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

A point P moves on the line 2x – 3y + 4 = 0. If Q(1, 4) and R (3, – 2) are fixed points, then the locus of the centroid of $$\Delta $$PQR is a line -

A

parallel to y-axis

B

with slope $${2 \over 3}$$

C

parallel to x-axis

D

with slope $${3 \over 2}$$

Let the centroid of $$\Delta $$PQR is (h, k) & P is ($$\alpha $$, $$\beta $$), then

$${{\alpha + 1 + 3} \over 3} = h\,$$ and $${{\beta + 4 - 2} \over 3} = k$$

$$\alpha = \left( {3h - 4} \right)$$ $$\beta = \left( {3k - 4} \right)$$

Point P($$\alpha $$, $$\beta $$) lies on the line 2x $$-$$ 3y + 4 = 0

$$ \therefore $$ 2(3h $$-$$ 4) $$-$$ 3 (3k $$-$$ 2) + 4 = 0

$$ \Rightarrow $$ locus is 6x $$-$$ 9y + 2 = 0

$${{\alpha + 1 + 3} \over 3} = h\,$$ and $${{\beta + 4 - 2} \over 3} = k$$

$$\alpha = \left( {3h - 4} \right)$$ $$\beta = \left( {3k - 4} \right)$$

Point P($$\alpha $$, $$\beta $$) lies on the line 2x $$-$$ 3y + 4 = 0

$$ \therefore $$ 2(3h $$-$$ 4) $$-$$ 3 (3k $$-$$ 2) + 4 = 0

$$ \Rightarrow $$ locus is 6x $$-$$ 9y + 2 = 0

2

If the line 3x + 4y – 24 = 0 intersects the x-axis at the point A and the y-axis at the point B, then the incentre of the triangle OAB, where O is the origin, is -

A

(3, 4)

B

(2, 2)

C

(4, 4)

D

(4, 3)

$$\left| {{{3r + 4r - 24} \over 5}} \right| = r$$

$$7r - 24 = \pm 5r$$

$$2r = 24$$ or $$12r + 24$$

$$r = 14,\,\,\,r = 2$$

then incentre is $$(2,2)$$

3

Two sides of a parallelogram are along the lines, x + y = 3 & x – y + 3 = 0. If its diagonals intersect at (2, 4), then one of its vertex is -

A

(2, 1)

B

(2, 6)

C

(3, 5)

D

(3, 6)

Solving

$$\matrix{ {x + y = 3} \cr {x - y = - 3} \cr } \,\, > \,\,A\left( {0,3} \right)$$

and $${{{x_1} + 0} \over 2} = 2;\,\,{x_i} = 4$$

similarly y

C $$ \Rightarrow $$ (4, 5)

Now equation of BC is x $$-$$ y = $$-$$ 1

and equation of CD is x + y = 9

Solving x + y = 9 and x $$-$$ y = $$-$$ 3

Point D is (3, 6)

4

Two vertices of a triangle are (0, 2) and (4, 3). If its orthocenter is at the origin, then its third vertex lies in which quadrant

A

third

B

fourth

C

second

D

first

m_{BD} $$ \times $$ m_{AD} = $$-$$ 1

$$ \Rightarrow $$ $$\left( {{{3 - 2} \over {4 - 0}}} \right) \times \left( {{{b - 0} \over {a - 0}}} \right) = - 1$$

$$ \Rightarrow $$ b + 4a = 0 . . . . (i)

m_{AB} $$ \times $$ m_{CF} = $$-$$ 1

$$ \Rightarrow $$ $$\left( {{{\left( {b - 2} \right)} \over {a - 0}}} \right) \times \left( {{3 \over 4}} \right) = - 1$$

$$ \Rightarrow $$ 3b $$-$$ 6 = $$-$$ 4a

$$ \Rightarrow $$ 4a + 3b = 6 . . . . .(ii)

From (i) and (ii)

a = $${{ - 3} \over 4}$$, b = 3

$$ \therefore $$ II^{nd} quadrant.

$$ \Rightarrow $$ $$\left( {{{3 - 2} \over {4 - 0}}} \right) \times \left( {{{b - 0} \over {a - 0}}} \right) = - 1$$

$$ \Rightarrow $$ b + 4a = 0 . . . . (i)

m

$$ \Rightarrow $$ $$\left( {{{\left( {b - 2} \right)} \over {a - 0}}} \right) \times \left( {{3 \over 4}} \right) = - 1$$

$$ \Rightarrow $$ 3b $$-$$ 6 = $$-$$ 4a

$$ \Rightarrow $$ 4a + 3b = 6 . . . . .(ii)

From (i) and (ii)

a = $${{ - 3} \over 4}$$, b = 3

$$ \therefore $$ II

Number in Brackets after Paper Name Indicates No of Questions

AIEEE 2002 (4) *keyboard_arrow_right*

AIEEE 2003 (5) *keyboard_arrow_right*

AIEEE 2004 (4) *keyboard_arrow_right*

AIEEE 2005 (2) *keyboard_arrow_right*

AIEEE 2006 (2) *keyboard_arrow_right*

AIEEE 2007 (3) *keyboard_arrow_right*

AIEEE 2008 (1) *keyboard_arrow_right*

AIEEE 2009 (3) *keyboard_arrow_right*

AIEEE 2010 (1) *keyboard_arrow_right*

AIEEE 2011 (1) *keyboard_arrow_right*

AIEEE 2012 (1) *keyboard_arrow_right*

JEE Main 2013 (Offline) (2) *keyboard_arrow_right*

JEE Main 2014 (Offline) (2) *keyboard_arrow_right*

JEE Main 2015 (Offline) (1) *keyboard_arrow_right*

JEE Main 2016 (Offline) (1) *keyboard_arrow_right*

JEE Main 2016 (Online) 9th April Morning Slot (2) *keyboard_arrow_right*

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JEE Main 2017 (Offline) (1) *keyboard_arrow_right*

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JEE Main 2018 (Offline) (1) *keyboard_arrow_right*

JEE Main 2018 (Online) 15th April Morning Slot (1) *keyboard_arrow_right*

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JEE Main 2020 (Online) 6th September Morning Slot (1) *keyboard_arrow_right*

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

JEE Main 2021 (Online) 25th February Morning Slot (1) *keyboard_arrow_right*

JEE Main 2021 (Online) 26th February Morning Shift (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*