Partial Differential equation and their Appliction
1. Find ∂z∂x where z=ax2+2by2+2bxy.
a) 3by
b) 2ax
c) 3(ax+by)
d) 2(ax+by)
View Answer
Answer:
d
2. Find ∂z∂x where z=sinx2×cosy2.
a) 2xsinx2
b) x sin2x
c) 2xsinx2 cosy2
d) 6xsinx2 cosy2
View Answer
Answer:
c
3. Find ∂u∂x where u=cos(x−−√+y√).
a) −12x√×tan(√x+√y)
b) −12x√×cos(√x+√y)
c) −12x√×sin(√x+√y)
d) −1x√×sin(√x+√y)
View Answer
Answer: c
4. If u=ex+yex−ey, what is ∂u∂x+u∂y?
a) 2((ex−ey)×ex+y)−(ex+y)(ex+ey) / (ex−ey)2
b) 2((ex−ey)×ex+y)−(ex+y)(ex+ey) / (ex+ey)2
c) 2((ex−ey)×ex+y)−(ex+y)(ex−ey) / (ex−ey)2
d) u
View Answer
Answer:
a
5. If θ=tne−r22t, find the value of n that satisfies the
equation, ∂θ∂t=1r2∂∂r(r2∂θ∂r).
a) 0
b) -1
c) 1
d) 3
View Answer
Answer: b
_____________________________________________
1. First order partial
differential equations arise in the calculus of variations.
a) True
b) False
View Answer
Answer:
a
2. The symbol used for
partial derivatives, ∂, was first used in mathematics by Marquis de Condorcet.
a) True
b) False
View Answer
Answer:
a
3. What is the order
of the equation, xy3(∂y∂x)2+yx2+∂y∂x=0?
a) Third Order
b) Second Order
c) First Order
d) Zero Order
Answer:
c
4. In the equation, y=
x2+c,c is known as the parameter and x and y are
known as the main variables.
a) True
b) False
View Answer
Answer:
a
5. Which of the
following is one of the criterions for linearity of an equation?
a) The dependent variable and its derivatives should be of second order
b) The dependent variable and its derivatives should not be of same order
c) Each coefficient does not depend on the independent variable
d) Each coefficient depends only on the independent variable
View Answer
Answer: d
6. Which of the
following is a type of Iterative method of solving non-linear equations?
a) Graphical method
b) Interpolation method
c) Trial and Error methods
d) Direct Analytical methods
View Answer
Answer:
b
7. Which of the
following is an example for first order linear partial differential equation?
a) Lagrange’s Partial Differential Equation
b) Clairaut’s Partial Differential Equation
c) One-dimensional Wave Equation
d) One-dimensional Heat Equation
View Answer
Answer:
a
8. What is the nature
of Lagrange’s linear partial differential equation?
a) First-order, Third-degree
b) Second-order, First-degree
c) First-order, Second-degree
d) First-order, First-degree
View Answer
Answer:
d
9. Find the general
solution of the linear partial differential equation, yzp+zxq=xy.
a) φ(x2-y2 – z2 )=0
b) φ(x2-y2, y2-z2 )=0
c) φ(x2-y2, y2-x2 )=0
d) φ(x2-z2, z2-x2 )=0
View Answer
Answer:
b
10. The equation 2dydx–xy=y−2, is an example for Bernoulli’s equation.
a) False
b) True
View Answer
Answer:
b
11. A particular
solution for an equation is derived by eliminating arbitrary constants.
a) True
b) False
View Answer
Answer:
b
12. A partial
differential equation is one in which a dependent variable (say ‘y’) depends on
one or more independent variables (say ’x’, ’t’ etc.)
a) False
b) True
View Answer
Answer: b
1. Which of the
following is an example of non-linear differential equation?
a) y=mx+c
b) x+x’=0
c) x+x2=0
d) x”+2x=0
View Answer
Answer:
c
2. Which of the
following is not a standard method for finding the solutions for differential
equations?
a) Variable Separable
b) Homogenous Equation
c) Orthogonal Method
d) Bernoulli’s Equation
View Answer
Answer: c
·
3. Solution of a
differential equation is any function which satisfies the equation.
a) True
b) False
View Answer
Answer:
a
4. A solution which
does not contain any arbitrary constants is called a general solution.
a) True
b) False
View Answer
Answer:
a
5. Which of the
following is a type of Iterative method of solving non-linear equations?
a) Graphical method
b) Interpolation method
c) Trial and Error methods
d) Direct Analytical methods
View Answer
Answer:
b
6. A particular
solution for an equation is derived by substituting particular values to the
arbitrary constants in the complete solution.
a) True
b) False
View Answer
Answer:
a
7. Singular solution
of a differential equation is one that cannot be obtained from the general
solution gotten by the usual method of solving the differential equation.
a) True
b) False
View Answer
Answer:
a
8. Which of the
following equations represents Clairaut’s partial differential equation?
a) z=px+f(p,q)
b) z=f(p,q)
c) z=p+q+f(p,q)
d) z=px+qy+f(p,q)
View Answer
Answer:
d
9. Which of the
following represents Lagrange’s linear equation?
a) P+Q=R
b) Pp+Qq=R
c) p+q=R
d) Pp+Qq=P+Q
View Answer
Answer:
b
10. A partial
differential equation is one in which a dependent variable (say ‘x’) depends on
an independent variable (say ’y’).
a) False
b) True
View Answer
Answer:
a
11. What is the
complete solution of the equation, q=e−pα?
a) z=ae−aαy
b) z=x+e−aαy
c) z=ax+e−aαy+c
d) z=e−aαy
View Answer
Answer:
c
12. A particular
solution for an equation is derived by eliminating arbitrary constants.
a) True
b) False
View Answer
Answer: b
1. Which of the
following is an example of non-linear differential equation?
a) y=mx+c
b) x+x’=0
c) x+x2=0
d) x”+2x=0
View Answer
Answer:
c
2. Which of the
following is not a standard method for finding the solutions for differential
equations?
a) Variable Separable
b) Homogenous Equation
c) Orthogonal Method
d) Bernoulli’s Equation
View Answer
Answer: c
3. Solution of a
differential equation is any function which satisfies the equation.
a) True
b) False
View Answer
Answer:
a
4. A solution which
does not contain any arbitrary constants is called a general solution.
a) True
b) False
View Answer
Answer: a
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5. Which of the
following is a type of Iterative method of solving non-linear equations?
a) Graphical method
b) Interpolation method
c) Trial and Error methods
d) Direct Analytical methods
View Answer
Answer:
b
6. A particular
solution for an equation is derived by substituting particular values to the
arbitrary constants in the complete solution.
a) True
b) False
View Answer
Answer:
a
7. Singular solution
of a differential equation is one that cannot be obtained from the general
solution gotten by the usual method of solving the differential equation.
a) True
b) False
View Answer
Answer:
a
8. Which of the
following is not an example of linear differential equation?
a) y=mx+c
b) x+x’=0
c) x+x2=0
d) x^”+2x=0
View Answer
Answer: c
9. Which of the
following represents Lagrange’s linear equation?
a) P+Q=R
b) Pp+Qq=R
c) p+q=R
d) Pp+Qq=P+Q
View Answer
Answer:
b
10.
A partial differential equation is one in which a dependent variable (say ‘x’)
depends on an independent variable (say ’y’).
a) False
b) True
View Answer
Answer:
a
11. What is the
complete solution of the equation, q=e−pα?
a) z=ae−aαy
b) z=x+e−aαy
c) z=ax+e−aαy+c
d) z=e−aαy
View Answer
Answer:
c
12. A particular
solution for an equation is derived by eliminating arbitrary constants.
a) True
b) False
View Answer
Answer: b
1. Non-homogeneous
which may contain terms which only depend on the independent variable.
a) True
b) False
View Answer
Answer: a
2. Which of the
following is a non-homogeneous equation?
a) ∂2u∂t2−c2∂2u∂x2=0
b) ∂2u∂x2+∂2u∂y2=0
c) ∂2u∂x2+(∂2u∂x∂y)2+∂2u∂y2=x2+y2
d) ∂u∂t−T∂2u∂x2=0
View Answer
Answer:
c
3. What is the general
form of the general solution of a non-homogeneous DE (uh(t)= general solution of the homogeneous equation, up(t)= any particular solution of the non-homogeneous equation)?
a) u(t)=uh (t)/up (t)
b) u(t)=uh (t)*up (t)
c) u(t)=uh (t)+up (t)
d) u(t)=uh (t)-up (t)
View Answer
Answer:
c
4. While an ODE of
order m has m linearly independent solutions, a PDE has infinitely many.
a) False
b) True
View Answer
Answer:
b
5. Which of the
following methods is not used in solving non-homogeneous equations?
a) Exponential Response Formula
b) Method of Undetermined Coefficients
c) Orthogonal Method
d) Variation of Constants
View Answer
Answer: c
6. What is the order
of the non-homogeneous partial differential equation,
∂2u∂x2+(∂2u∂x∂y)2+∂2u∂y2=x2+y2?
a) Order-3
b) Order-2
c) Order-0
d) Order-1
View Answer
Answer:
b
7. What is the degree
of the non-homogeneous partial differential equation,
(∂2u∂x∂y)5+∂2u∂y2+∂u∂x=x2−y3?
a) Degree-2
b) Degree-1
c) Degree-0
d) Degree-5
View Answer
Answer:
d
8. The Integrating
factor of a differential equation is also called the primitive.
a) True
b) False
View Answer
Answer:
b
9. A particular
solution for an equation is derived by substituting particular values to the
arbitrary constants in the complete solution.
a) True
b) False
View Answer
Answer:
a
10. What is the
complete solution of the equation, q=e−pα?
a) z=ae−aαy
b) z=x+e−aαy
c) z=ax+e−aαy+c
d) z=e−aαy
View Answer
Answer:
c
11. In recurrence
relation, each further term of a sequence or array is defined as a function of
its succeeding terms.
a) True
b) False
View Answer
Answer:
b
12. What is the degree
of the differential equation, x3-6x3 y3+2xy=0?
a) 3
b) 5
c) 6
d) 8
View Answer
Answer: c
1. What is the general
form of second order non-linear partial differential equations (x and y being
independent variables and z being a dependent variable)?
a) F(x,y,z,∂z∂x,∂z∂y,∂2z∂x2,∂2z∂y2,∂2z∂x∂y)=0
b) F(x,z,∂z∂x,∂z∂y,∂2z∂x2,∂2z∂y2)=0
c) F(y,z,∂z∂x,∂z∂y)=0
d) F(x,y)=0
View Answer
Answer:
a
2. The solution of the
general form of second order non-linear partial differential equation is
obtained by Monge’s method.
a) False
b) True
View Answer
Answer:
b
3. What is the reason
behind the non-existence of any real function which satisfies the differential
equation, (y’)2 + 1 = 0?
a) Because for any real function, the left-hand side of the equation will be
less than, or equal to one and thus cannot be zero
b) Because for any real function, the left-hand side of the equation becomes
zero
c) Because for any real function, the left-hand side of the equation will be
greater than, or equal to one and thus cannot be zero
d) Because for any real function, the left-hand side of the equation becomes
infinity
View Answer
Answer:
c
4. What is the order
of the partial differential equation, ∂2z∂x2−(∂z∂y)5+∂2z∂x∂y=0?
a) Order-5
b) Order-1
c) Order-4
d) Order-2
View Answer
Answer:
d
5. Which of the
following is the condition for a second order partial differential equation to
be hyperbolic?
a) b2-ac<0
b) b2-ac=0
c) b2-ac>0
d) b2-ac=<0
View Answer
Answer:
c
6. Which of the
following represents the canonical form of a second order parabolic PDE?
a) ∂2z∂η2+⋯=0
b) ∂2z∂ζ∂η+⋯=0
c) ∂2z∂α2+∂2z∂β2…=0
d) ∂2z∂ζ2+⋯=0
View Answer
Answer:
a
7. The condition which
a second order partial differential equation must satisfy to be elliptical is
b2-ac=0.
a) True
b) False
View Answer
Answer:
b
8. Which of the
following statements is true?
a) Hyperbolic equations have three families of characteristic curves
b) Hyperbolic equations have one family of characteristic curves
c) Hyperbolic equations have no families of characteristic curves
d) Hyperbolic equations have two families of characteristic curves
View Answer
Answer:
d
9. Which of the
following represents the family of the characteristic curves for parabolic
equations?
a) aζx+bζy=0
b) aζx+b=0
c) a+ζy=0
d) a(ζx+ζy)=0
View Answer
Answer:
a
10. The condition that
a second order partial differential equation should satisfy to be parabolic is
b2-ac=0.
a) True
b) False
View Answer
Answer:
a
11. Elliptic equations
have no characteristic curves.
a) True
b) False
View Answer
Answer:
a
12. Singular solution
of a differential equation is one that cannot be obtained from the general
solution gotten by the usual method of solving the differential equation.
a) True
b) False
View Answer
Answer:
a
13. In the formation
of differential equation by elimination of arbitrary constants, after
differentiating the equation with respect to independent variable, the
arbitrary constant gets eliminated.
a) False
b) True
View Answer
Answer: a
APPLICATION
1. By using the method
of separation of variables, the determination of solution to P.D.E. reduces to determination
of solution to O.D.E.
a) True
b) False
View Answer
Answer:
a
2. Separation of
variables, in mathematics, is also known as Fourier method.
a) False
b) True
View Answer
Answer:
b
3. Which of the
following equations cannot be solved by using the method of separation of
variables?
a) Laplace Equation
b) Helmholtz Equation
c) Alpha Equation
d) Biharmonic Equation
View Answer
Answer: c
4. The matrix form of
the separation of variables is the Kronecker sum.
a) True
b) False
View Answer
Answer:
a
5. For a partial
differential equation, in a function φ (x, y) and two variables x, y, what is
the form obtained after separation of variables is applied?
a) Φ (x, y) = X(x)+Y(y)
b) Φ (x, y) = X(x)-Y(y)
c) Φ (x, y) = X(x)Y(y)
d) Φ (x, y) = X(x)/Y(y)
View Answer
Answer:
c
6. What is the
solution of, ∂2u∂x2=2xet, after applying
method of separation of variables (u(0,t)=t,∂u∂x(0,t)=et)?
a) u=x33et+xet
b) u=x33et+xet+t
c) u=x33et+et+t
d) u=x22et+xet+t
View AnswerAnswer: b
7. Which of the following
is true with respect to formation of differential equation by elimination of
arbitrary constants?
a) The given equation should be differentiated with respect to independent
variable
b) Elimination of the arbitrary constant by replacing it using derivative
c) If ‘n’ arbitrary constant is present, the given equation should be
differentiated ‘n’ number of times
d) To eliminate the arbitrary constants, the given equation must be integrated
with respect to the dependent variable
View Answer
Answer: d
8. In the formation of
differential equation by elimination of arbitrary constants, after
differentiating the equation with respect to independent variable, the
arbitrary constant gets eliminated.
a) False
b) True
View Answer
Answer:
a
9. u (x, t) = e −
2π*2t*sin πx is the solution of the two-dimensional Laplace equation.
a) True
b) False
View Answer
Answer:
b
10. The symbol used
for partial derivatives, ∂, was first used in mathematics by Marquis de
Condorcet.
a) True
b) False
View Answer
Answer:
a
11. Separation of
variables was first used by L’Hospital in 1750.
a) False
b) True
View Answer
Answer:
b
12. A particular
solution for an equation is derived by eliminating arbitrary constants.
a) True
b) False
View Answer
Answer: b
1. The partial differential
equation of 1-Dimensional heat equation is ___________
a) ut = c2uxx
b) ut = puxx
c) utt = c2uxx
d) ut = – c2uxx
View Answer
Answer:
a
2. When using the
variable separable method to solve a partial differential equation, then the function
can be written as the product of functions depending only on one variable. For
example, U(x,t) = X(x)T(t).
a) True
b) False
View Answer
Answer:
a
3. The one dimensional
heat equation can be solved using a variable separable method. The constant which
appears in the solution should be __________
a) Positive
b) Negative
c) Zero
d) Can be anything
View Answer
Answer:
b
4. When solving the
1-Dimensional heat equation for the conduction of heat along the rod without
radiation with conditions:
i) u(x,t) is finite for t tends to infinite
ii) ux(0,t) = 0 and ux(l,t) = 0
iii) u(x,t) = x(l-x) for t=0 between x=0 and x=l, which condition is the best
to use in the first place?
a) ux(0,t) = ux(l,t) = 0
b) u(x,t) = x(l-x) for t=0 between x=0 and x=l.
c) u(x,t) = x(l-x) for x=0 between t=0 and t=l.
d) u(0,t) = u(l,t) = 0
View Answer
Answer:
a
5. Solve the
1-Dimensional heat equation for the conduction of heat along the rod without
radiation with conditions:
i) u(x,t) is finite for t tends to infinite
ii) ux(0,t) = 0 and ux(l,t) = 0
iii) u(x,t) = x(l-x) for t=0 between x=0 and x=l.
a) U(x,t) =l23/2+∑cos(nÏ€xl)e−c2n2Ï€2tl2−4l2(2m)2+Ï€2
b) U(x,t) =l23+∑cos(nÏ€xl)e−c2n2Ï€2tl2−4l2(2m)2+Ï€2
c) U(x,t) =l23+∑cos(nÏ€xl)e−c2n2Ï€2tl24l2(2m)2+Ï€2
d) U(x,t) =l23/2+∑cos(nÏ€xl)e−c2n2Ï€2tl24l2(2m)2+Ï€2
View AnswerAnswer: a
6. A rod of 30cm
length has its ends P and Q kept 20°C and 80°C respectively until steady state
condition prevail. The temperature at each point end is suddenly reduced to 0°C
and kept so. Find the conditions for solving the equation.
a) u(0,t) = 0 = u(30,t) and u(x,0) = 20 + 60/10 x
b) ux(0,t) = 0 = ux(30,t) and u(x,0) = 20 + 60/30 x
c) ut(0,t) = 0 = ut(30,t) and u(x,0) = 20 + 60/10 x
d) u(0,t) = 0 = u(30,t) and u(x,0) = 20 + 60/30 x
View Answer
Answer:
d
7. Is it possible to
have a solution for 1-Dimensional heat equation which does not converge as time
approaches infinity?
a) Yes
b) No
View Answer
Answer:
b
8. Solve the equation
ut = uxx with the
boundary conditions u(x,0) = 3 sin (nπx) and u(0,t)=0=u(1,t) where 0<x<1
and t>0.
a) 3∑∞n=1 e-n2 Ï€2 t cos(nÏ€x)
b) ∑∞n=1 e-n2 Ï€2 t sin(nÏ€x)
c) 3∑∞n=1 e-n2 Ï€2 t sin(nÏ€x)
d) ∑∞n=1 e-n2 Ï€2 t cos(nÏ€x)
View Answer
Answer:
c
9. If two ends of a
bar of length l is insulated then what are the conditions to solve the heat
flow equation?
a) ux(0,t) = 0 = ux(l,t)
b) ut(0,t) = 0 = ut(l,t)
c) u(0,t) = 0 = u(l,t)
d) uxx(0,t) = 0 = uxx(l,t)
View Answer
Answer:
a
10. The ends A and B
of a rod of 20cm length are kept at 30°C and 80°C until steady state prevails.
What is the condition u(x,0)?
a) 20 + 5⁄2 x
b) 30 + 5⁄2 x
c) 30 + 2x
d) 20 + 2x
View Answer
Answer: b
1. Solve ∂u∂x=6∂u∂t+u using the method of separation of
variables if u(x,0) = 10 e-x.
a) 10 e-x e-t/3
b) 10 ex e-t/3
c) 10 ex/3 e-t
d) 10 e-x/3 e-t
View Answer
Answer:
a
2. Find the solution of ∂u∂x=36∂u∂t+10u if ∂u∂x(t=0)=3e−2x using the method of separation of
variables.
a) −32e−2xe−t/3
b) 3exe−t/3
c) 32e2xe−t/3
d) 3e−xe−t/3
View Answer
Answer:
a
3. Solve the partial differential
equation x3∂u∂x+y2∂u∂y=0 using method of
separation of variables if u(0,y)=10e5y.
a) 10e52x2e5y
b) 10e−52y2e5x
c) 10e−52y2e−5x
d) 10e−52x2e5y
View Answer
Answer:
d
4. Solve the differential equation 5∂u∂x+3∂u∂y=2u using the method of separation of
variables if u(0,y)=9e−5y.
a) 9e175xe−5y
b) 9e135xe−5y
c) 9e−175xe−5y
d) 9e−135xe−5y
View Answer
Answer:
a
5. Solve the differential equation x2∂u∂x+y2∂u∂y=u using the method of separation of
variables if u(0,y)=e2y.
a) e−3ye2x
b) e3ye2x
c) e−3xe2y
d) e3xe2y
View Answer
Answer:
c
6. While solving a partial differential
equation using a variable separable method, we assume that the function can be
written as the product of two functions which depend on one variable only.
a) True
b) False
View Answer
Answer:
a
7. While solving a partial differential
equation using a variable separable method, we equate the ratio to a constant
which?
a) can be positive or negative integer or zero
b) can be positive or negative rational number or zero
c) must be a positive integer
d) must be a negative integer
View Answer
Answer:
b
8. When solving a 1-Dimensional wave equation
using variable separable method, we get the solution if _____________
a) k is positive
b) k is negative
c) k is 0
d) k can be anything
View Answer
Answer:
b
9. When solving a 1-Dimensional heat equation
using a variable separable method, we get the solution if ______________
a) k is positive
b) k is negative
c) k is 0
d) k can be anything
View Answer
Answer:
b
10. While solving any partial differentiation
equation using a variable separable method which is of order 1 or 2, we use the
formula of fourier series to find the coefficients at last.
a) True
b) False
View Answer
Answer: a
1. Who was the first
person to develop the heat equation?
a) Joseph Fourier
b) Galileo Galilei
c) Daniel Gabriel Fahrenheit
d) Robert Boyle
View Answer
Answer:
a
2. Which of the
following is not a field in which heat equation is used?
a) Probability theory
b) Histology
c) Financial Mathematics
d) Quantum Mechanics
View Answer
Answer: b
3. Under ideal
assumptions, what is the two-dimensional heat equation?
a) ut = c∇2 u = c(uxx + uyy)
b) ut = c2 uxx
c) ut = c2 ∇2 u = c2 (uxx + uyy)
d) ut = ∇2 u = (uxx + uyy)
View Answer
Answer:
c
4. In mathematics, an
initial condition (also called a seed value), is a value of an evolving
variable at some point in time designated as the initial time (t=0).
a) False
b) True
View Answer
Answer:
b
5. What is another
name for heat equation?
a) Induction equation
b) Condenser equation
c) Diffusion equation
d) Solar equation
View Answer
Answer:
c
6. Heat Equation is an
example of elliptical partial differential equation.
a) True
b) False
View Answer
Answer:
b
7. What is the
half-interval method in numerical analysis is also known as?
a) Newton-Raphson method
b) Regula Falsi method
c) Taylor’s method
d) Bisection method
View Answer
Answer:
d
8. Which of the
following represents the canonical form of a second order parabolic PDE?
a) ∂2z∂η2+⋯=0
b) ∂2z∂ζ∂η+⋯=0
c) ∂2z∂α2+∂2z∂β2…=0
d) ∂2z∂ζ2+⋯=0
View Answer
Answer:
a
9. Which of the
following is the condition for a second order partial differential equation to
be hyperbolic?
a) b2-ac<0
b) b2-ac=0
c) b2-ac>0
d) b2-ac=<0
View Answer
Answer:
c
10. What is the order
of the partial differential equation, ∂2z∂x2−(∂z∂y)5+∂2z∂x∂y=0?
a) Order-5
b) Order-1
c) Order-4
d) Order-2
View Answer
Answer: d
1. Who discovered the
one-dimensional wave equation?
a) Jean d’Alembert
b) Joseph Fourier
c) Robert Boyle
d) Isaac Newton
View Answer
Answer:
a
2. Wave equation is a
third-order linear partial differential equation.
a) True
b) False
View Answer
Answer:
b
3. In which of the
following fields, does the wave equation not appear?
a) Acoustics
b) Electromagnetics
c) Pedology
d) Fluid Dynamics
View Answer
Answer:
c
4. The wave equation
is known as d’Alembert’s equation.
a) True
b) False
View Answer
Answer:
a
5. Which of the
following statements is false?
a) Equations that describe waves as they occur in nature are called wave
equations
b) The problem of having to describe waves arises in fields like acoustics,
electromagnetics, and fluid dynamics
c) Jean d’Alembert discovered the three-dimensional wave equation
d) Jean d’Alembert discovered the one-dimensional wave equation
View Answer
Answer:
c
6. What is the order
of the partial differential equation, ∂z∂x−(∂z∂y)3=0?
a) Order-5
b) Order-1
c) Order-4
d) Order-2
View Answer
Answer:
b
7. The half-interval
method in numerical analysis is also known as __________
a) Newton-Raphson method
b) Regula Falsi method
c) Taylor’s method
d) Bisection method
View Answer
Answer:
d
8. Wave equation is a
linear elliptical partial differential equation.
a) False
b) True
View Answer
Answer:
a
9. Which of the
following is the condition for a second order partial differential equation to
be hyperbolic?
a) b2-ac < 0
b) b2-ac=0
c) b2-ac>0
d) b2-ac= < 0
View Answer
Answer:
c
10. Which of the
following statements is true?
a) Hyperbolic equations have three families of characteristic curves
b) Hyperbolic equations have one family of characteristic curves
c) Hyperbolic equations have no families of characteristic curves
d) Hyperbolic equations have two families of characteristic curves
View Answer
Answer: d
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