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1
8005-8008
7 What products would be formed when a nucleotide from DNA containing thymine is hydrolysed 10 8 When RNA is hydrolysed, there is no relationship among the quantities of different bases obtained What does this fact suggest about the structure of RNA
1
8006-8009
10 8 When RNA is hydrolysed, there is no relationship among the quantities of different bases obtained What does this fact suggest about the structure of RNA Summary Summary Summary Summary Summary Carbohydrates are optically active polyhydroxy aldehydes or ketones or molecules which provide such units on hydrolysis
1
8007-8010
8 When RNA is hydrolysed, there is no relationship among the quantities of different bases obtained What does this fact suggest about the structure of RNA Summary Summary Summary Summary Summary Carbohydrates are optically active polyhydroxy aldehydes or ketones or molecules which provide such units on hydrolysis They are broadly classified into three groups β€” monosaccharides, disaccharides and polysaccharides
1
8008-8011
What does this fact suggest about the structure of RNA Summary Summary Summary Summary Summary Carbohydrates are optically active polyhydroxy aldehydes or ketones or molecules which provide such units on hydrolysis They are broadly classified into three groups β€” monosaccharides, disaccharides and polysaccharides Glucose, the most important source of energy for mammals, is obtained by the digestion of starch
1
8009-8012
Summary Summary Summary Summary Summary Carbohydrates are optically active polyhydroxy aldehydes or ketones or molecules which provide such units on hydrolysis They are broadly classified into three groups β€” monosaccharides, disaccharides and polysaccharides Glucose, the most important source of energy for mammals, is obtained by the digestion of starch Monosaccharides are held together by glycosidic linkages to form disaccharides or polysaccharides
1
8010-8013
They are broadly classified into three groups β€” monosaccharides, disaccharides and polysaccharides Glucose, the most important source of energy for mammals, is obtained by the digestion of starch Monosaccharides are held together by glycosidic linkages to form disaccharides or polysaccharides Proteins are the polymers of about twenty different aaaaa-amino acids which are linked by peptide bonds
1
8011-8014
Glucose, the most important source of energy for mammals, is obtained by the digestion of starch Monosaccharides are held together by glycosidic linkages to form disaccharides or polysaccharides Proteins are the polymers of about twenty different aaaaa-amino acids which are linked by peptide bonds Ten amino acids are called essential amino acids because they cannot be synthesised by our body, hence must be provided through diet
1
8012-8015
Monosaccharides are held together by glycosidic linkages to form disaccharides or polysaccharides Proteins are the polymers of about twenty different aaaaa-amino acids which are linked by peptide bonds Ten amino acids are called essential amino acids because they cannot be synthesised by our body, hence must be provided through diet Proteins perform various structural and dynamic functions in the organisms
1
8013-8016
Proteins are the polymers of about twenty different aaaaa-amino acids which are linked by peptide bonds Ten amino acids are called essential amino acids because they cannot be synthesised by our body, hence must be provided through diet Proteins perform various structural and dynamic functions in the organisms Proteins which contain only a-amino acids are called simple proteins
1
8014-8017
Ten amino acids are called essential amino acids because they cannot be synthesised by our body, hence must be provided through diet Proteins perform various structural and dynamic functions in the organisms Proteins which contain only a-amino acids are called simple proteins The secondary or tertiary structure of proteins get disturbed on change of pH or temperature and they are not able to perform their functions
1
8015-8018
Proteins perform various structural and dynamic functions in the organisms Proteins which contain only a-amino acids are called simple proteins The secondary or tertiary structure of proteins get disturbed on change of pH or temperature and they are not able to perform their functions This is called denaturation of proteins
1
8016-8019
Proteins which contain only a-amino acids are called simple proteins The secondary or tertiary structure of proteins get disturbed on change of pH or temperature and they are not able to perform their functions This is called denaturation of proteins Enzymes are biocatalysts which speed up the reactions in biosystems
1
8017-8020
The secondary or tertiary structure of proteins get disturbed on change of pH or temperature and they are not able to perform their functions This is called denaturation of proteins Enzymes are biocatalysts which speed up the reactions in biosystems They are very specific and selective in their action and chemically majority of enzymes are proteins
1
8018-8021
This is called denaturation of proteins Enzymes are biocatalysts which speed up the reactions in biosystems They are very specific and selective in their action and chemically majority of enzymes are proteins Vitamins are accessory food factors required in the diet
1
8019-8022
Enzymes are biocatalysts which speed up the reactions in biosystems They are very specific and selective in their action and chemically majority of enzymes are proteins Vitamins are accessory food factors required in the diet They are classified as fat soluble (A, D, E and K) and water soluble (B group and C)
1
8020-8023
They are very specific and selective in their action and chemically majority of enzymes are proteins Vitamins are accessory food factors required in the diet They are classified as fat soluble (A, D, E and K) and water soluble (B group and C) Deficiency of vitamins leads to many diseases
1
8021-8024
Vitamins are accessory food factors required in the diet They are classified as fat soluble (A, D, E and K) and water soluble (B group and C) Deficiency of vitamins leads to many diseases Rationalised 2023-24 302 Chemistry Nucleic acids are the polymers of nucleotides which in turn consist of a base, a pentose sugar and phosphate moiety
1
8022-8025
They are classified as fat soluble (A, D, E and K) and water soluble (B group and C) Deficiency of vitamins leads to many diseases Rationalised 2023-24 302 Chemistry Nucleic acids are the polymers of nucleotides which in turn consist of a base, a pentose sugar and phosphate moiety Nucleic acids are responsible for the transfer of characters from parents to offsprings
1
8023-8026
Deficiency of vitamins leads to many diseases Rationalised 2023-24 302 Chemistry Nucleic acids are the polymers of nucleotides which in turn consist of a base, a pentose sugar and phosphate moiety Nucleic acids are responsible for the transfer of characters from parents to offsprings There are two types of nucleic acids β€” DNA and RNA
1
8024-8027
Rationalised 2023-24 302 Chemistry Nucleic acids are the polymers of nucleotides which in turn consist of a base, a pentose sugar and phosphate moiety Nucleic acids are responsible for the transfer of characters from parents to offsprings There are two types of nucleic acids β€” DNA and RNA DNA contains a five carbon sugar molecule called 2-deoxyribose whereas RNA contains ribose
1
8025-8028
Nucleic acids are responsible for the transfer of characters from parents to offsprings There are two types of nucleic acids β€” DNA and RNA DNA contains a five carbon sugar molecule called 2-deoxyribose whereas RNA contains ribose Both DNA and RNA contain adenine, guanine and cytosine
1
8026-8029
There are two types of nucleic acids β€” DNA and RNA DNA contains a five carbon sugar molecule called 2-deoxyribose whereas RNA contains ribose Both DNA and RNA contain adenine, guanine and cytosine The fourth base is thymine in DNA and uracil in RNA
1
8027-8030
DNA contains a five carbon sugar molecule called 2-deoxyribose whereas RNA contains ribose Both DNA and RNA contain adenine, guanine and cytosine The fourth base is thymine in DNA and uracil in RNA The structure of DNA is a double strand whereas RNA is a single strand molecule
1
8028-8031
Both DNA and RNA contain adenine, guanine and cytosine The fourth base is thymine in DNA and uracil in RNA The structure of DNA is a double strand whereas RNA is a single strand molecule DNA is the chemical basis of heredity and have the coded message for proteins to be synthesised in the cell
1
8029-8032
The fourth base is thymine in DNA and uracil in RNA The structure of DNA is a double strand whereas RNA is a single strand molecule DNA is the chemical basis of heredity and have the coded message for proteins to be synthesised in the cell There are three types of RNA β€” mRNA, rRNA and tRNA which actually carry out the protein synthesis in the cell
1
8030-8033
The structure of DNA is a double strand whereas RNA is a single strand molecule DNA is the chemical basis of heredity and have the coded message for proteins to be synthesised in the cell There are three types of RNA β€” mRNA, rRNA and tRNA which actually carry out the protein synthesis in the cell 10
1
8031-8034
DNA is the chemical basis of heredity and have the coded message for proteins to be synthesised in the cell There are three types of RNA β€” mRNA, rRNA and tRNA which actually carry out the protein synthesis in the cell 10 1 What are monosaccharides
1
8032-8035
There are three types of RNA β€” mRNA, rRNA and tRNA which actually carry out the protein synthesis in the cell 10 1 What are monosaccharides 10
1
8033-8036
10 1 What are monosaccharides 10 2 What are reducing sugars
1
8034-8037
1 What are monosaccharides 10 2 What are reducing sugars 10
1
8035-8038
10 2 What are reducing sugars 10 3 Write two main functions of carbohydrates in plants
1
8036-8039
2 What are reducing sugars 10 3 Write two main functions of carbohydrates in plants 10
1
8037-8040
10 3 Write two main functions of carbohydrates in plants 10 4 Classify the following into monosaccharides and disaccharides
1
8038-8041
3 Write two main functions of carbohydrates in plants 10 4 Classify the following into monosaccharides and disaccharides Ribose, 2-deoxyribose, maltose, galactose, fructose and lactose
1
8039-8042
10 4 Classify the following into monosaccharides and disaccharides Ribose, 2-deoxyribose, maltose, galactose, fructose and lactose 10
1
8040-8043
4 Classify the following into monosaccharides and disaccharides Ribose, 2-deoxyribose, maltose, galactose, fructose and lactose 10 5 What do you understand by the term glycosidic linkage
1
8041-8044
Ribose, 2-deoxyribose, maltose, galactose, fructose and lactose 10 5 What do you understand by the term glycosidic linkage 10
1
8042-8045
10 5 What do you understand by the term glycosidic linkage 10 6 What is glycogen
1
8043-8046
5 What do you understand by the term glycosidic linkage 10 6 What is glycogen How is it different from starch
1
8044-8047
10 6 What is glycogen How is it different from starch 10
1
8045-8048
6 What is glycogen How is it different from starch 10 7 What are the hydrolysis products of (i) sucrose and (ii) lactose
1
8046-8049
How is it different from starch 10 7 What are the hydrolysis products of (i) sucrose and (ii) lactose 10
1
8047-8050
10 7 What are the hydrolysis products of (i) sucrose and (ii) lactose 10 8 What is the basic structural difference between starch and cellulose
1
8048-8051
7 What are the hydrolysis products of (i) sucrose and (ii) lactose 10 8 What is the basic structural difference between starch and cellulose 10
1
8049-8052
10 8 What is the basic structural difference between starch and cellulose 10 9 What happens when D-glucose is treated with the following reagents
1
8050-8053
8 What is the basic structural difference between starch and cellulose 10 9 What happens when D-glucose is treated with the following reagents (i) HI (ii) Bromine water (iii) HNO3 10
1
8051-8054
10 9 What happens when D-glucose is treated with the following reagents (i) HI (ii) Bromine water (iii) HNO3 10 10 Enumerate the reactions of D-glucose which cannot be explained by its open chain structure
1
8052-8055
9 What happens when D-glucose is treated with the following reagents (i) HI (ii) Bromine water (iii) HNO3 10 10 Enumerate the reactions of D-glucose which cannot be explained by its open chain structure 10
1
8053-8056
(i) HI (ii) Bromine water (iii) HNO3 10 10 Enumerate the reactions of D-glucose which cannot be explained by its open chain structure 10 11 What are essential and non-essential amino acids
1
8054-8057
10 Enumerate the reactions of D-glucose which cannot be explained by its open chain structure 10 11 What are essential and non-essential amino acids Give two examples of each type
1
8055-8058
10 11 What are essential and non-essential amino acids Give two examples of each type 10
1
8056-8059
11 What are essential and non-essential amino acids Give two examples of each type 10 12 Define the following as related to proteins (i) Peptide linkage (ii) Primary structure (iii) Denaturation
1
8057-8060
Give two examples of each type 10 12 Define the following as related to proteins (i) Peptide linkage (ii) Primary structure (iii) Denaturation 10
1
8058-8061
10 12 Define the following as related to proteins (i) Peptide linkage (ii) Primary structure (iii) Denaturation 10 13 What are the common types of secondary structure of proteins
1
8059-8062
12 Define the following as related to proteins (i) Peptide linkage (ii) Primary structure (iii) Denaturation 10 13 What are the common types of secondary structure of proteins 10
1
8060-8063
10 13 What are the common types of secondary structure of proteins 10 14 What type of bonding helps in stabilising the a-helix structure of proteins
1
8061-8064
13 What are the common types of secondary structure of proteins 10 14 What type of bonding helps in stabilising the a-helix structure of proteins 10
1
8062-8065
10 14 What type of bonding helps in stabilising the a-helix structure of proteins 10 15 Differentiate between globular and fibrous proteins
1
8063-8066
14 What type of bonding helps in stabilising the a-helix structure of proteins 10 15 Differentiate between globular and fibrous proteins 10
1
8064-8067
10 15 Differentiate between globular and fibrous proteins 10 16 How do you explain the amphoteric behaviour of amino acids
1
8065-8068
15 Differentiate between globular and fibrous proteins 10 16 How do you explain the amphoteric behaviour of amino acids 10
1
8066-8069
10 16 How do you explain the amphoteric behaviour of amino acids 10 17 What are enzymes
1
8067-8070
16 How do you explain the amphoteric behaviour of amino acids 10 17 What are enzymes 10
1
8068-8071
10 17 What are enzymes 10 18 What is the effect of denaturation on the structure of proteins
1
8069-8072
17 What are enzymes 10 18 What is the effect of denaturation on the structure of proteins 10
1
8070-8073
10 18 What is the effect of denaturation on the structure of proteins 10 19 How are vitamins classified
1
8071-8074
18 What is the effect of denaturation on the structure of proteins 10 19 How are vitamins classified Name the vitamin responsible for the coagulation of blood
1
8072-8075
10 19 How are vitamins classified Name the vitamin responsible for the coagulation of blood 10
1
8073-8076
19 How are vitamins classified Name the vitamin responsible for the coagulation of blood 10 20 Why are vitamin A and vitamin C essential to us
1
8074-8077
Name the vitamin responsible for the coagulation of blood 10 20 Why are vitamin A and vitamin C essential to us Give their important sources
1
8075-8078
10 20 Why are vitamin A and vitamin C essential to us Give their important sources 10
1
8076-8079
20 Why are vitamin A and vitamin C essential to us Give their important sources 10 21 What are nucleic acids
1
8077-8080
Give their important sources 10 21 What are nucleic acids Mention their two important functions
1
8078-8081
10 21 What are nucleic acids Mention their two important functions 10
1
8079-8082
21 What are nucleic acids Mention their two important functions 10 22 What is the difference between a nucleoside and a nucleotide
1
8080-8083
Mention their two important functions 10 22 What is the difference between a nucleoside and a nucleotide 10
1
8081-8084
10 22 What is the difference between a nucleoside and a nucleotide 10 23 The two strands in DNA are not identical but are complementary
1
8082-8085
22 What is the difference between a nucleoside and a nucleotide 10 23 The two strands in DNA are not identical but are complementary Explain
1
8083-8086
10 23 The two strands in DNA are not identical but are complementary Explain 10
1
8084-8087
23 The two strands in DNA are not identical but are complementary Explain 10 24 Write the important structural and functional differences between DNA and RNA
1
8085-8088
Explain 10 24 Write the important structural and functional differences between DNA and RNA 10
1
8086-8089
10 24 Write the important structural and functional differences between DNA and RNA 10 25 What are the different types of RNA found in the cell
1
8087-8090
24 Write the important structural and functional differences between DNA and RNA 10 25 What are the different types of RNA found in the cell Exercises Exercises Exercises Exercises Exercises Rationalised 2023-24
1
1-4
vProofs are to Mathematics what calligraphy is to poetry Mathematical works do consist of proofs just as poems do consist of characters β€” VLADIMIR ARNOLD v A 1
1
2-5
Mathematical works do consist of proofs just as poems do consist of characters β€” VLADIMIR ARNOLD v A 1 1 Introduction In Classes IX, X and XI, we have learnt about the concepts of a statement, compound statement, negation, converse and contrapositive of a statement; axioms, conjectures, theorems and deductive reasoning
1
3-6
β€” VLADIMIR ARNOLD v A 1 1 Introduction In Classes IX, X and XI, we have learnt about the concepts of a statement, compound statement, negation, converse and contrapositive of a statement; axioms, conjectures, theorems and deductive reasoning Here, we will discuss various methods of proving mathematical propositions
1
4-7
1 1 Introduction In Classes IX, X and XI, we have learnt about the concepts of a statement, compound statement, negation, converse and contrapositive of a statement; axioms, conjectures, theorems and deductive reasoning Here, we will discuss various methods of proving mathematical propositions A
1
5-8
1 Introduction In Classes IX, X and XI, we have learnt about the concepts of a statement, compound statement, negation, converse and contrapositive of a statement; axioms, conjectures, theorems and deductive reasoning Here, we will discuss various methods of proving mathematical propositions A 1
1
6-9
Here, we will discuss various methods of proving mathematical propositions A 1 2 What is a Proof
1
7-10
A 1 2 What is a Proof Proof of a mathematical statement consists of sequence of statements, each statement being justified with a definition or an axiom or a proposition that is previously established by the method of deduction using only the allowed logical rules
1
8-11
1 2 What is a Proof Proof of a mathematical statement consists of sequence of statements, each statement being justified with a definition or an axiom or a proposition that is previously established by the method of deduction using only the allowed logical rules Thus, each proof is a chain of deductive arguments each of which has its premises and conclusions
1
9-12
2 What is a Proof Proof of a mathematical statement consists of sequence of statements, each statement being justified with a definition or an axiom or a proposition that is previously established by the method of deduction using only the allowed logical rules Thus, each proof is a chain of deductive arguments each of which has its premises and conclusions Many a times, we prove a proposition directly from what is given in the proposition
1
10-13
Proof of a mathematical statement consists of sequence of statements, each statement being justified with a definition or an axiom or a proposition that is previously established by the method of deduction using only the allowed logical rules Thus, each proof is a chain of deductive arguments each of which has its premises and conclusions Many a times, we prove a proposition directly from what is given in the proposition But some times it is easier to prove an equivalent proposition rather than proving the proposition itself
1
11-14
Thus, each proof is a chain of deductive arguments each of which has its premises and conclusions Many a times, we prove a proposition directly from what is given in the proposition But some times it is easier to prove an equivalent proposition rather than proving the proposition itself This leads to, two ways of proving a proposition directly or indirectly and the proofs obtained are called direct proof and indirect proof and further each has three different ways of proving which is discussed below
1
12-15
Many a times, we prove a proposition directly from what is given in the proposition But some times it is easier to prove an equivalent proposition rather than proving the proposition itself This leads to, two ways of proving a proposition directly or indirectly and the proofs obtained are called direct proof and indirect proof and further each has three different ways of proving which is discussed below Direct Proof It is the proof of a proposition in which we directly start the proof with what is given in the proposition
1
13-16
But some times it is easier to prove an equivalent proposition rather than proving the proposition itself This leads to, two ways of proving a proposition directly or indirectly and the proofs obtained are called direct proof and indirect proof and further each has three different ways of proving which is discussed below Direct Proof It is the proof of a proposition in which we directly start the proof with what is given in the proposition (i) Straight forward approach It is a chain of arguments which leads directly from what is given or assumed, with the help of axioms, definitions or already proved theorems, to what is to be proved using rules of logic
1
14-17
This leads to, two ways of proving a proposition directly or indirectly and the proofs obtained are called direct proof and indirect proof and further each has three different ways of proving which is discussed below Direct Proof It is the proof of a proposition in which we directly start the proof with what is given in the proposition (i) Straight forward approach It is a chain of arguments which leads directly from what is given or assumed, with the help of axioms, definitions or already proved theorems, to what is to be proved using rules of logic Consider the following example: Example 1 Show that if x2 – 5x + 6 = 0, then x = 3 or x = 2
1
15-18
Direct Proof It is the proof of a proposition in which we directly start the proof with what is given in the proposition (i) Straight forward approach It is a chain of arguments which leads directly from what is given or assumed, with the help of axioms, definitions or already proved theorems, to what is to be proved using rules of logic Consider the following example: Example 1 Show that if x2 – 5x + 6 = 0, then x = 3 or x = 2 Solution x2 – 5x + 6 = 0 (given) Appendix 1 PROOFS IN MATHEMATICS Rationalised 2023-24 MATHEMATICS 188 β‡’ (x – 3) (x – 2) = 0 (replacing an expression by an equal/equivalent expression) β‡’ x – 3 = 0 or x – 2 = 0 (from the established theorem ab = 0 β‡’ either a = 0 or b = 0, for a, b in R) β‡’ x – 3 + 3 = 0 + 3 or x – 2 + 2 = 0 + 2 (adding equal quantities on either side of the equation does not alter the nature of the equation) β‡’ x + 0 = 3 or x + 0 = 2 (using the identity property of integers under addition) β‡’ x = 3 or x = 2 (using the identity property of integers under addition) Hence, x2 – 5x + 6 = 0 implies x = 3 or x = 2
1
16-19
(i) Straight forward approach It is a chain of arguments which leads directly from what is given or assumed, with the help of axioms, definitions or already proved theorems, to what is to be proved using rules of logic Consider the following example: Example 1 Show that if x2 – 5x + 6 = 0, then x = 3 or x = 2 Solution x2 – 5x + 6 = 0 (given) Appendix 1 PROOFS IN MATHEMATICS Rationalised 2023-24 MATHEMATICS 188 β‡’ (x – 3) (x – 2) = 0 (replacing an expression by an equal/equivalent expression) β‡’ x – 3 = 0 or x – 2 = 0 (from the established theorem ab = 0 β‡’ either a = 0 or b = 0, for a, b in R) β‡’ x – 3 + 3 = 0 + 3 or x – 2 + 2 = 0 + 2 (adding equal quantities on either side of the equation does not alter the nature of the equation) β‡’ x + 0 = 3 or x + 0 = 2 (using the identity property of integers under addition) β‡’ x = 3 or x = 2 (using the identity property of integers under addition) Hence, x2 – 5x + 6 = 0 implies x = 3 or x = 2 Explanation Let p be the given statement β€œx2 – 5x + 6 = 0” and q be the conclusion statement β€œx = 3 or x = 2”
1
17-20
Consider the following example: Example 1 Show that if x2 – 5x + 6 = 0, then x = 3 or x = 2 Solution x2 – 5x + 6 = 0 (given) Appendix 1 PROOFS IN MATHEMATICS Rationalised 2023-24 MATHEMATICS 188 β‡’ (x – 3) (x – 2) = 0 (replacing an expression by an equal/equivalent expression) β‡’ x – 3 = 0 or x – 2 = 0 (from the established theorem ab = 0 β‡’ either a = 0 or b = 0, for a, b in R) β‡’ x – 3 + 3 = 0 + 3 or x – 2 + 2 = 0 + 2 (adding equal quantities on either side of the equation does not alter the nature of the equation) β‡’ x + 0 = 3 or x + 0 = 2 (using the identity property of integers under addition) β‡’ x = 3 or x = 2 (using the identity property of integers under addition) Hence, x2 – 5x + 6 = 0 implies x = 3 or x = 2 Explanation Let p be the given statement β€œx2 – 5x + 6 = 0” and q be the conclusion statement β€œx = 3 or x = 2” From the statement p, we deduced the statement r : β€œ(x – 3) (x – 2) = 0” by replacing the expression x2 – 5x + 6 in the statement p by another expression (x – 3) (x – 2) which is equal to x2 – 5x + 6