Joint Entrance Examination

Graduate Aptitude Test in Engineering

1

Subjective

7 relatives of a man comprises 4 ladies and 3 gentlemen ; his wife has also 7 relatives ; 3 of them are ladies and 4 gentlemen. In how many ways can they invite a dinner party of 3 ladies and 3 gentlemen so that there are 3 of man's relatives and 3 of the wife's relatives?

485

2

Subjective

m men and n women are to be seated in a row so that no two women sit together. If $$m > n$$, then show that the number of ways in which they can be seated is $$\,{{m!(m + 1)!} \over {(m - n + 1)!}}$$

solve it.

3

Subjective

Five balls of different colours are to be placed in there boxes of different size. Each box can hold all five. In how many different ways can be place the balls so that no box remains emply?

300

4

Subjective

Six X' s have to be placed in the squares of figure below in such a way that each row contains at least one X. In how many different ways can this be done.

26

On those following papers in Subjective

Number in Brackets after Paper Indicates No. of Questions

IIT-JEE 2005 (1)

IIT-JEE 2004 (1)

IIT-JEE 1994 (1)

IIT-JEE 1991 (1)

IIT-JEE 1986 (1)

IIT-JEE 1985 (1)

IIT-JEE 1983 (1)

IIT-JEE 1981 (1)

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