GATE ME 2011 | Calculus Question 30 | Engineering Mathematics

GATE ME 2011

MCQ (Single Correct Answer)

-0.3

If $$f(x)$$ is even function and a is a positive real number , then $$\int\limits_{ - a}^a {f\left( x \right)dx\,\,} $$ equals ________.

$$0$$

$$a$$

$$2a$$

$$2\int\limits_0^a {f\left( x \right)dx\,\,} $$

GATE ME 2011

MCQ (Single Correct Answer)

-0.3

A series expansion for the function $$\sin \theta $$ is _______.

$$1 - {{{\theta ^2}} \over {2!}} + {{{\theta ^4}} \over {4!}} - ......$$

$$\theta - {{{\theta ^3}} \over {3!}} + {{{\theta ^5}} \over {5!}} - ......$$

$$1 + \theta + {{{\theta ^2}} \over {2!}} + {{{\theta ^3}} \over {3!}} + ......$$

$$\theta + {{{\theta ^3}} \over {3!}} + {{{\theta ^5}} \over {5!}} + ......$$

GATE ME 2011

MCQ (Single Correct Answer)

-0.3

What is $$\mathop {Lim}\limits_{\theta \to 0} {{\sin \theta } \over \theta }\,\,$$ equal to ?

$$\theta $$

$$sin$$$$\theta $$

$$0$$

$$1$$

GATE ME 2010

MCQ (Single Correct Answer)

-0.3

The parabolic are $$y = \sqrt x ,1 \le x \le 2$$ is revolved around the $$x$$-axis. The volume of the solid of revolution is

$${\pi \over 4}$$

$${\pi \over 2}$$

$${{3\pi } \over 4}$$

$${{3\pi } \over 2}$$

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GATE ME Subjects

Engineering Mechanics

Engineering Mechanics Static and Dynamics

Machine Design

Bolted Riveted and Welded Joints Design For Static Loading Design of Brakes and Clutches Design of Spur Gears Design of Bearings Fatigue Strength

Strength of Materials

Springs Simple Stress and Strain Complex Stresses Pure Bending Moment of Inertia Shear Force and Bending Moment Stresses In Beams Deflection of Beams Columns and Struts Torsion Strain Energy Method Thin Cylinders

Heat Transfer

Conduction Fin Design and Transient Heat Conduction Convection Radiation Heat Exchangers

Production Engineering

Sheet Metal Forming Processes Metal Cutting Welding Process Metal Forming Casting Advance Machine Tools Machining Metrology and Inspection

Industrial Engineering

Queuing Production Planning and Control Line Balancing Forecasting Linear Programming Assignment Pert and Cpm Inventory Control Transportation Scheduling

Turbo Machinery

Theory of Machines

Vibrations Gears and Gear Trains Flywheel Analysis of Plane Mechanisms

Engineering Mathematics

Linear Algebra Calculus Vector Calculus Probability and Statistics Differential Equations Complex Variable Transform Theory Numerical Methods

Fluid Mechanics

Fluid Properties Fluid Statics Boundary Layer Turbulent Flow Laminar Flow Fluid Dynamics Fluid Kinematics

Thermodynamics

Properties of Pure Substances Basic Concepts and Zeroth Law First Law of Thermodynamics Calculation of Work and Heat Entropy and Irreversibility Rankine Cycle Availability Second Law of Thermodynamics

General Aptitude

Numerical Ability Logical Reasoning Verbal Ability