Let A = (1, -1, i, -i) be the set of four 4th roots of unity.
Question: Let A = (1, -1, i, -i) be the set of four 4th roots of unity. Prepare the composition table for multiplication on A and show that (i) $A$ is closed for multiplication, (ii) multiplication is associative on $A$, (iii) multiplication is commutative on $A$, (iv) 1 is the multiplicative identity, (v) every element in A has its multiplicative inverse. Solution: (i) A is said to be closed on * if all the elements of a*b A. composition table is $\left(\operatorname{as} i^{2}=-1\right)$ As tab...
Read More →The commercial name of polyacrylonitrile
Question: The commercial name of polyacrylonitrile is ______________. (i) Dacron (ii) Orlon (Acrilan) (iii) PVC (iv) Bakelite Solution: Option (ii)Orlon (Acrilan) is the answer....
Read More →Evaluate the following integral:
Question: Evaluate the following integral: $\int \frac{x}{\left(x^{2}+1\right)(x-1)} d x$ Solution: Denominator is factorized, so let separate the fraction through partial fraction, hence let $\frac{\mathrm{x}}{\left(\mathrm{x}^{2}+1\right)(\mathrm{x}-1)}=\frac{\mathrm{Ax}+\mathrm{B}}{\left(\mathrm{x}^{2}+1\right)}+\frac{\mathrm{Cx}+\mathrm{D}}{\mathrm{x}-1} \ldots \ldots$ (i) $\Rightarrow \frac{\mathrm{x}}{\left(\mathrm{x}^{2}+1\right)(\mathrm{x}-1)}=\frac{(\mathrm{Ax}+\mathrm{B})(\mathrm{x}-1)...
Read More →Which of the following is not a semisynthetic
Question: Which of the following is not a semisynthetic polymer? (i) cis-polyisoprene (ii) Cellulose nitrate (iii) Cellulose acetate (iv) Vulcanised rubber Solution: Option (i)cis-polyisoprene is the answer...
Read More →Which of the following polymers of glucose
Question: Which of the following polymers of glucose is stored by animals? (i) Cellulose (ii) Amylose (iii) Amylopectin (iv) Glycogen Solution: Option (iv)Glycogenis the answer....
Read More →Let A = N × N. Define * on A by
Question: Let A = N N. Define * on A by (a, b) * (c, d) = (a + c, b + d). Show that (i) $A$ is closed for $*$, (ii) $*$ is commutative, (iii) $*$ is associative, (iv) identity element does not exist in $\mathrm{A}$. Solution: (i) $A$ is said to be closed on $*$ if all the elements of $(a, b) *(c, d)=(a+c, b+d)$ belongs to $N \times N$ for $A$ $=\mathrm{N} \times \mathrm{N}$. Let a = 1, b = 3, c = 8, d = 2 $(1,3) *(8,2)=(1+8,3+2)$ $=(9,5) \in N \times N$ Hence A is closed for *. (ii) For commutat...
Read More →Let Q be the set of all rational numbers. Define an operation on
Question: Let $\mathrm{Q}$ be the set of all rational numbers. Define an operation on $\mathrm{Q}-\{-1\}$ by $\mathrm{a} * \mathrm{~b}=\mathrm{a}+\mathrm{b}+\mathrm{ab}$. Show that (i) $*$ is a binary operation on $\mathrm{Q}-\{-1\}$, (ii) * is Commutative, (iii) * is associative, (iv) zero is the identity element in $\mathrm{Q}-\{-1\}$ for $*$, Solution: (i) $*$ is an operation as $\mathrm{a}^{*} \mathrm{~b}=\mathrm{a}+\mathrm{b}+\mathrm{ab}$ where $\mathrm{a}, \mathrm{b} \in \mathrm{Q}-\{-1\}$...
Read More →Evaluate the following integral:
Question: Evaluate the following integral: $\int \frac{\mathrm{ax}^{2}+\mathrm{bx}+\mathrm{c}}{(\mathrm{x}-\mathrm{a})(\mathrm{x}-\mathrm{b})(\mathrm{x}-\mathrm{c})} \mathrm{dx}$, where $\mathrm{a}, \mathrm{b}, \mathrm{c}$ are distinct. Solution: Denominator is factorised, so let separate the fraction through partial fraction, hence let $\frac{\mathrm{ax}^{2}+\mathrm{bx}+\mathrm{c}}{(\mathrm{x}-\mathrm{a})(\mathrm{x}-\mathrm{b})(\mathrm{x}-\mathrm{c})}=\frac{\mathrm{A}}{(\mathrm{x}-\mathrm{a})}+...
Read More →How do you explain the presence
Question: How do you explain the presence of an aldehydic group in a glucose molecule? Solution: Glucose can be treated with bromine water, which undergoes mild oxidation to give the carboxylic acid gluconic acid, which confirms the presence of an aldehyde group....
Read More →The activation energy for the acid catalysed
Question: The activation energy for the acid catalysed hydrolysis of sucrose is 6.22 kJ mol1, while the activation energy is only 2.15 kJ mol1 when hydrolysis is catalyzed by the enzyme sucrase. Explain. Solution: Mainly the enzymes are biocatalyst which provides an alternative path to reduce the reactions activation energy. Using enzyme sucrase, the hydrolysis of sucrose is much faster than conventional acidic hydrolysis....
Read More →Protein found in a biological system with
Question: Protein found in a biological system with a unique three-dimensional structure and biological activity is called a native protein. When a protein in its native form, is subjected to a physical change like change in temperature or a chemical change like change in pH, denaturation of protein takes place. Explain the cause. Solution: The amino acid residues of proteins are joined by hydrogen bonds and various other intermolecular forces. On physical or chemical change, the hydrogen bonds ...
Read More →Structures of glycine and alanine
Question: Structures of glycine and alanine are given below. Show the peptide linkage in glycylalanine. Solution: The hydroxyl group of glycine is linked to the amine group of alanine by peptide (-CONH) linkage to form glycylalanine....
Read More →Amino acids behave like salts rather
Question: Amino acids behave like salts rather than simple amines or carboxylic acids. Explain. Solution: An amino acid contains an NH2 group as well as COOH. In aqueous solution of the amino acid, the COOH group loses a proton [H]+ and the NH2 gains a proton to form a zwitterion which is a salt....
Read More →Sucrose is dextrorotatory but the mixture
Question: Sucrose is dextrorotatory but the mixture obtained after hydrolysis is laevorotatory. Explain. Solution: Sucrose is dextrorotatory in its aqueous solution and rotates plane-polarized light entering the solution 66.5 to the right. When sucrose is hydrolysed with dilute acids or invertase enzyme, it gives two products in equimolar concentration, dextrorotatory D-(+)-glucose and laevorotatory D-(-)-fructose. Thus, hydrolysis of sucrose brings about a change in the sign of rotation, from D...
Read More →Why must vitamin C be supplied
Question: Why must vitamin C be supplied regularly in diet? Solution: Vitamin C is a water-soluble vitamin, and hence the excess is excreted regularly from the body. Since it cannot be stored in the body, vitamin C must be supplied regularly in the diet....
Read More →Why does compound (A)
Question: Why does compound (A) give below not form an oxime? Solution: The given compound is glucose pentaacetate. Glucose contains a free C=O group, and formation of oxime from glucose confirms the presence of a free carbonyl group. The given compound does not have a free carbonyl group and thus does not form an oxime on reaction with hydroxylamine....
Read More →How do you explain the presence
Question: How do you explain the presence of five OH groups in the glucose molecule? Solution: When glucose is treated with acetic anhydride (CH3CO)2O, in the presence of ZnCl2, it undergoes acetylation to form glucose pentaacetate which confirms the presence of five OH groups....
Read More →During curdling of milk,
Question: During curdling of milk, what happens to sugar present in it? Solution: During curdling of milk, which is caused due to bacteria, the sugar present in milk lactose, is converted to lactic acid....
Read More →Let Q+ be the set of all positive rational numbers.
Question: Let $\mathrm{Q}^{+}$be the set of all positive rational numbers. (i) Show that the operation $*$ on $\mathrm{Q}^{+}$defined by $\mathrm{a} * \mathrm{~b}=\frac{1}{2}(\mathrm{a}+\mathrm{b})$ is a binary operation. (ii) Show that $*$ is commutative. (iii) Show that * is not associative. Solution: (i) $*$ is an operation as $a^{*} b=\frac{1}{2}(a+b)$ where $a, b \in Q^{+} .$Let $a=1$ and $b=2$ two integers. $\mathrm{a}^{*} \mathrm{~b}=\frac{1}{2}(1+2) \Rightarrow \frac{3}{2} \in \mathrm{Q}...
Read More →Some enzymes are named after the reaction,
Question: Some enzymes are named after the reaction, where they are used. What name is given to the class of enzymes which catalyse the oxidation of one substrate with simultaneous reduction of another substrate? Solution: The name given to the class of enzymes which catalyse redox reactions is known as enzyme oxidoreductases. An example is Alcohol Dehydrogenase, which helps in reducing alcohol levels in the human body when alcohol is ingested....
Read More →α-Helix is a secondary structure of proteins
Question: -Helix is a secondary structure of proteins formed by twisting of the polypeptide chain into right-handed screw-like structures. Which type of interactions is responsible for making the a-helix structure stable? Solution: A stable -Helix is formed as a right-handed screw helix structure as the NH group of each amino acid residue hydrogen is bonded to the C=O of an adjacent turn of the helix....
Read More →Amino acids can be classified as α-, β-, -, δ- and
Question: Amino acids can be classified as -, -, -, - and so on depending upon the relative position of the amino group concerning the carboxyl group. Which type of amino acids forms polypeptide chain in proteins? Solution: -amino acids, alpha-amino acids, where the amino acid is linked to the -carbon in the molecule are the type of amino acids which form a polypeptide chain....
Read More →Which sugar is called invert sugar?
Question: Which sugar is called invert sugar? Why is it called so? Solution: Sucrose is also known as invert sugar. It is a naturally occurring sugar derived from sugarcane and sugarbeet. The hydrolysis of sucrose brings about a change in the sign of rotation, from Dextro (+) to laevo () and thus the product is named as invert sugar....
Read More →Aldopentoses named as ribose
Question: Aldopentoses named as ribose and 2-deoxyribose are found in nucleic acids. What is their relative configuration? Solution: The configuration of both the aldopentoses is D-configuration. Ribose is named -D-ribose and 2-deoxyribose is -D-2-deoxyribose....
Read More →On the set Q+ of all positive rational numbers, define an operation
Question: On the set $\mathrm{Q}^{+}$of all positive rational numbers, define an operation $*$ on $\mathrm{Q}^{+}$by $\mathrm{a} * \mathrm{~b}=\frac{\mathrm{ab}}{2}$ for all $\mathrm{a}$, $\mathrm{b} \in \mathrm{Q}^{+}$. Show that (i) $*$ is a binary operation on $\mathrm{Q}^{+}$, (ii) $*$ is commutative, (iii) * is associative. Find the identity element in $\mathrm{Q}^{+}$for $*$. What is the inverse of $\mathrm{a} \in \mathrm{Q}^{+}$? Solution: (i) $*$ is an operation as $\mathrm{a}^{*} \mathr...
Read More →