Biology 1st Year Chapter 2

Biological molecules are essential compounds in living organisms, including carbohydrates, proteins, lipids, and nucleic acids, which play key roles in cellular structure, energy storage, and genetic information. 1st year Biology Chapter 2 Notes ​When a protein undergoes a hydrolysis reaction the end-products are: Amino acid Glycerol is the back bone molecule for: Triglycerides To biological … Read more

Biology 1st Year Chapter 1

The introduction to the 1st year Biology chapter provides an overview of foundational concepts, including cell structure, genetics, ecology, and the diversity of life, setting the stage for deeper exploration of biological systems. 1st year Biology Notes Chapter 1 ​Which of the following is not related to cloning: Removal of piece of DNA or gene … Read more

Mathematics Class 12 Chapter 7

Vectors are mathematical objects that have both magnitude and direction. They are used in physics and engineering to represent quantities such as force, velocity, and displacement. Mathematics Notes for Class 12 Chapter 7 The vector, whose initial point is the origin Oand whose terminal point is P i.e., OP is called: Position vector The dot product of unit … Read more

Mathematics Class 12 Chapter 6

A conic section is a curve formed by the intersection of a plane and a double-napped cone. The four main types are circles, ellipses, parabolas, and hyperbolas, each with distinct properties and equations. Mathematics Notes For Class 12 Chapter 6 A function which is to be maximized or minimized is called an: Objective function The … Read more

Mathematics Class 12 Chapter 5

“Learn about linear inequalities and linear programming, techniques used to solve optimization problems by finding the best outcome within given constraints.” Mathematic 12 Class Chapter 5 Notes ​The inequality x < a is the closed half plane to the _________ of the boundary line x = a: Left A function which is to be maximized or minimized … Read more

Mathematics Class 12 Chapter 4

“Explore the basics of Analytic Geometry, which combines algebra and geometry to study shapes, lines, and curves using coordinate systems and equations.” Important questions of Chapter 4 Mathematics Class 12 ​Equation of horizontal line through (a, b) is: x = b The point of concurrency of medians of triangle is called: Centroid y = c … Read more

Mathematics Class 12 Chapter 3

“Discover integration in calculus, the process of finding the area under curves, summing infinitesimal changes, and solving problems related to accumulation and total quantities.” Mathematics Class 12 Chapter 3 Notes ? Cos(ax+b)dx=: (ax+b)n+1/a(n+1) +c The differentiate of x is given by: sin-1 (x/a) + c ? Sin(ax+b)dx=: y= -Cos x + c If y= x2-1 then dy =: … Read more

Mathematics Class 12 Chapter 2

“Learn about differentiation in calculus, a fundamental concept that explores how functions change, calculating the rate of change or slope at any given point.” Mathematics Chapter 2 Class 12 ​Derivative of ?x (cos x) w.r.t x is: Cos x /2?x -?xSin x If y = eax, then y4=: a4eax dy/dx = dy/dx . dx/du is called: … Read more

Mathematics Class 12 Chapter 1

“Explore the concepts of functions and limits in mathematics. Understand how functions map inputs to outputs and how limits describe the behavior of functions as they approach specific points.” Solutions of Mathematics Class 12 Chapter 1 ​If f(x) = x sec x, then f(0): 0 f(x) = sin x + cos x is ———— function: … Read more

11th Class Physics Chapter 5

Circular motion refers to the movement of an object along a circular path, where forces like centripetal force keep it in motion. It is key in understanding the dynamics of rotating systems and orbits. Physics Class 11 Chapter 5 Notes A satellite moving around the earth constitutes: non inertial frame of reference The close orbiting … Read more