Joint Entrance Examination

Graduate Aptitude Test in Engineering

Geomatics Engineering Or Surveying

Engineering Mechanics

Hydrology

Transportation Engineering

Strength of Materials Or Solid Mechanics

Reinforced Cement Concrete

Steel Structures

Irrigation

Environmental Engineering

Engineering Mathematics

Structural Analysis

Geotechnical Engineering

Fluid Mechanics and Hydraulic Machines

General Aptitude

1

Two circles with equal radii are intersecting at the points (0, 1) and (0, –1). The tangent at the point (0, 1) to one of the circles passes through the centre of the other circle. Then the distance between the centres of these circles is :

A

$$2\sqrt 2 $$

B

$$\sqrt 2 $$

C

2

D

1

In $$\Delta $$APO

$${\left( {{{\sqrt 2 r} \over 2}} \right)^2} + {1^2} = {r^2}$$

$$ \Rightarrow $$ $$r = \sqrt 2 $$

So distance between centres $$ = \sqrt 2 r = 2$$

2

If a variable line, 3x + 4y – $$\lambda $$ = 0 is such that the two circles x^{2} + y^{2} – 2x – 2y + 1 = 0 and x^{2} + y^{2} – 18x – 2y + 78 = 0 are on its opposite sides, then the set of all values of $$\lambda $$ is the interval :

A

(23, 31)

B

(2, 17)

C

[13, 23]

D

[12, 21]

Centre of circles are opposite side of line

(3 + 4 $$-$$ $$\lambda $$) (27 + 4 $$-$$ $$\lambda $$) < 0

($$\lambda $$ $$-$$ 7) ($$\lambda $$ $$-$$ 31) < 0

$$\lambda $$ $$ \in $$ (7, 31)

distance from S_{1}

$$\left| {{{3 + 4 - \lambda } \over 5}} \right| \ge 1 \Rightarrow \lambda \in ( - \infty ,2] \cup [(12,\infty ]$$

distance from S_{2}

$$\left| {{{27 + 4 - \lambda } \over 5}} \right| \ge 2 \Rightarrow \lambda \in ( - \infty ,21] \cup [41,\infty )$$

so $$\lambda \in \left[ {12,21} \right]$$

(3 + 4 $$-$$ $$\lambda $$) (27 + 4 $$-$$ $$\lambda $$) < 0

($$\lambda $$ $$-$$ 7) ($$\lambda $$ $$-$$ 31) < 0

$$\lambda $$ $$ \in $$ (7, 31)

distance from S

$$\left| {{{3 + 4 - \lambda } \over 5}} \right| \ge 1 \Rightarrow \lambda \in ( - \infty ,2] \cup [(12,\infty ]$$

distance from S

$$\left| {{{27 + 4 - \lambda } \over 5}} \right| \ge 2 \Rightarrow \lambda \in ( - \infty ,21] \cup [41,\infty )$$

so $$\lambda \in \left[ {12,21} \right]$$

3

Let C_{1} and C_{2} be the centres of the circles x^{2} + y^{2} – 2x – 2y – 2 = 0 and x^{2} + y^{2} – 6x – 6y + 14 = 0 respectively. If P and Q are the points of intersection of these circles, then the area (in sq. units) of the quadrilateral PC_{1}QC_{2} is:

A

4

B

6

C

9

D

8

Area = 2 $$ \times $$ $${1 \over 2}$$.4 = 2

4

If a circle of radius R passes through the origin O and intersects the coordinates axes at A and B, then the
locus of the foot of perpendicular from O on AB is :

A

(x^{2} + y^{2})^{2} = 4R^{2}x^{2}y^{2}

B

(x^{2} + y^{2}) (x + y) = R^{2}xy

C

(x^{2} + y^{2})^{2} = 4R^{}x^{2}y^{2}

D

(x^{2} + y^{2})^{3} = 4R^{2}x^{2}y^{2}

Slope of AB = $${{ - h} \over k}$$

Equation of AB is hx + ky = h

A $$\left( {{{{h^2} + {k^2}} \over h},0} \right),B\left( {0,{{{h^2} + {k^2}} \over k}} \right)$$

AB = 2R

$$ \Rightarrow $$ (h

$$ \Rightarrow $$ (x

Number in Brackets after Paper Name Indicates No of Questions

AIEEE 2002 (4) *keyboard_arrow_right*

AIEEE 2003 (2) *keyboard_arrow_right*

AIEEE 2004 (4) *keyboard_arrow_right*

AIEEE 2005 (4) *keyboard_arrow_right*

AIEEE 2006 (2) *keyboard_arrow_right*

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JEE Main 2013 (Offline) (1) *keyboard_arrow_right*

JEE Main 2014 (Offline) (1) *keyboard_arrow_right*

JEE Main 2015 (Offline) (2) *keyboard_arrow_right*

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JEE Main 2016 (Online) 9th April Morning Slot (1) *keyboard_arrow_right*

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JEE Main 2019 (Online) 12th April Morning Slot (1) *keyboard_arrow_right*

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JEE Main 2020 (Online) 7th January Evening Slot (1) *keyboard_arrow_right*

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JEE Main 2021 (Online) 24th February Evening Slot (1) *keyboard_arrow_right*

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Trigonometric Functions & Equations *keyboard_arrow_right*

Properties of Triangle *keyboard_arrow_right*

Inverse Trigonometric Functions *keyboard_arrow_right*

Complex Numbers *keyboard_arrow_right*

Quadratic Equation and Inequalities *keyboard_arrow_right*

Permutations and Combinations *keyboard_arrow_right*

Mathematical Induction and Binomial Theorem *keyboard_arrow_right*

Sequences and Series *keyboard_arrow_right*

Matrices and Determinants *keyboard_arrow_right*

Vector Algebra and 3D Geometry *keyboard_arrow_right*

Probability *keyboard_arrow_right*

Statistics *keyboard_arrow_right*

Mathematical Reasoning *keyboard_arrow_right*

Functions *keyboard_arrow_right*

Limits, Continuity and Differentiability *keyboard_arrow_right*

Differentiation *keyboard_arrow_right*

Application of Derivatives *keyboard_arrow_right*

Indefinite Integrals *keyboard_arrow_right*

Definite Integrals and Applications of Integrals *keyboard_arrow_right*

Differential Equations *keyboard_arrow_right*

Straight Lines and Pair of Straight Lines *keyboard_arrow_right*

Circle *keyboard_arrow_right*

Conic Sections *keyboard_arrow_right*