Joint Entrance Examination

Graduate Aptitude Test in Engineering

Strength of Materials Or Solid Mechanics

Structural Analysis

Construction Material and Management

Reinforced Cement Concrete

Steel Structures

Geotechnical Engineering

Fluid Mechanics and Hydraulic Machines

Hydrology

Irrigation

Geomatics Engineering Or Surveying

Environmental Engineering

Transportation Engineering

Engineering Mathematics

General Aptitude

1

An unbiased coin is tossed eight times. The probability of obtaining at least one head and at least one tail is :

A

$${{255} \over {256}}$$

B

$${{127} \over {128}}$$

C

$${{63} \over {64}}$$

D

$${{1} \over {2}}$$

An unbiased coin is tossed 8 times which is same as 8 coins tossed 1 times.

$$\therefore\,\,\,$$ Possible no. of out come = 2^{8}

$$\therefore\,\,\,$$ Sample space = 2^{8}

Here in this condition, all head or all tail out come is not acceptable.

No. of times all head can occur

(H H H H H H H H) = 1

$$\therefore\,\,\,$$ Probability (all head) = $${1 \over {{2^8}}}$$ = $${1 \over {256}}$$

No. of times all tail can occur

(T T T T T T T T) = 1

$$\therefore\,\,\,$$ Probability (all tail) = $${1 \over {{2^8}}}$$ = $${{1 \over {256}}}$$

$$\therefore\,\,\,$$ Required probability

= 1 $$-$$ (P (All head) + P (All tail))

= 1 $$-$$ ( $${{1 \over {256}}}$$ + $${{1 \over {256}}}$$)

= 1 $$-$$ $${{1 \over {128}}}$$

= $${{127} \over {128}}$$

$$\therefore\,\,\,$$ Possible no. of out come = 2

$$\therefore\,\,\,$$ Sample space = 2

Here in this condition, all head or all tail out come is not acceptable.

No. of times all head can occur

(H H H H H H H H) = 1

$$\therefore\,\,\,$$ Probability (all head) = $${1 \over {{2^8}}}$$ = $${1 \over {256}}$$

No. of times all tail can occur

(T T T T T T T T) = 1

$$\therefore\,\,\,$$ Probability (all tail) = $${1 \over {{2^8}}}$$ = $${{1 \over {256}}}$$

$$\therefore\,\,\,$$ Required probability

= 1 $$-$$ (P (All head) + P (All tail))

= 1 $$-$$ ( $${{1 \over {256}}}$$ + $${{1 \over {256}}}$$)

= 1 $$-$$ $${{1 \over {128}}}$$

= $${{127} \over {128}}$$

2

From a group of 10 men and 5 women, four member committees are to be formed each of which must contain at least one woman. Then the probability for these committees to have more women than men, is :

A

$${{21} \over {220}}$$

B

$${{3} \over {11}}$$

C

$${{1} \over {11}}$$

D

$${{2} \over {23}}$$

3

Let E and F be two independent events. The probability that both E and F happen is $${1 \over {12}}$$ and the probability that neither E nor F happens is $${1 \over {2}}$$, then a value of $${{P\left( E \right)} \over {P\left( F \right)}}$$ is :

A

$${4 \over 3}$$

B

$${3 \over 2}$$

C

$${1 \over 3}$$

D

$${5 \over 12}$$

4

A bag contains 4 red and 6 black balls. A ball is drawn at random from the bag, its colour is observed and
this ball along with two additional balls of the same colour are returned to the bag. If now a ball is drawn at
random from the bag, then the probability that this drawn ball is red, is :

A

$${3 \over 4}$$

B

$${3 \over 10}$$

C

$${2 \over 5}$$

D

$${1 \over 5}$$

If we follow path 1, then probability of getting 1st ball black $$ = {6 \over {10}}$$ and probability of getting 2nd ball red when there is 4 R and 8 B balls = $${4 \over {12}}$$.

So, the probability of getting 1st ball black and 2nd ball red = $${6 \over {10}} \times {4 \over {12}}$$.

If we follow path 2, then the probability of getting 1st ball red $$ = {4 \over {10}}$$ and probability of getting 2nd ball red when in the bag there is 6 red and 6 black balls = $${6 \over {12}}$$

$$\therefore\,\,\,$$ Probability of getting 2nd ball as red

$$ = {6 \over {10}} \times {4 \over {12}} + {4 \over {10}} \times {6 \over {12}}$$

$$ = {1 \over 5} + {1 \over 5}$$

$$ = {2 \over 5}$$

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*