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

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

2

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.

3

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".

4

The Boolean expression ((p $$ \wedge $$ q) $$ \vee $$ (p $$ \vee $$ $$ \sim $$ q)) $$ \wedge $$ ($$ \sim $$ p $$ \wedge $$ $$ \sim $$ q) is equivalent to :

A

p $$ \wedge $$ q

B

p $$ \wedge $$ ($$ \sim $$ q)

C

p $$ \vee $$ ($$ \sim $$ q)

D

($$ \sim $$ p) $$ \wedge $$ ($$ \sim $$ q)

((p $$ \wedge $$ q) $$ \vee $$ (p $$ \vee $$ $$ \sim $$ q)) $$ \wedge $$ ($$ \sim $$ p $$ \wedge $$ $$ \sim $$ q)

$$ \equiv $$ $$\left( {\left( {\left( {p \vee \left( {p \vee \sim q} \right)} \right)} \right) \wedge \left( {q \vee \left( {p \vee \sim q} \right)} \right)} \right) \wedge \left( { \sim p \wedge \sim q} \right)$$

$$ \equiv $$ $$\left( {\left( {p \vee \sim q} \right) \wedge \left( {q \vee \sim q \vee p} \right)} \right) \wedge \left( { \sim p \wedge \sim q} \right)$$

$$ \equiv $$ $$\left( {\left( {p \vee \sim q} \right) \wedge \left( {t \vee p} \right)} \right) \wedge \left( { \sim p \wedge \sim q} \right)$$

$$ \equiv $$ $$\left( {\left( {p \vee \sim q} \right) \wedge t} \right) \wedge \left( { \sim p \wedge \sim q} \right)$$

$$ \equiv $$ $$\left( {p \vee \sim q} \right) \wedge \left( { \sim p \wedge \sim q} \right)$$

$$ \equiv $$ $$\left( {p \wedge \sim p \wedge \sim q} \right) \vee \left( { \sim q \wedge \sim p \wedge \sim q} \right)$$

$$ \equiv $$ $$\left( {f \wedge \sim q} \right) \vee \left( { \sim q \wedge \sim p} \right)$$

$$ \equiv $$ $$f' \vee \left( { \sim q \wedge \sim p} \right)$$

$$ \equiv $$ $$\left( { \sim q \wedge \sim p} \right)$$

$$ \equiv $$ $$\left( {\left( {\left( {p \vee \left( {p \vee \sim q} \right)} \right)} \right) \wedge \left( {q \vee \left( {p \vee \sim q} \right)} \right)} \right) \wedge \left( { \sim p \wedge \sim q} \right)$$

$$ \equiv $$ $$\left( {\left( {p \vee \sim q} \right) \wedge \left( {q \vee \sim q \vee p} \right)} \right) \wedge \left( { \sim p \wedge \sim q} \right)$$

$$ \equiv $$ $$\left( {\left( {p \vee \sim q} \right) \wedge \left( {t \vee p} \right)} \right) \wedge \left( { \sim p \wedge \sim q} \right)$$

$$ \equiv $$ $$\left( {\left( {p \vee \sim q} \right) \wedge t} \right) \wedge \left( { \sim p \wedge \sim q} \right)$$

$$ \equiv $$ $$\left( {p \vee \sim q} \right) \wedge \left( { \sim p \wedge \sim q} \right)$$

$$ \equiv $$ $$\left( {p \wedge \sim p \wedge \sim q} \right) \vee \left( { \sim q \wedge \sim p \wedge \sim q} \right)$$

$$ \equiv $$ $$\left( {f \wedge \sim q} \right) \vee \left( { \sim q \wedge \sim p} \right)$$

$$ \equiv $$ $$f' \vee \left( { \sim q \wedge \sim p} \right)$$

$$ \equiv $$ $$\left( { \sim q \wedge \sim p} \right)$$

Number in Brackets after Paper Name Indicates No of Questions

AIEEE 2008 (2) *keyboard_arrow_right*

AIEEE 2009 (1) *keyboard_arrow_right*

AIEEE 2010 (1) *keyboard_arrow_right*

AIEEE 2011 (1) *keyboard_arrow_right*

AIEEE 2012 (1) *keyboard_arrow_right*

JEE Main 2013 (Offline) (1) *keyboard_arrow_right*

JEE Main 2014 (Offline) (1) *keyboard_arrow_right*

JEE Main 2015 (Offline) (1) *keyboard_arrow_right*

JEE Main 2016 (Offline) (1) *keyboard_arrow_right*

JEE Main 2016 (Online) 9th April Morning Slot (1) *keyboard_arrow_right*

JEE Main 2016 (Online) 10th April Morning Slot (1) *keyboard_arrow_right*

JEE Main 2017 (Offline) (1) *keyboard_arrow_right*

JEE Main 2017 (Online) 8th April Morning Slot (1) *keyboard_arrow_right*

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JEE Main 2018 (Offline) (1) *keyboard_arrow_right*

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JEE Main 2018 (Online) 15th April Evening Slot (1) *keyboard_arrow_right*

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JEE Main 2019 (Online) 9th January Morning Slot (1) *keyboard_arrow_right*

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JEE Main 2020 (Online) 7th January Morning Slot (1) *keyboard_arrow_right*

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JEE Main 2020 (Online) 5th September Morning Slot (1) *keyboard_arrow_right*

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JEE Main 2020 (Online) 6th September Morning Slot (1) *keyboard_arrow_right*

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JEE Main 2021 (Online) 24th February Morning Slot (1) *keyboard_arrow_right*

JEE Main 2021 (Online) 24th February Evening Slot (2) *keyboard_arrow_right*

JEE Main 2021 (Online) 25th February Morning Slot (1) *keyboard_arrow_right*

JEE Main 2021 (Online) 25th February Evening Shift (1) *keyboard_arrow_right*

JEE Main 2021 (Online) 26th February Evening Shift (1) *keyboard_arrow_right*

JEE Main 2021 (Online) 16th March Morning Shift (1) *keyboard_arrow_right*

JEE Main 2021 (Online) 17th March Morning Shift (1) *keyboard_arrow_right*

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JEE Main 2021 (Online) 20th July Morning Shift (1) *keyboard_arrow_right*

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JEE Main 2021 (Online) 31st August Morning Shift (1) *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*