Joint Entrance Examination

Graduate Aptitude Test in Engineering

1

MCQ (More than One Correct Answer)

Let $${L_1}$$ be a straight line passing through the origin and $${L_2}$$ be the straight line $$x + y = 1$$. If the intercepts made by the circle $${x^2} + {y^2} - x + 3y = 0$$ on $${L_1}$$ and $${L_2}$$ are equal, then which of the following equations can represent $${L_1}$$?

A

$$x + y = 0$$

B

$$x -y = 0$$

C

$$x + 7y = 0$$

D

$$x - 7y = 0$$

2

MCQ (More than One Correct Answer)

If the vertices $$P, Q, R$$ of a triangle $$PQR$$ are rational points, which of the following points of the triangle $$PQR$$ is (are) always rational point(s)?

A

centroid ( A rational point is a point both of whose co-ordinates are rational numbers.)

B

incentre. ( A rational point is a point both of whose co-ordinates are rational numbers.)

C

circumcentre ( A rational point is a point both of whose co-ordinates are rational numbers.)

D

orthocentre ( A rational point is a point both of whose co-ordinates are rational numbers.)

3

MCQ (More than One Correct Answer)

All points lying inside the triangle formed by the points $$\left( {1,\,3} \right),\,\left( {5,\,0} \right)$$ and $$\left( { - 1,\,2} \right)$$ satisfy

A

$$3x + 2y \ge 0$$

B

$$2x + y - 13 \ge 0$$

C

$$2x - 3y - 12 \le 0$$

D

$$ - 2x + y \ge 0$$

4

MCQ (More than One Correct Answer)

Three lines $$px + qy + r = 0$$, $$qx + ry + p = 0$$ and $$rx + py + q = 0$$ are concurrent if

A

$$p + q + r = 0$$

B

$${p^2} + {q^2} + {r^2} = qr + rp + pq$$

C

$${p^3} + {q^3} + {r^3} = 3pqr$$

D

none of these.

On those following papers in MCQ (Multiple Correct Answer)

Number in Brackets after Paper Indicates No. of Questions

IIT-JEE 1999 (1)

IIT-JEE 1998 (1)

IIT-JEE 1986 (1)

IIT-JEE 1985 (1)

Complex Numbers

Quadratic Equation and Inequalities

Permutations and Combinations

Mathematical Induction and Binomial Theorem

Sequences and Series

Matrices and Determinants

Vector Algebra and 3D Geometry

Probability

Trigonometric Functions & Equations

Properties of Triangle

Inverse Trigonometric Functions

Straight Lines and Pair of Straight Lines

Circle

Conic Sections

Functions

Limits, Continuity and Differentiability

Differentiation

Application of Derivatives

Indefinite Integrals

Definite Integrals and Applications of Integrals

Differential Equations