Formula Card

Concept of the Day
$\int \frac{1}{x} dx = \ln|x| + C$
Note: Essential for solving integration problems in Class 12 and JEE Prep.

Saturday, 2 May 2026

RTU Hojai Exam Prep: Plant Structure, Development, and Diversity

Botany Paper II: Embryology of Angiosperms and Gymnosperm Morphology

1. Explain the structure and Development of Embryo Sac


In the context of the Rabindranath Tagore University (RTU), Hojai, botanical questions regarding embryology often require a detailed, step-by-step explanation of Megasporogenesis and Megagametogenesis.

Here is a comprehensive breakdown of the structure and development of the female gametophyte (Embryo Sac) in Angiosperms.


1. Development of the Embryo Sac (Megagametogenesis)

The process of embryo sac formation usually follows the Polygonum type (monosporic), which is the most common pattern in flowering plants.

The Megaspore Formation

  • Starting Point: Inside the ovule's nucellus, a single cell differentiates into the Archesporial cell, which becomes the Megaspore Mother Cell (MMC).

  • Meiosis: The MMC undergoes meiosis to produce a linear tetrad of four haploid megaspores.

  • Degeneration: In most plants, the three megaspores toward the micropylar end degenerate, leaving only one functional megaspore at the chalazal end.

Nuclear Divisions

The functional megaspore expands and its nucleus undergoes three successive mitotic divisions without immediate cytokinesis:

  1. First Division: Produces 2 nuclei which move to opposite poles.

  2. Second Division: Produces 4 nuclei (2 at each pole).

  3. Third Division: Produces 8 nuclei (4 at each pole).

Cellular Organization

After the 8-nucleate stage, walls begin to form, organizing the cells into the final 7-celled, 8-nucleate structure.

JEE Main Units & Measurements PYQs (2021-2025) | Chapter-wise Solved Questions

JEE Main Previous Year Questions (2016-2025) on the topic of Units and Measurements:

Question 1 (JEE Main 2023)

Match List I with List II:

List I List II
A. Planck's constant ($h$) I. $[M^1 L^2 T^{-2}]$
B. Stopping potential ($V_s$) II. $[M^1 L^1 T^{-1}]$
C. Work function ($\phi$) III. $[M^1 L^2 T^{-1}]$
D. Momentum ($p$) IV. $[M^1 L^2 T^{-3} A^{-1}]$

Choose the correct answer from the options given below:

(1) A-I, B-III, C-IV, D-II

(2) A-III, B-I, C-II, D-IV

(3) A-II, B-IV, C-III, D-I

(4) A-III, B-IV, C-I, D-II

Friday, 1 May 2026

Imaginary and Complex numbers | Class 11 | CBSE, ICSE, AHSEC

Based on the NCERT chapter on Complex Numbers and Quadratic Equations, here is a simplified study guide designed to help you visualize and master the basics of Section 4.2.


4.2 Understanding Complex Numbers

1. Why do we need them?

In the real number system, we cannot solve equations like $x^2 + 1 = 0$ because $x^2 = -1$, and no real number squared results in a negative value. To solve this, mathematicians introduced the symbol $i$ (iota).

  • The Definition: $i = \sqrt{-1}$

  • The Property: $i^2 = -1$


2. What is a Complex Number?

A complex number ($z$) is a combination of a Real part and an Imaginary part. It is written in the form:

$$z = a + ib$$
Component Name Symbol
$a$ Real Part $Re(z)$
$b$ Imaginary Part $Im(z)$

Example: In $z = 2 + i5$

  • The Real part is 2.

  • The Imaginary part is 5.

Electric Potential and Potential Energy Worksheet

 Physics Worksheet - 11


Board: CBSE/ICSE/AHSEC

Topic(s): Electric Potential and Potential Energy

Total Marks: 20

Time: 30 minutes


Name: ____________________ Class: _______ Date: ___________


INSTRUCTIONS

• Answer all questions.

• Write neatly and legibly.

• For numerical problems, show your working and include units in your final answer.

• Use k = 8.99 × 10⁹ N m² C⁻² where required.

• Charge of an electron = -1.60 × 10⁻¹⁹ C.

• Charge of a proton = +1.60 × 10⁻¹⁹ C.


SECTION A: MULTIPLE CHOICE QUESTIONS


The definition of electric potential difference between two points is: (1 mark)

a) The force experienced per unit positive charge.

b) The work done in moving a unit positive charge between the points.

c) The product of the electric field and the distance between the points.

d) The total kinetic energy gained by a charge moving between the points.

Friday, 17 April 2026

BSc Zoology Major: Animal Diversity and Evolutionary Concepts (NEP RTU Hojai)

Chordata Study Notes: 


Osteichthyes (Bony Fish), Chondrichthyes (Cartilaginous Fish), General Characters: Agnatha, General Characters: Cephalochordata, Dipleurula Concept, Retrogressive Metamorphosis, Fish Migration, Snake Poisonous Apparatus, and Amphibian Parental Care


For your BSc Zoology Major under the NEP (New Education Policy) framework at Rabindranath Tagore University (RTU), Hojai, the study of Chordates typically falls under the Animal Diversity paper. Since your curriculum aligns closely with Gauhati University, these notes are structured for descriptive "Long Answer" type questions, emphasizing classification and comparative characteristics.


1. Osteichthyes (Bony Fish)

The name is derived from Greek (osteon = bone; ichthyes = fish). These are the most diverse group of vertebrates.

  • Endoskeleton: Primarily composed of bone (calcified).

  • Body Form: Usually streamlined/fusiform; skin is covered by cycloid, ctenoid, or ganoid scales (rarely placoid).

  • Mouth: Position is usually terminal (at the tip of the snout).

  • Respiration: Gills are covered by a protective bony flap called the operculum.

  • Buoyancy: Possess a swim bladder (air bladder) which helps them maintain depth without constant swimming.

  • Tail Fin: Usually homocercal (symmetrical lobes).

  • Reproduction: Mostly oviparous (lay eggs) with external fertilization.

  • Examples: Labeo rohita (Rohu), Exocoetus (Flying fish), Hippocampus (Sea horse).