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

Consider the statement : "P(n) : n^{2} – n + 41 is prime". Then which one of the following is true ?

A

P(5) is false but P(3) is true

B

Both P(3) and P(5) are true

C

P(3) is false but P(5) is true

D

Both P(3) and P(5) are false

P(n) : n^{2} $$-$$ n + 41 is prime

P(5) = 61 which is prime

P(3) = 47 which is also prime

P(5) = 61 which is prime

P(3) = 47 which is also prime

2

Consider the following three statements :

P : 5 is a prime number

Q : 7 is a factor of 192

R : L.C.M. of 5 and 7 is 35

Then the truth value of which one of the following statements is true ?

P : 5 is a prime number

Q : 7 is a factor of 192

R : L.C.M. of 5 and 7 is 35

Then the truth value of which one of the following statements is true ?

A

(P $$ \wedge $$ Q) $$ \vee $$ ($$ \sim $$ R)

B

P $$ \vee $$ ($$ \sim $$ Q $$ \wedge $$ R)

C

(~ P) $$ \wedge $$ ($$ \sim $$ Q $$ \wedge $$ R)

D

($$ \sim $$ P) $$ \vee $$ (Q $$ \wedge $$ R)

It is obvious

3

If q is false and p $$ \wedge $$ q $$ \leftrightarrow $$ r is true, then which one of the following statements is a tautology ?

A

P $$ \wedge $$ r

B

(p $$ \vee $$ r) $$ \to $$ (p $$ \wedge $$ r)

C

p $$ \vee $$ r

D

(p $$ \wedge $$ r) $$ \to $$ (p $$ \vee $$ r)

Given q is F and (p $$ \wedge $$ q) $$ \leftrightarrow $$ r is T

$$ \Rightarrow $$ p $$ \wedge $$ q is F which implies that r is F

$$ \Rightarrow $$ q is F and r is F

$$ \Rightarrow $$ (p $$ \wedge $$ r) is always F

$$ \Rightarrow $$ (p $$ \wedge $$ r) $$ \to $$ (p $$ \vee $$ r) is tautology.

$$ \Rightarrow $$ p $$ \wedge $$ q is F which implies that r is F

$$ \Rightarrow $$ q is F and r is F

$$ \Rightarrow $$ (p $$ \wedge $$ r) is always F

$$ \Rightarrow $$ (p $$ \wedge $$ r) $$ \to $$ (p $$ \vee $$ r) is tautology.

4

Contrapositive of the statement " 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 not equal

B

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

C

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

D

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

Number in Brackets after Paper Name Indicates No of Questions

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