Joint Entrance Examination

Graduate Aptitude Test in Engineering

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1

Subjective

Prove by permulation or otherwise $${{({n^2})!} \over {{{(n!)}^n}}}$$ is an integer $$(n \in {1^ + })$$.

solve it.

2

Subjective

A committee of 12 is to be formed from 9 women and 8 men. In how many ways this can be done if at least five women have to included in a committee? In how many of these committees? In how may of these committees

(a) The women are in majority?

(b) The men are in majority?

(a) The women are in majority?

(b) The men are in majority?

6072, (a) 2702, (b) 1008

3

Subjective

Eighteen guests have to be seated, half on each side of a long table. Four particular guests desire to sit on one particular side and three others on the other side. Determine the number of ways in which the sitting arrangements can be made.

$${}^{11}{C_5} \times 9\,!\, \times \,9\,!$$

4

Subjective

A box contains two white balls, three black balls and four red balls. In how many ways can three balls be drawn from the box if at least one black ball is to be included in the draw?

64

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