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TS Inter 1st Year Botany Study Material Chapter 2 Biological Classification

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TS Inter 1st Year Botany Study Material Chapter 2 Biological Classification

Very Short Answer Type Questions

Question 1.


What is the nature of cell walls in diatoms?


Answer:

  1. In Diatoms, the cell walls form two thin overlapping shells, epitheca over hypotheca which fit together as in a soap box.
  2. The walls are embedded with silica and are indestructible. The cell walls left behind by diatoms in their habitat and accumulate over billions of years as diatomaceous earth or kieselguhr.

Question 2.


How are Viroids different from Viruses?


Answer:

VirusesViroids
1) It is a nucleoprotein particle.1) It is a free RNA particle.
2) Nucleic acid can be DNA or RNA.2) Viroid is formed only by RNA.
3) Viruses infect all types of living organisms.3) Viroids infect only plants.

Question 3.


What do the terms phycobiont and mycobiont signify? [Mar. ’17, A.P. : Mar. ’13]?


Answer:


1) Phycobiont :
The group of Algae that live as symbionts in lichens.

2) Mycobiont :
The group of fungi that live as symbionts in lichens.

Question 4.


What do the terms ‘algal bloom’ and ‘red tides’ signify?


Answer:


1. Algal bloom :
Excessive growth of algae mostly cyanophyceae members due to the enrichment of excessive nutrients in a water body. t

2. Red tides :
Sea appears red due to the rapid multiplication of a dinoflagellate, Gonyaulax Red tides in Meditarrenian sea.

Question 5.


State two economically important uses of heterotrophic bacteria?


Answer:

  1. They help in making curd from milk.
  2. They are helpful in nitrogen fixation in roots of leguminous plants.

Question 6.


What is the principle underlying the use of cyanobacteria in agricultural fields for crop improvement? [Mar. 2019, ’15 A.P]?


Answer:

  1. Cyanobacteria Eg : Nostoc, Anabaena, can fix atmospheric nitrogen in specialised cells called heterocysts.
  2. They improve soil fertility by adding organic matter. ,

Question 7.


Plants are autotrophic. Name some plants which are partially heterotrophic?


Answer:

  1. Insectivorous plants are partially heterotrophic.
    Eg : Bladderwort and Venus fly trap.
  2. Parasitic plant, cuscuta is also partially heterotrophic.

Question 8.


Who proposed five kingdom classification ? How many kingdoms of this classification contain eukaryotes?


Answer:

  1. R.H. Whittaker (1969) proposed Five Kingdom Classification.
  2. Four kingdoms namely Protista, Fungi, Plantae and Animalia, consists of eukaryotes, while kingdom Monera consists of Prokaryotes.

Question 9.


Give the main criteria used for classification by Whittaker. [Mar. – 2020, 2018 • Mar. 15 – T.S.]?


Answer:


The main criteria for five kingdom classification of Whittaker are cell structure, thallus organisation, mode of nutrition, reproduction and phylogenetic relationships.

Question 10.


Name two diseases caused by Mycoplasmas. [May ’14]?


Answer:

  1. Witches broom in plants.
  2. Pleuropheumonia in cattle.
  3. Mycoplasmal urethritis in humans.

Question 11.


What are slime moulds? Explain what is meant by plasmodium with reference to slime moulds.?


Answer:


1. Slime moulds are saprophytic protists.

2. Plasmodium :
An aggregation formed by a slime mould under suitable conditions, which may grow and spread over several feet.

Short Answer Type Questions

Question 1.


What are the characteristic features of Euglenoids?


Answer:


Euglenoids:

  1. These are unicellular, flagellate, fresh water organisms found in stagnant water.
  2. Cell wall is absent.
  3. The body is covered by thin flexible pellicle.
  4. They bear two flagella, usually one long and one short. They swim actively by flagella.
  5. The anterior part of the cell bears an invagination consisting of cytostome (cell mouth), cytopharynx (gullet) and reservoir.
  6. A photosynthetic stigma or eye spot is present in the reservoir.
  7. Chloroplast is present. The pigments in it are identical to those present in higher plants. Performs photosynthesis.
  8. In the absence of sunlight they behave like heterotrophs depending on smaller organisms for food.,
  9. Reproduction is by longitudinal binary fission Palmella stage is found in Euglena.

Question 2.


What are the advantages and disadvantages of two kingdom classification?


Answer:


a) Two kingdom classification with Plantae and Animalia was developed during cinnaeues tissue, that included all plants and animals respectively.

AdvantagesDisadvantages
1) Organisms were easily classified into plants and animals and was easy to understand.1) But a large number of organisms did not fall into either of the two categories.
This system did not distinguish between the eukaryotes and prokeryotes; unicellular and multicellular organisms and photo-synthetic and non photosynthetic organisms.
2) All cell wall containing organisms were included in plantae kingdom. So Bacteria, Algae, Fungi, Bryophytes, Pteridophytes, gymno- sperms and angiosperms were placed under plants.2) This placed together groups which widely differed in other character- sties prokeryotic bacteria and Blue green algae were brought together and placed with other groups which are eukaryotic. It also grouped together the unicellular (eg.: Chlamydomonas) and multicellular, (eg : spirogyra) ones. This systems did not differentiate between the heterographic group, fungi and the autotrophic green plants. Fungi consists of chitin in their cell wall, while green plants have cellulosic cell walls.

Question 3.


Give the salient features and importance of Chrysophytes. [Mar. – 2018, Mar. ’15 – A.P. : Mar. ’13]?


Answer:

  1. This group includes diatoms and desmids (golden algae).
  2. They are green, microscopic, float in water currents.
  3. In diatoms the cell walls form two thin overlapping shells, epitheca and . hypotheca which fit together as in a soap box.
  4. The cell walls are embedded with silica which are indestructible. They pile at the bottom of water reservoir to form diatomaceous earth.
  5. Diatoms are divided into two types based oh symmetry.
    i) CentraIe diatoms are radially symmetrical.
    ii) Pennales are bilaterally symmetrical.
  6. Asexual reproduction is by binary fission and sexual reproduction is by the formation of gametes.

Question 4.


Give a brief account of Dinoflagellates. [Mar. 2019, ’17 – A.P, Mar. ’15 – T.S]?


Answer:

  1. Dinoflagellates are marine. They appear as yellow, green, brown, blue or red depending upon the pigments present in the cells.
  2. Cell wall is made up of cellulose plates.
  3. Two flagella are present. One lies longitudinally and the other lies transversely in the furrow between the wall plates.
  4. Flagella produce spinning movements. So these are called whirling whips.
  5. Nucleus is called Mesokaryon as chromosomes are condensed without histones.
  6. Example : Nostoc shows bioluminescence.
    Gonyaulax make the sea appear red.

Question 5.


Write the role of fungi in our daily life. [Mar. ’14]?


Answer:

  1. Mushroom and toadstools are edible fungus.
  2. Unicellular fungi like yeast are used to make beer and bread.
  3. Fungi like Rhizopus commonly grow on stale bread, pickles, jams, cheese, on moist food stuff and spoils them. They are called moulds.
  4. Fungi causes diseases in plants and animals.
    Eg : Wheat rust is caused by puccinia.
    Late blight of potato by phytopthora.
  5. Orange rot, Red rot in sugarcane are caused by fungus.
  6. White spots on mustard leaves are due to parasitic fungus. (Albugo)
  7. Some fungi are the source of antibiotics and peninllium.

Long Answer type Questions

Question 1.


Give the salient features and comparative account of different classes of Fungi studied by you.?


Answer:


img

Question 2.


Describe briefly different groups of Monerans you have studied?


Answer:


Kingdom Monera includes all prokarytes like Archebacteria, Eubacteria, Mycoplasma and Actinomycetes.

Archebacteria :

  1. These are different type of bacteria as they have a different cell wall structure. They can survive in extreme conditions like salty areas (halophiles), hot springs (thermacidophiles) and marshy areas (methanogens).
  2. The cell wall does not contain peptidoglycan as in bacteria but contain pseudomurein.
  3. The cell membrane contains branched lipid which is responsible for their survival in extreme conditions.
  4. Methanogens live in the guts of several ruminant animals like cowand buffaloes and help in their digestion.
  5. They help in the production of,biogas such as methane from the dungs of the animals.

Eubacteria:

  1. They occur everywhere even in extreme habitats.
  2. They live as parasites, and symbionts also.
  3. Basing on the shape bacteria are grouped under four categories. They are 1) Spherical coccus 2) Rod shaped Bacillus 3) Comma, shaped Vibrium 4) Spiral shape Spirillum
  4. In Bacteria, cell wall consists of peptidoglycan also called murein or ‘ mucopeptide.
  5. Infolding of cell membrane called mesosomes responsible for respiration.
  6. Cell organelles are absent except ribosome.
  7. As it is prokaryotic, the genetic material DNA is naked without nuclear membrane.
  8. It shows autotrophic and heterotrophic nutrition.
  9. Excessive growth of cyanobacteria due to nutrients present in sewage causes Algal blooms.
  10. Rapid growth of red dinoflagellate like Gonyaulax make sea appear red or red tides in Mediterianian sea.
  11. Chemo autotrophic bacteria oxidise various inorganic substances.
  12. Chemo heterotrophs are saprophytes which grow on dead organic matter and parasite which causes diseases.
  13. Asexual reproduction is mainly by binary fission or by spores during unfavourable condition. Sexual reproduction is done by transfer of genetic material from one bacteria to other.

Mycoplasma :

  1. Mycoplasma are the smallest living cells and can survive without oxygen.
  2. They do not have any cell wall.
  3. Mostly they are pathogenic in plants and animals. They cause witches broom in plants, pleuropneumonia in cattle and mycoplasmal urethritis in humans.

Actinomycetes :

  1. These are branched filamentous bacteria.
  2. Cell wall contains mycolic acid.
  3. Most of them are saprophytic and decomposers. Mycobacterium and Corynebacteriurn are parasites.
  4. Antibiotics are produced from the genus Streptomyces.

Question 3.


Enumerate the salient features of different groups of protista.?


Answer:


Kingdom Protista includes unicellular, aquatic, eukaryotes. It includes Chrysophytes, Dinoflagellates, Euglenoids, Slime moulds and Protozoans.
1. Chrysophytes:

  1. It includes diatoms and desmids (golden algae).
  2. They are green, microscopic, float in water currents.
  3. In Diatoms the cell walls form two thin overlapping shells, epitheca and hypotheca which fit together as soap box.
  4. The cell walls are embedded with silica which are indestructible. They pile at the bottom of water reservoir to form diatomaceous earth.
  5. Diatoms are divided into two types based on symmetry.
    i) Centrale diatoms are radially symmetrical.
    ii) Pennales are bilaterally symmetrical.
  6. Asexual reproduction is by binary fission and sexual reproduction is by the formation of gametes.

2. Dinoflagellates:

  1. Dinoflagellates are marine. They appear as yellow, green, brown, blue or red depending upon the pigments present in the cells.
  2. Cell wall is made up of cellulose plates.
  3. Two flagella are present. One lies longitudinally and the other lies transversely in the furrow between the wall plates.
  4. Flagella produce spinning movements. So these are called whirling whips.
  5. Nucleus is called Mesokaryon as chromosomes are condensed without histones.
  6. Example : Nostoc shows bioluminescence.
    Gonyaulax make the sea appear red.

3. Euglenoids :

  1. These are unicellular, flagellate, fresh water organisms found in stagnant water.
  2. Cell wall is absent.
  3. The body is covered by thin flexible pellicle.
  4. They bear two flagella, usually one long and one short. They swim actively by flagella.
  5. The anterior part of the cell bears an invagination consisting of Cytostome (cell mouth), Cytopharynx (gullet) and reservoir.
  6. A photosynthetic stigma on eye spot is present inthe reservoir.
  7. Chloroplast is present. The pigments in it are identical to those present in higher plants. Performs photosynthesis.
  8. In the absence of sunlight they behave like heterotrophs depending on smaller organisms for food.
  9. Reproduction is by longitudinal binary fission Palmella stage is found in Euglena.

4. Slime moulds:

  1. They show saprophytic nutrition.
  2. Slime moulds are multinucleated protoplasm surrounded by plasma membrane.
  3. They are aquatic; move along with decaying twigs.
  4. Under favourable Conditions they aggregate to form plasmodium. They may spread upto several feet.
  5. Under unfavourable conditions, plasmodium differentiates and forms fruiting bodies which bear spores at their tips. These spores are wind dispersed and can survive for many years.

5. Protozoans:
All protozoans are heterotrophs and live as parasites. The four major groups of protozoans are given below.
i) Amoeboid protozoans:

  1. These organisms live in fresh water, sea water or moist soil.
  2. They have locomotory organ called pseudopodia or false feet.
  3. Marine forms have silica shells on their surface. Example: Amoeba.

ii) Flagellated protozoans:

  1. These members are either free-living or parasitic.
  2. They have flagella.
  3. They cause diseases like sleeping sickness. Example : Trypanosoma.

iii) Ciliated protozoans:

  1. These are aquatic and actively moving organisms because of cilia.
  2. They have a cavity that opens to outside of the cell surface.
    Example : Paramecium.

iv) Sporozoans :
It includes diverse organisms that have an infectious sporelike stage in their life cycle. Example : Plasmodium.

InText Question Answers

Question 1.


State two economically important uses of?
a) Heterotrophic bacteria.
b) Archaebacteria.


Answer:


a) Use of heterotrophic bacteria :

  1. They help in making curd from milk.
  2. They convert dead plants and animals into simpler substances and make them available to plants.

b) Use of archaebacteria :
1) They live in the guts of several ruminant animals such as cow and buffaloes and help in their digestion.

Question 2.


Give a comparative account of the classes of Kingdom Fungi on the basis of the following i) Mode of nutrition ii) Mode of reproduction?


Answer:


img

Question 3.


Give a brief account of viruses with respect to their structure and nature of genetic material. Also name four common viral diseases?


Answer:

  1. Viruses are acellular, ultramicroscopic, nucleoprotein particles.
  2. Viruses are obligate parasites. They are inert outside the host cell.
  3. Viruses contain nucleic acid and protein.
  4. The protein part forms a coat called capsid. It is made up of small sub units called capsomeres.
  5. The nucleic acid which is genetic material may be DNA or RNA.
  6. No virus contains both DNA and RNA.
  7. Tobacco Mosaic Virus (TMV) and Human Immuno Virus (HIV) are examples for virus having RNA.
  8. Bacteriophages contain DNA as genetic material.
  9. Four common Viral Diseases : 1) AIDS, 2) Influenza 3) Small pox 4) Mumps.

Question 4.


Organise a discussion in your class on the topic. Are viruses living or non-living?


Answer:


The main points to be discussed in class :
a) Viruses can be regarded as living organisms because

  1. They are formed by macromolecules which occur in living beings.
  2. Presence of genetic material
  3. Ability to multiply or reproduce
  4. Occurrence of mutations
  5. Infectivity and host specificity
  6. Occurrence of antigenic property
  7. Viruses are killed by autoclaving and ultraviolet rays.
  8. Viruses are responsible for infectious diseases like common cold, influenza, chicken pox, mumps etc.

b) Viruses can be regarded as non-living organisms because

  1. Protoplasm absents
  2. Ability to get crystallized & TMV
  3. Inability to live independently
  4. High specific gravity which is found only in non-living objects
  5. Absence of respiration
  6. Absence of storing energy system
  7. Absence of growth and division.

Question 5.


Suppose you accidentally find an old preserved permanent slide without a label and in your effort to identify it, you place the slide under microscope and observe the following features?
a) unicellular body
b) well defined nucleus
c) biflagellate condition – one flagellum lying longitudinally and the other transversely.
What would you identify it as ? Can you name the kingdom it belongs to?


Answer:


It is identified as Dinoflagellates.
It belongs to kingdom : Protista.

Question 6.


Polluted water bodies have usually high abundance of plants like IMostoc and Oscillatoria. Give reasons.?


Answer:


Polluted water bodies have excessive growth of plants like Nostoc and Oscillatonia because of the excessive nutrients present in it. It results in algal booms.

Question 7.


Cyanobacteria and heterotrophic bacteria have been clubbed together in Eubacteria of kingdom Monera as per the five kingdom classification, even though the two are vastly different from each other. Is this grouping of the two types of taxa in the same kingdom justified? If so why?


Answer:


Yes. because both are unicellular prokaryotic organisms.

Question 8.


What observable features in Trypanosoma would make you classify under the kingdom Protista?


Answer:


They are aquatic, single-celled eukaryotes.

Question 9.


At a stage of their life cycle, ascomycetous fungi produce fruiting bodies like cleistothecium, perithecium or apothecium. How are these three types of fruiting bodies differ from each other?


Answer:

  1. The fruiting bodies are produced in Fungi.
  2. Ascomycetes are called Ascocarp.
  3. The globose ascocarp without opening is called cleistothecium.
  4. The flask-shaped ascocarp with an apical opening is called perithecium.
  5. The cup or saucer-shaped ascocarp is called apothecium.

CBSE Class 12th Time Table 2026 Reschedule Date Out: Download Pdf CBSE 12th Exam Date Sheet 2026 at Manabadi.co.in

Ramu
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CBSE Class 12th Time Table 2026 Reschedule Date Out: Download Pdf CBSE 12th Exam Date Sheet 2026 at Manabadi.co.in

It is hereby informed that the examinations of the subjects for Class X and Class XII, which were earlier scheduled on 03 March 2026, have been rescheduled due to administrative reasons. The revised dates are as follows:

Class X
Earlier Date: 03 March 2026
Revised Date: 11 March 2026

Class XII
Earlier Date: 03 March 2026
Revised Date: 10 April 2026

All other examination dates remain unchanged. Schools are requested to kindly disseminate this information to all concerned students and parents for their information and necessary action please.

Date Sheets are being amended accordingly and the revised dates will also be given in the Admit Cards when issued.

Your cooperation will be appreciated in ensuring smooth conduct of the examinations.

CBSE Class 10th Exam Reschedule Date

The Central Board of Secondary Education (CBSE) has officially released the CBSE Class 12th Time Table 2026 for all streams including Science, Commerce, and Arts. As per the CBSE Board notification, the Class 12th Board Exams 2026 will be conducted from February 17, 2026 to April 9, 2026 in offline mode across thousands of examination centers in India and abroad. Students appearing for the Higher Secondary examinations can now download the CBSE 12th Exam Date Sheet 2026 PDF from the official board website or from Manabadi.co.in for easy access.

The time table plays a crucial role in helping students start structured preparation, revise strategically, and maintain a proper study schedule. In this article, we provide complete details of the CBSE Class 12 Exam Schedule 2026, steps to download the timetable in PDF format, subject-wise exam dates, exam day guidelines, and preparation tips.

CBSE Class 12th Time Table 2026 – Download

CBSE 12th Board Exam 2026 Overview

FeatureDetails
Name of ExamCBSE Class 12 Board Examination 2026
Conducting AuthorityCentral Board of Secondary Education (CBSE)
Academic Session2025–26
Exam Start DateFeb 17, 2026
Exam End DateApril 10th 2026
Mode of ExamOffline (Pen & Paper)
StreamsScience, Commerce & Arts
Official Websitewww.cbse.gov.in
Download Time Table FromManabadi.co.in

CBSE Class 12 Exam Date Sheet 2026 (Subject-Wise Schedule)

Students can check the CBSE 10th final date sheet 2026 from below: 

DateSubject (Timings: 10:30 am to 1:30 pm)
17-Feb-2026 (Tue)Biotechnology; Entrepreneurship; Shorthand (English); Shorthand (Hindi)
18-Feb-2026 (Wed)Physical Education
19-Feb-2026 (Thu)Engineering Graphics; Bharatanatyam; Kuchipudi; Odissi; Manipuri; Kathakali; Horticulture; Cost Accounting
20-Feb-2026 (Fri)Physics
21-Feb-2026 (Sat)Automotive; Fashion Studies
23-Feb-2026 (Mon)Mass Media Studies; Design Thinking and Innovation
24-Feb-2026 (Tue)Accountancy
25-Feb-2026 (Wed)Beauty & Wellness; Typography & Computer Application
26-Feb-2026 (Thu)Geography
27-Feb-2026 (Fri)Painting; Graphics; Sculpture; Applied Art (Commercial Art)
28-Feb-2026 (Sat)Chemistry
02-Mar-2026 (Mon)Urdu Elective; Sanskrit Elective; Carnatic Music; Kathak; Urdu Core; Front Office Operations; Insurance; Geospatial Technology; Electrical Technology
05-Mar-2026 (Thu)Psychology
06-Mar-2026 (Fri)Punjabi; Bengali; Tamil; Telugu; Sindhi; Marathi; Gujarati; Manipuri; Malayalam; Odia; Assamese; Kannada; Arabic; Tibetan; German; Russian; Persian; Nepali; Limboo; Lepcha; Telugu (Telangana); Bodo; Tangkhul; Japanese; Bhutia; Spanish; Kashmiri; Mizo
07-Mar-2026 (Sat)Yoga; Electronics & Hardware
09-Mar-2026 (Mon)Mathematics; Applied Mathematics
10-Mar-2026 (Tue)Food Production; Office Procedures & Practices; Library & Information Science; Early Childhood Care & Education
11-Mar-2026 (Wed)Hindustani Music (Mel/Per Instrument); Health Care; Design
12-Mar-2026 (Thu)English Elective / English Core
13-Mar-2026 (Fri)Tourism; Air-conditioning & Refrigeration
14-Mar-2026 (Sat)Home Science
16-Mar-2026 (Mon)Hindi Elective / Hindi Core
17-Mar-2026 (Tue)Hindustani Music Vocal
18-Mar-2026 (Wed)Economics
19-Mar-2026 (Thu)Physical Activity Trainer
20-Mar-2026 (Fri)Marketing
23-Mar-2026 (Mon)Political Science
24-Mar-2026 (Tue)Retail; Artificial Intelligence
25-Mar-2026 (Wed)Informatics Practices; Computer Science; Information Technology
27-Mar-2026 (Fri)Biology
28-Mar-2026 (Sat)Business Studies; Business Administration
30-Mar-2026 (Mon)History
01-Apr-2026 (Wed)Financial Market Management; Agriculture; Medical Diagnostics; Salesmanship
02-Apr-2026 (Thu)National Cadet Corps (NCC); Food Nutrition & Dietetics
04-Apr-2026 (Sat)Sociology
06-Apr-2026 (Mon)Knowledge Tradition & Practices of India; Bhoti; Kokborok; Banking; Electronics Technology
07-Apr-2026 (Tue)Web Application
08-Apr-2026 (Wed)Sanskrit Core; French; Taxation
09-Apr-2026 (Thu)Multi-Media; Textile Design; Data Science
10-Apr-2026 (Fri)Legal Studies

How to Download CBSE Class 12th Time Table 2026 PDF at Manabadi.co.in

Follow the simple steps to access the date sheet:

  • Visit Manabadi.co.in
  • Find the CBSE Class 12 Time Table 2026 link on the homepage.
  • Click on the link labeled “Download CBSE 12th Exam Schedule 2026 PDF.”
  • The timetable will open in a new window.
  • Click on Download or Print for offline access.

Details Mentioned in CBSE 12th Date Sheet 2026

  • Board name
  • Examination name
  • Subjects
  • CBSE Class 10 exam date 2025
  • Exam time
  • Practical exam dates
  • Important instructions

Preparation Tips for CBSE Class 12 Board Exams 2026

  1. Follow NCERT Books Thoroughly
    Most questions in CBSE come directly or indirectly from NCERT textbooks.
  2. Solve Previous Year Papers
    Understanding question patterns helps boost confidence.
  3. Practice Sample Papers
    CBSE releases sample papers every year — practice them weekly.
  4. Make Revision Notes
    Short notes improve memory and help during final revision.
  5. Maintain Health
    Eat well, sleep well, and avoid late-night study habits before exams.

Guidelines for Students Appearing for the CBSE Board Exams 2026

  • Reach the examination center at least 30 minutes early.
  • Carry admit card, school ID card, and necessary stationery.
  • Mobile phones, calculators, and smart watches are strictly prohibited.
  • Follow writing and presentation formats as instructed.
  • Answer questions neatly and manage time across sections.

AP Inter 2nd Year Hall Ticket 2026: Download BIEAP II Yr Hall Ticket at manabadi.co.in

Ramu
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AP Inter 2nd Year Hall Ticket 2026: Download BIEAP II Yr Hall Ticket at manabadi.co.in

The Board of Intermediate Education, Andhra Pradesh (BIEAP) is set to conduct the AP Intermediate 2nd Year Public Examinations 2026 from February 23rd, 2026 to March 25th, 2026. Students appearing for these crucial board examinations must download their AP Inter 2nd Year Hall Ticket 2026 to gain entry into the examination hall.

The AP Inter II Year Hall Ticket 2026 will be released online through the official BIEAP portal and education websites like manabadi.co.in. This hall ticket is a mandatory document and contains essential details such as exam dates, subject-wise schedule, exam center address, and student information.

In this article, you will find complete details about the AP Inter 2nd Year Hall Ticket 2026, including release date, download steps, exam schedule, important instructions, and FAQs.

AP Intermediate 2nd Year Result 2026

Impact of AP Inter Reforms on the 2025 Hall Ticket

The numerous changes introduced by the Andhra Pradesh Intermediate Board for the academic year have a direct impact on the design, instructions, and information to be printed on the AP Inter 2025 Hall Ticket. With the introduction of a new question paper model, expanded answer booklets, and revised pass criteria, the hall ticket is expected to carry more detailed guidelines than in previous years.

One of the major changes influencing the 2025 hall ticket is the increase in answer booklet pages. Students of Mathematics, Physics, Chemistry, Economics, History, Political Science and Commerce will receive 32-page booklets, while Biology students will receive two separate 24-page booklets for Botany and Zoology. To avoid confusion in the exam hall, the hall ticket is likely to mention the type of answer booklet provided for each subject. This helps students mentally prepare for the length and structure of their examinations.

The introduction of one-mark questions for the first time and the increased number of questions also require the board to add instructions regarding the updated question pattern. Since there is no choice in one-mark and two-mark questions, this detail may be noted in the hall ticket or the accompanying instruction sheet so students clearly understand what to expect.

Revised pass rules—such as 29 marks being enough to pass out of 85 in first year, and overall 35% being calculated across both years—may also be included as advisory notes. This ensures students are aware of the new evaluation system before appearing for exams.

Subjects like Geography (75 marks but counted as 85) and the 30-mark practical exams in second year also require clear mention of exam timings and rules.

Overall, the AP Inter 2025 Hall Ticket will likely contain more comprehensive guidelines, reflecting all structural changes and helping students approach the examinations with clarity and confidence.

APBIE 2026 Inter 1st Year Exam Pattern Changes – Revised Marks Distribution & Question Paper Design

The APBIE (Andhra Pradesh Board of Intermediate Education) has introduced significant changes for the Inter 1st Year (Class 11) 2026 public exams, reflecting new exam pattern, marks distribution, and question paper design. These reforms align with national standards and focus on both conceptual clarity and higher-order thinking skills.

Revised Marks Distribution

  • Most subjects now follow a balanced split: theory papers generally carry 85–100 marks per subject, with practicals/internal assessment contributing an additional 15–30 marks depending on the stream (BiPC, MPC, etc.).​
  • For Biology, Botany and Zoology are split: Botany – 43 marks; Zoology – 42 marks. Practicals in science subjects have a separate weightage.​
  • Internal assessment weightage is now 20 marks per subject, focusing on continuous evaluation.​
  • Total score for each stream (MPC, BiPC, CEC, MEC, HEC) is either 500 or 485 marks in 1st year, with the remainder in 2nd year; practical marks are added separately where applicable.

Changed Question Paper Design

  • The blueprint introduces more application-based, analytical, and higher-order thinking (HOT) questions, reducing emphasis on rote memorization.​
  • Objective-type questions (MCQs, fill in the blanks, true/false) are included for conceptual clarity, with specific weightage per section.​
  • Descriptive questions (short and long answers) are retained for in-depth understanding.
  • One-mark questions will be present across all subjects to directly test conceptual knowledge.

AP Inter 1st Year Exams 2026 Changes in the Question Paper Design

Revised Distribution of Marks among Subjects

Comb.1 – M.P.C

Comb.2 – Bi.P.C

Comb.3 – M.E.C

Comb.4 – C.E.C

Comb.5 – H.E.C

AP Inter 2nd Year Hall Ticket 2026 Out at bie.ap.gov.in, Direct Link to Download BIEAP Halltickets

The Andhra Pradesh Board of Intermediate Education (BIEAP) 2nd Year exams will be conducted from february 24 to March 23, 2026, in a single shift from 9:00 AM to 12:00 noon. Students can download their hall tickets from the official website at bie.ap.gov.in.

AP Intermediate Public Examinations MARCH 2026 Second Year General Hall Ticket 2026 released on 20th February. Students can download from link given below:

Note: All the I & II year Intermediate students of General and Vocational courses and private candidates are hereby informed that the Intermediate Public Examination (Theory), 2026 Hall tickets are placed in their college login and also in public domain i.e., https://bie.ap.gov.in/. The students can download the Hall tickets by providing his/her previous hall ticket number or IPE March 2026 Hall Ticket Number or Aadhaar Number and Date of birth. Students can also download through Mana Mithra, Government of A.P, WhatsApp Number 9552300009 by selecting the Education Services option and entering the previous Hall ticket number or IPE March 2026 Hall ticket number or Aadhaar Number and Date of Birth.

The Andhra Pradesh Intermediate 2nd Year Hall Ticket 2026 can be accessed online, once released for the AP Intermediate examinations conducted by the Board of Intermediate Education, Andhra Pradesh (BIEAP). The hall ticket serves as an entry pass to the examination center and contains essential details such as the student’s name, roll number, exam center, and exam schedule. This article provides a step-by-step process to download the AP Inter Hall Ticket 2026 and important details students need to know.

Number of 1st Year General StudentsEducation counseling servicesInter 2nd Year guides500963
Number of 1st Year Vocational Students44581
Number of 2nd Year General Students471021
Number of 2nd Year Vocational Students42328
Total number of Students1058893
Number of Exam centers1535

The hall ticket is mandatory for appearing in the AP Intermediate 2nd Year examinations. Without Hall Ticket, students will not be allowed to enter the exam hall. It also helps verify the student’s identity and ensures that the examination process is conducted smoothly. Students must carry a printed copy of the hall ticket to the exam center along with a valid ID proof.

AP Inter 2nd Year Hall Tickets 2026 Overview

NameDescription
Name of BoardAndhra Pradesh State Board of Intermediate Education(APBIE)
Name of ExamIntermediate 2nd Year Annual Exams 2026
Exam Dates24-02-2026 to 23-03-2026
Exam Timings09:00 AM To 12:00 PM
StatusInter 2nd Year guidesEducation counseling servicesAvailable Soon
CategoryHall tickets
Hall tickets Release Date20th February 2026
Results Announcement DateApril 2026
Hall ticket Download LinkReleased on 20-02-2026
Official website Linkbie.ap.gov.in

Steps to Download AP Inter 2nd Year Hall Ticket 2026

Students can follow these simple steps to download their AP Intermediate 2nd Year Hall Ticket 2026:

  • Visit the official website – www.manabadi.co.in
  • On the homepage, look for the link titled “AP Inter 2nd Year Hall Ticket 2026 Download”.
  • Click on the link and choose your stream (General / Vocational).
  • Enter your Roll Number / Registration Number and Date of Birth.
  • Click on Submit.
  • Your AP Inter 2nd Year Hall Ticket 2026 will appear on the screen.
  • Verify all the details carefully.
  • Download and take a printout of the hall ticket for future reference.

AP Inter 2nd Year Exam Dates & Schedule 2026

DatesSubjects
24.02.2026 (Tuesday)Part-II: 2nd Language paper-II
26.02.2026 (Thursday)Part- I: English Paper-II
28.02.2026 (Saturday)BOTANY PAPER-II,
HISTORY PAPER-II
03.03.2026 (Tuesday)MATHEMATICS PAPER-IIA,
CIVICS PAPER-II
06.03.2026 (Friday)ZOOLOGY PAPER-II,
ECONOMICS PAPER-II
09.03.2026 (Monday)MATHEMATICS PAPER-IIB
11.03.2026 (Wednesday)COMMERCE PAPER-II,
SOCIOLOGY PAPER -II,
FINE ARTS, MUSIC PAPER-II
13.03.2026 (Friday)PHYSICS PAPER-II
16.03.2026 (Monday)MODERN LANGUAGE PAPER- II, GEOGRAPHY-II,
BRIDGE COURSE MATHEMATICS -II (FOR Bi.PC STUDENTS)
18.03.2026 (Wednesday)CHEMISTRY PAPER-II
23.03.2026 (Monday)PUBLIC ADMINISTRATION PAPER-II, LOGIC PAPER-II

Details Mentioned on the AP Inter 2nd Year Hall Ticket 2026

After downloading, students must check the details printed on the hall ticket. Any discrepancies should be immediately reported to the college principal or BIEAP authorities. The following details are typically mentioned:

  • Student’s Name
  • Roll Number
  • Hall Ticket Number
  • Photograph and Signature
  • College Name and Code
  • Exam Center Name and Address
  • Subject-wise Exam Dates
  • Timing of Examination
  • Important Instructions for Students
  • BIEAP Controller’s Signature

AP Inter 1st Year Hall Ticket 2026: Download BIEAP I Yr Hall Ticket at manabadi.co.in

Ramu
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AP Inter 1st Year Hall Ticket 2026: Download BIEAP I Yr Hall Ticket at manabadi.co.in

The Board of Intermediate Education, Andhra Pradesh (BIEAP) is set to conduct the AP Intermediate 1st Year Public Examinations 2026 from February 23, 2026, to March 25, 2026. Students who have registered for the examinations can soon download their AP Inter 1st Year Hall Ticket 2026 from the official website and popular education portals like manabadi.co.in.

The hall ticket is a mandatory document for all students appearing in the AP Inter I Year exams. Without it, candidates will not be allowed to enter the examination hall. In this article, you will find complete details about the AP Inter 1st Year Hall Ticket 2026 download process, exam dates, important instructions, details mentioned on the hall ticket, and FAQs.

AP Inter 1st Year Time Table 2026

Impact of AP Inter Reforms on the 2025 Hall Ticket

The numerous changes introduced by the Andhra Pradesh Intermediate Board for the academic year have a direct impact on the design, instructions, and information to be printed on the AP Inter 2025 Hall Ticket. With the introduction of a new question paper model, expanded answer booklets, and revised pass criteria, the hall ticket is expected to carry more detailed guidelines than in previous years.

One of the major changes influencing the 2025 hall ticket is the increase in answer booklet pages. Students of Mathematics, Physics, Chemistry, Economics, History, Political Science and Commerce will receive 32-page booklets, while Biology students will receive two separate 24-page booklets for Botany and Zoology. To avoid confusion in the exam hall, the hall ticket is likely to mention the type of answer booklet provided for each subject. This helps students mentally prepare for the length and structure of their examinations.

The introduction of one-mark questions for the first time and the increased number of questions also require the board to add instructions regarding the updated question pattern. Since there is no choice in one-mark and two-mark questions, this detail may be noted in the hall ticket or the accompanying instruction sheet so students clearly understand what to expect.

Revised pass rules—such as 29 marks being enough to pass out of 85 in first year, and overall 35% being calculated across both years—may also be included as advisory notes. This ensures students are aware of the new evaluation system before appearing for exams.

Subjects like Geography (75 marks but counted as 85) and the 30-mark practical exams in second year also require clear mention of exam timings and rules.

Overall, the AP Inter 2025 Hall Ticket will likely contain more comprehensive guidelines, reflecting all structural changes and helping students approach the examinations with clarity and confidence.

APBIE 2026 Inter 1st Year Exam Pattern Changes – Revised Marks Distribution & Question Paper Design

The APBIE (Andhra Pradesh Board of Intermediate Education) has introduced significant changes for the Inter 1st Year (Class 11) 2026 public exams, reflecting new exam pattern, marks distribution, and question paper design. These reforms align with national standards and focus on both conceptual clarity and higher-order thinking skills.

Revised Marks Distribution

  • Most subjects now follow a balanced split: theory papers generally carry 85–100 marks per subject, with practicals/internal assessment contributing an additional 15–30 marks depending on the stream (BiPC, MPC, etc.).​
  • For Biology, Botany and Zoology are split: Botany – 43 marks; Zoology – 42 marks. Practicals in science subjects have a separate weightage.​
  • Internal assessment weightage is now 20 marks per subject, focusing on continuous evaluation.​
  • Total score for each stream (MPC, BiPC, CEC, MEC, HEC) is either 500 or 485 marks in 1st year, with the remainder in 2nd year; practical marks are added separately where applicable.

Changed Question Paper Design

  • The blueprint introduces more application-based, analytical, and higher-order thinking (HOT) questions, reducing emphasis on rote memorization.​
  • Objective-type questions (MCQs, fill in the blanks, true/false) are included for conceptual clarity, with specific weightage per section.​
  • Descriptive questions (short and long answers) are retained for in-depth understanding.
  • One-mark questions will be present across all subjects to directly test conceptual knowledge.

AP Inter 1st Year Exams 2026 Changes in the Question Paper Design

Revised Distribution of Marks among Subjects

Comb.1 – M.P.C

Comb.2 – Bi.P.C

Comb.3 – M.E.C

Comb.4 – C.E.C

Comb.5 – H.E.C

AP Inter 1st Year Hall Ticket 2026 at bie.ap.gov.in, BIEAP Direct Link to Download Halltickets

The Andhra Pradesh Board of Intermediate Education (BIEAP) 1st Year exams will be conducted from 23rd Feb to 25th March, 2026. in a single shift from 9:00 AM to 12:00 noon. Students can download their hall tickets from the official website at bie.ap.gov.in.

AP Intermediate Public Examinations MARCH 2026 First Year General Hall Ticket 2026 released on 20th February. Students can download from link given below:

Those who have not downloaded their AP Inter Hall tickets can do so now. The site is accessible, as the servers are free, and everyone will receive their Hall tickets immediately.

Note: All the I & II year Intermediate students of General and Vocational courses and private candidates are hereby informed that the Intermediate Public Examination (Theory), 2026 Hall tickets are placed in their college login and also in public domain i.e., https://bie.ap.gov.in/. The students can download the Hall tickets by providing his/her previous hall ticket number or IPE March 2026 Hall Ticket Number or Aadhaar Number and Date of birth. Students can also download through Mana Mithra, Government of A.P, WhatsApp Number 9552300009 by selecting the Education Services option and entering the previous Hall ticket number or IPE March 2026 Hall ticket number or Aadhaar Number and Date of Birth.

Board of Intermediate Education, Andhra Pradesh (BIEAP) is responsible for conducting the AP Inter 1st Year Exams 2026 and releasing the hall tickets for students. The AP Inter Hall Ticket 2026 Download is a crucial document required for students to appear for their exams. It contains essential details like exam dates, exam center, and personal information.

Number of 1st Year General Students500963
Number of 1st Year Vocational Students44581
Number of 2nd Year General Students471021
Number of 2nd Year Vocational Students42328
Total number of Students1058893
Number of Exam centers1535

Steps to Download AP Inter 1st Year Hall Ticket 2026

Follow the step-by-step process to download your admit card easily:

  • Visit the official website — manabadi.co.in
  • On the homepage, click on “AP Inter 1st Year Hall Ticket 2026” link.
  • You’ll be redirected to the BIEAP admit card page.
  • Select your course (General/Vocational).
  • Enter your Roll Number / Previous Hall Ticket Number / Date of Birth.
  • Click on Submit.
  • Your AP Inter 1st Year Hall Ticket 2026 will appear on the screen.
  • Check all the details carefully and download the hall ticket.
  • Take two or three printouts for safety and future reference.

AP Inter 1st Year Exam 2026 Time Table Snapshot

Here’s a quick look at the tentative AP Inter 1st Year exam schedule 2026

DateSubject / Paper
February 26, 20262nd Language — Paper I
February 28, 2026English — Paper I
March 03, 2026Mathematics (Paper I A) / Botany Paper I / Civics Paper I
March 05, 2026Mathematics (Paper I B) / Zoology Paper I / History Paper I
March 07, 2026Physics — Paper I / Economics — Paper I
March 10, 2026Chemistry — Paper I / Commerce — Paper I / Sociology — Paper I
March 12, 2026Public Administration / Logic / Bridge Course Maths Paper I (BiPC)

Details Mentioned on AP Inter 1st Year Hall Ticket 2026

After downloading, students must check the information printed on their admit card. The following details should be verified:

  • Student’s Full Name
  • Roll Number / Hall Ticket Number
  • Photograph and Signature
  • College Name and Code
  • Subject-wise Exam Dates and Timings
  • Exam Centre Name and Address
  • Stream (MPC, BiPC, CEC, MEC, HEC, or Vocational)
  • Instructions for Students
  • BIEAP Seal and Signature

CBSE Class 10th Time Table 2026 Reschedule Date Out: Download PDF Exams Final Schedule at Manabadi.co.in

Ramu
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CBSE Class 10th Time Table 2026 Reschedule Date Out: Download PDF Exams Final Schedule at Manabadi.co.in

CBSE has been released the final Class 10 Date Sheet 2026. The board exams will be held from February 17 to March 10, 2026. Check the complete subject-wise schedule and download the CBSE 10th exam time table PDF here.

It is hereby informed that the examinations of the subjects for Class X and Class XII, which were earlier scheduled on 03 March 2026, have been rescheduled due to administrative reasons. The revised dates are as follows:

Class X
Earlier Date: 03 March 2026
Revised Date: 11 March 2026

Class XII
Earlier Date: 03 March 2026
Revised Date: 10 April 2026

All other examination dates remain unchanged. Schools are requested to kindly disseminate this information to all concerned students and parents for their information and necessary action please.

Date Sheets are being amended accordingly and the revised dates will also be given in the Admit Cards when issued.

Your cooperation will be appreciated in ensuring smooth conduct of the examinations.

CBSE Class 10th Exam Reschedule Date

The Central Board of Secondary Education (CBSE) has officially announced the CBSE Class 10th Time Table 2026, bringing clarity and relief to lakhs of students preparing for the board examinations. As per the released schedule, the CBSE Class 10th Board Exams 2026 are set to be conducted from February 17, 2026 to March 11, 2026. Students can now download the CBSE 10th Time Table 2026 PDF directly from the official website cbse.gov.in as well as from trusted educational portals like Manabadi.co.in.

CBSE Guidance to Class X students for Boards Examinations Notification

This detailed exam schedule allows students to plan their preparation strategically, ensuring they have sufficient time to revise all subjects thoroughly. In this article, we have presented the complete CBSE Class 10 Time Table 2026, step-by-step instructions to download the PDF, preparation tips, important guidelines, and examination day instructions.

CBSE Class 10th Time Table 2026 – Download

CBSE Class 10 Exam 2026 – Highlights

Event / DetailDescription
Conducting BodyCentral Board of Secondary Education (CBSE)
Academic Session2025–26
Exam NameCBSE Class 10 Board Examination 2026
Date Sheet Release Date30 October 2025
First Exam Date17 February 2026
Last Exam Date (Phase 1)11 March 2026
Exam Timing10:30 AM to 1:30 PM (for general theory papers)
Exam Duration2 to 3 hours (depending on subject)
Exam ModeOffline (Pen and Paper Mode)
Type of QuestionsObjective, Short Answer, Long Answer, and Case-Based Questions
Subjects CoveredAll major and minor subjects, including vocational and additional papers
Practical/Internal AssessmentsTo be conducted by schools prior to the theory exams (January–February 2026)
Official Websitecbse.gov.in

CBSE Class 10 Date Sheet 2026 – Subject-Wise Exam Schedule

Here is the subject-wise date sheet for CBSE Class 10 Board Exams 2026:

DateDayTimeSubject Code(s)Subject
17 Feb 2026Tuesday10:30 AM–1:30 PM041, 241Mathematics (Standard & Basic)
18 Feb 2026Wednesday10:30 AM–12:30 PM*064Home Science
20 Feb 2026Friday10:30 AM–12:30 PM*407, 412, 415, 416, 418, 419Beauty & Wellness; Marketing & Sales; Multi Skill Foundation; Physical Activity Trainer; Data Science
21 Feb 2026Saturday10:30 AM–1:30 PM101, 184English (Communicative); English (Language & Literature)
23 Feb 2026Monday10:30 AM–1:30 PM003, 004, 005, 006, 009, 010, 011, 089Urdu Course–A; Punjabi; Bengali; Tamil; Marathi; Gujarati; Manipuri; Telugu (Telangana)
24 Feb 2026Tuesday10:30 AM–1:30 PM154, 303Elements of Business; Urdu Course–B
25 Feb 2026Wednesday10:30 AM–1:30 PM086Science (General)
26 Feb 2026Thursday10:30 AM–12:30 PM*401, 403, 404, 405, 406, 408, 409, 419, 411, 413, 420, 421, 422Retail; Security; Automotive; Financial Markets; Tourism; Agriculture; Food Production; Front Office Operations; Banking & Insurance; Health Care; Apparel; Electronics & Hardware; Foundation Skills; Design Thinking & Innovation
27 Feb 2026Friday165, 402, 417Computer Applications; Information Technology; AI
28 Feb 2026Saturday10:30 AM–1:30 PM016, 119, 122, 131, 132, 133, 134Arabic; Sanskrit (Communicative); Rai; Gurung; Tamang; Shepa
2 Mar 2026Monday10:30 AM–1:30 PM002, 085Hindi Course-A; Hindi Course-B
5 Mar 2026Thursday10:30 AM–1:30 PM008, 012, 013, 014, 015, 091Sindhi; Malayalam; Odia; Kannada; Assamese; Kokborok
6 Mar 2026Friday10:30 AM–12:30 PM049Painting
7 Mar 2026Saturday10:30 AM–1:30 PM087Social Science
9 Mar 2026Monday10:30 AM–1:30 PM or 10:30 AM–12:30 PM007
021
023
024
025
026
031
032
033
034
035
036
136		TELUGU
RUSSIAN
PERSIAN
NEPALI
LIMBOO
LEPCHA
CARNATIC MUSIC (VOCAL)
CARNATIC MUSIC MEL INS.
CARNATIC MUSIC PER. INS.
HINDUSTANI MUSIC VOCAL
HINDUSTANI MUSIC (MEL INS)
HINDUSTANI MUSIC (PER INS)
THAI
10 Mar 2026Tuesday10:30 AM–1:30 PM018French
11 Mar 202610:30 AM–1:30 PM017, 020, 076, 088, 089, 090, 091TIBETAN
GERMAN
NATIONAL CADET CORPS
BHOTI
BODO
TANGKHUL
JAPANESE
BHUTIA
SPANISH
KASHMIRI
MIZO
BAHASA MELAYU
ELEMENTS OF BOOK KEEPING &
ACCOUNTANCY

How to Download CBSE Class 10th Time Table 2026 PDF from Manabadi.co.in

Follow the simple steps below:

  • Visit the website Manabadi.co.in
  • On the homepage, click on “CBSE Class 10 Time Table 2026” link.
  • A PDF file will open containing the complete exam schedule.
  • Click Download and save it on your device.
  • Take a printout for quick reference.

Alternatively, you can also download the PDF from CBSE’s official website.

Details Mentioned in CBSE 10th Date Sheet 2026

  • Board name
  • Examination name
  • Subjects
  • CBSE Class 10 exam date 2025
  • Exam time
  • Practical exam dates
  • Important instructions

Tips to Prepare for CBSE Class 10 Exams 2026

  1. Create a Smart Study Plan
    Distribute your daily study hours between theory subjects, math subjects, and revision. Keep weekly check-points to track progress.
  2. Solve Previous Year Question Papers
    This helps students understand actual exam patterns, marking scheme, and repeated question trends.
  3. Focus on NCERT Textbooks
    Most CBSE board exam questions come directly from NCERT. Ensure chapters, examples, and exercises are completed.
  4. Practice Time-Based Mock Tests
    Attempting mock papers helps improve speed and accuracy while reducing exam anxiety.
  5. Maintain Health and Sleep Schedule
    Healthy sleep boosts memory and concentration. Avoid late-night study habits close to exams.

Guidelines for Students Appearing for the CBSE Board Exams 2026

  • Reach the examination center at least 30 minutes early.
  • Carry admit card, school ID card, and necessary stationery.
  • Mobile phones, calculators, and smart watches are strictly prohibited.
  • Follow writing and presentation formats as instructed.
  • Answer questions neatly and manage time across sections.

CBSE Class 12th Admit Card 2026: Download Hall Ticket at manabadi.co.in

Ramu
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CBSE Class 12th Admit Card 2026: Download Hall Ticket at manabadi.co.in

The Central Board of Secondary Education (CBSE) conducts the Class 12 board examinations every year across India and in various CBSE-affiliated schools abroad. As one of the most crucial milestones in a student’s academic journey, the Class 12 exams require thorough preparation and timely awareness of important updates—especially regarding the CBSE Class 12th Admit Card 2026.

The admit card is not just a hall ticket; it acts as an identity document for students during their board exams. Without it, students will not be permitted to enter the examination hall under any circumstances. Therefore, downloading and checking the CBSE Class 12 admit card carefully is extremely important.

In 2026, students can download their Class 12 admit cards easily through manabadi.co.in, a popular and trusted website for educational information, result updates, and board exam hall tickets. This article provides complete details on how to download the CBSE 12th hall ticket, important instructions, exam guidelines, and what students should do after obtaining the admit card.

CBSE Class 12th Exam 2026 – Overview

FeatureDetails
BoardCentral Board of Secondary Education (CBSE)
Class12th (Senior Secondary)
Academic Year2025–2026
Exam modePen & Paper (Theory) • Practical/Project assessments as per school schedule
Admit Card release (expected)January–February 2026
Theory exam window17th Feb – 10th Apr 2026
Practical examsConducted by schools/centres from Jan 2026 (dates vary)
Result announcement (expected)May 2026
Where to download admit cardSchool distribution / CBSE portal for private candidates / educational portals such as Manabadi

How to Download CBSE Class 12th Admit Card 2026 from manabadi.co.in

While the admit card is officially released on the CBSE academic portal, manabadi.co.in acts as a reliable information platform offering:

  • Visit the website: https://www.manabadi.co.in
  • Navigate to the Education / Exams / CBSE Updates section.
  • Look for the link titled “CBSE 12th Admit Card 2026 Download”.
  • Click the link and you will be redirected to the CBSE portal.
  • Enter the required details (Application No / Password / Security Code).
  • Download and print the admit card for future reference.

Details Mentioned in CBSE Class 12th Admit Card

  • Student’s Full Name
  • Father’s Name
  • Mother’s Name
  • Date of Birth (DOB)
  • Gender
  • Roll Number
  • Enrollment / Registration Number
  • School Name and School Code
  • Class (12th) and Stream (Science / Commerce / Arts)
  • Exam Year and Session
  • Photograph of the Student
  • Student’s Signature
  • Exam Center Name and Center Code
  • Full Address of Examination Center
  • Subject Names and Subject Codes
  • Examination Dates and Time Schedule
  • Important Exam Day Instructions
  • QR Code for Verification (if applicable) CBSE Official Seal and Signature of Authorized Signatory

CBSE Class 12 Exam 2026 – Preparation Tips for Students

The Class 12 board exams are significant for college admissions, competitive exams, and career paths. Therefore, strategic preparation is essential.

1. Create a Study Time Table

Allocate time for each subject and revise regularly.

2. Focus on NCERT Textbooks

Most questions in CBSE exams are based on NCERT content.

3. Solve Previous Year Papers

This helps in understanding the question pattern and improving speed.

4. Take Mock Tests

Mock exams help in analyzing weaknesses and improving performance.

5. Revise Weak Topics Frequently

Regular revision helps in strengthening memory retention.

TS Inter 1st Year Study Material Textbook Solutions PDF Download: Telangana Board Intermediate I Year Books at manabadi.co.in

Junaid
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TS Inter 1st Year Study Material Textbook Solutions PDF Download: Telangana Board Intermediate I Year Books at manabadi.co.in

The Telangana State Board of Intermediate Education (TSBIE) plays a crucial role in shaping the academic future of Intermediate students. For Class 11 (Inter 1st Year) students, having the right study material is essential to build strong fundamentals for competitive exams and higher education. To support students, manabadi.co.in provides easy access to TS Inter 1st Year Textbook Solutions PDF downloads for all subjects.

In this article, you will find complete details about TS Inter 1st Year textbooks, subject-wise solutions, benefits of PDFs, exam preparation tips, and how to download Intermediate I Year books online.

Subjects Covered in TS SCERT Inter 1st Year Textbook Solutions

TS Inter provides solutions for all major Intermediate subjects, including Mathematics, Physics, Chemistry, Biology, Economics, Commerce, Accountancy, History, Political Science, and Languages. Both Telugu and English medium students can access subject-wise solutions according to their curriculum needs.

Subject NameSolutions
MathematicsMathematics Inter 1st Year Textbook Solutions
PhysicsPhysics Inter 1st Year Textbook Solutions
ChemistryChemistry Inter 1st Year Textbook Solutions
BiologyBiology Inter 1st Year Textbook Solutions
BotanyBotany Inter 1st Year Textbook Solutions
EconomicsEconomics Inter 1st Year Textbook Solutions
CommerceCommerce Inter 1st Year Textbook Solutions
AccountancyAccountancy Inter 1st Year Textbook Solutions
HistoryHistory Inter 1st Year Textbook Solutions
Political SciencePolitical Science Inter 1st Year Textbook Solutions
EnglishEnglish Inter 1st Year Textbook Solutions

About TS Inter 1st Year (Intermediate I Year)

The TS Intermediate 1st Year course is the foundation stage after Class 10 and is offered in different streams such as:

  • MPC (Maths, Physics, Chemistry)
  • BiPC (Biology, Physics, Chemistry)
  • MEC (Maths, Economics, Commerce)
  • CEC (Civics, Economics, Commerce)
  • HEC (History, Economics, Commerce)
  • Vocational Courses

The syllabus is designed by TSBIE to prepare students for board exams as well as entrance tests like TS EAPCET, NEET, JEE, CA Foundation, and other competitive exams.

Importance of TS Inter 1st Year Textbook Solutions

Textbook solutions are an essential learning resource for students aiming to score high marks. The TS Inter 1st Year Textbook Solutions PDFs available at manabadi.co.in help students in the following ways:

  • Clear explanation of concepts in simple language
  • Step-by-step answers as per board exam pattern
  • Helpful for self-study and revision
  • Improves answer-writing skills
  • Useful for exam-oriented preparation

By regularly practicing textbook solutions, students can gain confidence and accuracy in answering questions.

TS Inter 1st Year Subjects – Stream Wise

Science Stream (MPC & BiPC)

  • Mathematics IA
  • Mathematics IB
  • Physics
  • Chemistry
  • Botany
  • Zoology
  • English

Commerce & Arts Stream

  • Economics
  • Commerce
  • Civics
  • History
  • Sociology
  • Logic
  • Public Administration
  • English

All subject-wise Intermediate I Year textbook solutions PDFs are prepared according to the latest TSBIE syllabus.

TS Inter 1st Year Maths Textbook Solutions PDF

Mathematics is a scoring subject for MPC and MEC students. The TS Inter 1st Year Maths syllabus is divided into Maths IA and Maths IB.

Topics Covered:

  • Sets and Functions
  • Mathematical Induction
  • Trigonometric Functions
  • Complex Numbers
  • Permutations and Combinations
  • Straight Lines
  • Circles

The Maths solutions PDFs at manabadi.co.in provide detailed step-by-step answers, making problem-solving easier for students.

TS Inter 1st Year Physics Textbook Solutions PDF

Physics requires conceptual clarity and numerical practice. The Physics textbook solutions help students understand theories, laws, and numerical problems.

Key Units:

  • Physical World and Measurement
  • Laws of Motion
  • Work, Energy, and Power
  • Motion of System of Particles
  • Oscillations and Waves

These solutions are ideal for board exams and entrance test preparation.

TS Inter 1st Year Chemistry Textbook Solutions PDF

Chemistry is divided into Physical, Organic, and Inorganic Chemistry. Proper explanations are essential to understand reactions and formulas.

Important Chapters:

  • Atomic Structure
  • Chemical Bonding
  • States of Matter
  • Thermodynamics
  • Organic Chemistry – Basic Principles

The solutions PDFs provide clear reaction mechanisms and solved numerical problems.

TS Inter 1st Year Biology Textbook Solutions PDF

BiPC students can download Botany and Zoology solutions in PDF format.

Botany Topics:

  • Living World
  • Plant Kingdom
  • Morphology of Flowering Plants

Zoology Topics:

  • Animal Kingdom
  • Structural Organisation in Animals
  • Human Physiology

These solutions help in understanding diagrams, definitions, and long-answer questions.

TS Inter 1st Year Commerce, Economics & Arts Subjects Solutions

For MEC, CEC, and HEC students, textbook solutions are available for:

  • Economics (Micro Economics basics)
  • Commerce (Business fundamentals)
  • Civics (Political Science concepts)
  • History (Indian and World History)
  • Sociology & Logic

The content is written in a student-friendly manner, ensuring conceptual clarity and exam readiness.

TS Inter 1st Year English Textbook Solutions PDF

English is a compulsory subject for all streams. The English textbook solutions include:

  • Prose explanations
  • Poetry summaries
  • Grammar answers
  • Short and long questions

These PDFs help improve language skills and writing techniques.

How to Download TS Inter 1st Year Textbook Solutions PDF from manabadi.co.in

Follow these simple steps:

  1. Visit manabadi.co.in
  2. Search for “TS Inter 1st Year Textbook Solutions”
  3. Select your stream and subject
  4. Click on the PDF download link
  5. Save the file for offline use

The website provides latest and updated study material for Telangana Intermediate students.

Exam Preparation Tips for TS Inter 1st Year Students

  • Read textbooks thoroughly before referring to solutions
  • Practice numerical problems daily
  • Prepare short notes for revision
  • Solve previous years’ question papers
  • Focus on weak subjects
  • Follow a proper study timetable

Using textbook solutions along with regular practice can significantly improve exam performance.

CBSE Class 10th Admit Card 2026: Download Hall Ticket at manabadi.co.in

Ramu
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CBSE Class 10th Admit Card 2026: Download Hall Ticket at manabadi.co.in

The Central Board of Secondary Education (CBSE) is expected to release the CBSE Class 10th Admit Card 2026 in the month of February 2026. Students appearing for the Class 10 board examinations can download their Hall Ticket / Admit Card from the official CBSE academic portal. Additionally, many students prefer quickly accessing their admit card through trusted education portals such as manabadi.co.in which provides faster access, updates, and easy download links.

The CBSE Class 10 Admit Card 2026 is an essential document for all students going to appear in the board exams. Without the admit card, students will not be allowed to enter the examination hall. The admit card contains crucial exam-related details including student name, roll number, exam center, subject-wise exam schedule, guidelines, and other important instructions.

This article provides complete details on how to download the admit card, release date, important instructions, and a step-by-step guide for both regular and private students.

Highlights – CBSE Class 10th Admit Card 2026

FeaturesDetails
Board NameCentral Board of Secondary Education (CBSE)
Exam NameCBSE Class 10 Board Exams 2026
Article TypeAdmit Card / Hall Ticket
Academic Session2025-2026
Admit Card Release DateJanuary 2026 (Expected)
Exam Dates17th February – 11th March 2026
Official Websitewww.cbse.gov.in
Alternative Downloadwww.manabadi.co.in

How to Download CBSE Class 10 Hall Ticket 2026 at Manabadi.co.in

Manabadi is known for offering quick education updates, result links, hall ticket pages, and study resources.

  • Follow the steps:
  • Go to https://www.manabadi.co.in
  • Click on CBSE Class 10 Admit Card 2026 Link on the homepage.
  • Enter your details (Roll Number / Name / DOB).
  • Click on Download.
  • Save and print your hall ticket.

This method is especially useful during heavy traffic on CBSE servers.

Details Mentioned on CBSE Class 10 Admit Card 2026

Students must carefully verify every detail printed on the admit card. It includes:

  • Student Name
  • Roll Number
  • Photograph & Signature
  • Father’s & Mother’s Name
  • Date of Birth
  • School Name and Code
  • Exam Center Name & Code
  • Subject-wise Exam Dates & Timings
  • Important Exam Instructions Space for Invigilator & Student Signature

If any detail is incorrect, students must immediately contact their school authorities or CBSE Regional Office.

TS Inter 1st Year Botany Study Material Chapter 1 The Living World

Sandhya
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TS Inter 1st Year Botany Study Material Chapter 1 The Living World

Very Short Answer Type Questions

Question 1.


What does ICBINT stand for?


Answer:


ICBN stands for International Code for Botanical Nomenclature.

Question 2.


What is flora?

Aswer:

  1. Flora is the actual account of habitat, distribution and systematic listing of plants of a given area.
  2. It provides the index to the plant species found in a particular area.

Question 3.


Define Metabolism. What is the difference between anabolism and catabolism?


Aswer:

  1. Metabolism refers to the sum total of all the chemical reactions occurring in the body of a living organism.
  2. The constructive metabolic process in which complex molecules are formed from simpler molecules is called anabolism. The destructive metabolic process in which complex molecules are broken down into simpler molecules is called catabolism.

Question 4.


Which is the largest botanical garden in the world? Name a few well known botanical gardens in India?


Answer:

  1. Royal Botanical Garden (RBG) at Kew, England is the largest botanical garden in the world.
  2. Indian Botanical Garden, Howrah and National Botanical Research Institute, Lucknow are well known botanical gardens in India.

Question 5.


Define the terms couplet and lead in taxonomic key. [Mar. – 2018, Mar. 15, A.P.]?


Answer:


1) Couplet :
A pair of contrasting characters that represents the choice made between two opposite options.

2) Lead :
Each statement in the taxonomic key.

Question 6.


What is meant by manuals and monographs? [May ’17, May ’14]?


Answer:

  1. Manuals are recorded descriptions useful in providing information for identification of names of species found in an area.
  2. Monographs contain information on any one taxon.

Question 7.


What is systematics?


Answer:

  1. Systematics is the study of different kinds of organisms, their diversities and also the relationship among them.
  2. Systematics includes identification, nomenclature and classification. It takes into account evolutionary relationships between organisms.

Question 8.


Why are living organisms classified?


Answer:

  1. Classification is the process by which anything is grouped into convenient categories based on some easily observable characters.
  2. It is a device to study all the living organisms with ease.

Question 9.


What is the basic unit of classification? Define it. [Mar. ’20, ’17; Mar. 14, 13]?


Answer:

  1. Species is the basic unit of classification.
  2. Species can be defined as a group of individual organisms with fundamental similarities. Eg : Solanum tuberosum (Potato)

Question 10.


Give the scientific name of Mango. Identify the generic name and specific epithet.?


Answer:

  1. The scientificname of Mango is Mangifera indica.
  2. Mangifera is generic name and indica is specific epithet.

Question 11.


What is growth? What is the difference between the growth in living organisms and growth in non-living objects?


Answer:

  1. Growth may be defined as permanent and irreversible increase in size overtime.
  2. The growth in living organisms is from inside and by cell divisions. Whereas in non-living objects growth is due to accumulation of material on the surface.

Short Answer Type Questions

Question 1.


What is meant by identification and nomenclature? How is a key helpful in the identification and classification of an organism?


Answer:

  1. Determining whether a collected plant is entirely new or already known is called identification. Providing a correct scientific name to an identified plant is called nomenclature.
  2. Correct identification can be done by directly comparing the characters of the plant with an authentic herbarium specimen or indirectly with the help of key in floras.
  3. Key or taxonomic key is an artificial analytic device having a list of statements with dichotomatic table of alternate characteristics which is used in identifying organisms.
  4. Usually a couplet or two contrasting characters are used. The one present in the organism is chosen while the other is rejected.
  5. Taxonomic key is helpful in the identification and classification of an organism based on.the similarities and dissimilarities.
  6. Each statement in the key is called a lead.
  7. Separate taxonomic keys are required for each taxonomic category such as family, genus and Species for identification purpose.

Question 2.


What are taxonomical aids? Give the importance of herbaria and museums.?


Answer:


Herbarium, Botanical gardens, Zoological parks and Museums are taxonomical aids.

Herbarium:

  1. Herbarium is a store house of collected plant specimen.
  2. Plants identification can be done directly comparing the characters with an authentic herbarium specimen.
  3. Plant specimens that are collected are dried, pressed and preserved on the sheets.
  4. These sheets are arranged according to the system of classification.
  5. These sheets provide the information about the date, place of collection, English name, local name and scientific name, family name even the collector’s name etc.
  6. Herbaria serves as a quick referred system in taxonomic studies.
  7. Royal Botanical garden at Kew, England has largest herbarium. It is an international centre for plant identification.
  8. Nowadays herbarium is preserved as Digital herbarium. The digital images of the herbarium specimens and the related information is preserved and published on internet for wider use.

This digital herbarium is intended to take advantage of internet and digital photography technologies to provide online facility.

Museum :
Generally in schools and colleges biological museums are present. In these museums, they preserve the plants and animals specimens collected for study and reference. Specimens are preserved in the containers or jars in preservative solutions or they may be preserved as dry specimens.

Question 3.


Define a taxon. Give some examples of taxa at different hierarchial levels.?


Answer:


Any system of classification is made up of different units such as species, genus, family, order, class, division, kingdom which are arranged in a hierarchial sequence. Irrespective of its rank in the sequence every unit is called Taxon.

Hierarchy is the arrangement of organism in a definite sequence. The following is the taxonomical categories showing hierarchial arrangement in ascending order.

Examples of Taxa at different hierarchial levels :

KingdomPlant kingdomPlant kingdom
DivisionSpermatophytaSpermatophyta
ClassDicotyledonaeMonocotyledonae
OrderSapindalesPoales
FamilyAnacardiaceaePoaceae
GenusMangiferaTriticum
SpeciesIndicaVulgare
Common nameMangoWheat

Question 4.


How are botanical gardens useful in conserving biodiversity? Define the terms Flora, Manuals, Monographs and Catalogues.?


Answer:


Plants found in botanical gardens can be regarded as live specimens. Plants are grown in these gardens for identification purposes. Each plant is labelled indicating its botanical name and its family. Botanical gardens are useful in knowing our bioresources and their diversity.

Flora :
Flora is a book containing the details of the habitat and distribution of plants of a particular area. Every district in each state has its own flora.

Manuals :
These are small books useful in providing information for identification of names of species found in an area. It specially designed for ready reference.

Monograph :
They contain information on any one taxon.

Catalogues :
Books which help in correct identification of plants.

Question 5.


Explain binomial nomenclature.?


Answer:

  1. Every plant should have only one correct scientific name.
  2. Every scientific plant name has two components. They are the generic name and the specific,epithet. This system of providing a name with two components is called Binomial nomenclature.
  3. Scientific name should be in Latin or Latin derivative.
  4. Both the words’ when handwritten they must be underlined or printed in italics to indicate their Latin origin.
  5. The generic name will be in the noun form and always begins with capital letter. The specific name will be in the adjective form and starts with small letter. For example, Solanum tuberosum is the name of the potato plant in which “Solanum” is the genus and “tuberosum” is the species.
  6. The author’s name may be given in abbreviated form at the end of the scientific name.

For example :
Mangifera indica Linn. It indicates that the species was first described by Linnaeus.

Long Answer Type Questions

Question 1.


What is meant by living? Give a detailed account of any four defining features of life forms?


Answer:


Organisms which are self replicating, evolving and self regulating, having interactive systems, capable of responding to external stimuli are said to be living.

The defining features of life forms are
1. Metabolism :
All living organisms are made of chemicals. These chemicals undergo various chemical reactions. The sum total of all the chemical reactions occurring in the body of a living organism is called metabolism. Cellular organisation of the body required for metabolism is the defining feature of life forms.

2. Consciousness :
Response to external stimuli is called irritability. Plants repond to external factors like light, water/temperature, other organisms, pollutants etc. All organisms are aware of their surroundings. This is called consciousness. Consciousness is the defining property of living organisms/Human being is the only one who is aware of himself that means has self consciousness.

3. Interactions :
Properties of tissues are not present in the constituent cells but arise as a result of interactions among the constituent cells. Similarly properties of cellular organelles are not present in the molecular constituents of the organelle but arise as a result of interactions among the molecular components comprising the organelle. Such underlying molecular interactions are also apparent in macromolecules such as starch. These interactions result in emergent properties at a higher level of organisation.

4. Genetic material :
All living organisms present, past and future are linked to one another by the sharing of common genetic material.

Question 2.


Define the following terms with examples, (i) Class (ii) Family (iii) Order (iv) Genus (v) Division.?


Answer:


i) Class :
Class includes related orders. For example, in plant kingdom orders like Malvales, Rosales, Polemoniales etc., are included in the class : Dicotyledonae.

ii) Family :
Family is a group in which different genera of common characters are put together. Families are characterised on the basis of both vegetative and reproductive features of plant species. For example, three different genera Solanuim, Nicotiana, and Datura are placed in the family Solonaceae.

iii) Order :
Different families with similar characters are put into an order. The similar characters are less in number as compared to different genera included in a family. Plant families like Convolvulaceae, Solanaceae are included in the order Polemoniales mainly based on floral characters.

iv) Genus :
Genus is a group of different species with related characters. For example, potato and brinjal are two different species but belong to the genus-Solanum.

v) Division :
Different classes with similarities are grouped into division. Classes like Dicotyledonae and Monocotyledonae with a few similar characters are assigned to a higher category called division : Spermatophyta.

In the case of animals related classes are included in a phylum.

InText Question Answers

Question 1.


Some of the properties of tissues are not constituents of their cells. Give two examples to support the statement?


Answer:

  1. Vascular tissues like xylem and phloem help in conduction of water, mineral salts and organic substances from one place to other.
  2. Sclerenchyma tissue gives mechanical support to the plant body.

Question 2.


What do we learn from identification of individuals and populations?


Answer:

  1. From the identification of individuals and population we learn their correct scientific names and the description of the organisms.
  2. Identification is useful in agriculture, forestry to know our bioresources and their diversity.
  3. Identification helps to determine whether a collected organism is entirely new or already known.

Question 3.


Given below is the scientific name of Mango. Identify the correctly written name, (i) Mangifera Indica (ii) Mangifera indica?


Answer:


Mangifera indica.

Question 4.


Can you identify the correct sequence of taxonomical categories ?


a) Species, Order, Division, Kingdom.
b) Genus, Species, Order, Kingdom.
c) Species, Genus, Order, Phylum.


Answer:


a) Species, Order, Division, Kingdom.

Question 5.


Define the following terms?
(i) Species (ii) Class (iii) Family (iv) Order (v) Genus.


Answer:


Species :
Species is the basic unit of classification. All those plants which are identical in all respects are regarded as species.

Class :
Class includes related orders. For example, in plant kingdom orders like Malvales, Rosales, Polemoniales etc., are included in the class : Dicotyledonae.

Family :
Family is a group in which different genera of comfhon characters are put together. Families are characterised on the basis of both vegetative and reproductive features of plant species. For example, three different genera Solanum, Nicotiana, and Datura are placed in the family Solonaceae.

Order :
Different families with similar characters are put into an order. The similar characters are less in number as compared to different genera included in a family. Plant families like Convolvulaceae, Solanaceae are included in the order Polemoniales mainly based on floral characters.

Genus :
Genus is a group of different species with related characters. For example: Potato and brinjal are two different species but belong to the Genus : Solanum.

Question 6.


Illustrate the taxonomical hierarchy with suitable examples of a plant?


Answer:


Flierarchy of categories is the arrangement of organisms in a definite sequence of categories. Descending order starts from kingdom to species. Ascending order starts from species to kingdom. This hierarchial system of classification was introduced by Linnaeus. The hierarchy includes seven categories – kingdom, division, or phylum, class, order, family, genus and species.

Question 7.


What are the distinctive characteristics exhibited by living organisms? Describe them in brief.?


Answer:


The distinctive characters exhibited by living organisms are Growth, reproduction, irritability, metabolism, ability to self replicate, self organise, interaction and emergence.

Growth :
Living organisms grow by cell division. In animals growth is seen up to a certain age. However, cell division occurs in certain tissue to replace lost cells. In plants growth is present throughout the life.

Reproduction :
Production of progeny is referred on reproduction. Progeny are more or less similar to parents. Reproduction may be vegetative, asexual and sexual methods.

Irritability :
Response to stimuli is called irritability. Plants respond to external factors like light, water temperature etc. All organisms are aware of their surroundings and this is called consciousness.

Metabolism :
The sum total of all the chemical reactions occurring in the body of the living organism is called Metabolism.

Interaction and emergence :
Properties of cellular organelles are not present in the molecular constituents but as a result of interactions they emerge properties at next higher level of organisation.

Question 8.

Answer:


Life forms exhibit ‘unity in diversity’ :
Discuss with your teacher.

Question 9.


List out the principles followed to provide scientific names for newly found organism?


Answer:

  1. Every plant should have only one correct scientific name.
  2. Every scientific plant name has two components. They are the generic name and the specific epithet. This system of providing a name with two components is called Binomial nomenclature.
  3. Scientific name should be in Latin or Latin derivative.
  4. Both the words, when hand written they must be underlined or printed in italics to indicate their Latin origin.
  5. The generic name will be in the noun form and always begins with capital letter. The specific name will be in the adjective form and starts with small letter. For example, Solanum tuberosum is the name of the potato plant in which “Solanum” is the genus and “tuberosum” is the species.
  6. The author’s name may be given in abbreviated form at the end of the scientific name.

For example :
Mangifera indica Linn. It indicates that the species was first described by Linnaeus.

TS Inter 1st Year Maths 1A Solutions Chapter 2 Mathematical Induction Ex 2(a),TG Inter 1st Year Maths 1A Mathematical Induction Solutions Exercise 2(a)Using Mathematical Induction prove each of the following statement for all n ∈ N.

Junaid
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TS Inter 1st Year Maths 1A Solutions Chapter 2 Mathematical Induction Ex 2(a),TG Inter 1st Year Maths 1A Mathematical Induction Solutions Exercise 2(a)Using Mathematical Induction prove each of the following statement for all n ∈ N.

Question 1.
12 + 22+ 32 + …………. + n2 = n(n+1)(2n+1)/6

Answer:
Let S(n) be the given statement
12 + 22 + 32 + …………. + n2 = n(n+1)(2n+1)/6
Since 12 = 1(1+1)(2+1)/6
⇒ 1 = 1; the statement is true for n = 1
Suppose the statement is true for n = k then
(12 + 22 + 32 + ………….. + k2) + k(k+1)(2k+1)/6
We have to prove that the statement is true for n = k + 1 also then
(12 + 22 + 32 + …………… + k2) + (k + 1)2

∴ The statement is true for n = k + 1 also.
∴ By the principle of Finite Mathematical Induction S(n) is true for all n ∈ N.
i.e., 12 + 22 + 32 + ……….. + n2 = n(n+1)(2n+1)/6, ∀ n ∈ N

Question 2. 2.3 + 3.4 + 4.5 + ………………. upto n terms = n(n2+6n+11)/3 (March 13, May 06)

Answer:
Let S(n) be the statement.
The nth term of 2.3 + 3.4 + 4.5 + …………… is (n + 1) (n + 2)
∴ 2 . 3 + 3 . 4 + 4 . 5 + …………….. + (n + 1) (n + 2)
= n(n2+6n+11)/3
Now S(1) = 2 . 3 = 1(12+6+11)/3 = 6
∴ The statement is true for n = 1.
Suppose that the statement is true for n = k, then 2.3 + 3.4 + 4.5 + …………….. + (k + 1) (k + 2)
= k(k2+6k+11)/3
Adding (k + 1) th term of L.H.S both sides
S(k + 1) = 2.3 + 3.4 + 4.5 + ……………. + k (k + 1) (k + 2) + (k + 2) (k + 3)

∴ S(k + 1) = 1/3 (k + 1) [k2 + 2k + 1 + 6 (k + 1) + 11]
= 1/3 (k + 1) [(k + 1)2 + 6(k + 1) + 11]
∴ The statement is true for n = k + 1
So by the principle of Finite Mathematical Induction S(n) is true ∀ n ∈ N
∴ 2 . 3 + 3 . 4 + 4 . 5 + ……………. + (n + 1) (n + 2) = n(n2+6n+11)/3

Question 3. 1/1⋅3+1/3⋅5+1/5⋅7 + ……………. + 1/(2n−1)(2n+1) = n2n/+1 (May 2014)

Answer:
Let Sn be the statement
1/1⋅3+1/3⋅5+1/5⋅7 + ……………. + 1/(2n−1)(2n+1)
Then S(1) = 1/1⋅3=1/2(1)+1=1/3
∴ S(1) is true.
Suppose the statement is true for n = k, then
S(K) = 1/1⋅3+1/3⋅5+1/5⋅7+….+1(2k−1)(2k+1) = k/2k+1
We have to show that the statement is true for n = k + 1 also,

The statement S(n) is true for n = k + 1
∴ By the principle of Mathematical Induction S(n) is true for all n ∈ N.
∴ 1/1⋅3+1/3⋅5+1/5⋅7 + ……………. + 1/(2n−1)(2n+1) = n/2n+1

Question 4. 43 + 83 + 123 + ………… + upto n terms = 16n2 (n + 1)2

Answer:
4, 8, 12, are in A.P. and nth term of A.P. is = a + (n – 1) d
= 4 + (n – 1) 4 = 4n
Let S(n) be the statement
43 + 83 + 123 + ……………… + (4n)3 = 16n2 (n + 1)2
Let n = 1, then
S(1) = 43 = 16 (1 + 1)2 = 64
∴ The statement is true for n = 1 also.
Suppose the statement is true for n = k then
43 + 83 + 123+ ……………… + (4k)3 = 16k2 (k + 1)2
We have to prove that the result is true for n = k + 1 also. Adding (k + 1) th term
= [4 (k + 1)]3 = [4k + 4]3 both sides
43 + 83 + 123 + ……………….. + (4k)3 + (4k + 4)3
= 16k3 (k + 1)2 + [4 (k + 1)]3
= 16 (k + 1)2 [k2 + 4k + 4]
= 16 (k + 1)2 (k + 2)2
= 16 (k + 1)2 [(k + 1) + 1]2
Hence the result is true for n = k + 1.
∴ By the principle of Mathematical Induction S(n) is true ∀ n ∈ N.
∴ 43 + 83 + 123 + ……………….. + (4n)3 = 16n2 (n + 1)2

Question 5.
a + (a + d) + (a + 2d) + ……………… upto n terms = n/2 [2a + (n – 1) d]

Answer:
Let S(n) be the statement
a + (a + d) + (a + 2d) + + [a + (n – 1) d] = n/2 [2a + (n – 1) d]
Now S(1) is a = 1/2 [2a + 0 (d)] = a
∴ S(1) is true.
Assume that the statement is true for n = k
∴ S(k) = a + (a + d) + (a + 2d) + ……………….. + [a + (k – 1) d]
= k/2 [2a + (k – 1) d]
We have to prove that the statement is true for n = k + 1 also.
Adding a + kd both sides
a + (a + d) + ……………. + [a + (k – 1) d] + [a + kd]

∴ The statement is true for n = k + 1 also
∴ By the principle of Mathematical Induction.
S(n) is true for all n ∈ N
∴ a + (a + d) + (a + 2d) + + [a + (n – 1) d] = n/2 [2a + (n -1) d]

Question 6.
a + ar + ar2 + ………………… + n terms = a(rn−1)/r−1, r ≠ 1 (March 2011)

Answer:
Let S(n) be the statement
a + ar + ar2 + ………….. + arn – 1 = (rn−1)/r−1, r ≠ 1
Then S(1) = a = a(r1−1)/r−1 = a
∴ The result is true for n = 1
Suppose the statement is true for n = k then
a + ar + ar2 + …………… + ar = a(rk−1)/r−1, r ≠ 1
We have to prove that the result is true for n = k + 1 also.
Adding ark both sides
(a + ar + ar2 + ………….. + ark – 1 + ark)

∴ The statement is true for n = k + 1 also
∴ By the principle of Mathematical Induction p(n) is true for all n ∈ N
a + ar + ar2 + ………………… + n terms = a(rn−1)/r−1, r ≠ 1

Question 7.
2 + 7 + 12 + ………. + (5n – 3) = n(5n−1)/2

Answer:
Let S(n) be the statement
2 + 7 + 12 + ………. + (5n – 3) = n(5n−1)/2 = 1(5−1)/2 = 2,
Since S(1) = 2,
S(1) is true.
Suppose the statement is true for n k then
(2 + 7 + 12 + ………….. + (5k – 3) = k(5k−1)/2
We have to show that S(n) is true for n = k + 1 also.
Adding (k + 1)th term 5 (k + 1) – 3 = 5k + 2 both sides
[2 + 7 + 12 + ……. + 5k – 3)] + (5k + 2)

∴ S(n) is true for n = k + 1 also
∴ By the principal of Mathematical Induction
S(n) is true ∀ n ∈ N
∴ 2 + 7 + 12 + …………… + (5n – 3) = n(5n−1)/2.

Question 8.
(1 + 3/1)(1 + 5/4)(1 + 7/9)………(1 + 2n+1/n2) = (n + 1)2 (March 2015-A.P)


Answer:
Let Sn be the statement

∴ S(n) is true for n = 1
Suppose Sn is true for n = k then
(1 + 3/1)(1 + 5/4)(1 + 7/9)……(1 + 2k+1/k2)
= (k + 1)2 ………………. (1)
We have to prove that the statement is true for n = k + 1 also
(k + 1) th term is

= k2 + 4k + 4
= (k + 2)2
∴ S(n) is true for n = k + 1 also
∴ By the principal of Mathematical Induction S(n) is true for ∀ n ∈ N


Question 9.
(2n + 1) < (n + 3)2

Answer:
Let S(n) be the statement
When n = 1, then 9 < 16 ∴ S(n) is true for n = 1 Suppose S(n) is true for n = k then(2k + 7) < (k + 3)2 …………….. (1)
We have to prove that the result is true for n = k + 1
i.e., 2(k + 1) + 7 < (k + 4)2
∴ 2 (k + 1) + 7 = 2k + 2 + 7 = (2k + 7) + 2 < (k + 3)2 + 2 (From (1))
= k2 + 6k + 9 + 2
= k2 + 6k + 11 < (k2 + 6k + 11) + (2k + 5)
= k2 + 8k + 16
= (k + 4)2
∴ S(n) is true for n = k + 1 also
By principle of Mathematical Induction
S(n) is true ∀ n ∈ N


Question 10.
12 + 22 + ……………. + n2 > n3/3

Answer:
Let S(n) be the statement
When n = 1, then 1 > 1/3
∴ S(n) is true for n = 1
Assume S(n) to be true for n = k then
12 + 22 + ……………. + k2 > k3/3
We have to prove that the result is true for n = k + 1 also.

∴ S(n) is true for n = k + 1 also
∴ By principle of Mathematical Induction.
S(n) is true ∀ n ∈ N

Question 11.
4n – 3n – 1 is divisible by 9

Answer:
Let S(n) be the statement,
4n – 3n – 1 is divisible by 9
For n = 1, 4 – 3 – 1 = 0 is divisible by 9
∴ Statement S(n) is true for n = 1.
Suppose the statement S(n) is true for n = k
Then 4k – 3k – 1 is divisible by 9.
∴ 4k – 3k – 1 = 9t for t ∈ N ……………. (1)
We have to show that statement is true for n = k + 1 also.
From (1), 4k = 9t + 3k + 1
∴ 4k + 1 – 3 (k + 1) – 1 = 4 . 4k – 3 (k + 1) – 1
= 4 (9t + 3k + 1) – 3k – 3 – 1
= 4 (9t) + 9k
= 9 (4t + k) divisible by 9
(∵ 4t + k is an integer)
Hence, S(n) is true for n = k + 1 also.
∴ 4k + 1 – 3 (k + 1) – 1 is divisible by 9
∴ The statement is true for n = k + 1
∴ By the principle of Mathematical Induction.
S(n) is true for all n e K
∴ 4n – 3n – 1 is divisible by 9

Question 12.
3.52n + 1 + 23n + 1 is divisible by 17 (May 2012, 2008)

Answer:
Let Sn be the statement
3.52n + 1 + 23n + 1 is divisible by 17
S(1) is 3 . 52(1) + 1 + 23 (1) + 1
= 3 . 53 + 24 = 3 (125) + 16
= 375 + 16 = 391 is divisible by 17
Hence, S(n) is true for n = 1.
Suppose that the statement is true for n = k, then
3.52k + 1 + 23k + 1 is divisible by 17 and
3.52k + 1 + 23k + 1 = 17t for t ∈ N
then we have to show that the result is true for n = k + 1 also
Consider 3.52(k + 1) + 1 + 23(k + 1) + 1
= 3.52k + 1 . 52 + 23(k + 1) . 2
= (17t – 23k + 1) 52 + 23k + 3 . 2
= 17t (25) – 23k (50) + 23k (16)
= 17 t (25) + 23k (16 – 50)
= 17 t (25) – 34 23k
= 17 [25t – 23k + 1
25t – 23k + 1 is an integer.
∴ 3.52(k + 1) + 1 + 23 (k + 1) + 1 is divisible by 17.
∴ The statement S(n) is true for n = k + 1 also.
∴ By the principle of Mathematical induction S(n) is true for ∀n ∈ N
∴ 3.52n + 1 + 23n + 1 is divisible by 17

Question 13.
1.2.3 + 2.3.4 + 3.4.5 + ……………. upto n terms = n(n+1)(n+2)(n+3)/4. (March 2015-T.S) (Mar. 08)

Answer:
The nth term of the given series is n (n + 1) (n + 2) and let Sn be the statement.
1.2.3 + 2.3.4 + 3.4.5 + ……………. + n (n + 1) (n + 2)
= n(n+1)(n+2)(n+3)/4
For n = 1
S(1) = 1.2.3 = 6
= 1(1+1)(1+2)(1+3)/4
= 2(3)(4)/4 = 6
∴ S(n) is true for n = 1
Let S(n) is true for n = k then
1.2.3 + 2.3.4 + 3.4.5 + ……………. + k (k + 1) (k + 2)
= k(k+1)(k+2)(k+3)/4 …………….. (1)
We have to prove that the result is true for n = k + 1 also.
Adding (k + 1) th term, (k + 1) (k + 2) (k + 3) both sides we get
1.2.3 + 2.3.4 + 3.4.5 + ……………. + k(k + 1)(k + 2) + (k + 1) (k + 2) (k + 3)

∴ S(n) is true for n = k + 1 also.
Hence by the principle of Mathematical Induction.
S(n) is true for ∀n ∈ N
∴ 1.2.3 + 2.3.4 + 3.4.5 + ……………. + n (n + 1) (n + 2) = n(n+1)(n+2)(n+3)4

Question 14.
13/1 + 13+23/1+3 + 13+23+33/1+3+5 + ……………… upto n terms = n/24 (2n2 + 9n + 13). (Mar. 14, 04, 05)

Answer:
The nth term of the given series is

Question 15.
12 + (12 + 22) + (12 + 22 + 32) + ……………. upto n terms = n(n+1)2(n+2)/12. (March 2012)

Answer:
Let S(n) be the statement and
nth term of series is 12 + 22 + 32 + ……………… + n2
∴ S(n) = 12 + (12 + 22) + (12 + 22 + 32) + ……… + (12 + 22 + 32 + ………………. + n2)

∴ S(n) is true for n = 1.
Suppose S(n) is true for n = k then
12 + (12 + 22) + (12 + 22 + 32) + ……… + (12 + 22 + 32 + ………………. + k2) = k(k+1)2(k+2)/12
Now we have to prove that S(k + 1) is true.
So 12 + (12 + 22) + (12 + 22 + 32) + ……… + (12 + 22 + 32 + ………………. + k2) + (12 + 22 + 32 + ……………. + k2 + (k + 1)2

∴ The statement S(n) hold for n = k + 1 also
∴ By the principle of Mathematical Induction S(n)is true ∀n ∈ N.
∴ 12 + (12 + 22) + (12 + 22 + 32) + (12 + 22 + 32 + …………… + n2) = n(n+1)2(n+2)/12

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