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 a triangular plot ABC with sides AB = 7m, BC = 5m and CA = 6m. A vertical lamp-post at the mid point D of AC subtends an angle 30^{o} at B. The height (in m) of the lamp-post is -

A

$$2\sqrt {21} $$

B

$${3 \over 2}\sqrt {21} $$

C

$$7\sqrt {3} $$

D

$${2 \over 3}\sqrt {21} $$

BD = hcot30

So, 7

$$ \Rightarrow $$ 37 = 3h

$$ \Rightarrow $$ 3h

$$ \Rightarrow $$ h = $$\sqrt {{{28} \over 3}} = {2 \over 3}\sqrt {21} $$

2

With the usual notation, in $$\Delta $$ABC, if $$\angle A + \angle B$$ = 120^{o}, a = $$\sqrt 3 $$ $$+$$ 1, b = $$\sqrt 3 $$ $$-$$ 1 then the ratio $$\angle A:\angle B,$$ is -

A

9 : 7

B

7 : 1

C

5 : 3

D

3 : 1

A + B = 120^{o}

$$\tan {{A - B} \over 2} = {{a - b} \over {a + b}}\cot \left( {{c \over 2}} \right)$$

$$ = {{\sqrt 3 + 1 - \sqrt 3 + 1} \over {2\left( {\sqrt 3 } \right)}}\cot \left( {{{30}^o}} \right) = {1 \over {\sqrt 3 }}.\sqrt 3 = 1$$

$${{A - B} \over 2} = {45^o}$$

$$ \Rightarrow A - B = {90^o}$$

$$ \ A + B = {120^o}$$

$$2A = {210^o}$$

$$A = {105^o}$$

$$B = {15^o}$$

$$ \therefore $$ $$\angle A:\angle B,$$ = 7 : 1

$$\tan {{A - B} \over 2} = {{a - b} \over {a + b}}\cot \left( {{c \over 2}} \right)$$

$$ = {{\sqrt 3 + 1 - \sqrt 3 + 1} \over {2\left( {\sqrt 3 } \right)}}\cot \left( {{{30}^o}} \right) = {1 \over {\sqrt 3 }}.\sqrt 3 = 1$$

$${{A - B} \over 2} = {45^o}$$

$$ \Rightarrow A - B = {90^o}$$

$$ \ A + B = {120^o}$$

$$2A = {210^o}$$

$$A = {105^o}$$

$$B = {15^o}$$

$$ \therefore $$ $$\angle A:\angle B,$$ = 7 : 1

3

In a triangle, the sum of lengths of two sides is x and the product of the lengths of the same two sides is y. If x^{2} – c^{2} = y, where c is the length of the third side of the triangle, then the circumradius of the triangle is :

A

$${y \over {\sqrt 3 }}$$

B

$${c \over 3}$$

C

$${c \over {\sqrt 3 }}$$

D

$${3 \over 2}$$y

Given a + b = x and ab = y

If x^{2} $$-$$ c^{2} = y $$ \Rightarrow $$ (a + b)^{2} $$-$$ c^{2} = ab

$$ \Rightarrow $$ a^{2} + b^{2} $$-$$ c^{2} = $$-$$ ab

$$ \Rightarrow $$ $${{{a^2} + {b^2} - {c^2}} \over {2ab}} = - {1 \over 2}$$

$$ \Rightarrow \cos C = - {1 \over 2}$$

$$ \Rightarrow \angle C = {{2\pi } \over 3}$$

$$R = {c \over {2\sin C}} = {c \over {\sqrt 3 }}$$

If x

$$ \Rightarrow $$ a

$$ \Rightarrow $$ $${{{a^2} + {b^2} - {c^2}} \over {2ab}} = - {1 \over 2}$$

$$ \Rightarrow \cos C = - {1 \over 2}$$

$$ \Rightarrow \angle C = {{2\pi } \over 3}$$

$$R = {c \over {2\sin C}} = {c \over {\sqrt 3 }}$$

4

Given $${{b + c} \over {11}} = {{c + a} \over {12}} = {{a + b} \over {13}}$$ for a $$\Delta $$ABC with usual notation.

If $${{\cos A} \over \alpha } = {{\cos B} \over \beta } = {{\cos C} \over \gamma },$$ then the ordered triad ($$\alpha $$, $$\beta $$, $$\gamma $$) has a value

If $${{\cos A} \over \alpha } = {{\cos B} \over \beta } = {{\cos C} \over \gamma },$$ then the ordered triad ($$\alpha $$, $$\beta $$, $$\gamma $$) has a value

A

(19, 7, 25)

B

(7, 19, 25)

C

(5, 12, 13)

D

(3, 4, 5)

b + c = 11$$\lambda $$, c + a = 12$$\lambda $$, a + b = 13$$\lambda $$

$$ \Rightarrow $$ a = 7$$\lambda $$, b = 6$$\lambda $$, c = 5$$\lambda $$

(using cosine formula)

cosA = $${1 \over 5},$$ cosB = $${19 \over 35},$$ cosC = $${5 \over 7},$$

$$\alpha $$ : $$\beta $$ : $$\gamma $$ $$ \Rightarrow $$ 7 : 19 : 25

$$ \Rightarrow $$ a = 7$$\lambda $$, b = 6$$\lambda $$, c = 5$$\lambda $$

(using cosine formula)

cosA = $${1 \over 5},$$ cosB = $${19 \over 35},$$ cosC = $${5 \over 7},$$

$$\alpha $$ : $$\beta $$ : $$\gamma $$ $$ \Rightarrow $$ 7 : 19 : 25

Number in Brackets after Paper Name Indicates No of Questions

AIEEE 2002 (2) *keyboard_arrow_right*

AIEEE 2003 (3) *keyboard_arrow_right*

AIEEE 2004 (2) *keyboard_arrow_right*

AIEEE 2005 (2) *keyboard_arrow_right*

AIEEE 2007 (1) *keyboard_arrow_right*

AIEEE 2008 (1) *keyboard_arrow_right*

AIEEE 2010 (1) *keyboard_arrow_right*

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

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

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

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

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

JEE Main 2018 (Online) 16th April Morning Slot (1) *keyboard_arrow_right*

JEE Main 2019 (Online) 10th January Morning Slot (1) *keyboard_arrow_right*

JEE Main 2019 (Online) 10th January Evening Slot (1) *keyboard_arrow_right*

JEE Main 2019 (Online) 11th January Morning Slot (1) *keyboard_arrow_right*

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JEE Main 2019 (Online) 12th January Evening Slot (1) *keyboard_arrow_right*

JEE Main 2019 (Online) 8th April Evening Slot (2) *keyboard_arrow_right*

JEE Main 2019 (Online) 9th April Evening Slot (1) *keyboard_arrow_right*

JEE Main 2019 (Online) 10th April Morning Slot (1) *keyboard_arrow_right*

JEE Main 2019 (Online) 10th April Evening Slot (1) *keyboard_arrow_right*

JEE Main 2019 (Online) 12th April Evening Slot (1) *keyboard_arrow_right*

JEE Main 2020 (Online) 4th September Morning Slot (1) *keyboard_arrow_right*

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

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

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

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

JEE Main 2021 (Online) 18th March Evening Shift (1) *keyboard_arrow_right*

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

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JEE Main 2021 (Online) 25th July Morning Shift (1) *keyboard_arrow_right*

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

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*