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

To find the focal length of a convex mirror, a student records the following data :

The focal length of the convex lens is f_{1} and that of mirror is f_{2}. Then taking index correction to be negligibly small, f_{1} and f_{2} are close to :

Object Pin |
Convex Lens |
Convex Mirror |
Image Pin |
---|---|---|---|

22.2 cm | 32.2 cm | 45.8 cm | 71.2 cm |

The focal length of the convex lens is f

A

f_{1} = 12.7 cm f_{2} = 7.8 cm

B

f_{1} = 7.8 cm f_{2} = 12.7 cm

C

f_{1} = 7.8 cm f_{2} = 25.4 cm

D

f_{1} = 15.6 cm f_{2} = 25.4 cm

For lens :

u_{1} = $$-$$ (32.2 $$-$$ 22.2) cm

= $$-$$ 10 cm

v_{1} = (71.2 $$-$$ 32.2) cm

= 39 cm

$$ \therefore $$ $${1 \over {{f_1}}}$$ = $${1 \over {{v_1}}} - {1 \over {{u_1}}}$$

= $${1 \over {39}}$$ + $${1 \over {10}}$$

= $${{49} \over {390}}$$

$$ \therefore $$ f_{1} = 7.8 cm

For mirror :

R = (71.2 $$-$$ 45.8) cm

= 25.4 cm

$$ \therefore $$ f_{2} = $${R \over 2}$$ = $${{25.4} \over 2}$$ = 12.7 cm

u

= $$-$$ 10 cm

v

= 39 cm

$$ \therefore $$ $${1 \over {{f_1}}}$$ = $${1 \over {{v_1}}} - {1 \over {{u_1}}}$$

= $${1 \over {39}}$$ + $${1 \over {10}}$$

= $${{49} \over {390}}$$

$$ \therefore $$ f

For mirror :

R = (71.2 $$-$$ 45.8) cm

= 25.4 cm

$$ \therefore $$ f

2

In an experiment a sphere of aluminium of mass 0.20 kg is heated upto 150^{o}^{}C. Immediately, it is put into water of volume 150 cc at 27^{o}C kept in a calorimeter of water equivalent to 0.025 kg. Final temperature of the system is 40^{o}C. The specific heat of aluminium is : (take 4.2 Joule = 1 calorie)

A

378 J/kg $$-$$^{o}C

B

315 J/kg $$-$$^{o}C

C

476 J/kg $$-$$^{o}C

D

434 J/kg $$-$$^{o}C

Let specific heat of aluminium = S,

As we know from principle of calorimetry,

Q_{given} = Q_{used}

$$\therefore\,\,\,$$ 0.2 $$ \times $$ S $$ \times $$ (150 $$-$$ 40) =

150 $$ \times $$ 1 $$ \times $$ (40 $$-$$ 27) + 25 $$ \times $$ (40$$-$$27)

$$ \Rightarrow $$$$\,\,\,$$ 0.2 $$ \times $$ S $$ \times $$ 110 = 150 $$ \times $$ 13 + 25 $$ \times $$ 13

$$ \Rightarrow $$$$\,\,\,$$ S = 434 J/kg -^{o}C

As we know from principle of calorimetry,

Q

$$\therefore\,\,\,$$ 0.2 $$ \times $$ S $$ \times $$ (150 $$-$$ 40) =

150 $$ \times $$ 1 $$ \times $$ (40 $$-$$ 27) + 25 $$ \times $$ (40$$-$$27)

$$ \Rightarrow $$$$\,\,\,$$ 0.2 $$ \times $$ S $$ \times $$ 110 = 150 $$ \times $$ 13 + 25 $$ \times $$ 13

$$ \Rightarrow $$$$\,\,\,$$ S = 434 J/kg -

3

In an experiment a convex lens of focal length 15 cm is placed coaxially on an optical bench in front of a convex mirror at a distance of 5 cm from it. It is found that an object and its image coincide, if the object is placed at a distance of 20 cm from the lens. The focal length of the convex mirror is :

A

27.5 cm

B

20.0 cm

C

25.0 cm

D

30.5 cm

4

In an experiment to determine the period of a simple pendulum of length 1 m, it is attached to different spherical bobs of radii r_{1}
and r_{2} . The two spherical bobs have uniform mass distribution. If the relative difference in the periods, is found to be
5×10^{−4} s, the difference in radii, $$\left| {} \right.$$r_{1} $$-$$ r_{2} $$\left| {} \right.$$ is best given by :

A

1 cm

B

0.05 cm

C

0.5 cm

D

0.01 cm

Number in Brackets after Paper Name Indicates No of Questions

AIEEE 2005 (1) *keyboard_arrow_right*

AIEEE 2008 (3) *keyboard_arrow_right*

AIEEE 2009 (2) *keyboard_arrow_right*

AIEEE 2011 (1) *keyboard_arrow_right*

AIEEE 2012 (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 2017 (Online) 8th April Morning Slot (1) *keyboard_arrow_right*

JEE Main 2017 (Online) 9th April Morning Slot (2) *keyboard_arrow_right*

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

Units & Measurements *keyboard_arrow_right*

Motion *keyboard_arrow_right*

Laws of Motion *keyboard_arrow_right*

Work Power & Energy *keyboard_arrow_right*

Simple Harmonic Motion *keyboard_arrow_right*

Impulse & Momentum *keyboard_arrow_right*

Rotational Motion *keyboard_arrow_right*

Gravitation *keyboard_arrow_right*

Properties of Matter *keyboard_arrow_right*

Heat and Thermodynamics *keyboard_arrow_right*

Waves *keyboard_arrow_right*

Vector Algebra *keyboard_arrow_right*

Electrostatics *keyboard_arrow_right*

Current Electricity *keyboard_arrow_right*

Magnetics *keyboard_arrow_right*

Alternating Current and Electromagnetic Induction *keyboard_arrow_right*

Ray & Wave Optics *keyboard_arrow_right*

Atoms and Nuclei *keyboard_arrow_right*

Electronic Devices *keyboard_arrow_right*

Communication Systems *keyboard_arrow_right*

Practical Physics *keyboard_arrow_right*

Dual Nature of Radiation *keyboard_arrow_right*