When exams are around the corner, all engineering aspirants think only one question “how to cover all important topics of all subjects in just few days?”. They can’t study complete books just before few days of UPSEE entrance examination.

To help UPSEE aspirants, Subject Experts of Mathematics have prepared concise chapter notes of chapter** Circles** including important concepts, formulae and some previous year solved questions for coming UPSEE/UPTU entrance examination 2018. About **1-2 questions** are always asked from this topic in the examination.

These notes contain all important topics related to chapter Circles like **definition of circle, general equation of circle, equation of circle with the end points of diameter, equation of tangent to a circle, equation of normal to a circle, equation of a circle passing through a line and touching a line, length of tangent from an external point, equation of chord, orthogonal circles** etc.

These notes are based on the latest syllabus and pattern of UPSEE entrance examination.

**UPSEE: Important Questions and Preparation Tips – Permutation and Combination**

**Important Concepts:**

**UPSEE: Important Questions and Preparation Tips – Sequence and Series**

**Some previous year solved questions are given below:**

**Question 1:**

**Solution 1:**

Hence, the correct option is (a).

**UPSEE: Important Questions and Preparation Tips – Relations and Functions**

**Question 2:**

**Solution 2:**

Hence, the correct option is (b).

**UPSEE: Important Questions and Preparation Tips - Complex Numbers**

**Question 3:**

**Solution 3:**

Hence, the correct option is (a).

**UPSEE: Important Questions and Preparation Tips - Matrices and Determinants**

**Question 4:**

**Solution 4:**

Hence, the correct option is (d).

**UPSEE: Important Questions and Preparation Tips – Limits**

**Question 5:**

**Solution 5:**

Hence, the correct option is (d).

**UPSEE: Important Questions and Preparation Tips – Application of Derivatives**