Joint Entrance Examination

Graduate Aptitude Test in Engineering

1

MCQ (Single Correct Answer)

A circle C of radius 1 is inscribed in an equilateral triangle PQR. The points of contact of C with the sides PQ, QR, RP are D, E, F, respectively. The line PQ is given by the equation $$\sqrt 3 x\, + \,y\, - \,6 = 0$$ and the point D is $$\left( {{{3\,\sqrt 3 } \over 2},\,{3 \over 2}} \right)$$. Further, it is given that the origin and the centre of C are on the same side of the line PQ.

The equation of circle C is

A

$${\left( {x\, - 2\sqrt 3 \,} \right)^2} + {(y - 1)^2} = 1$$

B

$${\left( {x\, - 2\sqrt 3 \,} \right)^2} + {(y + {1 \over 2})^2} = 1$$

C

$${\left( {x\, - \sqrt 3 \,} \right)^2} + {(y + 1)^2} = 1$$

D

$${\left( {x\, - \sqrt 3 \,} \right)^2} + {(y - 1)^2} = 1$$

2

MCQ (Single Correct Answer)

ABCD is a square of side length 2 units. $${C_1}$$ is the circle touching all the sides of the square ABCD and $${C_2}$$ is the circumcircle of square ABCD. L is a fixed line in the same plane and R is a fixed point.

$${{P{A^2}\, + \,P{B^2}\, + P{C^2}\, + P{D^2}} \over {Q{A^2} + \,Q{B^2}\, + Q{C^2}\, + Q{D^2}}}$$ is equal to

If P is any point of $${C_1}$$ and Q is another point on $${C_2}$$, then

$${{P{A^2}\, + \,P{B^2}\, + P{C^2}\, + P{D^2}} \over {Q{A^2} + \,Q{B^2}\, + Q{C^2}\, + Q{D^2}}}$$ is equal to

A

0.75

B

1.25

C

1

D

0.5

3

MCQ (Single Correct Answer)

ABCD is a square of side length 2 units. $$C_1$$ is the circle touching all the sides of the square ABCD and $$C_2$$ is the circumcircle of square ABCD. L is a fixed line in the same plane and R is a fixed point.

A line L' through A is drawn parallel to BD. Point S moves such that its distances from the BD and the vertex A are equal. If locus of S cuts L' at $$T_2$$ and $$T_3$$ and AC at $$T_1$$, then area of $$\Delta \,{T_1}\,{T_2}\,{T_3}$$ is

A

$${1 \over 2}\,sq.\,units$$

B

$${2 \over 3}\,sq.\,units$$

C

1 sq. units

D

2 sq.units

4

MCQ (Single Correct Answer)

ABCD is a square of side length 2 units. $$C_1$$ is the circle touching all the sides of the square ABCD and $$C_2$$ is the circumcircle of square ABCD. L is a fixed line in the same plane and R is a fixed point.

If a circle is such that it touches the line L and the circle $$C_1$$ externally, such that both the circles are on the same side of the line, then the locus of centre of the circle is

A

ellipse

B

hyper bola

C

parabola

D

pair of straight line

On those following papers in MCQ (Single Correct Answer)

Number in Brackets after Paper Indicates No. of Questions

JEE Advanced 2021 Paper 2 Online (2)

JEE Advanced 2021 Paper 1 Online (1)

JEE Advanced 2019 Paper 1 Offline (1)

IIT-JEE 2012 Paper 2 Offline (2)

IIT-JEE 2012 Paper 1 Offline (1)

IIT-JEE 2011 Paper 2 Offline (1)

IIT-JEE 2009 (1)

IIT-JEE 2008 (4)

IIT-JEE 2006 (3)

IIT-JEE 2005 Screening (1)

IIT-JEE 2004 Screening (1)

IIT-JEE 2003 Screening (1)

IIT-JEE 2002 Screening (1)

IIT-JEE 2001 Screening (2)

IIT-JEE 2000 Screening (2)

IIT-JEE 1999 (1)

IIT-JEE 1996 (1)

IIT-JEE 1994 (1)

IIT-JEE 1993 (1)

IIT-JEE 1992 (1)

IIT-JEE 1989 (2)

IIT-JEE 1988 (1)

IIT-JEE 1984 (1)

IIT-JEE 1983 (2)

IIT-JEE 1980 (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