Scoring good marks in an entrance examination is an art where more than one subject questions are being asked. Students should choose the subjects very carefully where they can score marks confidently. In general, Mathematics is a subject which can be the suitable subject to score good marks.

There are only few months left for JEE Main entrance examination. This is the time when students should focus more on solving practice paper than to study. Solving practice papers help them to decide which strategies they should adopt in the examination.

In this article, Subject Experts bring to you Solved Practice Paper of Mathematics after analyzing the pattern and syllabus of the examination.

**About the paper:**

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

2. Each question carries equal marks.

3. For each correct answer you will be awarded by 4 marks while for the incorrect answer 1 mark will be deducted from your total score.

4. No mark will be awarded for any unattempted question.

5. Questions have been taken from different topics like Sets, Relations and Functions, Trigonometric Functions, Complex Numbers and Quadratic Equations, Linear Inequalities, Permutations and Combinations, Binomial Theorem, Sequences and Series, Straight Lines, Conic Sections, 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.

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

7. Detail solution for all the questions.

**JEE Main Mathematics Syllabus: 2017 – 2018**

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

**Question:**

The locus of the point of intersection of any two perpendicular tangents to the hyperbola is a circle which is called the director circle of the hyperbola, then the equation of this circle is

(a) x^{2} + y^{2} = a^{2} + b^{2}

(b) x^{ 2} + y^{2} = a^{2} - b^{2 }

(c) x^{2} + y^{2} = 2ab

(d) none of these

**Sol. (a)**

**Question:**

Three dice are thrown at the same time. The probability of getting three two’s, if it is known that the sum of the numbers on the dice was six is

(a) 1/5

(b) 1/8

(c) 1/12

(d) 1/10

**Sol.(d)**** **

On a throw of three dice, we have sample space [*n*(*S*)] = 6^{3} = 216

Let *E*_{1} is the event when the sum of numbers on the dice was six and *E*_{2}* *is the event when three two’s occurs.

⇒ (*E*_{1} = {(1, 1, 4), (1, 2, 3), (1, 3, 2), (1, 4, 1), (2, 1, 3) (2, 2, 2), (2, 3, 1),(3, 1, 2), (3, 2, 1), (4, 1, 1)

⇒ *n*(*E*_{1}) = 10 and *E _{2} *={2, 2, 2}

⇒ *n*(*E*_{1}) *= *1

Also, (*E*_{1} ∩ *E*_{2}) = 1

**Question:**

The approximate value of (1.999)^{5} is

(a) 31.920

(b) 31.290

(c) 30.920

(d) 33.920

**Sol. (a)**

**Question:**

OABC is a tetrahedron, OA = 3, BC = 2 and the shortest distance between OA and BC is 2. If the angle between OA and BC is 30^{o}, then its volume is

**Question:**

The area of the region bounded by the curve *y* = *x*^{3}, *y* = *x + *6 and *x *= 0* *is

(a) 10 sq. units

(b) 12 sq. units

(c) 14 sq. units

(d) 16 sq. units

**Sol. (d)*** *

We have, *y = x*^{3}*, y = x + *6 and *x = *

∴ *x*^{3} = *x + *6

⇒ *x*^{3} - *x = *6

⇒ *x*^{3} - *x* -6 = 0

⇒ *x*^{2}(*x* - 2) + 2*x*(*x* - 2) + 3(*x* - 2) = 0

⇒ (*x* - 2) (*x*^{2 }+ 2*x *+ 3) = 0

⇒ *x* = 2, with two imaginary points

**Question:**

The equation of a plane which bisects perpendicularly the line joining the points *A *(2*, *3, 4) and *B *(4, 5, 8) at right angles is

(a) *x + *2*y+ *2*z* = 19

(b) *x + y+ *2*z* = 19

(c) 2*x + y+ *2*z* = 19

(d) 2*x + y+ *2*z* = 19

**Sol. (b)**

Since, the equation of a plane is bisecting perpendicular the line joining the points

*A *(2, 3, 4) and *B *(4, 5, 8) at right angles.

**Question:**

In triangle ABC, AB = AC = m and D is a point on BC such that BD = 9, DC = 21 and AD = n. If m and n are integers then m – n can be

(a) 2

(b) 5

(c) 6

(d) 7

**Sol. (d)**

**Question:**

A ladder, 5 m long, standing on a horizontal floor, leans against a vertical wall. If the top of the ladder slides downwards at the rate of 10 cm/s, then the rate at which the angle between the floor and the ladder is decreasing when lower end of ladder is 2 m from the wall is

(a) 1/10 rad/s

(b) 1/20 rad/s

(c) 20 rad/s

(d) 10 rad/s

**Sol.(b)**

Let the angle between floor and the ladder be q.

Let *AB = x *cm and *BC = y *cm

**Question:**

Let S be the sum of all two – digit number each of which contains one odd and one even digits. Then S is divisible by

(a) 5

(b) 3

(c) 4

(d) 6

**Sol.(a)**

The sum of all two-digit number

**Conclusion:**

This practice paper will help students to manage speed and accuracy in the examination. Students will get to know about the latest pattern of the coming JEE examination. In this practice paper, students will find the questions from the complete syllabus of Mathematics.

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