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

Two integers are selected at random from the set {1, 2, ...., 11}. Given that the sum of selected numbers is even, the conditional probability that both the numbers are even is

A

$${2 \over 5}$$

B

$${1 \over 2}$$

C

$${7 \over 10}$$

D

$${3 \over 5}$$

Since sum of two numbers is even so either both are odd or both are even. Hence number of elements in reduced samples space = ^{5}C_{2} + ^{6}C_{2}

so required probability = $${{{}^5{C_2}} \over {{}^5{C_2} + {}^6{C_2}}}$$

so required probability = $${{{}^5{C_2}} \over {{}^5{C_2} + {}^6{C_2}}}$$

2

Let S = {1, 2, . . . . . ., 20}. A subset B of S is said to be "nice", if the sum of the elements of B is 203. Then the probability that a randonly chosen subset of S is "nice" is :

A

$${5 \over {{2^{20}}}}$$

B

$${7 \over {{2^{20}}}}$$

C

$${4 \over {{2^{20}}}}$$

D

$${6 \over {{2^{20}}}}$$

7,

1, 6

2, 5

3, 4

1, 2, 4

3

A bag contains 30 white balls and 10 red balls. 16 balls are drawn one by one randomly from the bag with replacement. If X be the number of white balls drawn, then $$\left( {{{mean\,\,of\,X} \over {s\tan dard\,\,deviation\,\,of\,X}}} \right)$$ is equal to :

A

4

B

$$3\sqrt 2 $$

C

$${{4\sqrt 3 } \over 3}$$

D

$$4\sqrt 3 $$

p (probability of getting white ball) = $${{30} \over {40}}$$

q = $${1 \over 4}$$ and n = 16

mean = np = 16.$${3 \over 4}$$ = 12

and standard diviation

= $$\sqrt {npq} $$ = $$\sqrt {16.{3 \over 4}.{1 \over 4}} = \sqrt 3 $$

$$ \because $$ $$mean \over standard\,deviation$$ = $$12\over{\sqrt3}$$ = $$4{\sqrt3}$$

q = $${1 \over 4}$$ and n = 16

mean = np = 16.$${3 \over 4}$$ = 12

and standard diviation

= $$\sqrt {npq} $$ = $$\sqrt {16.{3 \over 4}.{1 \over 4}} = \sqrt 3 $$

$$ \because $$ $$mean \over standard\,deviation$$ = $$12\over{\sqrt3}$$ = $$4{\sqrt3}$$

4

In a random experiment, a fair die is rolled until two fours are obtained in succession. The probability that the experiment will end in the fifth throw of the die is equal to :

A

$${{200} \over {{6^5}}}$$

B

$${{225} \over {{6^5}}}$$

C

$${{150} \over {{6^5}}}$$

D

$${{175} \over {{6^5}}}$$

$$\underline {} \,\,\,\underline {} \,\,\,\underline {} \,\,\underline 4 \,\,\underline 4 $$

$${1 \over {{6^2}}}\left( {{{{5^3}} \over {{6^3}}} + {{2{C_1}{{.5}^2}} \over {{6^3}}}} \right) = {{175} \over {{6^5}}}$$

$${1 \over {{6^2}}}\left( {{{{5^3}} \over {{6^3}}} + {{2{C_1}{{.5}^2}} \over {{6^3}}}} \right) = {{175} \over {{6^5}}}$$

Number in Brackets after Paper Name Indicates No of Questions

AIEEE 2002 (3) *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*