# Current Affairs 11th Class

#### Notes - Mathematics Olympiads - Matrices and Determinant

Matrices and Determinant   Key Points to Remember
• Matrices & Determinant
Let us consider the linear equation   ${{a}_{1}}x+{{b}_{1}}y={{c}_{1}}$                                    (i) ${{a}_{2}}x+{{b}_{2}}y={{c}_{2}}$                                    (ii)   We have one of the methods to solve these equation by cross multiplication method.   $\frac{x}{{{b}_{1}}{{c}_{2}}-{{b}_{2}}{{c}_{1}}}=\frac{y}{{{c}_{1}}{{a}_{2}}-{{c}_{2}}{{a}_{1}}}=\frac{1}{{{a}_{1}}{{b}_{2}}-{{a}_{2}}{{b}_{1}}}$   Now we modify this method & convert this method into standard form (matrix form)
• Matrix: Actually it is the shorthend of mathematics. It is an operator as addition, multiplication etc. Every matrix has come into existence through the solution of linear equations.
Given linear equation can be solved by matrix method & it is written as, $AX=B$
• Definition: It is the arrangement of mn things into horizontal (row) vertical (column) wise.
Generally matrix is represented by [ ] (square bracket) or ( ) etc.   Generally, it is represented as $A=[{{a}_{ij}}]$          $i=1,\,2,\,3,....m$                                     $j=1,\,2,\,3,....n$             Here subscript i denotes no. of row. & subsrcipt j determines no. of column. & ${{a}_{ij}}\to$ represent the position of element a in the given matrix e.g. $A=[{{a}_{ij}}]$ & if         $i\le 3$ and       $i\le 2$
• Order of Matrix: It is the symbol which represent how many rows and columns the matrixs has. In the above example,
Order of matrix $A=3\times 2$ in which 3 determine number of row & 2 determine no. of column of given matrix.
• Operation of Matrix

• Subtraction of matrix
• Multiplication of matrix
• Inverse of matrixes.
•
Let $A={{[{{a}_{ij}}]}_{m\times n}}$ & $B={{[{{b}_{ij}}]}_{m\times n}}$ be two matrices, having same order. Then $A+B$ or $B+A$ is a matrix whose elements be formed through corresponding addition of elements of two given matrices   $A+B=B+A$               Similarly for subtraction operation, we can subtracted two matrices. But $A-B\ne B-A$ i.e. $A-B=-(B-A)$   Note: For addition or substraction operation of two or more than two matrices. They (given matrix) should be the same order.
• Multiplication operation: Let $A={{[{{a}_{ij}}]}_{m\times \text{K}}}$ is a matrix of mx k order & $B={{[{{a}_{ij}}]}_{\text{K}\times \text{P}}}$ is a matrix of $\text{k}\times p$ order.
For multiplication of two matrices, no. of column of 1st matrix should be equal to no. of row of 2nd matrix. Otherwise multiplication of two matrix does not hold. Then   $A\times B-[{{c}_{ij}}]$be a matrix whose order will be$m\times p$.   e.g.       $A={{\left[ \xrightarrow[2\,\,\,\,\,\,\,\,\,2\,\,\,\,\,\,\,1]{2\,\,\,\,\,\,\,\,\,1\,\,\,\,\,\,\,\,3} \right]}_{2\times 3}}$     $\therefore \,\,\,A\times B$         more...

#### Notes - Mathematics Olympiads - Three Dimensional Plane

Three Dimensional Plane   In three dimensional Geometry, it is not a new geometry though it is the refined or extension form of the two dimension geometry. In 3-dimensional geometry. Three axes i.e. x-axis, y-axis and z-axis are perpendicular to each other is considered. Let $X'OX',Y'OY$ & $Z'OZ$ be three mutually perpendicular lines which be intersect at 0. It is called origin.                                   $X'OX\xrightarrow{{}}x-axis$   $Y'OY\xrightarrow{{}}y-axis$   $Z'OZ\xrightarrow{{}}z-axis$   Plane XOY is called xy plane YOZ is called yz plane and ZOX is called zx plane In 3-D, there are 8 quadrents Equation of x-axis be y= 0 & z =0 Equation of y-axis be x = 0 & z = 0 and equation of z-axis be x=0 & y=0   Note: In 3-D, a straight line is represented by two equations where as a plane is represented by single equation in at most three variables.
• Some basic formula which are used in 3-dimension. The distance between points $A({{x}_{1}},\,{{y}_{1}},\,{{z}_{1}})$ and $B({{x}_{1}},\,{{y}_{2}},\,{{z}_{3}})$be
$AB=\sqrt{{{({{x}_{2}}-{{x}_{1}})}^{2}}+{{({{y}_{2}}-{{y}_{1}})}^{2}}+{{({{z}_{2}}-{{z}_{1}})}^{2}}}$   e.g. Let two points are A (2, 3, 1) & B = (- 5, 2-1)               $\therefore \,\,\,\,AB=\sqrt{{{(-5-2)}^{2}}+{{(2-3)}^{2}}+{{(-1-1)}^{2}}}$               $=\sqrt{49+5}=\sqrt{54}$
• Section Formula: The coordinate of the point P dividing the line joining $A({{x}_{1}},\,{{y}_{1}},\,{{z}_{1}})$ & $({{x}_{2}},\,{{y}_{2}},\,{{z}_{2}})$ in the ratio m:n internally are
$P=\left( \frac{m{{x}_{2}}+n{{x}_{1}}}{m+n},\frac{m{{y}_{2}}+n{{y}_{1}}}{m+n},\frac{m{{z}_{2}}+n{{z}_{1}}}{m+n} \right)$   The co-ordinate of the point P dividing the line joining $A({{x}_{1}},\,{{y}_{1}},\,{{z}_{1}})$ and $({{x}_{2}},\,{{y}_{2}},\,{{z}_{2}})$ in the ratio m:n externally are                         $P=\left( \frac{m{{x}_{2}}-n{{x}_{1}}}{m-n},\frac{m{{y}_{2}}-n{{y}_{1}}}{m-n},\frac{m{{z}_{2}}-n{{z}_{1}}}{m-n} \right)$   Midpoint of AB be               $P=\left( \frac{{{x}_{1}}+{{x}_{2}}}{2},\frac{{{y}_{1}}+{{y}_{2}}}{2},\frac{{{z}_{1}}+{{z}_{2}}}{2} \right).$   e.g.       Find the co-ordinate of the point which divides the line segment joining the point (-2, 3, 5) & (1, - 4, 6) in the ratio (i) 2: 3 internally (ii) 2:3 externally.   Sol.      Here, Let A= (-2, 3, 5) & B= (1, -4, 6) and m:n =2:3 internally Let P divides AB in the ratio m: n internally                                     $\therefore \,\,\,P=\left( \frac{m{{x}_{2}}+n{{x}_{1}}}{m+n},\frac{m{{y}_{2}}+n{{y}_{1}}}{m+n},\frac{m{{z}_{2}}+m{{z}_{1}}}{m+n} \right)$               $=\left( \frac{2.1+3(-2)}{2+3},\frac{2(-4)+3.3}{2+3},\frac{2\times 6-3\times 5}{2+3} \right)$               $=\left( \frac{-4}{5},\frac{1}{5},\frac{27}{5} \right)$   When P divides AB in the ratio m : n externally                                     $\therefore \,\,\,P=\left( \frac{2.1-3(-2)}{2-3},\frac{2(-4)-3.3}{2-3},\frac{2\times 6-3\times 5}{2-3} \right)$               $P=(-8,+17,3).$
• Controid of triangle: The co-ordinate of the centroid of the triangle ABC, whose vertices are
$A({{x}_{1}},\,{{y}_{1}},\,{{z}_{1}}),$ $B({{x}_{2}},\,{{y}_{2}},\,{{z}_{2}}),$ & $C({{x}_{2}},\,{{y}_{2}},\,{{z}_{3}}),$ are   $\left( \frac{{{x}_{1}}+{{x}_{2}}+{{x}_{3}}}{3},\frac{{{y}_{1}}+{{y}_{2}}+{{y}_{3}}}{3},\frac{{{z}_{1}}+{{z}_{2}}+{{z}_{3}}}{3} \right)$
• Centroid of the tetrahedran: If $({{x}_{1}},\,{{y}_{1}},\,{{z}_{1}}),$ $({{x}_{2}},\,{{y}_{2}},\,{{z}_{2}}),$ $({{x}_{3}},\,{{y}_{3}},\,{{z}_{3}})\,a({{x}_{4}},\,{{y}_{4}},\,{{z}_{4}})$ be the vertices of the tetrahedran, then its centroid G is given by
$\left( \frac{{{x}_{1}}+{{x}_{2}}+{{x}_{3}}+{{x}_{4}}}{4},\frac{{{y}_{1}}+{{y}_{2}}+{{y}_{3}}+{{y}_{4}}}{4},\frac{z1+z2+z3+z4}{4} \right)$
• A point R with x-coordinate 4 lies on the segment joining the points $\mathbf{P(2,-3,4)}$ & $\mathbf{Q(8,0,1,0)}\mathbf{.}$
• Find the co-ordinate of the point R.   Sol:      Let $P(2,-3,4)$ and $Q(8,0,1,0).$ Let R divides PQ in the ratio l: 1 internally   $\therefore \,\,\,\,R=\left( \frac{8\lambda +2}{\lambda +1},\frac{0.\lambda +(-3)}{\lambda +1},\frac{10\lambda +1\times 4}{\lambda +1} \right)$…………  (1) Here x co-ordinate =4 more...

#### Notes - Mathematics Olympiads - Probability

Probability
• Probability: Actually, Probability is the mathematical modelling of chances or outcome of the events. In other, it is the branch of mathematics in which we study the occurrence of any element in the numerically form. It always lies between 0 & 1.
i.e.        $0\le P(E)\le 1$ Where P (E) = Probability of occurrence of the event E.
• Some basic terms and its concepts
Random experiment of Trial: An experiment of event or trial of event does not follow any rule of system is said to be random experiments, e.g. throwing a dice in which one of {1, 2, 3, 4, 5, 6} will be occurred. We cannot predict that in it throwing if integer 4 is occurred then the next throwing dice. 3 or 4 or any certain number will be occurred. It cannot be predicted. It is the random experiment and not to consider, throwing dice follows any rule/system.
• Outcome and Sample Space: A possible result of a random experiment is said to be its outcome/results.

• Sample space: The set of all possible outcome of an experiment is called a sample space.
Generally, it is denoted by S. e.g. when a coin is tossed then, whatever, H (Head) or T (Tale) is occurred, i.e. S = {H,T}.
• Event: An event is the subset of the sample space.
• g. when a dice is thrown the 6 is appeared then i.e. the occurrence of 6 is an event. In other word
To throw a dice then Sample space S = {1, 2, 3, 4, 5, 6} and an event E = {6}.   Note:    Here, we will study the probability which is based on set theory.
• Probability of an event: Here, we will define the probability into two ways:
• Mathematical (or a priori) definition
• Statistical (or empirical) definition.
•
• Mathematical definition of Probability: Probability of an event A, denoted as P(A), is defined as P(A)
$=\frac{Number\,\,of\,\,cases\,\,favourable\,\,to\,\,A}{Number\,\,of\,possible\,\,outcome}$   e.g.       To throw a dice, what is the probability of occurrence of even numbers. Usually, someone can ask this type of question. Then Sample Space, S = {1, 2, 3, 4, 5, 6} E = event of occurrence of even numbers = {2, 4, 6} n(S) = total o. of element/member of sample space = 6 n (E) = no. of element of event = 3 So, P (E) = Probability of occurrence of even no.             $=\frac{n(E)}{n(S)}=\frac{3}{6}=\frac{1}{2}$
• A coin is tossed once, what are the all possible outcome? What is the probability of the coin coming of tails?
•   Sol.      When, a coin is tossed, as usually, head (H) or Tail (T) can be appeared, i.e. Net consider sample other things that coin will be standard strictly. Only we have to think fruitfully more...

#### Notes - Mathematics Olympiads - Statistics

Statistics   Statistics history is very old. Early statistics is considered as the imposed form of applied mathematics.
• Statistics is used as singular and plural: Statistics used as singlular. It is the science in which we collect, analysis, interprete the data.

• Statistics used as plural
(i)         Statistics are aggregate of facts. (ii)        Statistics are affected by a number of factors. (iii)       Statistics are collected in systematic manner. (iv)       Statistics must be reasonable accurate. It is both art and science.
• Science: Systematised body of knowledge is said to be science.
• Art: Handling of the fact of given information to skill up the knowledge about the matter is said to be art.
Note: Statistics without science has no fruit and science without statistics has no roots.   Measure of Central Tendency
• Central Tendency: The properties of finding and the average value of the data is said to Central Tendency.
The commanly used measure of central tendency are:   (a) Arithmetic Mean                                (b) Geometric Mean (c) harmonic Mean                                 (d) Median (e) Mode
• Arithmetic Mean: Mean of unclassified/Raw data/Individual
Let ${{x}_{1}},\,{{x}_{2}},\,{{x}_{3}}.....{{x}_{n}}$ are n observations. Then their arithmetic mean is written as             $\overline{x}=\frac{x1+x2+x3+....xn}{n}=\frac{1}{n}.\sum\limits_{i=1}^{n}{xi}$             $=\frac{Sum\,\,o\text{f}\,\,\text{observations}}{no.\,\,o\text{f}\,\,\text{observations}}$
• Mean of Classified Data: Let ${{x}_{1}},\,{{x}_{2}},\,{{x}_{3}},\,{{x}_{4}},....{{x}_{n}}$ and let ${{\text{f}}_{1}},\,{{\text{f}}_{2}},\,{{\text{f}}_{3}},....{{\text{f}}_{n}}$ are their corresponding frequencies. Then
$\overline{x}=\frac{\sum{\text{f}\text{.x}}}{\sum{\text{f}}}$   Weighted Arithmetic Mean: If ${{w}_{1}},\,{{w}_{2}},\,{{w}_{3}},\,......{{w}_{n}}$ are the weights assigned to the values ${{x}_{1}},\,{{x}_{2}},\,{{x}_{3}},\,{{x}_{4}}\,......{{x}_{n}}$ respectively. Then the weighted average, or weighted               $A.M==\frac{{{w}_{1}}{{x}_{1}}+{{w}_{2}}{{x}_{2}}+{{w}_{3}}{{x}_{3}}+......{{w}_{n}}{{x}_{n}}}{{{w}_{1}}+{{w}_{2}}+{{w}_{3}}+.....{{w}_{n}}}$
• Combined Mean: If we are given the A.M. of two data sets and their sizes, then the combined
A.M of two data sets can be obtained as.             ${{\overline{x}}_{12}}=\frac{{{n}_{1}}{{\overline{x}}_{1}}+{{n}_{2}}{{\overline{x}}_{2}}}{{{n}_{1}}+{{n}_{2}}}$   Where, ${{\overline{x}}_{12}}=$ combined mean of the two data sets 1 and 2 0 Mean of 1st data ${{\overline{x}}_{2}}=$Mean of the 2nd data ${{n}_{1}}=$size of the 1st data. ${{n}_{2}}=$size of the 2nd data. Some properties about A.M. In statistical data, sum of the deviation of individual values from A.M. is always zero.             i.e.        $\sum\limits_{i=1}^{n}{\text{f}i}({{x}_{1}}-\overline{x})=0$   Where $\text{f}i=$ frequencies of $xi\,\,\{1\le i\le n\}$ A.M is written s             $A.M\,\,=\overline{x}=\frac{{{x}_{1}}{{\text{f}}_{\text{1}}}+{{x}_{2}}{{\text{f}}_{2}}+...{{x}_{n}}{{\text{f}}_{n}}}{{{\text{f}}_{1}}+{{\text{f}}_{2}}+{{\text{f}}_{3}}+....{{\text{f}}_{n}}}=\frac{\sum\limits_{i=1}^{n}{{{\text{f}}_{i}}{{x}_{i}}}}{\sum\limits_{i=1}^{n}{\text{f}i}}$
• Short-cut Method: For a given data, we suitably choose a term, usually the middle term and call it the assumed mean, to be denoted by A.
Then, we find deviation, ${{d}_{i}}=({{x}_{i}}-A)$ for each term. Thus $A.M=\overline{x}=A+\frac{\sum{{{\text{f}}_{i}}{{d}_{i}}}}{{{\text{f}}_{i}}}$   where A = Assumed Mean, f = frequency
• Step-Deviation: $A.M,\,\,\overline{x}=A+\frac{\Sigma {{\text{f}}_{i}}{{d}_{i}}}{N}\times h$
Where A = Assumed mean   ${{d}_{i}}=\frac{{{x}_{i}}-A}{h}=$deviation of any variate from A   h = width of the class-interval and $N=\Sigma {{\text{f}}_{i}}$ In a statistical date, the sum of square of deviations of individual values from A.M. is least.   i.e.        $\sum\limits_{i=1}^{n}{\text{f}i{{(x-\overline{x})}^{2}}=}$ least value             If each of the given observation is doubled then their arithmetic mean is doubled If more...

#### Nucleic Acids

Nucleic acids are the polymers of nucleotide made up of carbon, hydrogen, oxygen, nitrogen and phosphorus and which controls the basic functions of the cell. These were first reported by Friedrich Miescher (1871) from the nucleus of pus cell. Altmann called it first time as nucleic acid. Nuclein was renamed nucleic acid by Altman in (1889). They are found in nucleus. They help in transfer of genetic information. Types of nucleic acids : On the basis of nucleotides i.e., sugars, phosphates and nitrogenous bases, nucleic acids are of two types which are further subdivided. These are DNA (Deoxyribonucleic acid) and RNA (Ribonucleic acid). (1) DNA (Deoxyribonucleic acids) : Term DNA was given by Zacharis.  (i) Types of DNA : It may be linear or circular in eukaryotes and prokaryotes respectively. Palindromic DNA : The DNA helix bears nucleotide in a serial arrangement but opposite in two strands. $-T-T-A-A-C-G-T-T-A-A.......$ $-A-A-T-T-G-C-A-A-T-T......$ Repetitive DNA : This type of arrangement is found near centromere of chromosome and is inert in RNA synthesis. The sequence of nitrogenous bases is repeated several times. Satellite DNA : It may have base pairs up to $160\,\,bp$and are repetitive in nature. Microsatellite has $16\,\,bp$and minisatellite has $1160\,\,bp.$ They are used in DNA matching or finger printing (Jefferey). In eukaryotes, DNA is deutrorotatory and sugars have pyranose configuration. (ii) Chargaff’s rule : Quantitatively the ratio of adenine (A) to thymine (T) and guanine (G) to cytosine (C) is equal. i.e., “Purines are always equal to pyrimidine”. (iii) C value : It is the total amount of DNA in a genome or haploid set of chromosomes. (iv) Sense and Antisense strand : Out of two DNA strand one which carries genetic information in its cistrons is called sense strand while the other strand does not carry genetic information, therefore, doesn’t produce mRNA. The non-functional DNA strand is called antisense strand. (v) Heteroduplex DNA : Hybrid DNA formed as a result of recombination is called heteroduplex DNA. It contains mismatched base pair of heterologous base sequence. X-Ray crystallography study of DNA : It was done by Wilkins. It shows that the two polynucleotide chains of DNA show helical configuration. Single stranded DNA (ssDNA) : It is single helixed circular. And isolated from bacteriophage $\phi \times 174$ by Sinsheimer (1959). It does not follow chargaff’s rule. The replicative form (RF) has plus – minus DNA helix. e.g., parvovirus. Double helical model of DNA: It is also known as Watson and Crick model. (2) RNA or Ribonucleic acid : RNA is second type of nucleic acid which is found in nucleus as well as in cytoplasm i.e., mitochondria, plastids, ribosomes etc. They carry the genetic information in some viruses. They are widely distributed in the cell. Genomic RNA was discovered by Franklin and Conrat (1957).

#### Cell Division / Cell Reproduction / Cell Cycle

It is the process by which a mature cell divides and forms two nearly equal daughter cells which resemble the parental cell in a number of characters. In unicellular organisms, cell division is the means of reproduction by which the mother cell produces two or more new cells. In multicellular organism also, new individual develop from a single cell. Cell division is central to life of all cell and is essential for the perpetuation of the species. Discovery : Prevost and Dumans (1824) first to study cell division during the cleavage of zygote of frog. Nagelli (1846) first to propose that new cells are formed by the division of pre-existing cells. Rudolf Virchow (1859) proposed “omnis cellula e cellula” and “cell lineage theory”. A cell divides when it has grown to a certain maximum size which disturb the karyoplasmic index (KI)/Nucleoplasmic ratio (NP)/Kernplasm connection. Cell cycle : Howard and Pelc (1953) first time described it. The sequence of events which occur during cell growth and cell division are collectively called cell cycle. Cell cycle completes in two steps: (1) Interphase,                  (2) M-phase/Dividing phase (1) Interphase : It is the period between the end of one cell division to the beginning of next cell division. It is also called resting phase or not dividing phase. But, it is actually highly metabolic active phase, in which cell prepares itself for next cell division. In case of human beings it will take approx 25 hours. Interphase is completed in to three successive stages. G1 phase/Post mitotic/Pre-DNA synthetic phase/gap Ist : In which following events take place. (i) Intensive cellular synthesis. (ii) Synthesis of rRNA, mRNA ribosomes and proteins. (iii) Metabolic rate is high. (iv) Cells become differentiated. (v) Synthesis of enzymes and ATP storage. (vi) Cell size increases. (vii) Decision for a division in a cell occurs. (viii) Substances of G stimulates the onset of next S – phase. (ix) Synthesis of NHC protein, carbohydrates, proteins, lipids. (x) Longest and most variable phase. (xi) Synthesis of enzyme, amino acids, nucleotides etc. but there is no change in DNA amount. S-phase/Synthetic phase (i) DNA replicates and its amount becomes double $(2C-4C).$ (ii) Synthesis of histone proteins and NHC (non-histone chromosomal proteins). (iii) Euchromatin replicates earlier than heterochromatin. (iv) Each chromosome has 2 chromatids. G2-phase/Pre mitotic/Post synthetic phase/gap-IInd (i) Mitotic spindle protein (tubulin) synthesis begins. (ii) Chromosome condensation factor appears. (iii) Synthesis of 3 types of RNA, NHC proteins, and ATP mole. (iv) Duplication of mitochondria, plastids and other cellular macromolecular complements. (v) Damaged DNA repair occur. (2) M-phase/Dividing phase/Mitotic phase : It is divided in to two phases, karyokinesis and cytokinesis.      Duration of cell cycle : Time period for ${{G}_{1}},S,{{G}_{2}}$ and M-phase is species specific under specific environmental conditions. e.g., 20 minutes for bacterial cell, 8-10 hours for intestinal epithelial cell, and onion root tip cells may take 20 hours. ${{\mathbf{G}}_{\mathbf{0}}}\mathbf{-}$phase (Lajtha, 1963) : The cells, which are not to divide further, do more...

#### Metabolically Inactive Cell Inclusions

Within the cytoplasm of a cell there occur many different kinds of non-living structures which are called inclusions or ergastic / Deutoplasmic substances. (1) Vacuoles : The vacuole in plants was discovered by Spallanzani. It is a non-living reservoir, bounded by a differentially or selectively permeable membrane, the tonoplast. The vacuole is filled with cell sap or tonoplasm. They contain water, minerals and anthocyanin pigments. Some protozoans have contractile vacuoles which enlarge by accumulation of fluid or collapse by expelling them from the cell. The vacuoles may be sap vacuoles, contractile vacuoles or gas vacuoles (pseudo vacuoles). Function of vacuoles : Vacuole maintains osmotic relation of cell which is helpful in absorption of water. Turgidity and flaccid stages of a cell are due to the concentrations of sap in the vacuole. (2) Reserve food material The reserve food material may be classified as follows : (i) Carbohydrates : Non-nitrogenous, soluble or non- soluble important reserve food material. Starch cellulose and glycogen are all insoluble. (a) Starch : Found in plants in the form of minute solid grains. Starch grains are of two types : Assimilation starch : It is formed as a result of photosynthesis of chloroplasts. Reserve starch : Thick layers are deposited around an organic centre called hilum. (b) Glycogen : Glycogen or animal starch occurs only in colourless plants like fungi. (c) Inulin : It is a complex type of polysaccharide, soluble and found dissolved in cell sap of roots of Dahlia, Jaruslem, Artichoke, Dandelion and members of compositae. (d) Sugars : A number of sugars are found in solution of cell sap. These include glucose, fructose, sucrose, etc. (e) Cellulose : Chemical formula is ${{({{C}_{6}}{{H}_{10}}{{O}_{5}})}_{n}}.$The cell wall is made up of cellulose. It is insoluble in water. (ii) Fats and Oils : These are important reserve food material. These are always decomposed into glycerol and fatty acids by enzymatic action. Fat is usually abundant in cotyledons than in the endosperm. e.g., flax seed produce linseed oil, castor produce castor oil, cotton seeds produce cottonseed oil, etc. (iii) Proteins and Amides (Aleurone grains) : Storage organ usually contain protein in the form of crystalline bodies known as crystalloids (potato). Proteins may be in the form of aleurone grains as in pea, maize, castor, wheat, etc. (3) Excretory Products : The organic waste products of plants are by-product of metabolism. They are classified as : (i) Resins : They are believed to be aromatic compounds consisting of carbon, hydrogen and oxygen and are acidic in nature. Sometimes they are found in combination with gums and are called gum resin. e.g., Asafoetida (heeng). (ii) Tannins : They are complex nitrogenous compounds of acid nature having an astringent taste. Presence of tannin in plants makes its wood hard durable and germ proof. (iii) Alkaloids : These are organic, basic, nitrogenous substance. They occur in combination with organic acids and most of them are poisonous. From plants, cocaine, hyoscine, morphine, nicotine, quinine, atropine, strychnine and daturine etc. are extracted. (iv) Glucosides more...

#### Nucleus

The nucleus also called director of the cell. It is the most important part of the cell which directs and controls all the cellular function. Discovery : The nucleus was first observed by Robert Brown (1831), in orchid root cells. Nucleus plays determinative (in heredity) role in cell and organism, that was experimentally demonstrated by Hammerling (1934) in surgical experiments with green marine unicelled algae Acetabularia. Occurence : A true nucleus with definite nuclear membrane and linear chromosome, is present in all the eukaryotes except mature mammalian RBCs, sieve tube cell of phloem, tracheids and vessels of xylem. The prokaryotes have an incipient nucleus, called nucleoid or prokaryon or genophore or false nucleus. Number : Usually there is a single nucleus per cell i.e., mononucleate condition, e.g., Acetabularia. (1) Anucleate (without nucleus) : RBCs of mammals, phloem sieve tube, trachids and vessels of xylam. (2) Binucleate : e.g., Ciliate, Protozoans like Paramecium. (3) Polynucleate : e.g., fungal hyphae of Rhizopus, Vaucheria. Polynucleate condition may be because of fusion of a number of cells. i.e., syncytium, coconut endosperm or by free nuclear divisions without cytokinesis i.e., coenocyte. Shape : It varies widely, generally spherical e.g., cuboidal germ cells, oval e.g., columnar cells of intestine, bean shaped  in paramecium, horse-shoe shaped in Vorticella, bilobed, e.g., WBCs (acidophils), 3 lobed e.g., basophil, multilobed e.g., neutrophils, long and beaded form (moniliform) e.g., stentor and branched in silk spinning cells of platy phalyx insect larva. Size : The size of nucleus is variable i.e., $530\mu .$ In metabolically active cells size of the nucleus is larger than metabolically inactive cells. Chemical composition Proteins $=80%,\text{ }DNA=12%,\text{ }RNA=5%,\text{ }Lipids=3%$ Enzymes like polymerases are abundantly present and help in synthesis of DNA and RNA. Ultrastructure : The nucleus is composed of following structure. (1) Nuclear membrane : It is also called nuclear envelope or nucleolemma or karyotheca, was first discovered by Erclab (1845). Structure : It is a bilayered envelope. Each membrane is about 60-90Å thick lipoproteinous and trilaminar. Outer membrane, called ectokaryotheca (with ribosome) and inner membrane is called endokaryotheca (without ribosome). Two membranes are separated by a fluid-filled intermembranous perinuclear space (about $100-300{AA}$). Nuclear membrane is porous and has $1,000-10,000$ octagonal nuclear pores. Each nuclear pore is about $400-1,000\text{ }{AA}$ in diameter (average size is $800\text{ }{AA}$). Callan and Tamlin (1950) first to observe nuclear pore in nuclear membrane. The nuclear pares are enclosed by circular structure are called annuli. The pore and annuli together are called pore complex or pore basket.     Origin : It is formed by the fusion of ER elements during the telophase of cell division. Functions (i) It regulates the nucleo-cytoplasmic interactions. (ii) It allows the passage of inorganic ions, small organic molecules, ribosomal subunits, RNAs and proteins through nuclear pores. (iii) It maintains the shape of the nucleus. (2) The nucleolus (Little nucleus plasmosome) : It was first observed by Fontana (1781) in the skin cells of an eel. Bowman (1840) more...

#### Micromolecules

These are molecules of low molecular weight and have higher solubility. These include minerals, water, amino acid, sugars and nucleotides. All molecules or chemicals functional in life activity are called biomolecules. (1) Elements : On the basis of presence and requirement in plants and animals, they are grouped into major $(Ca,P,Na,Mg,S,K,N)$ and minor $(Fe,Cu,Co,Mn,Mo,Zn,I)$ bioelements. On the basis of function, they may be of following types :– (i) Framework elements : Carbon, oxygen and hydrogen. (ii) Protoplasmic elements : Protein, nucleic acid, lipids, chlorophyll, enzymes, etc. (iii) Balancing elements : Ca, Mg and K. (2) Biological compounds (i) Inorganic compounds : Water 80%, inorganic salts 1-3%. (ii) Organic compounds : Carbohydrates (1.0%), Lipids (3.5%), Proteins (12.0%) Nucleotides (2.0%), Other compounds (0.5). (3) Cellular pool : Aggregated and interlinked  various kinds of biomolecules in a living system. So cell is called cellular pool. It includes over 5000 chemicals. Inorganic chemicals are present mostly in aqueous phase while organic in both, aqueous and non-aqueous. Cellular pool comprises of both crystelloid and colloidal particles. Hence called as crystal colloids. (4) Water : Liquid of life, major constituent of cell (about 60-90%) and exists in intracellular, intercellular and in vacuoles. In cells it occurs in free state or bound state (KOH, CaOH etc.). Properties of water : It is colourless, transparent, tastless and odourless, neutral (pH-7) liquid.  It is universal solvent, as it can dissolve both polar and non-polar solutes. High boiling point due to hydrogen bonding. Shows high degree of cohesion and adhesion. It can undergo three states of matter i.e., solid$\rightleftharpoons$liquid$\rightleftharpoons$gas.  It is dense and heaviest at 4C and solid below it. (5) Carbohydrates : e.g., sugars, glycogen (animal starch), plant starch and cellulose. Source of carbohydrate : Mainly photosynthesis. It exists only in 1% but constitutes 80% of the dry weight of plants. Composition : It consists of carbon, hydrogen and oxygen in the ratio ${{C}_{n}}{{H}_{2n}}{{O}_{n}}.$ It is also called saccharide and sugars are their basic components. Classification of carbohydrates are : (i) Monosaccharides : These are single sugar units which can not be hydrolysed furthur into smaller carbohydrates. General formula is ${{C}_{n}}{{H}_{2n}}{{O}_{n}},$e.g., Trioses-3C, (Glyceraldehyde, dihydroxyacetone etc.), tetroses-4C, pentoses-5C, hexoses-6C etc. Important Hexoses Glucose : ${{C}_{6}}{{H}_{12}}{{O}_{6}}.$ Grape sugar is dextrose. Grape is sour due to presence of tartaric acid. Fructose is called fruit sugar (sweetest among natural sugars) and glucose is called "sugar of body" (blood sugar). Normal level of blood glucose is 80-120mg/100ml. If it exceeds then condition is called "glucosuria". Fructose : Occurs naturally in fruit juices and honey. Hydrolysis of cane sugar in body also yields fructose. Galactose : It is called as brain sugar. It's an important constituent of glycolipids and glycoproteins. Properties of monosaccharide
• Monosaccharides are colourless, sweet tasting, solids and show oxidation, esterification and fermentation.
• Due to asymmetric carbon, they exist in different isomeric forms. They can rotate polarized light hence they are dextrorotatory and laevorotatory.
• D-glucose after reduction gives rise to a mixture of polyhydroxy alcohol, sorbitol or mannitol.
• more...

#### Macromolecules

Macromolecules are polymerisation product of micromolecuels, have high molecular weight and low solubility. They include mainly polysaccharide, protein and nucleic acids. (1) Polysaccharide : They are branched or unbranched polymers of monosaccharides jointed by glycosidic bond.  Their general formula is ${{({{C}_{6}}{{H}_{10}}{{O}_{5}})}_{n}}.$ Polysaccharides are amorphous, tasteless and insoluble or only slightly soluble in water and can be easily hydrolysed to monosaccharide units. Types of polysaccharides (i) On the basis of structure Homopolysaccharides : These are made by polymerisation of single kind of monosaccharides. e.g., starch, cellulose, glycogen, etc. Heteropolysaccharide : These are made by condensation of two or more kinds of monosaccharides. e.g., chitin, pectin, etc. (ii) On the basis of functions Food storage polysaccharides : They serve as reserve food. e.g., starch and glycogen. Structural polysaccharides : These take part in structural framework of cell wall e.g., chitin and cellulose. Description of some polysaccharides Glycogen : It is a branched polymer of glucose and contain 30,000 glucose units. It is also called animal starch. It is also found as storage product in blue green algae, slime moulds, fungi and bacteria. It is a non-reducing sugar and gives red colour with iodine. In glycogen, glucose molecule are linked by $14$ glycosidic linkage in straight part and $16$ linkage in the branching part glycogen has branch points about every $8-10$ glucose units. Starch : Starch is formed in photosynthesis and function as energy storing substance. It is found abundantly in rice, wheat, legumes, potato (oval and ecentric shaped), banana, etc. Starch is of two types. Straight chain polysaccharides known as amylose and branched chain as amylopectin. Both composed of $D$glucose units jointed by $\alpha -1-4$ linkage and $\alpha -1-6$ linkage. It is insoluble in water and gives blue colour when treated with iodine. Inulin : Also called “dahlia starch”(found in roots). It has unbranched chain of 30 – 35 fructose units linked by $\beta -2-1$ glycosidic linkage between 1 and 2 of carbon atom of D– fructose unit. Cellulose : An important constituent of cell wall $(2040%),$ made up of unbranched chain of $6000\,\beta D$glucose units linked by 1 – 4 glycosidic linkage. It is fibrous, rigid and insoluble in water. It doesn’t give any colour when treated with iodine. It is a most abundant polysaccharide. Chitin : It is a polyglycol consisting of $N-$acetyl$D$glucosamine units connected with $\beta -1,\,4$ glycosidic linkage. Mostly it is found in hard exoskeleton of insects and crustaceans and some times in fungal cell wall. Second most abundant carbohydrate. It is a most abundant heteropolysaccharide. Agar-Agar : It is a galactan, consisting of both D and L galactose and it is used to prepare bacterial cultures. It is also used as luxative and obtained from cell wall of red algae e.g., Gracilaria, Gelidium etc. Pectin : It is a cell wall material in collenchyma tissue may also be found in fruit pulps, rind of citrus fruits etc. It is water soluble and can undergo sol $\rightleftharpoons$ gel transformation. It contain arabinose, galactose and galacturonic acid. Neutral more...

#### Trending Current Affairs

LIMITED OFFER HURRY UP! OFFER AVAILABLE ON ALL MATERIAL TILL TODAY ONLY!

You need to login to perform this action.
You will be redirected in 3 sec