Joint Entrance Examination

Graduate Aptitude Test in Engineering

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1

Subjective

The sides of a triangle are three consecutive natural numbers and its largest angle is twice the smallest one. Determine the sides of the triangle.

$$4, 5, 6$$

2

Subjective

In a triangle of base a the ratio of the other two sides is $$r\left( { < 1} \right)$$. Show that the altitude of the triangle is less than of equal to $${{ar} \over {1 - {r^2}}}$$

Solve it.

3

Subjective

A man notices two objects in a straight line due west. After walking a distance $$c$$ due north he observes that the objects subtend an angle $$\alpha $$ at his eye; and, after walking a further distance $$2c$$ due north, an angle $$\beta $$. Show that the distance between the objects is $${{8c} \over {3\cot \beta - \cot \alpha }}$$; the height of the man is being ignored.

Solve it.

4

Subjective

A vertical tower $$PQ$$ stands at a point $$P$$. Points $$A$$ and $$B$$ are located to the South and East of $$P$$ respectively. $$M$$ is the mid point of $$AB$$. $$PAM$$ is an equilateral triangle; and $$N$$ is the foot of the perpendicular from $$P$$ and $$AB$$. Let $$AN$$$$=20$$ mrtres and the angle of elevation of the top of the tower at $$N$$ is $${\tan ^{ - 1}}\left( 2 \right)$$. Determine the height of the tower and the angles of elevation of the top of the tower at $$A$$ and $$B$$.

$$40\sqrt 3 \,\,\,m,\,\,\,{60^ \circ },\,\,\,{45^ \circ }$$

On those following papers in Subjective

Number in Brackets after Paper Indicates No. of Questions

IIT-JEE 2003 (1)

IIT-JEE 2001 (1)

IIT-JEE 2000 (1)

IIT-JEE 1999 (1)

IIT-JEE 1998 (2)

IIT-JEE 1994 (3)

IIT-JEE 1993 (1)

IIT-JEE 1992 (1)

IIT-JEE 1991 (3)

IIT-JEE 1990 (1)

IIT-JEE 1989 (1)

IIT-JEE 1988 (1)

IIT-JEE 1986 (1)

IIT-JEE 1985 (2)

IIT-JEE 1984 (2)

IIT-JEE 1983 (1)

IIT-JEE 1982 (1)

IIT-JEE 1981 (1)

IIT-JEE 1980 (3)

IIT-JEE 1979 (2)

IIT-JEE 1978 (1)

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