JEE Main 2018 is scheduled to be held on April 8 in offline mode while the online exam will be conducted on April 15 and 16. There is almost one month left for the examination. This one month will surely affect your marks and ranking in JEE Main 2018.

Students already covered most of the syllabus. Now, they are searching for the practice paper to boost their preparation. Students should try to get solved practice paper. It will help you to match your answer or concept with the solution.

In this article, engineering aspirants will get solved practice paper of Mathematics which will help you to know the difficulty level of the questions which can be asked in JEE Main Examination 2018.

**About the paper:**

1. There are 30 multiple choice questions with only one correct option in this practice paper.

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.

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

**Question: **

If α is a complex cube root of unity and (1 + α)^{7} = *X + Y**ω**, *then *X* and *Y* are respectively

equal to

(a) 0, 1

(b) 1, 1

(c) 1, 0

(d) 1, 1

**Sol. (d)**

**Question: **

Let a die is loaded in such a way that prime number drawn are twice as likely to occur as a

non prime number face. The probability that an odd number will be show up when the die is

tossed is

(a) 1 / 3

(b) 2 / 3

(c) 4 / 9

(d) 5 / 9

**Sol. (d) **

**Question: **

Three boys and two girls stand in a queue. The probability that the number of boys ahead of every girl is at least one more than the number of girls ahead of her, is

(a) 1/2

(b) 1/3

(c) 2/3

(d) 3/4

**Sol. (a)**

The number of arrangement of 3 boys and 2 girls is 5!

Let *B*_{1}, *B*_{2}, *B*_{3} be the boys and *G*_{1},*G*_{2} be girls

According to given condition, following case may arise

1. *G*_{1} *G*_{2} *B*_{1} *B*_{2} *B*_{3}

2. *G*_{1} *B*_{1} *G*_{2} *B*_{2} *B*_{3}

3. *G*_{1} *B*_{1} *B*_{2}_{ }*G*_{3} *B*_{3}

4. *B*_{1} *G*_{1} *G*_{2}_{ }*B*_{2} *B*_{3}

5. *B*_{1} *G*_{1} *B*_{2}_{ }*G*_{2}_{ }*B*_{3}

**Question: **

The maximum value of the sum of the *AP* 50, 48, 46,,... is

(a) 620

(b) 550

(c) 520

(d) 650

**Sol. (d) **

For maximum value of the sum of given sequence to *n* terms, is when the *n*th term is either

zero or the smallest positive number of the sequence

*i.e.*, 50 + (*n* – 1) (−2) = 0

*n* = 26

**Question: **

If the number of ways of selecting *n* cards out of unlimited number of cards bearing the number 0, 1, 2, so that they cannot be used to write the number 201 is 93, then *n* is equal to

(a) 2

(b) 3

(c) 4

(d) 5

**Sol. (d) **

We cannot write 201, if in the selection of *n* cards, we get either (2 or 1), (2 or 0), ( 0 or 1), (only 0), (only 1) or (only 2)

** **

**Question: **

Find the equation of a curve passing through the point (2, 1), if the tangent drawn at any point *P*(*x, y*)* *on the curve meets the coordinate axes at *A *and *B *such that *P *is the mid-point of *AB.*

(a) *xy* = 2

(b) *y* = *x*

(c) *x *= 2

(d) *xy* = 1

**Sol. (a)**

**Conclusion:**

After doing a lot of research on previous years’ papers of JEE Main, the subject experts of Mathematics have designed this solved practice paper. Students can also find the detailed solution of each question and save their precious time. It will also help students to track their progress.

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