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A scalar quantity has

Magnitude

Del Operator is

same as gradient operator and vector differential operator

Divergence of vector field is not outward flux of a vector per unit

volume

In the cyclindrical coordinate system, φ ranges from

0 to less than 2π

The function F(x) = [x] denotes the greatest integer function, is continuous at

1.5

f(x) = [f(x) - f(x - h)]/h is called

Backward Difference Quotient

The following differential equation is known as x(1 - x)y'' + [c - (1 + a + 1)x]y' - aby = 0

Hypergeometric Differential Equation

At the point of discontinuity ____ component of magnetic flux density is continuous

Normal

In a cartesian coordinate system, axes x, y, and z are at ____ to each other.

90 degrees

Divergence at a point is positive if field lines are ____

Diverging

A differential equation is considered to be ordinary if it has

one independent variable

Suppose the potential function is a step function. The equation that gets satisfied is

Laplace Equation

The cross product of same vector is

Zero

Multiplication of two vectors is

Either vector or scalar

Divergence Theorem relates _____ integral to _____ integral

Surface, Volume

Spherical Coordinate System is _____

Right handed system

Spherical coordinates are represented in terms of

r, θ, φ

If Laplace equation satisfies, then which of the following statement is true?

Current will be infinite

According to this law, the induced current acts to produce an opposing flux.

Lenz' Law

Gradient can be replaced by

Differential Equation

A toroid is ___ selenoid

a long

In the cylindrical coordinate system, z ranges from

- ∞ to + ∞

Laplacian Operator ____

can be a scalar or vector function

Given f a continuous function on interval (a, b) such that f(a) is not equal to f(b). The concept that states that for every number c between a and b such that f(x) = c is known as

Intermediate Value Theorem

A unit vector has ___ direction to that of the main vector

same

Laplacian of a scalar is ___

scalar

What do you call a method of finding zeros of f(x) in numerical analysis wherein the following formula is utilized, X = Xo - f(Xo)/f'(Xo)

Newton-Raphson Method

In a spherical coordinate system, φ is __

Azimuthal angle

____ of two vectors uses the Law of Parallelogram

Addition

____ product is governed by the Right Hand rule.

Vector

Cylindrical Coordinates are represented in terms of _____

r, φ, z

The following differential equation is known as: x²y'' + xy' + (x² - n²)y = 0

Bessel Differential Equation

A vector quantity has

magnitude and direction

In free space, Poisson Equation becomes

Laplace Equation

Cylindrical coordinate 'z' is related to the Cartesian coordinate as

In a spherical coordinate system, φ is given as

tan^-1 (y/x)

f(x) = [f(x+h) - f(x - h)]/2h is called

Centered Difference Quotient

If a researcher uses an alpha level of 0.05 in an ANOVA test, they are essentially saying that they are willing to accept 5% chance of making

Type I Error

Consider the ANOVA Table below. Compute the MSE, Mean Square of Error.

1.454

Divergence of a vector at a point in a vector field is ___ quantity.

Scalar

Laplace equation is what type of Partial Differential Equation?

Elliptic

"r" in Cylindrical coordinates corresponding to Cartesian coordinates (3, 4, 5) is

For transformation from the Cartesian coordinate system to Spherical coordinate system, ap should be equal to

cos θ

Which of the following is/are scalar quantity?

Displacement

Divergence Theorem is applicable for a ____ that is bounded by a ____

Volume, Surface

Cylindrical coordinate "r" is related to the Cartesian coordinate as

√(x² + y²)

Divergence of a gradient of a vector function is

Laplacian operation

If two vectors are orthogonal, then their scalar product is ___

zero

Which of the following is/are vector quantity

All of the above

It relates a line integral around a simple closed curve C to a double integral over plane region D bounded by C

Green's Theorem

Metal have their conductivity

> 1

The following differential equation is known as: xy'' + (1 - x)y' + λy = 0

Laguerre Differential Equation

A scalar field is harmonic in a given region, its Laplacian is

Find the fourier transform of cos (nt)

π δ(ω + n) + π δ(ω - n)

Line integral of an electric field around a closed loop is

Zero

Which is the following is true about Type II Error?

Nonrejection of the null hypothesis when it is false

Maxwell's equations in ____ form give information at point of discontinuity in electromagnetic fields.

Integral

A unit vector has its magnitude as

In terms of Spherical coordinate system, variables y of Cartesian coordinate system is given as

r sin θ sin φ

Stoke's Theorem relates _____ integral to ___ integral

Line, Surface

If z = e^(jθ), what is the real part of z^n + 1/z^n

2 cos (nθ)

What type of partial differential equation is the wave equation?

Hyperbolic

Fo the function f(x, y, z) = xy - x²z + y²z. Which of the following is false?

It has one independent variable

Vector product obeys ____ law

Distributive

Laplacian of a given vector is ___ of gradient of its given divergence and its curl of curl

difference

Curl of gradient of a vector is

Null Vector

On the basis of magnetic behavior, materials are classified into ____ categories

A harmonic function is defined as function which:

Laplacian is zero

In cylindrical coordinate system, unit vector is

directed outwards radially and normal to cylindrical surface at a point

If the rate at which field lines enter into a small volume and also leave then divergence is ____

Which of the following is true about Type I Error?

Rejection of the null hypothesis when it is true

Curl of electrostatic field is

Gradient represents the ____ of maximum space rate of increase of a scalar field

magnitude and direction

Insulators have their conductivity

< 1

Permeability of vacuum is given as ____

4 x 10^-7 H/m

Which of the following theorem relates a surface integral to a volume Integral.

Gauss' Divergence Theorem

Which of the following is not possible for a given population

mean is positive and standard deviation is negative

Curl measures

rate of change of vector and circular motion

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