Plus Two Zoology Chapter Wise Previous Questions Chapter 4 Molecular Basis of Inheritance

Kerala State Board New Syllabus Plus Two Zoology Chapter Wise Previous Questions and Answers Chapter 4 Molecular Basis of Inheritance.

Kerala Plus Two Zoology Chapter Wise Previous Questions Chapter 4 Molecular Basis of Inheritance

Question 1.
Observe the diagram below: (MAY-2010)
Plus Two Zoology Chapter Wise Previous Questions Chapter 4 Molecular Basis of Inheritance 1
Which among the following is the complimentary sequence of the DNA fragment shown above?
a) 5′ -> ATTCG -> 3′
b) 3′ -> ATTCG -> 5′
c) 3′ -> TAAGC -> 5′
d) 3′ -> CGAAT -> 5′
Answer:
3′ -> TAAGC -> 5′

Question 2.
DNA sequence is provided below:   (MAY-2010)
TACGAGTTATATATACAT
a) Write down the triplet codon- it codes for.
b) If a nitrogen base is added in between 4th & 5th nitrogen bases, what will be its effect on transcription?
Answer:
a) AUG / CUC / AAU / AUA / UAU / GUA
OR
TAC / GAG / TTA / TAT / ATA / CAT
b) Frame shift mutation / point mutation/Mutation / Entire amino acid sequence changed / incorrect protein produced / change in protein structure / incorrect transcription and translation /abnormal protein.

Question 3.
In a paternity dispute, the VNTR DNA samples of parent and child were DNA finger printed. The diagrammatic representation of the DNA fingerprint is shown below.  (MAY-2010)
Plus Two Zoology Chapter Wise Previous Questions Chapter 4 Molecular Basis of Inheritance 2
a) What is your opinion about the paternity of child? Substantiate your opinion.
b) List down any four major steps of molecular biological procedures adopted for this.
Answer:
a) Paternity is confirmed
VNTR bands / finger print bands / bands are similar.
b) Steps of DNA finger printing techniques are
i) Isolation of DNA
ii) Digestion of DNA by restriction endo nuclease
iii) Seperation of DNA fragment by Electrophoresis,
iv) Plotting of DNA fragment into Nitro cellulose
v) Ditection of hybridised DNA by Auto radiography

Question 4.
A transcriptional unit is given below. Observe it and answer the questions.  (MARCH-2012)
Plus Two Zoology Chapter Wise Previous Questions Chapter 4 Molecular Basis of Inheritance 3
a) How can you identify the coding strand?
b) Write the sequence of RNA formed from this unit?
c) What would happen if both strands of the DNA act as templates for transcription?
Answer:
a) Coding strand has 5′ end at the promoter or 5’TCAGTACA3′
b) 5′ UCAGUACA 3′
c) The two RNA will be complimentary and may form double stranded RNA and it prevents the translation.

Question 5.
In E.coli lactose catabolism is controlled by Lac operon. Lac operon in the absence of inducer (lactose) is given below. (MARCH-2012)
Plus Two Zoology Chapter Wise Previous Questions Chapter 4 Molecular Basis of Inheritance 4
a) What is ‘P’?
b) Name the enzymes produced by the structural genes ‘Z’, ‘Y’ and ‘a’?
c) Redraw the diagram in the presence of an inducer.
Answer:
a) Promoter
Z-Bgalactosidase
b) Y – Permease
a-Transacetylase
c)
Plus Two Zoology Chapter Wise Previous Questions Chapter 4 Molecular Basis of Inheritance 5

Question 6.
Following are the first two steps in Griffith transformation experiment: (MAY-2012)
1) S strain 2 Inject into mice 2 mice live
2) R strain 2 Inject into mice 2 mice die
a) If there is any mistake correct it.
b) Write the remaining steps.
Answer:
a) 1. S strain -> inject into mice -> mice die
2. R strain inject into mice -> mice live
b) When Griffith was injected heat-killed S strain into mice, bacteria did not kill them. But he injected a mixture of heat-killed S and live R bacteria, the mice died .

Question 7.
DNA is better genetic material than RNA. Do you agree with this statement ? Substantiate. (MAY-2012)
Answer:
The 2-OH group present at the nucleotide in RNA is a reactive group and makes RNA labile and easily degradable. Hence DNA is less reactive and structurally more stable when compared to RNA. Therefore, among the two nucleic acids, the DNA is a better genetic material.

Question 8.
Given below is the diagrammatic representation of first stage of a process in bacteria. (MAY-2012)
Plus Two Zoology Chapter Wise Previous Questions Chapter 4 Molecular Basis of Inheritance 6
a) Identify the process.
b) Name the enzyme catalyses this process.
c) What are the additional complexities in Eukaryotes for this process?
Answer:
a) Prokaryotic transcription
b) RNA polymerase
c) In eukaryotes hnRNA undergo additional processing called as splicing, capping and tailing.
In splicing the introns are removed and exons are joined together. In capping methyl guanosine triphosphate is added to the 5-end of hnRNA. In tailing, adenylate residues are added at 3-end in a template.The fully processed hnRNA, called as mRNA, that is transported out of the nucleus for translation.

Question 9.
The flow of genetic information is shown below. (MARCH-2013)
Plus Two Zoology Chapter Wise Previous Questions Chapter 4 Molecular Basis of Inheritance 7
Name the processes a, b, c
Answer:
a) Replication
b) Transcription
c) Translation
d) Reverse transcription

Question 10.
RNA is not an ideal molecule as genetic material because ________. (MARCH-2013)
a) 2’OH group of ribose is reactive and make it labile
b) It is catalytic and hence reactive
c) Both (a) and (b)
d) None of the above
Answer:
c) Both a and b

Question 11.
Presence of lactose enhances the production of (3 galactosidase and other enzymes in bacteria, how will you explain this phenomenon? (MAY-2013)
Answer:
In lac operon,lactose is the inducer.Inducer binds with repressor protein but repressor cannot bind to op-erator gene,the free operator gene induces the RNA polymerase to bind with promoter and initiates tran-scription Three structural genes synthesise three mRNAs to produce enzymes.

Question 12.
A DNA sequence needed for coding a peptide is given below. (MAY-2013)
CAAGTAAATTGAGGACTC
(Hint: Codons and Aminoacids)
CAAGTAAATTGAGGACTC
UUA-Leu
CCU – Pro
CAU – His
ACU-Thr
GUU-Val
GAG-Glu
a) Write the complementary mRNA coding sequence for this.
b) Find out the amonoacid sequence of the peptide chain using the codons given in the hints.
c) If a mutation cause a change in the sixth codon CTC to CAC. It leads to a mendelian disorder. Identify the disease and write the specific characteristics of the diseasie.
Answer:
a) GUUCAUUUAACUCCUGAG
b) Val,His,Leu,Thr,Pro,Glu
c) Sickle cell anaemia, RBC become sickle shaped and unable to take oxygen .These are destroyed more rapidly leading to anaemia.

Question 13.
Draw a flow chart showing the steps of southern blot hybridization using radio labelled VNTR. (MAY-2013)
Answer:
Plus Two Zoology Chapter Wise Previous Questions Chapter 4 Molecular Basis of Inheritance 8

Question 14.
“Prediction of the sequence of amino acids from the nucleotide sequence in mRNA is very easy, but the exact prediction of the nucleotide sequence in m RNA from the sequence of amino aids coded by mRNA is difficult”.(MARCH-2014)
a) Which properties of the genetic code is the reason for the above condition? Explain.
b) Which are the stop codons in DNA replication?
Answer:
a) Degeneracy – A single aminoacid is represented by many codons (degenerate codons)
b) Stop codons are UAA,UAG,UGA

Question 15.
Diagrammatic representation of Central dogma’ is given below: Observe the diagram carefully and redraw it making appropriate corrections. (MARCH-2014)
Plus Two Zoology Chapter Wise Previous Questions Chapter 4 Molecular Basis of Inheritance 9
Answer:
Plus Two Zoology Chapter Wise Previous Questions Chapter 4 Molecular Basis of Inheritance 10

Question 16.
Explain the phenomenon shown in the following figure and the reason for difference in the production of  II recombinants in Cross A and Cross B as explained by morgan. (MARCH-2014)
Plus Two Zoology Chapter Wise Previous Questions Chapter 4 Molecular Basis of Inheritance 11
Difference in chromosome number of some human beings A, B. C and D are given below:
A) 22 pairs of Autosomes
B) 22 pairs of Autosomes+XO
C) 22 pairs of Autosomes + 1 Autosome
D) 22 pairs of Autosomes+XXY
OR
a) Identify the person who suffers from Klinefelter’s syndrome. Write its symptoms.
b) Differentiate between aneuploidy and polyploidy.
Answer:
The percentage of cross over depends upon the distance between the genes.
The genes are closer in cross A,so the less number of recombinants are produced. This is called link-age.
In cross B, genes are distantly located so more number of recombinants are produced.
OR
a) 22 pairs of autosomes+XXY, Sterile male, poorly developed testis and mental retardation
b) Aneuploidy-failure of separation of chromosomes during cell division results in-the gain or loss of chromosome.
Polyploidy – Failure of cytokinesis aftertelophase results in the increase in a whole set of chromosome

Question 17.
Correct the amino acid sequence of sickle cell haemoglobin. (MAY-2014)
Plus Two Zoology Chapter Wise Previous Questions Chapter 4 Molecular Basis of Inheritance 12
Answer:
Plus Two Zoology Chapter Wise Previous Questions Chapter 4 Molecular Basis of Inheritance 13

Question 18.
Diagram of components of DNA are given below: Identify and differentiate the two diagrams I and II. (MAY-2014)
Plus Two Zoology Chapter Wise Previous Questions Chapter 4 Molecular Basis of Inheritance 14
Answer:
I- Nucleotide II- Nucleoside

Question 19.
a) Identify the diagram and explain. (MAY-2014)
Plus Two Zoology Chapter Wise Previous Questions Chapter 4 Molecular Basis of Inheritance 15
b) In same cases DNA is produced from RNA. Name this process and give example.
Answer:
a) Central Dogma in molecular biology
b) Reverse transcription

Question 20.
a) Define mutation. (MAY-2014)
b) What are the different types of mutation?
Answer:
a) Mutation is a phenomenon which results in alteration of DNA sequences and consequently results in changes in the genotype and the phenotype of an organism
b) physical mutation and chemical mutation

Question 21.
a) Paternity or maternity can be determined by certain scientific methods. What is it? Define. (MAY-2014)
b) Briefly write the* methodology involved in the technique.
c) Comment on its other applications.
Answer:
a) DNA fingerprinting. DNA fingerprinting involves identifying differences in some specific regions in DNA sequence
b) i) isolation of DNA
ii) digestion of DNA by restriction endonucleases
iii) separation of DNA fragments by electrophoresis
iv) transferring (blotting) of separated DNA fragments to synthetic membranes, such as nitrocellulose or nylon
v) hybridisation using labelled VNTR probe
vi) detection of hybridised DNA fragments by autoradiography
c) It is also used in forensic science

Question 22.
Fill in the blanks: (MARCH-2015)
a) _________is a metabolic disorder that occurs due to the lack of an enzyme, that converts phenylalanine to tyrosine.
b) _______is a disease caused by the substitution of Glutamic acid by valine at 6th position.
Plus Two Zoology Chapter Wise Previous Questions Chapter 4 Molecular Basis of Inheritance 16
Answer:
a) Phenylketonuria
b) Sickle-cell anaemia

Question 23.
The flow of genetic information is shown below. Name the process of (a) and (b). (MARCH-2015)
Plus Two Zoology Chapter Wise Previous Questions Chapter 4 Molecular Basis of Inheritance 17
Answer:
a) Trancription
b) Translation

Question 24.
Explain transcription. A transcription unit in DNA is defined primarily by three regions. Write the names of any two regions. (MARCH-2015)
Answer:
Information contained in DNA is copied down to mRNA is called Transcription – Promoter and structural gene.

Question 25.
Observe the diagram and answer the questions: (MAY-2015)
Plus Two Zoology Chapter Wise Previous Questions Chapter 4 Molecular Basis of Inheritance 18
a) What is the difference in the replication processes in A strand and B strand?
b) What is the role of DNA ligase in the replication process in B strand?
c) What is meant by Replication fork?
Answer:
a) In A, replication is continuous and form leading strand but in B replication is discontinuous and form lagging strand.
b) In B, short stretch of Okazaki fragments are connected with the help of DNA ligase and form continuous strand
c) The replication occur within a small opening of the DNA helix, referred to as replication fork. It appears as Y shaped forked structure.

Question 26.
Observe the following diagram and answer the questions: (MAY-2015)
Plus Two Zoology Chapter Wise Previous Questions Chapter 4 Molecular Basis of Inheritance 19
a) Diagrammatically represent the changes take place when lactose is added to the medium.
b) What is the role of z, y and a genes in this metabolic pathway?
Answer:
a)
Plus Two Zoology Chapter Wise Previous Questions Chapter 4 Molecular Basis of Inheritance 30
b) The z gene codes for beta-galactosidase which is responsible for the hydrolysis of the disaccharide, lactose into galactose and glucose. The y gene codes for permease, which increases permeability of the cell to beta-galactosides.The a gene encodes a transacetylase

Question 27.
Read carefully the sequence of codons in the mRNA unit and answer the questions. (MARCH-2016)
Plus Two Zoology Chapter Wise Previous Questions Chapter 4 Molecular Basis of Inheritance 20
a) What change in needed in the first codon to start the translation process?
b) If translation starts by that change, till which codon it can continuous? Why?
Answer:
a) AUG is needed
b) UGA, Termination of translation occurs

Question 28.
Schematic representation of DNA fingerprints are shown below: (MARCH-2016)
Plus Two Zoology Chapter Wise Previous Questions Chapter 4 Molecular Basis of Inheritance 21
[Hints : C is a sample taken from a crime scene, A and B from two suspected individuals]
a) Which one of the suspected individual may involved in the crime?
b) Write any other use of DNA fingerprinting.
Answer:
a) suspected person is B
b) disputed parentage determining population and genetic diversities.

Question 29.
Observe the figure of mRNA and answer the questions: (MAY-2016)
Plus Two Zoology Chapter Wise Previous Questions Chapter 4 Molecular Basis of Inheritance 22
a) Find the start and stop codons.
b) How many amino acids will be present in the protein translated from this mRNA?
c) The additional sequences that are not translated in mRNA are called _______.
Answer:
a) Start codon – AUG
Stop codon – UAG
b) 4
UTR- Untranslated region

Question 30.
a) The hints of the lac operon is given below: (MAY-2016)
Hints:
Inducer, Repressor,
Structural genes, operator Regulatory gene
i) Which substance is acting as inducer in this operon?
ii) Explain the working of operon in presence of the inducer.
OR
b) With the help of the figure given, explain the processing of hnRNA to mRNA in eukaryotes.
Plus Two Zoology Chapter Wise Previous Questions Chapter 4 Molecular Basis of Inheritance 23
Answer:
a) i) lactose inducer
ii) If lactose is present in a medium, it has to be breakdown into glucose and galactose,for this positive control of operon works and structural genes transcribe. The switch on condition of operator gene is due to the binding of RNA polymerase with promotersite. In +ve control, repressor from regulator gene is inactivated due to the presence of lactose.
OR
b) 1) Splicing-the introns are removed and exons are joined together.
2) capping -methyl guanosine triphosphate is added to the 5-end of hnRNA.
3) Tailing- adenylate residues (200-300) are added at 3-end in a template
After these three process, fully processed mRNA is released from nucleus into cytoplasm for protein synthesis.

Question 31.
Examine the following fragment of beta globin chain in human haemoglobin and identify the hereditary disease with reason. (MARCH-2017)
Plus Two Zoology Chapter Wise Previous Questions Chapter 4 Molecular Basis of Inheritance 24
Answer:
Sickle cell anaemia
The defect is caused by the substitution of Glutamic acid by Valine at the sixth position of the beta globin chain of the haemoglobin molecule The mutant haemoglobin molecule under low oxygen tension causing the change in the shape of the RBC from biconcave disc to elongated sickle like structure.

Question 32.
Which of the following combinations do not apply to DNA? (MARCH-2017)
a) Deoxyribose, Guanine
b) Ribose, Adenine
c) Deoxyribose, Uracil
d) Guanine, Thymine
1) (a) and (b)
2) (b) and (c)
3) (c) and (d)
4) (a) and (d)
Answer:
2) b) and c)

Question 33.
Examine the diagram of mRNA given below. Mark the ‘5’ and ‘3’ ends of the mRNA by giving reasons. (MARCH-2017)
Plus Two Zoology Chapter Wise Previous Questions Chapter 4 Molecular Basis of Inheritance 25
Answer:
Polyadynilation always at 3′ end of m RNA ,so the other must be 5′ end.

Question 34.
A small fragment of skin of a different person was extracted from the nails of a murdered person. This fragment of skin led the crime investigators to the murderer. Based on this incident answer the following questions: (MARCH-2017)
1) What technique was used by the investigators?
2) What is the procedure involved in this technique?
OR
In an E. coli culture lactose is used as food instead of glucose. If so, answer the following questions:
1) How do the bacteria respond to the above situation at genetic level?
2) If lactose is removed from the medium what will happen?
Answer:
1) DNA finger printing
2) The technique, is based on following procedure
i) isolation of DNA,
ii) digestion of DNA by restriction endonucleases,
iii) separation of DNA fragments by electrophoresis,
iv) transferring (blotting) of separated DNA fragments to synthetic membranes, such as nitrocellulose or nylon,
v) hybridisation using labelled VNTR probe, and vi) detection of hybridised DNA fragments by autoradiography
OR
In this closely associated genes function as unit called operon If lactose is present in a medium, it has to be breakdown into glucose and galactose ,for this positive control of operon works and structural genes transcribe with the help of switch on condition of operator gene. This is due to binding of RNA polymerase on promoter site of DNA.

Question 35.
Find the odd one and write the common feature of others. (MAY-2017)
Cytidine, Adenine, Thymine, Guanine.
Answer:
Cytidine, All others are nitrogen bases.

Question 36.
Observe the diagram:  (MAY-2017)
Plus Two Zoology Chapter Wise Previous Questions Chapter 4 Molecular Basis of Inheritance 26
a) Redraw the diagram correctly if any mistake is there.
b) What does the diagram indicate?
c) What is the function of DNA ligase in this process?
Answer:
a)
Plus Two Zoology Chapter Wise Previous Questions Chapter 4 Molecular Basis of Inheritance 27
b) Replication fork.
c) Discontinuously synthesised fragments of DNA are joined by DNA ligase.

Question 37.
Read the codon sequence in the mRNA unit which is undergoing translation.  (MAY-2017)
Plus Two Zoology Chapter Wise Previous Questions Chapter 4 Molecular Basis of Inheritance 28
a) What will happen if the nitrogen base ‘U’ in the sixth position is replaced by ‘A’ by point mutation?
b) Name and define this type of mutation.
c) Draw the base sequence in the coding DNA strand from which the above mRNA is transcribed.
Answer:
a) Translation stop as UAA is a stop codon.
b) In this point mutation one nitrogen base is deleted.
c)
Plus Two Zoology Chapter Wise Previous Questions Chapter 4 Molecular Basis of Inheritance 29

Plus Two Zoology Chapter Wise Previous Questions Chapter 3 Principles of Inheritance and Variation

Kerala State Board New Syllabus Plus Two Zoology Chapter Wise Previous Questions and Answers Chapter 3 Principles of Inheritance and Variation.

Kerala Plus Two Zoology Chapter Wise Previous Questions Chapter 3 Principles of Inheritance and Variation

Question 1.
Polypeptide chains of two haemoglobin molecules are shown below. One of the chains shows an abnormality. Observe the diagram and answer the following questions. (MARCH-2010)
Plus Two Zoology Chapter Wise Previous Questions Chapter 3 Principles of Inheritance and Variation 1
a) Which of the polypeptide chain in haemoglobin is abnormal leading to a disease?
b) What is the reason for this abnormality?
c) What will be the effect of this change in polypeptide chain?
Answer:
a) A
b) Substitution of glutamic acid by valine in the 6th position of polypeptide chain.
c) The RBC become sickle shaped causing a disease sickle cell anaemia / Affect the o2 carrying capacity of RBC.

Question 2.
To find out the unknown genotype of a violet flowered pea plant a researcher done the following cross. Observe the diagram and answer the following questions: (Hint: Violet flower colourin pea plant is dominant over white). (MARCH-2010)
Plus Two Zoology Chapter Wise Previous Questions Chapter 3 Principles of Inheritance and Variation 2
a) What would be the above cross called?
b) Can you determine the unknown genotype of violet flowered parent by drawing Punnet square?
Answer:
a) Test cross
b)
Plus Two Zoology Chapter Wise Previous Questions Chapter 3 Principles of Inheritance and Variation 3
Genotype of unknown parent Ww/ Heterozygous.

Question 3.
Some genetic abnormalities, their genotypes and features are distributed in columns A, B and C respectively. Match them correctly. (MAY-2010)
Plus Two Zoology Chapter Wise Previous Questions Chapter 3 Principles of Inheritance and Variation 4
Answer:
Plus Two Zoology Chapter Wise Previous Questions Chapter 3 Principles of Inheritance and Variation 5

Question 4.
The flow charts A and B given below represents the inheritance of normal haemoglobin and sickle cell haemoglobin: (MAY-2010)
Plus Two Zoology Chapter Wise Previous Questions Chapter 3 Principles of Inheritance and Variation 6
a) Observe flow chart A and complete the flow chart B.
b) Note down the genotype of a sickel cell anaemia patient and mention the symptom of the disease.
c) Mention the peculiarity of HbA Hbs phenotype.
Plus Two Zoology Chapter Wise Previous Questions Chapter 3 Principles of Inheritance and Variation 7
Answer:
a)
Plus Two Zoology Chapter Wise Previous Questions Chapter 3 Principles of Inheritance and Variation 8
b) Sickle cell Anemia genotype is homozygous for Hbs (HbsHbs).
Symptoms
SevereAnemia
Oxygen shortage etc.
Haemoglobin becomes sickle shaped.
c) HbA Hbs indicate heterozygous individuals, who are the carrier of sickle cell Anemia, but unaffected ones.

Question 5.
After analyzing’the karyotype of a short statured round headed person with mental retardation, a general physician noticed an addition of autosomal chromosome. (MARCH-2011)
Answer the following questions.
a) Addition or deletion of chromosome generally results in ______
b) What may be the possible syndrome or disorder of the above person should suspected to be?
c) Suggest two / more morphological peculiarities to confirm the chromosome disorder in that person.
Answer:
a) Aneuploidy / Chromosomal disorders/ Chromo-somal abberrations/Chromosomal mutations.
b) Down’s syndrome / Mongolism / Trisomy 21st / 45A + xx / xy.
c) Furrowed tongue, partially opened mouth, Broad palm, Skin fold at the corner of the eye.
Two correct points.

Question 6.
The frequency of occurrence of Royal disease or . haemophilia is high in the pedigree of royal families of Queen Victoria. Which of the following cannot be generally inferred from this? (MARCH-2011)
a) Queen Victoria was not homozygous forthe disease.
b) Many heterozygous females were there in the Royal families.
c) Non-Royal families were not affected with haemophilia.
d) There is less possibility to become a female diseased.
e) Generally a diseased female cannot survive after the first menstruation.
f) Pedigreee analysis is the study of inheritance patterns of traits in human females.
Answer:
‘C’ and ‘f ’ c1 non royal families were not affected with haemophilia.
f2 Pedegree analysis is the study of inheritance pattern of traits in human females.

Question 7.
A couple have two daughters. The blood group of husband and wife is ‘O’ (MARCH-2011)
a) What is the possible blood groups of the children should have?
b) Whether any change in blood group will occur if they have two sons instead of daughters.
Substantiate your answer.
Answer:
a) O group
b) No.
There is no sex specificity in blood group alleles / Co-dominance / Homozygous recessive. Not related to sex chromosomes or autosomes /

Question 8.
Complete the table using suitable terms. (MARCH-2012)
Turner’s syndrome (a) ______ Sterile female
(b) __________44A + XXY (c) _________
(d) __________ Trisomy 21 Mental retardation
Answer:
a) 44A + X0
b) Klinefelters Syndrome
c) Sterile male
d) Down’s Syndrom

Question 9.
In pea plant the gene for yellow seed colour is dominant over green and round seed shape is dominant over wrinkled. Write the four types of gametes formed in a heterozygous pea plant with yellow and round seeds. (Yy Rr).
Answer:
YR Yr yR yr

Question 10.
The first child of a couple is affected with phenylketonuria. During the second pregnancy they visited a genetic counsellor and he prepared a pedigree chart of their family. (MARCH-2012)
a) What is pedigree analysis?
b) Draw the symbols for
i) Affected female.
ii) Sex unspecified.
iii) Consanguineous mating.
Answer:
a) It is the study of inheritance of a trait for several generation of a family.
b)
Plus Two Zoology Chapter Wise Previous Questions Chapter 3 Principles of Inheritance and Variation 9
Question 11.
Diagrammatic representation of chromosome map of Drosophila is given below: (MARCH-2012)
Plus Two Zoology Chapter Wise Previous Questions Chapter 3 Principles of Inheritance and Variation 10
Y – Yellow
W – White
M – Miniature
a) Which genes are more linked?
b) Who mapped the chromosome firstly?
c) Tightly linked genes show low recombination. Why?
Answer:
a) y and w
b) Alfred Sturtevant
c) Crossing over rarely takes between genes

Question 12.
Work of a student is given below:  (MAY-2012)
Plus Two Zoology Chapter Wise Previous Questions Chapter 3 Principles of Inheritance and Variation 11
a) From the above give an example for genotype and phenotype.
b) Complete the work’using punnett square and find out the phenotypic ratio in the F2 generation.
Answer:
a) First filial generation Genotype-RrYy,Phenotype- round yellow
Plus Two Zoology Chapter Wise Previous Questions Chapter 3 Principles of Inheritance and Variation 12

Question 13.
Identify the traits from the pedigree chart. Give one example each.  (MAY-2012)
Plus Two Zoology Chapter Wise Previous Questions Chapter 3 Principles of Inheritance and Variation 13
Answer:
a) Autosomal dominant trait
Eg. Muscular dystrophy
b) Autosomal recessive trait
Eg. Sickle cell anaemia

Question 14.
A poultry farm manager was cursing his hens for producting lion share of cocks in its progeny. Hearing this, Kumar – farm attender starts to blame his wife for delivering consecutive girl children. Analyze the situtations scientifically and state whether you agree with kumar.  (MARCH-2013)
Answer:
No, During spermatogenesis two types of gametes are produced of which 50 per cent carry the X- chromosome and the rest 50 per cent has Y- chromosome besides the autosomes. Females produce only one type of ovum with an X- chromosome.
In case the ovum fertilises with a sperm carrying X- chromosome the zygote develops into a female (XX) and with Y-chromosome results into a male offspring. Thus the genetic makeup of the sperm that determines the sex of the child.

Question 15.
In the given pedigree the shaded figures denote individuals expressing a specific trait. (MARCH-2013)
Plus Two Zoology Chapter Wise Previous Questions Chapter 3 Principles of Inheritance and Variation 14
Which of the following is the most probable mode of inheritance of this trait.
Answer:
Principles of inheritance & Variation
A – Simple Mendelian Recessive
B – Co dominant relationship of a single pair of alleles.
C- X – linked recessive transmission
D – X- linked dominant transmission
E – Polygenic inheritance.
X-Linked recessive transmission

Question 16.
“Gopalan argues that if father is of A’ blood group, mother is of ‘B’ blood group. Their children can only be A’ group, B group or AB’ group.” (MARCH-2014)
a) Do you agree with Gopalan’s Argument ?
b) Give reason for your answer.
Answer:
a) No ,All groups are possible including O group
b) Plus Two Zoology Chapter Wise Previous Questions Chapter 3 Principles of Inheritance and Variation 15

Question 17.
Identify the syndrome from the genotype given below: (MAY-2014)
1) 44 Autosomes + XXY
2) 44 Autosomes + XO
Answer:
1) Klinefelters syndrome
2) Turners syndrome

Question 18.
The family of Queen Victoria shows a number of haemophilic descendants as she was the carrier of the disease. Name the pattern of inheritance of this royal disease. (MAY-2014)
Answer:
Sex linked inheritance .
The heterozygous female (carrier) for haemophilia may transmit the disease to sons.
(Criss cross inheritance)

Question 19.
Plus Two Zoology Chapter Wise Previous Questions Chapter 3 Principles of Inheritance and Variation 16
a) Identify the syndrome from the diagram, and write the genotype. (MARCH-2015)
b) It occurs in both sexes (male and female)? Write the reason.
Answer:
a) Downs syndrome , 45 A+XX or 45A+XY
b) The cause of this genetic disorder is the presence of an additional copy of the chromosome number 21 (trisomy of 21).

Question 20.
It is evident that, it is the genetic make up of the sperm that determine the sex of the child in human beings. Substantiate. (MARCH-2015)
Answer:
During spermatogenesis among males, two types of gametes are produced. 50% of the total sperm produced carry the X-chromosome and the rest 50 per cent has Y-chromosome besides the autosomes. In case the ovum fertilises with a sperm carrying X- chromosome the zygote develops into a female (XX) and the fertilisation of ovum with Y-chromosome carrying sperm results into a male offspring. Hence the genetic makeup of the sperm that determines the sex of the child.

Question 21.
Diagrammatic representation of the pedigree analysis of the inheritance of sickle cell anaemia is shown below: (MAY-2015)
Plus Two Zoology Chapter Wise Previous Questions Chapter 3 Principles of Inheritance and Variation 27
a) Name the type of inheritance shown in the figure.
b) Write the genotype of A and B.
(Hint: Disease is controlled by a pair of alleles HbA & Hbs)
Represent pedigree analysis of an X-linked recessive inheritance diagrammatically.
Answer:
a) Mendalian inheritance
b) A-HbA Hbs B- HbA Hbs

Question 22.
Observe the inheritance shown in A (MAY-2015)
Plus Two Zoology Chapter Wise Previous Questions Chapter 3 Principles of Inheritance and Variation 17
a) Name the type of inheritance shown in A and B.
b) What is the difference between the two types of inheritance.?
Answer:
a) A- Dominance B-Co dominance
b) In dominance , dominant gene mask the expression of recessive gene and tall character in F1 progenies but in co dominance both dominant gene express together and shows AB blood group.

Question 23.
Results of a famous experiment is given in the figure. Answer the questions. (MARCH-2016)
Plus Two Zoology Chapter Wise Previous Questions Chapter 3 Principles of Inheritance and Variation 18
a) Identify the experiment.
b) Which property of the DNA is proved by this experiment?
Answer:
a) Semiconservative DNA replication experiment
b) During DNA replication one parent strand is conserved

Question 24.
Which of the following is not a Mendelian disorder? (MARCH-2016)
i) Colourblindess
ii) Down’s syndrome
iii) Haemophilia
iv) Thalassemia
Answer:
ii) Down’s syndrome

Question 25.
Study the following cross and answer the questions. (MARCH-2016)
Plus Two Zoology Chapter Wise Previous Questions Chapter 3 Principles of Inheritance and Variation 19
[Hint: ABO blood group in man is controlled by three alleles IA, IB, and i]

a) Write the geno types of Father, Mother and Son.
b) The type of dominance of human blood group inheritance is ________.
Answer:
Father-IA i or i i Mother-IB or i i Son-i i

Question 26.
Observe the figures and answer the questions. (MARCH-2016)
Plus Two Zoology Chapter Wise Previous Questions Chapter 3 Principles of Inheritance and Variation 20
a) Identify the syndromes A and B.
b) What is the chromosome numbers in A and B?
Answer:
a) A-KlinefelterSyndrome;
B- Turner’s Syndrome
b) A-47 B-45

Question 27.
a) Complete the flow chart of chromosomal disorder by filling the blank boxes (A and B). (MAY-2016)
Plus Two Zoology Chapter Wise Previous Questions Chapter 3 Principles of Inheritance and Variation 21
b) What is an euploidy?
Answer:
a) A-monosomy of sex chromosome B – Klinefelters syndrome
b) Failure of separation of homologous chromosomes during anaphase I of meosis lead to gain or loss of chromosome, it is called aneupoidy.

Question 28.
Observe the figure below and answer the questions following: (MAY-2016)
Plus Two Zoology Chapter Wise Previous Questions Chapter 3 Principles of Inheritance and Variation 22
a) Identify the figure
b) What shows the shaded symbols used?
Answer:
a) Pedigree analysis or Autosomal dominant trait
b) Individuals with genetic disorder (male and female)

Question 29.
The following table shows the F2 generation of a dihybrid cross, identify the ‘Phenotype’ with homozygous recessive genotype.(MARCH-2017)
Find out A : B : C : D.
Plus Two Zoology Chapter Wise Previous Questions Chapter 3 Principles of Inheritance and Variation 23
Answer:
B , Genotype A: B:C:D: = 3:1:9:3 OR 9:3:3:1

Question 30.
Which of the following do not have similar sex chromosomes? (Homogametic) (MARCH-2017)
a) Human female
b) Drosophila female
c) Bird female
d) Bird male
Answer:
c) Bird female

Question 31.
Observe the following diagram and answer the questions: (Hint: Steps in making a cross in pea plant) (MAY-2017)
Plus Two Zoology Chapter Wise Previous Questions Chapter 3 Principles of Inheritance and Variation 24
a) Name the process marked as A and write its significance.
b) Diagrammatically represent a monohybrid cross between Tall and dwarf pea plants.
Answer:
a) Removal of anthers from female plants
Significance –It prevents self pollination and fertilization
Plus Two Zoology Chapter Wise Previous Questions Chapter 3 Principles of Inheritance and Variation 25

Question 32.
Observe the diagrammatic representation of the following pedigree analysis and answer the questions (MAY-2017)
a) Describe the type of inheritance shown in the diagram.
b) Distinguish between Mendelian disorder and chromosomal disorder with example.
Plus Two Zoology Chapter Wise Previous Questions Chapter 3 Principles of Inheritance and Variation 26
Answer:
a) Sex linked inheritance
b) Mendelian disorder is determined by mutation in the single gene.
These disorders are transmitted to off springs in the same line as the principles of inheritance.

Plus Two Zoology Chapter Wise Previous Questions Chapter 2 Reproductive Health

Kerala State Board New Syllabus Plus Two Zoology Chapter Wise Previous Questions and Answers Chapter 2 Reproductive Health.

Kerala Plus Two Zoology Chapter Wise Previous Questions Chapter 2 Reproductive Health

Question 1.
Diagram shown below is a surgical method used for female sterilization. (MARCH-2010)
a) What is the method shown in diagram?
b) Mention any two Intra uterine devices to prevent conception.
c) What is the surgical method of male sterilization called?
Plus Two Zoology Chapter Wise Previous Questions Chapter 2 Reproductive Health 1
Answer:
a) Tubectomy
b) Any two methods (Cu-T, Cu-7, loop, Multibad-375, Hormone producing progestogent, LNG-20 etc)
c) Vasectomy

Question 2.
Select the Assisted Reproductive Technique that uses an early embryo with upto 8 blastomeres.   (MAY-2010)
a) ZIFT
b) IUT
c) GIFT
d) IUI
Answer:
a) ZIFT

Question 3.
One among the contraceptive method is peculiar. Find the odd one. What is common among others?  (MARCH-2011)
a) Periodic abstinence
b) Coitus interruptus
c) Lactational amenorrhea
d) lUD’s
Answer:
d) lUD’s
Others are natural contraceptives/Natural methods/ Others have more chance of conception / IUD is the barrier method.

Question 4.
The treatment facility advertised on the brochure of a private clinic is shown below.  (MARCH-2011)
a) Can you suggest what type of a clinic it is ?
b) Make a brief note on any three of the treatment procedure.
Plus Two Zoology Chapter Wise Previous Questions Chapter 2 Reproductive Health 2
Answer:
a) Infertility clinic / Fertility treatment clinic / Assisted Reproductive clinic or Hospital.
b) IVF-Invitro Fertilization
ZIFT – Zygote Intra Fallopian Transfer
GIFT – Gamete Intra Fallopian Transfer
IUI – Intra Uterine Insemination.

Question 5.
“STDs present a major health concern in both industralized and developing countries.”  (MARCH-2012)
a) What do you mean by STDs?
b) Name two STDs.
c) Suggest two preventive measures.
Answer:
a) Sexually transmitted diseases
b) Gonorrhoea and Syphilis
c) Avoid sex with unknown partners and use condom during coitus.

Question 6.
Find out the odd one from the following, write the reason.  (MAY-2012)
a) CuT
b) Cu7
c) LNG-20
d) Multiload – 375
Answer:
LNG-20

Question 7.
One couple came to know that they have a girl child during fourth month of pregnancy and they decide to do MTP.  (MAY-2012)
a) What is MTP ?
b) At which stage of pregnancy MTP relatively safe?
c) How will you respond to the decision of female foeticide by the couple?
Answer:
a) Medical termination of pregnancy
b) MTPs are safe during the first trimester, i.e., upto 12 weeks of pregnancy.
c) MTPs must be essential where continuation of the pregnancy could be harmful or even fatal either to the mother or to the foetus.

Question 8.
One of your friend argued that anti-retroviral drugs are effective medicine to treat AIDS.  (MAY-2012)
a) What is your opinion about it?
b) How HIV affect out immunity?
Answer:
a) It prevents the growth and multiplication of viruses
b) HIV enters into helper T-lymphocytes (TH), replicates and produce progeny viruses. The progeny viruses released in the blood attack other helper T-lymphocytes, as result the patient becomes immuno-deficient

Question 9.
Most often HIV infection occur due to conscious behaviour patterns. Do you agree with this statement? Substantiate your answer.  (MARCH-2013)
Answer:
No,
1) blood transfusion
2) During birth of child
Yes,
1) sexual contact
2) Intraveinous injection

Question 10.
Suggest the ART which may be successful in the following conditions. (MARCH-2013)
a) A female cannot produce ovum, but can provide suitable environment for fertilization and further development.
b) Male partner is unable to inseminate the female or has very low sperm count.
c) Fusion of gametes and zygote formation does not occur within the body of the female.
Answer:
a) Transfer of an ovum collected from a donor into the fallopian tube (GIFT – gamete intra fallopian transfer) of another female who cannot produce one, but provide suitable environment for fertilisation and further development
b) Intra cytoplasmic sperm injection (ICSI) Here a sperm is directly injected into the ovum. It is the procedure to form an embryo in the laboratory
c) In vitro fertilisation (IVF—fertilisation outside the body in almost similar conditions as that in the body) followed by embryo transfer (ET).

Question 11.
Prepare a pamphlet for Adolescent children to make them aware of alcohol and drug abuse. (MAY-2013)
Answer:
Education and counseling, moral education, Avoid undue peer pressure .visual publicity through TV, seeking professional and medical help etc.

Question 12.
One of your neighbour is suffering from itching, fluid discharge, slight pain and swelling in genital region. (MARCH-2014)
a) What do you think the disease he is suffering from?
b) What measures are to be taken to prevent such diseases?
Answer:
a) Sexually transmitted disease (STD) Eg-gonor- rhoea, syphilis etc.
b) 1) Avoid unknown sexual partner
2) Use condoms during coitus

Question 13.
Expand the following abbreviations which are commonly used in reproductive health: (MARCH-2014)
a) ART
b) ZIFT
Answer:
a) ART – Assisted reproductive techonology
b) ZIFT – Zygote intra fallopian transfer

Question 14.
______ and _____ are two surgical contraceptive methods in males and females respectively. (MAY-2014)
Answer:
Vasectomy,Tubectomy

Question 15.
Sex of the baby is determined by the father, not by the mother. Substantiate. (MAY-2014)
Answer:
ovum fertilises with a sperm carrying X- chromosome the zygote develops into a female (XX) and the fertilisation of ovum with Y-chromosome carrying sperm results into a male offspring. Hence the genetic make up of the sperm that determines the sex of the child.

Question 16.
Amniocentesis for sex determination is banned in our country? Is this ban necessary? Comment. One use of amniocentesis. (MAY-2014)
Answer:
Yes, Ban on amniocentesis for sex-determination to legally check increasing female foeticides. It is a foetal sex determination test based on the chromosomal pattern in the amniotic fluid surrounding the developing embryo.

Question 17.
Identify the diagram and write how it acts? (MARCH-2015)
Plus Two Zoology Chapter Wise Previous Questions Chapter 2 Reproductive Health 3
Answer:
Copper T (CuT), lUDs increase phagocytosis of sperms within the uterus and the Cu ions released suppress sperm motility and the fertilising capacity of sperms.

Question 18.
Foetal sex can be determined by a test based on the chromosomal pattern from the amniotic fluid.  (MARCH-2015)
a) What is this test?
b) Revealing of sex determination through this test is banned. Is this ban necessary? Comment.
c) Invitro fertilization followed by embryo transfer is known as _____.
Answer:
a) Aminocentesis
b) Yes, Ban on amniocentesis for sex- determination to legally check increasing female foeticides.
c) Test tube baby programme

Question 19.
If proper care and attention is not given by adults, adolescents may become addicted to drugs/ alcohol.” What is your opinion about this statement? Substantiate your answer.  (MAY-2015)
Answer:
Adolescence is a bridge linking childhood and adulthood. It is the very vulnerable phase of mental and psychological development of an individual. Repeated use of drugs, the tolerance level of the receptors present in our body increases. Consequently the receptors respond only to higher doses of drugs or alcohol leading to greater intake and addiction.

Question 20.
Some techniques commonly used for infertility treatment are given below. Read them carefully and answer the questions.  (MAY-2015)
ZIFI , GJFF, ICSI, IUI, IVF
a) Which of the above technique is used forthe collection of sperm from the husband or a healthy donor and artificially introduced into the vagina or uterus of the female?
b) Distinguish between ZIFT and GIFT.
c) Write the common term used to denote ‘ tech-niques given above
Answer:
a) IUI
b) ZIFT- Ova from the wife/donor (female) and sperms from the husband/donor (male) are collected and are induced to form zygote under simulated conditions in the laboratory. The zygote or early embryos (with upto 8 blastomeres) are transferred into the fallopian tube
b) GIFT-Transferof an ovum collected from a donor into the fallopian tube of another female who cannot produce it ,but can provide suitable environment for fertilisation
c) Assisted reproductive technologies (ART)

Question 21.
Categorise the given birth control methods into three groups with proper heads.  (MARCH-2016)
Cervical caps, Vasectomy, Cu T, Tubectomy, Diaphragms, Condom, Lippes Loop
Answer:
lUDs- Cu T, LiPPes loop
Barrier method- Diaphrams, Condoms Cervical caps, surgical method – Vasectomy, Tubectomy,

Question 22.
Diagnostic report of two couples having infertility problems are given below:  (MAY-2016)
1) The woman cannot produce ovum.
2) The man has very low sperm count in semen. Suggest a suitable Assisted Reproductive Technologies (ART) for each problem in expanded form
Answer:
1) GIFT -Gamete intra fallopian transfer
2) lUI-Intra uterine insemination/AI-Artificial insemination.

Question 23.
Which of the following pairs of STDs is completely curable?  (MARCH-2017)
1) HIV, Hepatitis-B
2) Hepatitis-B, Gonorrhoea
3) Syphilis, Gonorrhoea
4) Chlamydomonas, genital-herpes
Answer:
3) syphilis, gonorrohea

Question 24.
a) What is ART?  (MARCH-2017)
b) Categorize the following ARTs based on their applications in male sterility and female sterility:
GIFT, Al
Answer:
a) In the case of infertility, the couples could be assisted to have children through certain special techniques commonly known as assisted reproductive technologies (ART),
b) GIFT-Female,
Al – Male

Plus Two Zoology Chapter Wise Previous Questions Chapter 1 Human Reproduction

Kerala State Board New Syllabus Plus Two Zoology Chapter Wise Previous Questions and Answers Chapter 1 Human Reproduction.

Kerala Plus Two Zoology Chapter Wise Previous Questions Chapter 1 Human Reproduction

Question 1.
Given below is the diagrammataic representation of human blastocyst. Observe the diagram and answer the following questions: (MARCH-2010)
Plus Two Zoology Chapter Wise Previous Questions Chapter 1 Human Reproduction 1
a) Identify A and B
b) Write the functions of A and B.
Answer:
a) A – Inner cell mass, B – Trophoblast
b) A – Differentiate into embryo germ layers/gastrula B – Attachment to endometrium / form different embryonic membranes/ placenta formation/ nutritional supply.

Question 2.
When the urine sample of a lady is tested, presence of Human Chorionic Gonadotropin (HCG) is detected. (MARCH-2010)
a) What does the presence of HCG indicate?
b) Which is the source of HCG?
Answer:
a) Pregnancy
b) Placenta

Question 3.
The graph shown below shows the levels of LH and FSH at various stages of menstrual cycle. (MAY-2010)
Plus Two Zoology Chapter Wise Previous Questions Chapter 1 Human Reproduction 2
a) Name the source of LH and FSH.
b) The level of LH is maximum during the middle day of the cycle. Mention its effect.
c) Note the function of LH in males.
Answer:
a) Pituitary gland
b) Helps for ovulation
c) Stimulates the synthesis of horrnones (androgens)

Question 4.
Plus Two Zoology Chapter Wise Previous Questions Chapter 1 Human Reproduction 3
The above graph shows the level of ovarian hormones in a normally menstruacing woman during the follicular phase. (MARCH-2011)
a) Name ‘a’ and ‘b’
b) Mention the role of pituitary hormones in maintaining this condition.
c) Reconstruct the graph for Luteal phase.
Answer:
a) i) Estrogens
ii) Progesterone
b) FSH / Follicle stimulating Hormone, LH / Luteinizing Hormone
OR
Gonadotropins
One function each of FSH and LH.
c)
Plus Two Zoology Chapter Wise Previous Questions Chapter 1 Human Reproduction 4

Question 5.
Some stages of the embryonic development are given below. Observe these diagrams and answer the questions. (MAY-2011)
Plus Two Zoology Chapter Wise Previous Questions Chapter 1 Human Reproduction 5
a) What is A & B?
b) Name thetwo types of cells found in the blastocyst.
c) Which layer of blastocyst is attached to the endometrium? And name that process.
Answer:
a) A – Blastomere B – Morula
b) Trophoblast and inner cell mass
c) Trophoblast, Implantation

Question 6.
Observe the diagram provided (Do not copy the picture) (MARCH-2012)
Plus Two Zoology Chapter Wise Previous Questions Chapter 1 Human Reproduction 6
a) Label A and B
b) On which day of menstrual cycle Graafian follicle rupture.
c) Name the process induces the rupture of Graafian follicle.
d) Write the name and function of the structure forming inside the ovary after the rupture of Graafian follicle.
Answer:
a) A – Primary follicle B – Tertiary follicle
b) 14th day
c) The rupture of Graafian follicle and the release of ovum is called ovulation.
d) The corpus luteum secretes large amounts of progesterone which helps in the maintenance of the endometrium.

Question 7.
The following statements compares the process of oogenesis and spermatogenesis. Which one is not true?  (MAY-2012)
a) Production of ovum ceases at certain age, but sperm production continues even in old men.
b) Oogenesis begins in the embryonic stages, but spermatogenesis starts at the onset of puberty.
c) Meiotic arrest occurs both in Oogenesis and spermatogenesis.
d) Polar bodies are formed in oogenesis.
Answer:
a) Replication
b) Transcription
c) Translation
d) Reverse transcription

Question 8.
The diagram represents a process of gametogenesis. Closely observe it and answer the following  (MARCH-2013)
Plus Two Zoology Chapter Wise Previous Questions Chapter 1 Human Reproduction 7
Is it spermatogenesis or Oogenesis?
What does the smaller shaded circle represent? Write down two significance of production of the same.
Answer:
a) oogenesis
b) polar bodies
c) Retention of cytoplasm in ovum Maintaining one functional haploid ovum

Question 9.
Though one ovum is produced from a primary oocyte it can result into a male or female child after fertilization. But in the case of spermatocyte though 4 sperms are produced only two of them can result to a female child after fertilization”. Justify.  (MARCH-2013)
Answer:
Two types of sperms are produced one with x chromosomes and other withy chromosome. Sperm with x chromosome after fertilization results in the formation of female baby

Question 10.
Sterilization and IUDS are effective birth control measures, but lactational amenorrhea may not be so effective.  (MAY-2013)
a) How the sterilization procedure of males differ from that of females in preventing pregnancy?
b) Which part of the female reproductive organ is utilized for the IUD procedure? How this procedure prevents pregnancy?
c) Why the lactational amenorrhea is not so effective?
Answer:
a) In males the sterilization method is called vasectomy but in females it is called Tubectomy
b) uterus, lUDs suppresses sperm motility and fertilizing capacity of sperm or they make uterus unsuitable for implantation.
c) During intense lactation, menstrual cycle does not occur. Therefore the chance of conception is almost nil. But the method is effective only upto six months following delivery

Question 11.
Observe the diagram, and answer the questions: (MARCH-2013)
a) Identify A and B.
b) What is the function of C ?
c) In which of the marked part reduction division takes place? What is the significance of it?
Plus Two Zoology Chapter Wise Previous Questions Chapter 1 Human Reproduction 8
Answer:
a) A – Spermatozoa, B-Primary spermatocyte
b) Sertoli cells provide nutrition to the germ cells.
c) Primary spermatocyte, chromosome number reduced to half

Question 12.
Diagram of a mammalian sperm’is given. Label the parts marked. (MAY-2014)
Plus Two Zoology Chapter Wise Previous Questions Chapter 1 Human Reproduction 9
Answer:
A – Acrosome
B – Nucleus containing chromosomal material

Question 13.
Schematic representation of gametogenesis is given below. Identify A. Write one difference between A& B. (MARCH-2015)
Plus Two Zoology Chapter Wise Previous Questions Chapter 1 Human Reproduction 10
Answer:
A) Spermatogenesis – It results 4 spermatozoa
B) Oogenesis – It results one ovum and polar body

Question 14.
1) In which part of the human reproductive system the following events occur? (MARCH-2015)
a) Fertilisation
b) Implantation
2) Diagram of a human biastocyst is given below. Identify A & B.
Plus Two Zoology Chapter Wise Previous Questions Chapter 1 Human Reproduction 11
Answer:
a) ampullary-isthmicjunction
b) Endometrium of the uterus
A – inner cell mass
B – trophoblast

Question 15.
Choose the odd one from the following and write the common feature of others; (MAY-2015)
a) Estrogen
b) Androgen
c) Relaxin
d) Progesterone
Answer:
Androgen.
Others are ovarian hormones.

Question 16.
Complete the flow chart showing spermatogenesis by filling A and B and answer the questions: (MAY-2015)
Plus Two Zoology Chapter Wise Previous Questions Chapter 1 Human Reproduction 12
a) What is the chromosome number of primary spermatocyte
b) What is the significance of reduction division in spermatocyte?
Answer:
A- Spermatogonia
B- Spermatids
a) Primary spermatocyte-Diploid number, in man it is 23 pair, spermatids-haploid number, in man it is 23
b) Reduction division helps to reduce chromosome number as half in gametes (haploid).
It helps keep chromosome number species as constant for many generations.

Question 17.
Match the columns A and B: (MARCH-2016)
Plus Two Zoology Chapter Wise Previous Questions Chapter 1 Human Reproduction 13
Answer:
Plus Two Zoology Chapter Wise Previous Questions Chapter 1 Human Reproduction 14

Question 18.
The process of fusion of a sperm with ovum is called _______. (MAY-2016)
Answer:
Fertilisation

Question 19.
Match columns A and B.  (MAY-2016)
Plus Two Zoology Chapter Wise Previous Questions Chapter 1 Human Reproduction 15
Answer:
Plus Two Zoology Chapter Wise Previous Questions Chapter 1 Human Reproduction 16

Question 20.
LH and FSH are gonadotrophins. Distinguish their roles in males and females.  (MARCH-2017)
Answer:
LH acts at the Leydig cells and stimulates synthesis and secretion of androgens.
Androgens stimulate the process of spermato-genesis.
FSH acts on the Sertoli cells and stimulates secretion of some factors which help in the process of spermiogenesis.
Female Rapid secretion of LH leading to rupture of Graafian follicle and release ovum (ovulation). FSHhelpsinthe growth and development of ovarian follicle.

Question 21.
Human female possess 44 + XX chromosome number. The chromosome number of secondary oocyte is  (MAY-2017)
a) 44 + X
b) 22 + X
c) 44 +XX
d) 22 +XX
Answer:
b) 22 + X

Question 22.
Observe the diagram and answer the questions:  (MAY-2017)
Plus Two Zoology Chapter Wise Previous Questions Chapter 1 Human Reproduction 17
a) Identify A and B
b) Write the function of B.
Answer:
a) A – peri vitelline space
B- zona pellucida
b) Prevent the entry of further sperms after fertilization

Plus One Maths Notes Chapter 16 Probability

Kerala State Board New Syllabus Plus One Maths Notes Chapter 16 Probability.

Kerala Plus One Maths Notes Chapter 16 Probability

I. Random Experiments
An experiment is called a random experiment if it satisfies the following two conditions:

  • It has more than one outcome.
  • It is not possible to predict the outcome in advance.

Sample space: The set of all possible outcomes of a random experiment is called sample space. Generally denoted by S.

Event: Any subset E of a sample space S is called an event.

Types of Events:
1. Impossible event and sure event: The empty set φ and the sample space S describe the impossible event and sure event respectively.

2. Simple event: An event E having only one sample point of a sample space.

3. Compound event: An event having more than one sample point of a sample space.

Algebra of events:

  1. Event ‘not A’ = A’
  2. Event ‘A or B’ = A ∪ B
  3. Event ‘A and B’ = A ∩ B
  4. Event ‘A but not B’ = A ∩ \(\bar{B}\) = A – B

If A ∩ B = φ, then A and B are mutually exclusive events or disjoint events.

If E1 ∪ E2 ∪ E3 ∪ …… ∪ En = S, then we say that E1, E2, E3, …….., En are exhaustive events.

If E1 ∪ E2 ∪ E3 ∪ …… ∪ En = S, and Ei ∩ Ej = φ, i ≠ j then we say that E1, E2, E3,…….., En are mutually exclusive events and exhaustive events.

II. Probability of an Event
Let S is a sample space and E be an event, such that n(S) = n and n(E) = m. If each outcome is equally likely, then it follows that P(E) = \(\frac{m}{n}\).

P(Impossible event) = 0 and P(Sure event) = 1, hence 0 ≤ P(E) ≤ 1.

If A and B are any two events, then P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

If A and B are mutually exclusive events, then P(A ∪ B) = P(A) + P(B)

If A is any events, then P(A’) = 1 – P(A)

P(A ∩ \(\bar{B}\)) = P(A) – P(A ∩ B)

Plus One Maths Notes Chapter 15 Statistics

Kerala State Board New Syllabus Plus One Maths Notes Chapter 15 Statistics.

Kerala Plus One Maths Notes Chapter 15 Statistics

Statistics deals with data collected for specific purposes and making decisions about the data by analyzing and interpreting it.

I. Measure of Dispersion
This gives a measure of the dispersion of the observation around the measure of central tendency of the data collected.

1. Range = Maximum value – Minimum value.
2. Mean Deviation.
Plus One Maths Notes Chapter 15 Statistics 1
Where,
xi – observations
a – Any measure of central tendency.
Plus One Maths Notes Chapter 15 Statistics 2
Grouped data:
i. Discrete frequency distribution.
ii. Continuous frequency distribution.
Plus One Maths Notes Chapter 15 Statistics 3
Where,
xi – Observations/midpoints of class intervals
a – Any measure of central tendency.
Plus One Maths Notes Chapter 15 Statistics 4
Median class is the class in which the \(\left(\frac{N}{2}\right)^{t h}\) observation lies.
Plus One Maths Notes Chapter 15 Statistics 5
l – The lower limit of the median class.
f0 – Cumulative frequency of the class preceding the median class.
f1 – Frequency of the median class.
C – Width of the class interval.
Plus One Maths Notes Chapter 15 Statistics 6
3. Variance and Standard Deviations.
Standard Deviation (σ) = √Variance
Ungrouped data:
Plus One Maths Notes Chapter 15 Statistics 7
Where, xi – observations
\(\bar{x}\) – Mean
n – number of observations

Grouped data:
i) Discrete frequency distribution.
ii) Continuous frequency distribution.
Plus One Maths Notes Chapter 15 Statistics 8
Where,
xi – Observations/mid points of class intervals.
\(\bar{x}\) – Mean
fi – Frequency.

Short cut method of finding variance and standard deviation:
Let A be the assumed mean and the scale be reduced to \(\frac{1}{h}\) times (h being the width of class intervals). Let the new value be yi and prepare the required tables using yi. i.e; yi = \(\frac{x_{i}-A}{h}\)
Find the variance and standard deviation of yi using the above-mentioned method, let it
Plus One Maths Notes Chapter 15 Statistics 10

II. Coefficient of Variation
Plus One Maths Notes Chapter 15 Statistics 9
The distribution having greater CV has more variability around the central value than the distribution having a smaller value of the CV.

Less the CV more consistent is the data.

For distributions with equal means, the distribution with lesser standard deviation is more consistent or less scattered.

Plus One Maths Notes Chapter 14 Mathematical Reasoning

Kerala State Board New Syllabus Plus One Maths Notes Chapter 14 Mathematical Reasoning.

Kerala Plus One Maths Notes Chapter 14 Mathematical Reasoning

I. Statement
The basic unit involved in mathematical reasoning is a mathematical sentence.

A sentence is called a mathematically acceptable statement if it is either true or false but not both. Usually denoted by small letters p, q, r, ……..

Denial of a statement is called the negation of the statement. While forming the negation of a statement, phrases like, “It is not the case” or “it is false that” are also used. The negation of a statement p is denoted by ~p.

II. Compound Statement
Many mathematical statements are obtained by combining one or more statements using some connective words like “and”, “or”, etc.
Plus One Maths Notes Chapter 14 Mathematical Reasoning 1

Contrapositive statement: the contrapositive of a statement p ⇒ q is the statement ~q ⇒ ~p.

Converse of a statement: Converse of a statement p ⇒ q is the statement q ⇒ p.

III. Validity of Statement
A statement is said to be valid or invalid according to it is true or false.
Plus One Maths Notes Chapter 14 Mathematical Reasoning 2

Plus One Maths Notes Chapter 13 Limits and Derivatives

Kerala State Board New Syllabus Plus One Maths Notes Chapter 13 Limits and Derivatives.

Kerala Plus One Maths Notes Chapter 13 Limits and Derivatives

Calculus is that branch of mathematics which mainly deals with the study of change in the value of a function as the points in the domain changes.

I. Limit
Limit of a function f(x) at x = a is the behaviors of f(x) at x = a.

x → a: Means that ‘x’ takes values less than ‘a’ but not ‘a’.

x → a+: Means that ‘x’ takes values greater than ‘a’ but not ‘a’.

x → a: Read as ‘x’ tends to ‘a’, means that ‘x’ takes values very close to ‘a’ but not ‘a’.

\(\lim _{x \rightarrow a^{-}} f(x)=A\): Read as left limit of f(x) is ‘A’, means that f(x) → A as x → a. To evaluate the left limit we use the following substitution \(\lim _{x \rightarrow a^{-}} f(x)=\lim _{h \rightarrow 0} f(a-h)\)

\(\lim _{x \rightarrow a^{+}} f(x)=B\): Read as right limit of f(x) is ‘B’, means that f(x) → B as x → a+. To evaluate the left limit we use the following substitution \(\lim _{x \rightarrow a^{+}} f(x)=\lim _{h \rightarrow 0} f(a+h)\).

If left limit and right limit of f(x) at x = a are equal, then we say that the limit of the function f(x) exists at x = a and is denoted
by lim \(\lim _{x \rightarrow a} f(x)\). Otherwise we say that \(\lim _{x \rightarrow a} f(x)\) does not exist.

II. Evaluation Methods

  1. Direct substitution method
  2. Factorisation method
  3. Rationalisation method
  4. Using standard results.

III. Algebra of Limits:
For functions f and g the following holds;
Plus One Maths Notes Chapter 13 Limits and Derivatives 1
Plus One Maths Notes Chapter 13 Limits and Derivatives 2

IV. Standard Results

\(\lim _{x \rightarrow a} k=k\), where k is constant.

\(\lim _{x \rightarrow a} f(x)=f(a)\), if f(x) is a polynomial function.

1. \(=\frac{0}{0}\), if possible we can factorise the numerator and denominator and then, cancel the common factors and again put x = a. This factorization method is not possible in all cases so we are studying some standard limits.
Plus One Maths Notes Chapter 13 Limits and Derivatives 3

V. Derivatives
A derivative of f at a: Suppose f is a real-valued function and a is a point in its domain of definition. The derivative of f at a is defined by \(\lim _{h \rightarrow 0} \frac{f(a+h)-f(a)}{h}\)
Provided this limit exists. A derivative of f (x) at a is denoted by f'(a).
Derivative of f at x. Suppose f is a real-valued function, the function defined by \(\lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}\)

Wherever this limit exists is defined as the derivative of f at x and is denoted by f”(x) |\(\frac{d y}{d x}\)| |y1| y’. This definition of derivative is also called the first principle of the derivative.

VI. Algebra of Derivatives
For functions f and g are differentiable following holds;
Plus One Maths Notes Chapter 13 Limits and Derivatives 4

VII. Standard Results
Plus One Maths Notes Chapter 13 Limits and Derivatives 5

Plus One Maths Notes Chapter 12 Introduction to Three Dimensional Geometry

Kerala State Board New Syllabus Plus One Maths Notes Chapter 12 Introduction to Three Dimensional Geometry.

Kerala Plus One Maths Notes Chapter 12 Introduction to Three Dimensional Geometry

Introduction
To refer to a point in space we require a third axis (say z-axis) which leads to the concept of three-dimensional geometry. In this chapter, we study the basic concept of geometry in three-dimensional space.

I. Octant
Consider three mutually perpendicular planes meet at a point O. Let these three planes intercept along three lines XOX’, YOY’ and ZOZ’ called the x-axis, y-axis, and z-axis respectively. These three planes divide the entire space into 8 compartments called Octants. These octants could be named as XOYZ, XOYZ’, XOYZ, X’OYZ, XOY’Z’, X’OYZ, X’OYZ’, X’OYZ’.
Plus One Maths Notes Chapter 12 Introduction to Three Dimensional Geometry 1

Plus One Maths Notes Chapter 12 Introduction to Three Dimensional Geometry 2
Distance between two points: The distance between the points (x1, y1, z1) and (x2, y2, z2) is Plus One Maths Notes Chapter 12 Introduction to Three Dimensional Geometry 3

Section formula:
1. Internal: The coordinate of the point R which divides the line segment joining the points (x1, y1, z1) and (x2, y2, z2) internally in the ratio l : m is Plus One Maths Notes Chapter 12 Introduction to Three Dimensional Geometry 4

2. External: The coordinate of the point R which divides the line segment joining the points (x1, y1, z1) and (x2, y2, z2) externally in the ratio l : m is Plus One Maths Notes Chapter 12 Introduction to Three Dimensional Geometry 5

3. Midpoint: The coordinate of the point R which is the midpoint of the line segment joining the points (x1, y1, z1) and (x2, y2, z2) is Plus One Maths Notes Chapter 12 Introduction to Three Dimensional Geometry 6

4. Centroid: The coordinate of the centroid of a triangle whose vertices are given by the points (x1, y1, z1), (x2, y2, z2) and (x3, y3, z3) is Plus One Maths Notes Chapter 12 Introduction to Three Dimensional Geometry 7

Plus One Maths Notes Chapter 11 Conic Sections

Kerala State Board New Syllabus Plus One Maths Notes Chapter 11 Conic Sections.

Kerala Plus One Maths Notes Chapter 11 Conic Sections

I. Circle
A circle is the set of all points in a plane that are equidistant from a fixed point in the plane. The fixed point is the centre and the fixed distance is the radius.
Equation of a circle with centre origin and radius r is x2 + y2 = r2.

Equation of a circle with centre (h, k) and radius r is (x – h)2 + (y – k)2 = r2.

General form of the equation of a circle is x2 + y2 + 2gx + 2fy + c = 0 with centre (-g, -f) and radius \(\sqrt{g^{2}+f^{2}-c}\).

II. Conic
A conic is the set of all points in a plane which moves so that the distance from a fixed point is in a constant ratio to its distance from a fixed-line. The fixed point is the focus and fixed line is directrix and the constant ratio is eccentricity, denoted by ‘e’.

III. Parabola (e = 1)

y2 = 4ax
Plus One Maths Notes Chapter 11 Conic Sections 1
Vertex: (0, 0)
Focus(S): (a, 0)
Length of Latusrectum: (LL’) = 4a
Equation of directrix (DD’) is x = -a

y2 = -4ax
Plus One Maths Notes Chapter 11 Conic Sections 2
Vertex: (0, 0)
Focus(S): (-a, 0)
Length of Latusrectum (LL’) = 4a
Equation of directrix (DD’) is x = a

x2 = 4ay
Plus One Maths Notes Chapter 11 Conic Sections 3
Vertex: (0, 0)
Focus(S): (0, a)
Length of Latusrectum (LL’) = 4a
Equation of directrix (DD’) is y = -a

x2 = -4ay
Plus One Maths Notes Chapter 11 Conic Sections 4
Vertex: (0, 0)
Focus(S): (0, -a)
Length of Latusrectum (LL’) = 4a
Equation of directrix (DD’) is y = a

IV. Ellipse (e < 1)

\(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\), a > b
Plus One Maths Notes Chapter 11 Conic Sections 5
1. Eccentricity, e = \(\frac{\sqrt{a^{2}-b^{2}}}{a}\)
(ae)2 = a2 – b2 ⇒ c2 = a2 – b2
2. b2 = a2(1 – e2)
3. Length of Latusrectum (LL’) = \(\frac{2 b^{2}}{a}\)
4. Focii, S(ae, 0) and S'(-ae, 0) or S(c, 0), S'(-c, 0)
5. Centre (0, 0)
6. Vertices A(a, 0) and A'(-a, 0)
7. Equation of directrix (DD’) is x = \(\frac{a}{e}\) and x = \(-\frac{a}{e}\)
8. Length of major axis (AA’) = 2a
9. Length of minor axis'(BB’) = 2b

\(\frac{x^{2}}{b^{2}}+\frac{y^{2}}{a^{2}}=1\), a > b
Plus One Maths Notes Chapter 11 Conic Sections 6
1. Eccentricity, e = \(\frac{\sqrt{a^{2}-b^{2}}}{a}\)
(ae)2 = a2 – b2 ⇒ c2 = a2 – b2
2. b2 = a2(1 – e2)
3. Length of Latus rectum (LL’) = \(\frac{2 b^{2}}{a}\)
4. Focii, S(0, ae) and S'(0, -ae) or S(0, c), S'(0, -c)
5. Centre (0, 0)
6. Vertices A(0, a) and A'(0, -a)
7. Equation of directrix (DD’) is y = \(\frac{a}{e}\) and y = \(-\frac{a}{e}\)
8. Length of major axis (AA’) = 2a
9. Length of minor axis (BB’) = 2b

V. Hyperbola (e > 1)

\(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1\)
Plus One Maths Notes Chapter 11 Conic Sections 7
1. Eccentricity, e = \(\frac{\sqrt{a^{2}+b^{2}}}{a}\)
(ae)2 = a2 + b2 ⇒ c2 = a2 + b2
2. b2 = a2(e2 – 1)
3. Length of Latus rectum (LL’) = \(\frac{2 b^{2}}{a}\)
4. Focii, S(ae, 0) and S'(-ae, 0) or S(c, 0), S'(-c, 0)
5. Centre (0, 0)
6. Vertices A(a, 0) and A'(-a, 0)
7. Equation of directrix (DD’) is x = \(\frac{a}{e}\) and x = \(-\frac{a}{e}\)

\(\frac{y^{2}}{a^{2}}-\frac{x^{2}}{b^{2}}=1\)
Plus One Maths Notes Chapter 11 Conic Sections 8
1. Eccentricity, e = \(\frac{\sqrt{a^{2}+b^{2}}}{a}\)
(ae)2 = a2 + b2 ⇒ c2 = a2 + b2
2. b2 = a2(e2 – 1)
3. Length of Latus rectum (LL’) = \(\frac{2 b^{2}}{a}\)
4. Focii, S(0, ae) and S'(0, -ae) or S(0, c), S'(0, -c)
5. Centre (0, 0)
6. Vertices A(0, a) anti A'(0, -a)
7. Equation of directrix (DD’) is y = \(\frac{a}{e}\) and y = \(-\frac{a}{e}\)

Plus One Maths Notes Chapter 10 Straight Lines

Kerala State Board New Syllabus Plus One Maths Notes Chapter 10 Straight Lines.

Kerala Plus One Maths Notes Chapter 10 Straight Lines

I. Slope of Line
The slope of a line is the ‘tan’ of the angle the line makes with the positive direction of the x-axis. If θ is the angle then, slope = tan θ.

The slope of the x-axis is zero and that of the y-axis is not defined.

Parallel lines have the same slope.

The product of the slopes of perpendicular lines is -1.

The slope is positive if θ < 90°. The slope is negative if θ > 90°.

The slope of a line passing through two points (x1, y1) and (x2, y2) is \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)

If three points A, B, and C are collinear, then AB and BC have the same slope.

If m1 and m2 be slopes of two lines then, θ the angle between is given by tan θ = \(\left|\frac{m_{2}-m_{1}}{1+m_{1} m_{2}}\right|\), 1 + m1m2 ≠ 0

II. Equation of a Line
Equation of x-axis is y = 0.

Equation of y-axis is x = 0.

The equation of a horizontal line is y = a. If ‘a’ is positive then the line is above the x-axis and if negative it will be below the x-axis.

The equation of a vertical line is x = a. If ‘a’ is positive then the line is to the right of the x-axis and if negative it will be to the left of the x-axis.

Point-slope form: y – y1 = m(x – x1), where ‘m’ is the slope and (x1, y1) is a point on the line.

Two-Point form:
y – y1 = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\) (x – x1) where (x1, y1) and(x2, y2) are two point on the line.

Slope intercept form:
1. y = mx + c, where ‘m’ is the slope and ‘c’ is the y-intercept.
2. y = m(x – d), where ‘m’ is the slope and ‘d’ is the x-intercept.

Intercept form: \(\frac{x}{a}+\frac{y}{b}=1\) = 1, where ‘a’ and ‘b‘ are x and y intercept respectively.

Normal form: x cos θ + y sin θ = p, where ‘p’ is the length of the normal from the origin to the line and ‘θ’ is the angle the normal makes with the positive direction of the x-axis.

General equation of a Line: ax + by + c = 0, where a, b and c are real constants.
1. Slope of the line ax + by + c = 0 is \(-\frac{a}{b}\)

2. Parallel lines differ in constant term, i.e; a line parallel to ax + by + c = 0 is ax + by + k = 0.

3. A line perpendicular to ax + by + c = 0 is bx – ay + k = 0.

4. The equation of the family of lines passing through the intersection of the lines a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 is of the form a1x + b1y + c1 + k(a2x + b2y + c2) = 0.

5. The perpendicular distance of a point (x1, y1) from the line ax + by + c = 0 is \(\left|\frac{a x_{1}+b y_{1}+c}{\sqrt{a^{2}+b^{2}}}\right|\)

6. The distance between the parallel lines ax + by + c = 0 and ax + by + k = 0 is \(\left|\frac{c-k}{\sqrt{a^{2}+b^{2}}}\right|\)

7. Normal form of the equation ax + by + c = 0 is x cos θ + y sin θ = p;
Where cos θ = \(\pm \frac{a}{\sqrt{a^{2}+b^{2}}}\); sin θ = \(\pm \frac{b}{\sqrt{a^{2}+b^{2}}}\) and p = \(\pm \frac{c}{\sqrt{a^{2}+b^{2}}}\)

Proper choice of signs is made so that p should be positive.

III. Shifting of Origin
An equation corresponding to a set of points with reference to a system of coordinate axes by shifting the origin is shifted to a new point is called a translation of axes.

Let us take a point P (x, y) referred to the axes OX and OY. Let (h, k) be the coordinates of origin and P(X, Y) be the coordinate of P(x, y) with respect to the new axis. Then, the transformation relation between the old coordinates (x, y) and the new coordinates (X, Y) are given by X = x + h and Y = y + k.

Plus One Maths Notes Chapter 7 Permutation and Combinations

Kerala State Board New Syllabus Plus One Maths Notes Chapter 7 Permutation and Combinations.

Kerala Plus One Maths Notes Chapter 7 Permutation and Combinations

I. Fundamental Principle of Counting
If an event can occur in ‘m’ different ways, following which another event can occur in ‘n’ different ways, then the total number of occurrences of the events in the given order is m × n.

II. Permutation
A permutation is the arrangement of some or all of a number of different objects.

Factorial notation: The notation n! represents the product of first n natural numbers,
ie; n! = n(n – 1 )(n – 2) ….. 3.2.1
1. 1! = 1
2. 0! = 1

The number of permutation of ‘n’ different objects taken ‘r’ at a time, where the objects do not repeat is n(n – 1)(n – 2)……(n – r + 1) which is denoted by nPr.
Plus One Maths Notes Chapter 7 Permutation and Combinations 1
The number of permutation of ‘n’ different objects taken ‘r’ at a time, where repetition is allowed is nr.

Permutation when all the objects are not distinct.
1. The number of permutations of ‘n’ objects, where ‘p’ objects are of the same kind and rest all different = \(\frac{n !}{p !}\)

2. The number of permutations of ‘n’ objects, where ‘p1’ objects are of one kind, ‘p2’ objects are of the second kind, …….., ‘pk‘ objects are of a kth kind and rest all different = \(\frac{n !}{p_{1} ! p_{2} ! \ldots p_{k} !}\)

III. Combinations
A combination is a selection of some or all of a number of different objects (the order of selection is not important). The number of selection of ‘n’ things taken ‘r’ at a time is nCr.
Plus One Maths Notes Chapter 7 Permutation and Combinations 2

Plus One Maths Notes Chapter 5 Complex Numbers and Quadratic Equations

Kerala State Board New Syllabus Plus One Maths Notes Chapter 5 Complex Numbers and Quadratic Equations.

Kerala Plus One Maths Notes Chapter 5 Complex Numbers and Quadratic Equations

we have studied linear equations in one and two variables and quadratic equations in one variable. We have seen that the equation x2 + 1 = 0 has no real solution since the root of a negative number does not exist in a real number. So, we need to extend the real number system to a larger number system to accommodate such numbers.

I. Complex Numbers
A number of the form a + ib, where a and b are real numbers and i = √-1.
Usually, a complex number is denoted by z, a is the real part of z denoted by Re(z) and b is the imaginary part of z denoted by Im(z).

II. Algebra of Complex Numbers

Addition: Let z1 = a + ib and z2 = c + id be two complex numbers. Then the sum z1 + z2 is obtained by adding the real and imaginary parts.

1. z1 + z2 = z2 + z1, commutative.
2. z1 + (z2 + z3) = (z1 + z2) + z3, associative.
3. 0 + i0 is the identity element.
4. -z is the inverse of z.

Multiplication: Let z1 = a + ib and z2 = c + id be two complex numbers.
Then the product z1z2 is defined as follows:
z1z2 = (ac – bd) + i(ad + bc).

1. z1z2 = z2z1, commutative.
2. z1(z2z3) = (z1z2)z3, associative.
3. 1 + i0 is the identity element.
4. \(\frac{1}{z}\) is the inverse of z.
5. z1(z2 + z3) = z1z2 + z1z3, distributive law.

Power of ‘i’: i3 = -i, i4 = 1
In general i4k = 1, i4k+1 = i, i4k+2 = -1, i4k+3 = -i

Identities:
Plus One Maths Notes Chapter 5 Complex Numbers and Quadratic Equations 1
Plus One Maths Notes Chapter 5 Complex Numbers and Quadratic Equations 2

The Modulus and Conjugate of a complex number:
Consider a complex number z = a + ib . Then, the conjugate of z is denoted by \(\bar{z}\), defined as \(\bar{z}\) = a – ib and the modulus of z is denoted by |z|, defined as \(\sqrt{a^{2}+b^{2}}\).

Properties:
Plus One Maths Notes Chapter 5 Complex Numbers and Quadratic Equations 3

III. Representation of Complex Number

Argand Plane:
Plus One Maths Notes Chapter 5 Complex Numbers and Quadratic Equations 4
A complex number z = a + ib which corresponds to the ordered pair (a, b) can be represented geometrically as the unique point P(a, b) in the XY-plane, where the real part is taken along the x-axis and the imaginary part along the y-axis. Such a plane is called the Argand Plane or Complex plane.

Polar Form:
Plus One Maths Notes Chapter 5 Complex Numbers and Quadratic Equations 5
Let the point P represent the non-zero complex number z = x + iy. Let the directed line segment OP be of length ‘r’ and be the angle which OP makes with the positive direction of the x-axis. Then, P is determined by the unique ordered pair of a real number (r, θ) called polar coordinate of the point P, where x = r cos θ, y = r sin θ and therefore the polar form of z can be represented as z = r(cos θ + i sin θ).
The principle argument of z is value ‘θ’ such that -x ≤ θ ≤ π, denoted by arg z.
To find the principle argument, we find tan α = |\(\frac{y}{x}\)|, 0 ≤ α ≤ \(\frac{\pi}{2}\)

The quadrant on which ‘P’ liesarg z =
Iα
IIπ – α
IIIα – π
IV
Positive real axis0
Negative real axisπ
Positive imaginary axis\(\frac{\pi}{2}\)
Negative imaginary axis\(-\frac{\pi}{2}\)

Plus One Maths Notes Chapter 4 Principle of Mathematical Induction

Kerala State Board New Syllabus Plus One Maths Notes Chapter 4 Principle of Mathematical Induction.

Kerala Plus One Maths Notes Chapter 4 Principle of Mathematical Induction

Induction means the generalization from a particular case or facts. In contrast to deductive reasoning, inductive depends on working with each case and developing a conjecture by observing incidences till we have observed each and every case. In algebra or in another discipline of mathematics, there are certain results or statements that are formulated in terms of n, where n is a positive integer. To such statements, the well-suited principle that is based on the specific technique is known as the principle of mathematical induction.

The Principle of Mathematical Induction:
Suppose there is a statement P(n) involving the natural number n such that

1. The statement is true for n = 1, i.e; P(1) is true, and

2. If the statement is true for n = k (where k is some positive integer), then the statement is also true for n = k + 1, i.e; the truth of P(k) implies the truth of P(k+1). Then, P(n) is true for all natural numbers n.

Plus One Maths Notes Chapter 3 Trigonometric Functions

Kerala State Board New Syllabus Plus One Maths Notes Chapter 3 Trigonometric Functions.

Kerala Plus One Maths Notes Chapter 3 Trigonometric Functions

I. Angles
The measure of an angle is the amount of rotation performed to get the terminal side from the initial side.

1. Degree measure: If a rotation from the initial side to terminal side is \(\left(\frac{1}{360}\right)^{t h}\) of a revolution, the angle is said to have a measure of one degree, written as 1°. 1° = 60′ and f = 60″.

2. Radian measure: An angle subtended at the center by an arc of length 1 unit in a unit circle is said to be of 1 radian. Radian measure is a real number corresponding to degree measure.

180° = π radians

Radian measure = \(\frac{\pi}{180}\) × Degree measure

Degree measure = \(\frac{180}{\pi}\) × Radian measure

l = rθ, where l = arc length, r = radius of the circle and θ = angle in radian measure.

II. Trigonometric Function
Consider a unit circle with centre at the origin of the coordinate axis.
Let P (a, b) be any point on the circle which makes an angle θ° with the x-axis. Let x be the corresponding radian measure of the angle θ°, i.e; x is the arc length corresponding to θ°.

Plus One Maths Notes Chapter 3 Trigonometric Functions 1

From the ∆OMP’m the figure we get;
sin θ = sin x = \(\frac{b}{1}\) = b and cos θ = cos x = \(\frac{b}{1}\) = a
This means that for each real value of x we get corresponding unique ‘sin’ and ‘cosine’ value which is also real. Hence we can define the six trigonometric functions as follows.

1. f : R → [-1, 1] defined by f(x) = sin x
Plus One Maths Notes Chapter 3 Trigonometric Functions 2

2. f : R → [-1, 1] defined by f(x) = cos x
Plus One Maths Notes Chapter 3 Trigonometric Functions 3

3. f : R – {nπ, n ∈ Z} → R – (-1, 1) defined by f(x) = \(\frac{1}{\sin x}\) = cosec x
Plus One Maths Notes Chapter 3 Trigonometric Functions 4

4. f : R – {(2n + 1) \(\frac{\pi}{2}\)} → R – (-1, 1) defined by f(x) = \(\frac{1}{\cos x}\) = sec x
Plus One Maths Notes Chapter 3 Trigonometric Functions 5

5. f : R – {(2n + 1)π, n ∈ Z} → R defined by f(x) = \(\frac{\sin x}{\cos x}\) = tan x
Plus One Maths Notes Chapter 3 Trigonometric Functions 6

6. f : R – {nπ, n ∈ Z} → R defined by f(x) = \(\frac{\cos x}{\sin x}\) = cot x
Plus One Maths Notes Chapter 3 Trigonometric Functions 7

Sign of trigonometric functions in different quadrants;
Plus One Maths Notes Chapter 3 Trigonometric Functions 8
For odd multiple of \(\frac{\pi}{2}\) trignometric functions changes as given below.
sin → cos
cos → sin
sec → cosec
cosec → sec
tan → cot
cot → tan

The value of trigonometric functions for some specific angles;
Plus One Maths Notes Chapter 3 Trigonometric Functions 9

III. Compound Angle Formula

sin(x + y) = sin x cos y + cos x sin y

sin(x – y) = sin x cos y – cos x sin y

cos(x + y) = cos x cos y – sin x sin y

cos(x – y) = cos x cos y + sin x sin y
Plus One Maths Notes Chapter 3 Trigonometric Functions 10
sin(x + y) sin(x – y) = sin2 x – sin2 y = cos2 x – cos2 y

cos(x + y) cos(x – y) = cos2 x – sin2 y
Plus One Maths Notes Chapter 3 Trigonometric Functions 11

IV. Multiple Angle Formula

cos2x = cos2 x – sin2 x
= 1 – 2sin2 x
= 2 cos2 x – 1
= \(\frac{1-\tan ^{2} x}{1+\tan ^{2} x}\)

Plus One Maths Notes Chapter 3 Trigonometric Functions 12

V. Sub-Multiple Angle Formula
Plus One Maths Notes Chapter 3 Trigonometric Functions 13

Plus One Maths Notes Chapter 3 Trigonometric Functions 14

VI. Sum Formula
Plus One Maths Notes Chapter 3 Trigonometric Functions 16

VII. Product Formula

2 sin x cos y = sin(x + y) + sin(x – y)

2 cos x sin y = sin(x + y) – sin(x – y)

2 cos x cos y = cos(x + y) + cos(x – y)

2 sin x sin y = cos(x – y) – cos(x + y)

VIII. Solution of Trigonometric Equations

sin x = 0 gives x = nπ, where n ∈ Z

cos x = 0 gives x = (2n + 1)π, where n ∈ Z

tanx = 0 gives x = nπ, where n ∈ Z

sin x = sin y ⇒ x = nπ + (-1)n y, where n ∈ Z

cos x = cos y ⇒ x = 2nπ ± y, where n ∈ Z

tan x = tan y ⇒ x = nπ + y, where n ∈ Z

Principal solution is the solution which lies in the interval 0 ≤ x ≤ 2π.

IX. Sine and Cosine formulae

Let ABC be a triangle. By angle A we mean the angle between the sides AB and AC which lies between 0° and 180°. The angles B and C are similarly defined. The sides AB, BC, and CA opposite to the vertices C, A, and B will be denoted by c, a, and b, respectively.

Theorem 1 (sine formula): In any triangle, sides are proportional to the sines of the opposite angles. That is, in a triangle ABC
\(\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}\)

Theorem 2 (Cosine formulae): Let A, B and C be angles of a triangle and a, b and c be lengths of sides opposite to angles A, B, and C, respectively, then
a2 = b2 + c2 – 2bc cos A
b2 = c2 + a2 – 2ca cos B
c2 = a2 + b2 – 2ab cos C

A convenient form of the cosine formulae, when angles are to be found are as follows:
Plus One Maths Notes Chapter 3 Trigonometric Functions 15