - Metals and Non-metals
CBSE NOTES : terms & Definitions
Metals are the elements which are usually hard, malleable and ductile. They are sonorous and have metallic lustre. Metals are also good conductors of heat and electricity.
Metals are mostly solids with high density and high melting and boiling points. They can loose electrons easily from positive ions.
1. Some metals like sodium and potassium, magnesium are the only metals which can be cut with knife.
2. Mercury is the only metal which is liquid at room temperature.
3. Lead, Sodium, Potassium and Lithium are the only metals which are not ductile.
4. Pb and Hg are poor conductors of heat.
The process of forming oxide layer on the surface of metal is called anodising. For example, aluminium forms an oxide layer on its surface when exposed to air. This layer of aluminium oxide protects aluminium from corrosion. The layer can be made thicker with the help of anodising.
Aqua Regia

Aqua Regia is a mixture of conc. HCl and conc. HNO3 in the ratio of 3:1. It can dissolve gold and platinum although none of these two metals react with conc. HCl or conc. HNO3 alone. Aqua Regia is a strong oxidising agent due to the formation of NOCl  (Nitrosyl Chloride) and Chlorine produced by a reaction of two acids. It is highly corrosive and fuming liquid. Therefore, Aqua Regia should be kept away from eyes and skin.
Non-metals are those materials which are found in all the three states  (solid, liquid and gas), non-lustrous, non-sonorous, and neither malleable nor ductile. These are bad conductors of heat and electricity. The oxides of non-metals are acidic in nature. Non-metal elements tend to gain electrons and form negative ions (anion).
Non-metals have generally low melting and boiling points except diamond, graphite, boron and Silicon which have high melting and boiling points.
These are homogeneous mixture of two or more metals, or a metal and a non-metal. For example, brass is an alloy of Cu and Zn. Alloying is a very good method of improving the properties of a metal:
(i) Alloys do not get corroded or corroded to very less extent.
(ii) They are harder and stronger than pure metal, e.g., gold mixed with copper is harder than pure gold.
(iii) Alloys are less conducting than pure metals, e.g., copper is a good conductor of heat and electricity whereas its alloys like - brass and bronze are not good conductors.
(iv) The melting point of an alloy is less than that of pure metals. For example, Solder, which is an alloy of lead and tin, has lower melting points than either tin or lead. Solder is used for soldering (welding) of electrical wires.
In an alloy, if one of the metals is Mercury then the alloy is known as amalgam.
Minerals are the natural materials in which metals occur in the form of their compounds. Minerals are found in the earth's crust and also in sea water.
It is a process in which the sulphide ores are converted into oxides by heating strongly in presence of excess air. For example,

It is a process in which the carbonate ores are changed into oxides by heating strongly either in limited or in absence of air. This process also helps to remove moisture or volatile impurities. For example,
The substance which reacts with gangue to form a fusible mass which can easily be removed, is known as flux. For example, in the extraction of iron from ore, CaO  (as lime) is used as flux to remove SiO2 (Silica) which is present as gangue.
This is the fusible mass formed by the reaction of flux and gangue is known as slag.
Slag is lighter than molten metal and so floats over the molten metal and can be easily removed. It prevents metal from oxidation.
Froth Flotation
Froth flotation is a concentration process of selectively separating hydrophobic valuable minerals from hydrophilic waste gangue. In mineral processing, Froth Flotation method is used for the concentration of sulphide ores. The sulphide ore is mixed with water and pine oil. The mixture is then agitated with the blast of compressed air. In this process sulphide ore gets collected in Froth and gangue particles settled at the bottom of the tank. Sulphide ore is thus, separated and dried.
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CBSE Class 10 Science - Metals and Non-metals