In this article, engineering section is providing you JEE Main Solved Mathematics Practice Paper. After doing a lot of research on previous years’ papers of JEE Main, the subject experts of Mathematics have designed this practice paper.

**About the paper:**

1. There are 30 multiple choice questions with only one correct option.

2. Questions have been taken from different chapters like Relations and Functions, Trigonometric Functions, Complex Numbers and Quadratic Equations, Permutations and Combinations, Binomial Theorem, Sequences and Series, Straight Lines, Limits and Derivatives, Probability, Inverse Trigonometric Functions, Matrices, Determinants, Continuity and Differentiability, Application of Derivatives, Integrals, Application of Integrals, Differential Equations, Vector Algebra, Three Dimensional Geometry.

3. Detail solution for all the questions.

**Importance of solved practice paper:**

1. It helps students to get familiar with the pattern and difficulty level of the exam.

2. Students can learn new ways of managing speed and accuracy in the examination.

3. It also helps students to brush up their knowledge.

4. Students can find the detailed solution of each question and save their precious time.

5. Students need to solve lot of practice papers to overcome the fear of exam.

**Few sample questions from the solved practice paper are given below:**

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**Question:**

A box of oranges is inspected by examining three randomly selected oranges drawn without replacement. If all the three oranges are good, the box is approved for sale, otherwise, it is rejected. Find the probability that a box containing 15 oranges out of which 12 are good and 3 are bad ones will be approved for sale.

(a) 25/46

(b) 4/25

(c) 44/91

(d) 4/81

**Sol. (c)**

The correct option is C

Let A = first drawn orange is good

B = second drawn orange is good

C = third drawn orange is good

The oranges are not replaced.

Thus,

**Question:**

The line passing through the extremity *A* of the major axis and extremity *B* of the minor axis of the ellipse *x*^{2} + 9*y*^{2} = 9 meets its auxiliary circle at the point *M*. Then the area of the triangle with vertices at *A*, *M* and the origin *O* is

(a) 31/10

(b) 29/10

(c) 21/10

(d) 27/10

**Sol. (d)**

**Question:**

For the curve *y* = 4*x*^{3} − 2*x*^{5}, find all the points at which the tangents passes through the origin.

(a) (0, 0), (1, 2), and (1, −2)

(b) (0, 0), (1, 2), and (−1, −2)

(c) (0, 0), (1, 2), and (−1, 2)

(d) (0, 0), (1, −2), and (−1, −2)

**Sol.(b)**

**Question:**

The slope of the line touching both the parabolas *y*^{2} = 4*x* and *x*^{2} = −32*y* is

(a) 1/2

(b) 3/2

(c) 1/8

(d) 2/3

**Sol. (b) **

**Question:**

The sum of the first 20 term of the sequence 0.7, 0.77, 0.777,…, is

**Sol. (a)**

**Conclusion:**

This solved practice paper will help students to manage speed and accuracy. It will also help students to track their progress. Students can find the detailed solution of each question and save their precious time.