Joint Entrance Examination

Graduate Aptitude Test in Engineering

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1

Subjective

(a) If a circle is inscribed in a right angled triangle $$ABC$$ with the right angle at $$B$$, show that the diameter of the circle is equal to $$AB+BC-AC$$.

(b) If a triangle is inscribed in a circle, then the product of any two sides of the triangle is equal to the product of the diameter and the perpendicular distance of the third side from the opposite vertex. Prove the above statement.

Solve it.

2

Subjective

(a) A balloon is observed simultaneously from three points $$A, B$$ and $$C$$ on a straight road directly beneath it. The angular elevation at $$B$$ is twice that at $$A$$ and the angular elevation at $$C$$ is thrice that at $$A$$. If the distance between $$A$$ and $$B$$ is a and the distance between $$B$$ and $$C$$ is $$b$$, find the height of the balloon in terms of $$a$$ and $$b$$.

(b) Find the area of the smaller part of a disc of radius $$10$$ cm, cut off by a chord $$AB$$ which subtends an angle of at the circumference.

(a) $${a \over {2b}}\sqrt {\left( {a + b} \right)\left( {3b - a} \right)} $$

(b) $$3.91$$ sq. cm.

3

Subjective

A triangle $$ABC$$ has sides $$AB=AC=5$$ cm and $$BC=6$$ cm Triangle $$A'B'C'$$ is the reflection of the triangle $$ABC$$ in a line parallel to $$AB$$ placed at a distance $$2$$ cm from $$AB$$, outside the triangle $$ABC$$. Triangle $$A''B''C''$$ is the reflection of the triangle $$A'B'C'$$ in a line parallel to $$BC$$ placed at a distance of $$2$$ cm from $$B'C'$$ outside the triangle $$A'B'C'$$. Find the distance between $$A$$ and $$A''$$.

$$8\sqrt {{{17} \over 5}} $$

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