Joint Entrance Examination

Graduate Aptitude Test in Engineering

Strength of Materials Or Solid Mechanics

Structural Analysis

Construction Material and Management

Reinforced Cement Concrete

Steel Structures

Geotechnical Engineering

Fluid Mechanics and Hydraulic Machines

Hydrology

Irrigation

Geomatics Engineering Or Surveying

Environmental Engineering

Transportation Engineering

Engineering Mathematics

General Aptitude

1

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

2

If in a parallelogram ABDC, the coordinates of A, B and C are respectively (1, 2), (3, 4) and (2, 5), then the
equation of the diagonal AD is :

A

5x + 3y – 11 = 0

B

5x – 3y + 1 = 0

C

3x – 5y + 7 = 0

D

3x + 5y – 13 = 0

co-ordinates of point D are (4, 7)

$$ \Rightarrow $$ line AD is 5x $$-$$ 3y + 1 = 0

$$ \Rightarrow $$ line AD is 5x $$-$$ 3y + 1 = 0

3

If the straight line, 2x – 3y + 17 = 0 is perpendicular to the line passing through the points (7, 17) and (15, $$\beta $$), then $$\beta $$ equals :

A

$${{35} \over 3}$$

B

$$-$$ 5

C

$$-$$ $${{35} \over 3}$$

D

5

$${{17 - \beta } \over { - 8}} \times {2 \over 3} = - 1$$

$$\beta $$ = 5

$$\beta $$ = 5

4

If a straight line passing through the point P(–3, 4) is such that its intercepted portion between the coordinate axes is bisected at P, then its equation is :

A

x – y + 7 = 0

B

4x – 3y + 24 = 0

C

4x + 3y = 0

D

3x – 4y + 25 = 0

Let the line be $${x \over a} + {y \over b} = 1$$

($$-$$ 3, 4) = $$\left( {{a \over 2},{b \over 2}} \right)$$

a = $$-$$6, b = 8

equation of line is 4x $$-$$ 3y + 24 = 0

Number in Brackets after Paper Name Indicates No of Questions

AIEEE 2002 (4) *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*