Joint Entrance Examination

Graduate Aptitude Test in Engineering

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1

MCQ (Single Correct Answer)

Consider a branch of the hyperbola
$$${x^2} - 2{y^2} - 2\sqrt 2 x - 4\sqrt 2 y - 6 = 0$$$

with vertex at the point $$A$$. Let $$B$$ be one of the end points of its latus rectum. If $$C$$ is the focus of the hyperbola nearest to the point $$A$$, then the area of the triangle $$ABC$$ is

A

$$1 - \sqrt {{2 \over 3}} $$

B

$$\sqrt {{3 \over 2}} - 1$$

C

$$1 + \sqrt {{2 \over 3}} $$

D

$$\sqrt {{3 \over 2}} + 1$$

2

MCQ (Single Correct Answer)

Let $$a$$ and $$b$$ be non-zero real numbers. Then, the equation $${x^2}{\cos ^2}\theta - {y^2}{\sin ^2}\theta = 0$$ represents

A

four straight lines, when $$c=0$$ and $$a, b$$ are of the same sign.

B

two straight lines and a circle, when $$a=b$$, and $$c$$ is of sign opposite to that of $$a$$

C

two straight lines and a hyperbola, when $$a$$ and $$b$$ are of the same sign and $$c$$ is of sign opposite to that of $$a$$

D

a circle and an ellipse, when $$a$$ and $$b$$ are of the same sign and $$c$$ is of sign opposite to that of $$a$$

3

MCQ (Single Correct Answer)

**STATEMENT-2:** A parabola is symmetric about its axis.

A

Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1

B

Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1

C

Statement-1 is True, Statement-2 is False

D

Statement-1 is False, Statement-2 is True.

4

MCQ (Single Correct Answer)

Consider the circle $${x^2} + {y^2} = 9$$ and the parabola $${y^2} = 8x$$. They intersect at $$P$$ and $$Q$$ in the first and the fourth quadrants, respectively. Tangent to the circle at $$P$$ and $$Q$$ intersect the $$x$$-axis at $$R$$ and tangents to the parabola at $$P$$ and $$Q$$ intersect the $$x$$-axis at $$S$$.

The radius of the incircle of the triangle $$PQR$$ is

A

$$4$$

B

$$3$$

C

$${8 \over 3}$$

D

$$2$$

On those following papers in MCQ (Single Correct Answer)

Number in Brackets after Paper Indicates No. of Questions

JEE Advanced 2020 Paper 1 Offline (1)

JEE Advanced 2019 Paper 2 Offline (2)

JEE Advanced 2018 Paper 2 Offline (1)

JEE Advanced 2018 Paper 1 Offline (2)

JEE Advanced 2017 Paper 1 Offline (3)

JEE Advanced 2016 Paper 2 Offline (2)

JEE Advanced 2014 Paper 2 Offline (3)

JEE Advanced 2013 Paper 2 Offline (3)

IIT-JEE 2012 Paper 1 Offline (1)

IIT-JEE 2011 Paper 2 Offline (2)

IIT-JEE 2010 Paper 1 Offline (2)

IIT-JEE 2010 Paper 2 Offline (3)

IIT-JEE 2009 (3)

IIT-JEE 2008 (2)

IIT-JEE 2007 (5)

IIT-JEE 2006 (2)

IIT-JEE 2005 Screening (2)

IIT-JEE 2004 Screening (3)

IIT-JEE 2003 Screening (3)

IIT-JEE 2002 Screening (3)

IIT-JEE 2001 Screening (2)

IIT-JEE 2000 Screening (2)

IIT-JEE 1999 (3)

IIT-JEE 1998 (2)

IIT-JEE 1995 Screening (2)

IIT-JEE 1994 (2)

IIT-JEE 1981 (2)

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