After covering most of the syllabus, now students are looking for the practice paper which can help them in understanding the pattern and difficulty level of the coming JEE Main entrance examination 2018.

To fulfil this need of the students, Subject Experts of Mathematics bring to you Solved Practice Paper of Mathematics after analyzing the pattern and syllabus of the examination.

**About the paper:**

1. There are 30 questions in this paper.

2. Questions have been taken from different topics like Trigonometric Functions, Conic Sections, Relations and Functions, Inverse Trigonometric Functions, Matrices, Determinants, Continuity and Differentiability, Application of Derivatives, Integrals, Application of Integrals, Differential Equations, Vector Algebra, Three Dimensional Geometry, Probability etc.

3. Questions are of different level i.e., easy, moderate and tough.

4. All questions are of objective level with only one correct option.

5. Detail solution for all the questions.

**Few sample questions from the Practice Paper are given below:**

**Question:**

The maximum number of equivalence relations on the set *A* = {1, 2, 3} is

(a) 1

(b) 2

(c) 3

(d) 5

**Sol.(d)**

**Question:**

The sum of integers from 1 to 100 that are divisible by 2 or 5 is

(a) 3000

(b) 3050

(c) 4050

(d) None of these

**Sol.(b)**

The sum of integers from 1 to 100 that are divisible by 2 or 5 = sum of series divisible by 2 + sum of series divisible by 5 - sum of series divisible by 2 and 5.

**Question:**

Three normals are drawn from the point (c, 0) to the curve y^{2} = x. If two of the normals are perpendicular to each other, then c =

(a) 1/4

(b) 1/2

(c) 3/4

(d) 1

**Sol. (c)**

**Question:**

The curve *y* = *x*^{l/5} has at (0, 0)

(a) a vertical tangent (parallel to *Y*-axis)

(b) a horizontal tangent (parallel to *X*-axis)

(c) an oblique tangent

(d) no tangent

**Sol. (a) **

**Question:**

If matrix *A* = [a_{ij}] _{2x2}, where a_{ij} = 1, if *i *¹* j *=0* *and if *i* = *j*, then , *A*^{2} is equal to

(a) *I*

(b) *A*

(c) 0

(d) None of these

**Sol. (a)**

**Conclusion:**

This practice paper will help students to practice a new set of questions of Mathematics. Students can revise all the topics where they have stuck while attempting it. It will help them to manage speed and accuracy in the examination.