Joint Entrance Examination

Graduate Aptitude Test in Engineering

Geomatics Engineering Or Surveying

Engineering Mechanics

Hydrology

Transportation Engineering

Strength of Materials Or Solid Mechanics

Reinforced Cement Concrete

Steel Structures

Irrigation

Environmental Engineering

Engineering Mathematics

Structural Analysis

Geotechnical Engineering

Fluid Mechanics and Hydraulic Machines

General Aptitude

1

If all the words, with or without meaning, are written using the letters of the word QUEEN and are arranged as in English dictionary, then the position of the word QUEEN is :

A

44^{th}

B

45^{th}

C

46^{th}

D

47^{th}

2

The number of ways in which 5 boys and 3 girls can be seated on a round table if a
particular boy B_{1} and a particular girl G_{1} never sit adjacent to each other, is :

A

5 $$ \times $$ 6!

B

6 $$ \times $$ 6!

C

7!

D

5 $$ \times $$ 7!

Number of ways = Total - when B_{1} and G_{1} sit together

Total ways to seat 8 people on round table = (8 - 1)! = 7!

When B_{1} and G_{1} sit together then assume B_{1} and G_{1} are one people, so total 7 people are there and among B_{1} and G_{1} they can sit 2! ways.

So total no of ways when B_{1} and G_{1} sit together

= (7 - 1)! $$ \times $$ 2! = 6! $$ \times $$ 2!

Number of ways = 7! - 6! $$ \times $$ 2! = 6!$$ \times $$(7 - 2) = 5 $$ \times $$ 6!

Total ways to seat 8 people on round table = (8 - 1)! = 7!

When B

So total no of ways when B

= (7 - 1)! $$ \times $$ 2! = 6! $$ \times $$ 2!

Number of ways = 7! - 6! $$ \times $$ 2! = 6!$$ \times $$(7 - 2) = 5 $$ \times $$ 6!

3

From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and
arranged in a row on a shelf so that the dictionary is always in the middle. The number of such
arrangements is :

A

at least 750 but less than 1000

B

at least 1000

C

less than 500

D

at least 500 but less than 750

From 6 different novels 4 novels can be chosen = $${}^6{C_4}$$ ways

And from 3 different dictionaries 1 can be chosen = $${}^3{C_1}$$ ways

$$\therefore$$ From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary can be chosen = $${}^6{C_4} \times {}^3{C_1}$$ ways

Let 4 novels are N_{1}, N_{2}, N_{3}, N_{4} and 1 dictionary is D_{1}.

Dictionary should be in the middle. So the arrangement will be like this

_ _ D_{1} _ _

On those 4 blank places 4 novels N_{1}, N_{2}, N_{3}, N_{4} can be placed. And 4 novels can be arrange $$4!$$ ways.

$$\therefore$$ Total no of ways = $${}^6{C_4} \times {}^3{C_1}$$$$ \times 4!$$ = 1080

And from 3 different dictionaries 1 can be chosen = $${}^3{C_1}$$ ways

$$\therefore$$ From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary can be chosen = $${}^6{C_4} \times {}^3{C_1}$$ ways

Let 4 novels are N

Dictionary should be in the middle. So the arrangement will be like this

_ _ D

On those 4 blank places 4 novels N

$$\therefore$$ Total no of ways = $${}^6{C_4} \times {}^3{C_1}$$$$ \times 4!$$ = 1080

4

n$$-$$digit numbers are formed using only three digits 2, 5 and 7. The smallest value of n for which 900 such distinct numbers can be formed, is :

A

6

B

7

C

8

D

9

In n digit number first place can be filled with any one of 2, 5, 7. So no of ways first digit can be filled = 3

Similarly,

no of ways 2nd digit can be filled = 3 ways

.

.

.

.

- - - - - - nth - - - - - - - = 3 ways

$$ \therefore $$ Total numbers = 3 $$ \times $$ 3 $$ \times $$ 3 .... n times

= 3^{n}

$$ \therefore $$ According to question, for smallest value of n,

3^{n} > 900

3^{6} = 729 < 900

3^{7} = 2187 > 900

$$ \therefore $$ n = 7

Similarly,

no of ways 2nd digit can be filled = 3 ways

.

.

.

.

- - - - - - nth - - - - - - - = 3 ways

$$ \therefore $$ Total numbers = 3 $$ \times $$ 3 $$ \times $$ 3 .... n times

= 3

$$ \therefore $$ According to question, for smallest value of n,

3

3

3

$$ \therefore $$ n = 7

Number in Brackets after Paper Name Indicates No of Questions

AIEEE 2002 (4) *keyboard_arrow_right*

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Trigonometric Functions & Equations *keyboard_arrow_right*

Properties of Triangle *keyboard_arrow_right*

Inverse Trigonometric Functions *keyboard_arrow_right*

Complex Numbers *keyboard_arrow_right*

Quadratic Equation and Inequalities *keyboard_arrow_right*

Permutations and Combinations *keyboard_arrow_right*

Mathematical Induction and Binomial Theorem *keyboard_arrow_right*

Sequences and Series *keyboard_arrow_right*

Matrices and Determinants *keyboard_arrow_right*

Vector Algebra and 3D Geometry *keyboard_arrow_right*

Probability *keyboard_arrow_right*

Statistics *keyboard_arrow_right*

Mathematical Reasoning *keyboard_arrow_right*

Functions *keyboard_arrow_right*

Limits, Continuity and Differentiability *keyboard_arrow_right*

Differentiation *keyboard_arrow_right*

Application of Derivatives *keyboard_arrow_right*

Indefinite Integrals *keyboard_arrow_right*

Definite Integrals and Applications of Integrals *keyboard_arrow_right*

Differential Equations *keyboard_arrow_right*

Straight Lines and Pair of Straight Lines *keyboard_arrow_right*

Circle *keyboard_arrow_right*

Conic Sections *keyboard_arrow_right*