Joint Entrance Examination

Graduate Aptitude Test in Engineering

Geotechnical Engineering

Transportation Engineering

Irrigation

Engineering Mathematics

Construction Material and Management

Fluid Mechanics and Hydraulic Machines

Hydrology

Environmental Engineering

Engineering Mechanics

Structural Analysis

Reinforced Cement Concrete

Steel Structures

Geomatics Engineering Or Surveying

General Aptitude

1

Contrapositive of the statement

‘If two numbers are not equal, then their squares are not equal’, is :

‘If two numbers are not equal, then their squares are not equal’, is :

A

If the squares of two numbers are equal, then the numbers are equal.

B

If the squares of two numbers are equal, then the numbers are not equal.

C

If the squares of two numbers are not equal, then the numbers are not equal.

D

If the squares of two numbers are not equal, then the numbers are equal.

Let,

p : two numbers are not equal

q : squares of two numbers are not equal

Contrapositive of p $$ \to $$ q is $$ \sim $$q $$ \to $$ $$ \sim $$p.

$$ \therefore $$ $$ \sim $$q $$ \to $$ $$ \sim $$p means "If the squares of two numbers are equal, then the numbers are equal".

p : two numbers are not equal

q : squares of two numbers are not equal

Contrapositive of p $$ \to $$ q is $$ \sim $$q $$ \to $$ $$ \sim $$p.

$$ \therefore $$ $$ \sim $$q $$ \to $$ $$ \sim $$p means "If the squares of two numbers are equal, then the numbers are equal".

2

The Boolean expression

$$ \sim \left( {p \vee q} \right) \vee \left( { \sim p \wedge q} \right)$$ is equvalent to

$$ \sim \left( {p \vee q} \right) \vee \left( { \sim p \wedge q} \right)$$ is equvalent to

A

$${ \sim q}$$

B

$${ \sim p}$$

C

p

D

q

From the table you can see ~p and

~(p $$ \vee $$ q) $$ \vee $$ (~p $$ \wedge $$ q) are equivalent.

3

If (p $$ \wedge $$ $$ \sim $$ q) $$ \wedge $$ (p $$ \wedge $$ r) $$ \to $$ $$ \sim $$ p $$ \vee $$ q is false, then the truth values of $$p, q$$ and $$r$$ are, respectively :

A

F, T, F

B

T, F, T

C

T, T, T

D

F, F, F

From the truth table you can see (p $$ \wedge $$ ~q) $$ \wedge $$ (p $$ \wedge $$ r) $$\to$$ ~p $$\vee$$ q is

4

Consider the following two statements :

**Statement p :**

The value of sin 120^{o} can be derived by taking $$\theta = {240^o}$$ in the equation

2sin$${\theta \over 2} = \sqrt {1 + \sin \theta } - \sqrt {1 - \sin \theta } $$

**Statement q :**

The angles A, B, C and D of any quadrilateral ABCD satisfy the equation

cos$$\left( {{1 \over 2}\left( {A + C} \right)} \right) + \cos \left( {{1 \over 2}\left( {B + D} \right)} \right) = 0$$

Then the truth values of p and q are respectively :

The value of sin 120

2sin$${\theta \over 2} = \sqrt {1 + \sin \theta } - \sqrt {1 - \sin \theta } $$

The angles A, B, C and D of any quadrilateral ABCD satisfy the equation

cos$$\left( {{1 \over 2}\left( {A + C} \right)} \right) + \cos \left( {{1 \over 2}\left( {B + D} \right)} \right) = 0$$

Then the truth values of p and q are respectively :

A

F, T

B

T, F

C

T, T

D

F, F

sin 120

So, $$\sqrt {1 + \sin {{240}^o}} - \sqrt {1 - \sin {{240}^o}} $$

$$ = \sqrt {{{1 - \sqrt 3 } \over 2}} - \sqrt {{{1 + \sqrt 3 } \over 2}} \ne \sqrt 3 $$

So, A + B + C + D = 2$$\pi $$

$$ \Rightarrow $$ $${{A + C} \over 2} + {{B + D} \over 2} = \pi $$

$$ \Rightarrow $$ cos$$\left( {{{A + C} \over 2}} \right) + \cos \left( {{{B + D} \over 2}} \right)$$

= cos $$\left( {{{A + C} \over 2}} \right)$$ $$-$$ cos$$\left( {{{A + C} \over 2}} \right) = 0$$

Therefore, statement p is false and statement q is true.

Number in Brackets after Paper Name Indicates No of Questions

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Straight Lines and Pair of Straight Lines *keyboard_arrow_right*

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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*

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