Find **JEE (Main) Mathematics Practice Paper** for the year 2016 JEE exam. These questions not only help the students to prepare for exams in a better manner but also help them in understanding the depth with which a topic should be studied. At the and of the paper, student can find the answer for each question.

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

**Q.** If the roots of the equation a(b – c)*x*^{2} + b(c – a)* x* + c (a – b) =0 are equal, then a, b and c are in:

(a) AP

(b) GP

(c) HP

(d) All of these

**Q.** (1 + i) * ^{x} *+ (1 + i

^{3})

*+ (1 + i*

^{x}^{5})

*+ (1 + i*

^{y}^{7})

*will be real number, if and only if:*

^{y}(a) *x *= *y* + 1

(b) *x* = *y *– 1

(c) *x* = *y*

(d) *x* > 0, *y *> 0

**Q.** If *a _{1}, a_{2}, a_{3}* as well as

*b*are in G.P. with the same common ratio, then the points

_{1}, b_{2}, b_{3}*(a*and

_{1}, b_{1}), (a_{2}, b_{2})*(a*

_{3}, b_{3}):(a) are vertices of a triangle

(b) lie on parabola

(c) lie on a circle

(d) lie on a straight line

**Q.** Number of matrices of 2 × 2 matrices A, which are satisfying the relation A + A^{T} = I and AA^{T }= I:

(a) 1

(b) 2

(c) 3

(d) 4

**Q.** Let *x*_{1} and *x*_{2} be m^{th} roots of unity which subtend a right angle at the origin. Then ‘m’ must be of the form:

(a) 4k + 1

(b) 4k + 2

(c) 4k + 3

(d) 4k

**Q.** Find the equation of the plane through the line of intersection of the planes *x* + *y* + *z* = 1 and 2*x* +3*y* + 4*z* = 5 which is perpendicular to the plane *x *– *y *+ *z* = 0

(a) x - z - 2 = 0

(b) x - y + 2 = 0

(c) x - z + 2 = 0

(d) y - z + 2 = 0

**Q. **A manufacturer produces nuts and bolts. It takes 1 hour of work on machine A and 3 hours on machine B to produce a package of nuts. It takes 3 hours on machine A and 1 hour on machine B to produce a package of bolts. He earns a profit, of Rs 17.50 per package on nuts and Rs. 7.00 per package on bolts. How many packages of each should be produced each day so as to maximize his profit, if he operates his machines for at the most 12 hours a day?

(a) 3 packages of nuts and 6 packages of bolts

(b) 3 packages of nuts and 3 packages of bolts

(c) 6 packages of nuts and 3 packages of bolts

(d)3 packages of nuts and 8 packages of bolts

**Q.** The length *x* of a rectangle is decreasing at the rate of 5 cm/minute and the width *y* is increasing at the rate of 4 cm/minute. When *x* = 8 cm and *y* = 6 cm, which of the following is true?

(a) Perimeter is decreasing at the rate of 2 cm/min

(b) Area of the rectangle is increasing at the rate of 2 cm^{2}/min

(c) Both A & B

(d) None of these