Joint Entrance Examination

Graduate Aptitude Test in Engineering

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1

Subjective

Find three numbers $$a,b,c$$ between $$2$$ and $$18$$ such that

(i) their sum is $$25$$

(ii) the numbers $$2,$$ $$a, b$$ are consecutive terms of an A.P. and

(iii) the numbers $$b,c,18$$ are consecutive terms of a G.P.

(i) their sum is $$25$$

(ii) the numbers $$2,$$ $$a, b$$ are consecutive terms of an A.P. and

(iii) the numbers $$b,c,18$$ are consecutive terms of a G.P.

$$5, 8, 12$$

2

Subjective

Does there exist a geometric progression containing $$27, 8$$ and $$12$$ as three of its terms? If it exits, how many such progressions are possible ?

$$ \Rightarrow $$ yes infinite

3

Subjective

The interior angles of a polygon are in arithmetic progression. The smallest angle is $${120^ \circ }$$, and the common difference is $${5^ \circ }$$, Find the number of sides of the polygon.

9

4

Subjective

The harmonic mean of two numbers is 4.Their arithmetic mean $$A$$ and the geometric mean $$G$$ satisfy the relation. $$2A + {G^2} = 27$$

$$3$$ and $$6$$ or $$6$$ and $$3$$

On those following papers in Subjective

Number in Brackets after Paper Indicates No. of Questions

IIT-JEE 2006 (1)

IIT-JEE 2003 (1)

IIT-JEE 2002 (1)

IIT-JEE 2001 (1)

IIT-JEE 2000 (1)

IIT-JEE 1999 (1)

IIT-JEE 1996 (1)

IIT-JEE 1991 (2)

IIT-JEE 1987 (1)

IIT-JEE 1985 (1)

IIT-JEE 1984 (2)

IIT-JEE 1983 (1)

IIT-JEE 1982 (1)

IIT-JEE 1980 (1)

IIT-JEE 1979 (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