Class 11 Maths NCERT solutions

In this article, you will find Class 11 Maths NCERT solutions in PDF format. These are notes thoroughly organized by HashLearn teachers making it ideal for exams like JEE & other state engineering examsCBSE and ICSE Board exams.

Class 12 Maths NCERT solutions

Students preparing for various competitive exam often dive directly into the subject without having a look at the syllabus first. A deep understanding of the syllabus can help with familiarizing the subject, understanding its depth, difficulty level and so on. Hence, the first step in your preparation process is to have a deep understanding of the syllabus.

Descartes’ Rule of Signs explained by an IITian

This explanation of Descartes’ Rule of Signs was submitted by Ayush, a HashLearn tutor from IIT, Dhanbad.

Consider a polynomial equation p(x)=0 (descending powers of x)
i) Number of positive roots of the equation p(x)=0 cannot exceed the number of changes of sign in p(x).…

Study Tips: Maxima and Minima

This tip on calculus was contributed by one of our top tutors, Darshan Maheshwari.

The last edition of study tips, we posted an interesting trick to differentiate an infinite series. This time we’re following it up with helpful formulae to quickly find maxima or minima for functions involving two variables.…

Study Tips: Differentiation of an Infinite Series

This tip on calculus was contributed by one of our top tutors, Shashwat.

What you will learn from this tip:
The trick to differentiate an infinite series.

Want more tips like this? Request a session on HashLearn now (it’s free!) Consider the following question:
A function y is defined as Find at x = 0.…

Study Tips: Finding the Roots of Unity

This tip on roots of an equation, and complex numbers was contributed by one of our top tutors, Sudheer Naidu.

What you will learn from this tip:
• An understanding of the relation between complex numbers and the roots of unity.
• The trick to calculate the nth roots of unity.

Study Tips: Sum of Infinite Telescoping Series

This tip on sequences and series was contributed by one of our top tutors, Rushil Shah.

What you will learn from this tip:
• An understanding of a telescoping series
• The trick to calculate the sum of a telescoping series

Telescoping series

A telescoping series is any series where nearly every term cancels with a preceding or following term.…

Trick to solve seating arrangement problems

This tip to solve permutation and combinations problems was submitted by Ayush, a HashLearn tutor from IIT, Dhanbad.

In this tip, you will learn how to quickly solve one kind of seating arrangement problems.

Question

n people are sitting on a round table.…

Study Tips: Finding Values For Trigonometric Identities

With this tip, you will learn:

• The 4 types of trigonometric identities
• The formulae to find maximum & minimum values for trigonometric identities for each type
• An example problem to solve

Study Tips: Properties of Triangles That You Need To Know

This Coordinate Geometry tip was contributed by Kshitij of BITS Pilani, Goa Campus.

What you will learn from this tip:
— Formulae to calculate trigonometric ratios of half-angles
— The properties of every triangle

Trigonometric ratios of half-angles

Here are some important formulae that you should note down to calculate the trigonometric ratios of half-angles.…