The vector field F = x - y&jcirc; (where and &jcirc; are unit vector) is

neither divergence free nor irrotational

divergence free, but not irrotational

irrotational, but not divergence free

divergence free and irrotational

neither divergence free nor irrotational

x + 2y + z = 4 2x + y + 2z = 5 x y + z = 1 The system of algebraic given below has

A unique solution of x = 1, y = 1 and z = 1

only the two solutions of (x = 1, y = 1, z = 1) and (x = 2, y = 1, z = 0)

Consider the function f(x) = |x| in the interval 1 < x 1. At the point x = 0, f(x) is

neither continuous nor differentiable

non-continuous and differentiable

continuous and non-differentiable

neither continuous nor differentiable

exponentially distributed with mean 2

exponentially distributed with mean 1/6

exponentially distributed with mean 2

normally distributed with mean 3/4

normally distributed with mean 1/6

The function y = |2 3x|

is continuous x & epsilon; R except x = 3 and differentiable x & epsilon; R

is continuous x & epsilon; R and differentiable x & epsilon; R

is continuous x & epsilon; R and differentiable x & epsilon; R except at x = 3/2

is continuous x & epsilon; R and differentiable x & epsilon; R except at x = 2/3

is continuous x & epsilon; R except x = 3 and differentiable x & epsilon; R

218 + Mcqs in Engineering Mathematics Miscellaneous in Engineering Mathematics Page 2 McqOptions

51.	The integral ∮_c(ydx - xdy) is evaluated along the circle x + y = 1/4 traversed in counter clockwise direction. The integral is equal to
A.	0
B.	- /4
C.	- /2
D.	/4
Answer» D. /4

Discussion

52.	Consider the continuous random variable with probability density function f(t) = 1 + t for 1 t 0 = 1 t for 0 t 5 1 The standard deviation of the random variable is
A.	1/
B.	1/
C.
D.	1/3
E.	1/6
Answer» C.

Discussion

53.

The value of the integral
² ₀ (x - 1) sin(x - 1) dx is
(x - 1) + cos(x - 1)

A.

3

B.

0

C.

1

D.

2

Answer» C. 1

Discussion

54.	The value of the following definite integral is _____ (round off to there decimal places). ^e ₁(xInx)dx
A.	2.15
B.	3.12
C.	2.097
D.	2.01
Answer» D. 2.01

Discussion

55.

Given a vector U = 1 (-y + x &jcirc; + z k)
3
and n as the unit normal vector to the surface of the hemisphere (x + y + z = 1; z 0), the value of integral ( u) n dS evaluated on the curved surface of the hemisphere S is

A.

- /2

B.

C.

/2

D.

/3

Answer» D. /3

Discussion

56.

Consider the differential equation x d y + x dy - 4y = 0
dx dx

with the boundary conditions of y(0) with the boundary conditions of y(0) = 0 and y(1) = 1. The complete solution of the differential equation is

A.

x

Answer» B.

Discussion

57.	The vector field F = x - yĵ (where and ĵ are unit vector) is
A.	divergence free, but not irrotational
B.	irrotational, but not divergence free
C.	divergence free and irrotational
D.	neither divergence free nor irrotational
Answer» D. neither divergence free nor irrotational

Discussion

58.	The directional derivative of the function f(x, y) = x + y along a line directed from (0, 0) to (1, 1), evaluated at the point x = 1, y = 1 is
A.	2
B.	4
C.	2
D.
Answer» D.

Discussion

59.

The solution to the differential equation d u - k du = 0
dx dx

is where k is constant, subjected to the boundary conditions u(0) = 0 and u(L) = U, is

A.

B.

Answer» C.

Discussion

60.

If y = f(x) is the solution of d y = 0
dx

with the boundary conditions y = 5 at x = 0, and dy = 2
dx

at x = 10, f(15) = _______.

A.

25

B.

35

C.

28

D.

32

Answer» C. 28

Discussion

61.

Finding the solution of d y + 16y = 0 for y(x) with the two boundary
dx

conditions dy |_x=0 = 1 and dy |_{x= /2} = - 1 has
dx dx

A.

no solution

B.

exactly two solutions

C.

exactly one solution

D.

infinitely many solutions

Answer» B. exactly two solutions

Discussion

62.	The set of equations x + y + z = 1 a ay + 3z = 5 5x 3y + az = 6 has infinite solution, if a =
A.	4
B.	3
C.	4
D.	3
Answer» D. 3

Discussion

63.	The parabolic arc y = x, 1 x 2 is revolved around the x-axis. The volume of the solid of revolution is
A.	/4
B.	/2
C.	3 /4
D.	3 /2
Answer» E.

Discussion

64.	The value of the definite integral ^e ₁ x In (x)dx is
A.
B.
C.
Answer» D.

Discussion

65.

Consider a spatial curve in three-dimensional space given in parametric form by x(t) = cos t, y(t) = sin t,
z(t) = 2 t , 0 t The length of the curve is ___________.
2

A.

0.8622

B.

1.8622

C.

11.8622

D.

1.81622

Answer» C. 11.8622

Discussion

66.	Consider the system of simultaneous equations x + 2y + z = 6 2x + y + 2z = 6 x + y + z = 5 This system has
A.	unique solution
B.	infinite number of solutions
C.	no solution
D.	exactly two solutions
Answer» D. exactly two solutions

Discussion

67.	Consider the following system of equations 2x₁ + x₂ + x₃ = 0 x₂ x₃ = 0 x₁ + x₂ = 0 this system has
A.	a unique solution
B.	no solution
C.	infinite number of solutions
D.	five solutions
Answer» D. five solutions

Discussion

68.	x + 2y + z = 4 2x + y + 2z = 5 x y + z = 1 The system of algebraic given below has
A.	A unique solution of x = 1, y = 1 and z = 1
B.	only the two solutions of (x = 1, y = 1, z = 1) and (x = 2, y = 1, z = 0)
C.	infinite number of solutions
D.	No feasible solution
Answer» D. No feasible solution

Discussion

69.	For what value of a, if any, will the following system of equation in x, y and z have a solution? 2x + 3y = 4 x + y + z = 4 x + 2y z = a
A.	any real number
B.	0
C.	1
D.	There is no such value
Answer» C. 1

Discussion

70.	Equation of the line normal to function f(x) = (x 8)^{2 / 3} + 1 at P(0, 5) is
A.	y = 3x 5
B.	y = 3x + 5
C.	3y = x + 15
D.	3y = x 15
Answer» C. 3y = x + 15

Discussion

71.	If, y = x + x + x + x + ......
A.	4 or 1
B.	4 only
C.	1 only
D.	undefined
Answer» C. 1 only

Discussion

72.	The best approximation of the minimum value attained by e^x sin (100 x) for x > 0 is ______.
A.	0.9844
B.	1.9844
C.	11.91844
D.	None of these
Answer» B. 1.9844

Discussion

73.	At x = 0, the function f(x) = x³ + 1 has
A.	a maximum value
B.	a minimum value
C.	a singularity
D.	a point of inflection
Answer» E.

Discussion

74.

For the equation dy + 7x²y = 0 , if y(0) = 3 / 7 ,
dx

then the value of y(1) is

A.

B.

Answer» B.

Discussion

75.

If y is the solution of the differential equation y³ dy + x³ = 0 ,
dx

y(0) = 1 the value of y( 1) is

A.

2

B.

1

C.

0

D.

1

Answer» D. 1

Discussion

76.

Consider the following differential equation :
dy = -5y ; initial condition; y = 2 at t = 0 The value of y at t = 3 is
dt

A.

-5e

B.

2e

C.

2e

D.

-15e

Answer» D. -15e

Discussion

77.	The distance between the origin and the point nearest it on the surface z² = 1 + xy is
A.	1
B.
C.	2
Answer» B.

Discussion

78.	The root of the function f(x) = x³ + x 1 obtained after first iteration on application of Newton Raphson scheme using an initial guess of x₀ = 1 is
A.	0.682
B.	0.686
C.	0.750
D.	1.000
Answer» D. 1.000

Discussion

79.	Newton-Raphson method is used to find the roots of the equation, x³ + 2x² + 3x 1 = 0. If the initial guess is x₀ = 1, then the value of x after 2nd iteration is ________.
A.	0.3043
B.	0.2043
C.	1.2043
D.	1.3043
Answer» B. 0.2043

Discussion

80.	The root of the function f(x) = x
A.	0.682
B.	0.686
C.	0.750
D.	1.000
Answer» D. 1.000

Discussion

81.	Newton-Raphson method is used to find the roots of the equation, x
A.	0.3043
B.	0.2043
C.	1.2043
D.	1.3043
Answer» B. 0.2043

Discussion

82.	The real root of the equation 5x 2 cosx 1 = 0 (up to two decimal accuracy) is _______.
A.	0.5424
B.	0.5423
C.	1.5424
D.	1.5423
Answer» B. 0.5423

Discussion

83.	Let X and Y be two independent random variables. Which one of the relations between expectation (n), variance (Var) and covariance (Cov) given below is FALSE?
A.	E (XY) = E(X) E(Y)
B.	Coy (X, Y) = 0
C.	Var (X+ Y) = Var (X) + Var (Y)
D.	E(X Y ) = (E (X)) (E (Y))
Answer» E.

Discussion

84.	Solve the equation x = 10 cos(x) using the Newton-Raphson method. The initial guess is x = / 4. The value of the predicted root after the first iteration, up to second decimal, is _____.
A.	0.75
B.	0.76
C.	0.74
D.	0.78
Answer» B. 0.76

Discussion

85.	The general solution of the differential equation (dy / dx) = cos(x + y), with c as a constant, is
A.	y + sin (x + y) = x + c
B.	<table><tr><td rowspan="2">tan</td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/aptitude/1-sym-oparen-h1.gif"></td><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;">x + y</td><td rowspan="2">= y + c</td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-cparen-h1.gif"></td><td rowspan="2"></td> </tr><tr><td style="text-align: center;">2</td></tr></table>
C.	<table><tr><td rowspan="2">cos</td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/aptitude/1-sym-oparen-h1.gif"></td><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;">x + y</td><td rowspan="2">= x + c</td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-cparen-h1.gif"></td><td rowspan="2"></td> </tr><tr><td style="text-align: center;">2</td></tr></table>
D.	<table><tr><td rowspan="2">tan</td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/aptitude/1-sym-oparen-h1.gif"></td><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;">x + y</td><td rowspan="2">= x + c</td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-cparen-h1.gif"></td><td rowspan="2"></td> </tr><tr><td style="text-align: center;">2</td></tr></table>
Answer» E.

Discussion

86.	Consider the function f(x) = \|x\| in the interval 1 < x 1. At the point x = 0, f(x) is
A.	continuous and differentiable
B.	non-continuous and differentiable
C.	continuous and non-differentiable
D.	neither continuous nor differentiable
Answer» D. neither continuous nor differentiable

Discussion

87.	Evaluation of
A.	63
B.	55
C.	45
D.	51
Answer» B. 55

Discussion

88.	P(0, 3), Q(0.5, 4) and R(1, 5) are three points on the curve defined by f(x). Numerical integration is carried out using both Trapezoidal rule and Simpson's rule within limits x = 0 and x = 1 for the curve. The difference between the two results will be
A.	0
B.	0.25
C.	0.5
D.	1
Answer» B. 0.25

Discussion

89.	The error in numerically computing the integral
A.	0.1860
B.	0.1863
C.	0.18
D.	0.1163
Answer» C. 0.18

Discussion

90.	Consider the differential equation (dy / dx) = (1 + y )x. The general solution with constant c is
A.	<table><tr><td rowspan="2">y = tan</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>x<sup>2</sup></center></td><td rowspan="2">+ tanc</td></tr><td align="center">2</td></table>
B.	<table><tr><td rowspan="2">y = tan </td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/aptitude/1-sym-oparen-h1.gif"></td><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;">x</td><td rowspan="2">+ c</td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-cparen-h1.gif"></td><td rowspan="2"></td> </tr><tr><td style="text-align: center;">2</td></tr></table>
C.	<table><tr><td rowspan="2">y = tan </td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/aptitude/1-sym-oparen-h1.gif"></td><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;">x</td><td rowspan="2"></td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-cparen-h1.gif"></td><td rowspan="2">+ c</td> </tr><tr><td style="text-align: center;">2</td></tr></table>
D.	<table><tr><td rowspan="2">y = tan</td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/aptitude/1-sym-oparen-h1.gif"></td><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;">x </td><td rowspan="2">+ c</td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-cparen-h1.gif"></td><td rowspan="2"></td> </tr><tr><td style="text-align: center;">2</td></tr></table>
Answer» E.

Discussion

91.	Using a unit step size, the volume of integral
A.	0.693
B.	0.669
C.	0.653
D.	0.623
Answer» B. 0.669

Discussion

92.	If x is the mean of data 3, x, 2 and 4, then the mode is
A.	6
B.	5
C.	3
D.	4
Answer» D. 4

Discussion

93.	Let X
A.	exponentially distributed with mean 1/6
B.	exponentially distributed with mean 2
C.	normally distributed with mean 3/4
D.	normally distributed with mean 1/6
Answer» B. exponentially distributed with mean 2

Discussion

94.	The function y = \|2 3x\|
A.	is continuous x & epsilon; R and differentiable x & epsilon; R
B.	is continuous x & epsilon; R and differentiable x & epsilon; R except at x = 3/2
C.	is continuous x & epsilon; R and differentiable x & epsilon; R except at x = 2/3
D.	is continuous x & epsilon; R except x = 3 and differentiable x & epsilon; R
Answer» D. is continuous x & epsilon; R except x = 3 and differentiable x & epsilon; R

Discussion

95.	A machine produces 0, 1 or 2 defective pieces in a day with associated probability of 1/6, 2/3 and 1/6, respectively. The mean value and the variance of the number of defective pieces produced by the machine in a day, respectively, are
A.	1 and 1/3
B.	1/3 and 1
C.	1 and 4/3
D.	1/3 and 4/3
Answer» B. 1/3 and 1

Discussion

96.

If x dy + 2xy =
2ln(x) , and y(1) = 0, then what is y(e)?
dx x

A.

e

B.

1

C.

1/e

D.

1/e

Answer» E.

Discussion

97.

The solution of x dy + y = x⁴ with the condition y(1) = 6 is
dx 5

A.

B.

C.

D.

Answer» B. <table><tr><td rowspan="2">y =</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>x<sup>4</sup></center></td><td rowspan="2">+</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>4</center></td><td rowspan="2"></td></tr><td align="center">5</td><td align="center">5x</td></table>

Discussion

98.	The solution of dy/dx = y with initial value y(0) = 1 bounded in the interval
A.	x
B.	x 1
C.	x < 1, x >1
D.	2 x 2
Answer» D. 2 x 2

Discussion

99.	Which one of the following equations is a correct identity for arbitrary 3 3 real matrices P, Q and R?
A.	P(Q + R) = PQ + RP
B.	(P Q) = P 2PQ + Q
C.	det (P + Q) = detP + detQ
D.	(P + Q) = P + PQ + QP + Q
Answer» E.

Discussion

100.	Match the items in columns I and II
A.	P 3, Q 1, R 4, S 2
B.	P 2, Q 3, R 4, S 1
C.	P 3, Q 2, R 5, S 4
D.	P 3, Q 4, R 2, S 1
Answer» B. P 2, Q 3, R 4, S 1

Discussion

Explore topic-wise MCQs in Engineering Mathematics.

The integral ∮c(ydx - xdy) is evaluated along the circle x + y = 1/4 traversed in counter clockwise direction. The integral is equal to

Consider the continuous random variable with probability density function f(t) = 1 + t for 1 t 0 = 1 t for 0 t 5 1 The standard deviation of the random variable is

The value of the integral 2 0(x - 1) sin(x - 1)dx is(x - 1) + cos(x - 1)

The value of the following definite integral is _____ (round off to there decimal places). e 1(xInx)dx

Given a vector U = 1 (-y + x &jcirc; + z k)3 and n as the unit normal vector to the surface of the hemisphere (x + y + z = 1; z 0), the value of integral ( u) n dS evaluated on the curved surface of the hemisphere S is

Consider the differential equation x d y + xdy - 4y = 0 dx dxwith the boundary conditions of y(0) with the boundary conditions of y(0) = 0 and y(1) = 1. The complete solution of the differential equation is

The vector field F = x - yĵ (where and ĵ are unit vector) is

The directional derivative of the function f(x, y) = x + y along a line directed from (0, 0) to (1, 1), evaluated at the point x = 1, y = 1 is

The solution to the differential equationd u - kdu = 0 dx dxis where k is constant, subjected to the boundary conditions u(0) = 0 and u(L) = U, is

If y = f(x) is the solution of d y = 0dx with the boundary conditions y = 5 at x = 0, and dy = 2dxat x = 10, f(15) = _______.

Finding the solution of d y + 16y = 0 for y(x) with the two boundarydx conditions dy |x=0 = 1 and dy |x= /2 = - 1 hasdxdx

The set of equations x + y + z = 1 a ay + 3z = 5 5x 3y + az = 6 has infinite solution, if a =

The parabolic arc y = x, 1 x 2 is revolved around the x-axis. The volume of the solid of revolution is

The value of the definite integral e 1 x In (x)dx is

Consider a spatial curve in three-dimensional space given in parametric form by x(t) = cos t, y(t) = sin t, z(t) = 2t , 0 t The length of the curve is ___________. 2

Consider the system of simultaneous equations x + 2y + z = 6 2x + y + 2z = 6 x + y + z = 5 This system has

Consider the following system of equations 2x1 + x2 + x3 = 0 x2 x3 = 0 x1 + x2 = 0 this system has

x + 2y + z = 4 2x + y + 2z = 5 x y + z = 1 The system of algebraic given below has

For what value of a, if any, will the following system of equation in x, y and z have a solution? 2x + 3y = 4 x + y + z = 4 x + 2y z = a

Equation of the line normal to function f(x) = (x 8)2 / 3 + 1 at P(0, 5) is

If, y = x + x + x + x + ......

The best approximation of the minimum value attained by e x sin (100 x) for x > 0 is ______.

At x = 0, the function f(x) = x3 + 1 has

For the equation dy + 7x2y = 0 , if y(0) = 3 / 7 ,dx then the value of y(1) is

If y is the solution of the differential equation y3dy + x3 = 0 ,dx y(0) = 1 the value of y( 1) is

Consider the following differential equation : dy = -5y ; initial condition; y = 2 at t = 0 The value of y at t = 3 isdt

The distance between the origin and the point nearest it on the surface z2 = 1 + xy is

The root of the function f(x) = x3 + x 1 obtained after first iteration on application of Newton Raphson scheme using an initial guess of x0 = 1 is

Newton-Raphson method is used to find the roots of the equation, x3 + 2x2 + 3x 1 = 0. If the initial guess is x0 = 1, then the value of x after 2nd iteration is ________.

The root of the function f(x) = x

Newton-Raphson method is used to find the roots of the equation, x

The real root of the equation 5x 2 cosx 1 = 0 (up to two decimal accuracy) is _______.

Let X and Y be two independent random variables. Which one of the relations between expectation (n), variance (Var) and covariance (Cov) given below is FALSE?

Solve the equation x = 10 cos(x) using the Newton-Raphson method. The initial guess is x = / 4. The value of the predicted root after the first iteration, up to second decimal, is _____.

The general solution of the differential equation (dy / dx) = cos(x + y), with c as a constant, is

Consider the function f(x) = |x| in the interval 1 < x 1. At the point x = 0, f(x) is

Evaluation of

P(0, 3), Q(0.5, 4) and R(1, 5) are three points on the curve defined by f(x). Numerical integration is carried out using both Trapezoidal rule and Simpson's rule within limits x = 0 and x = 1 for the curve. The difference between the two results will be

The error in numerically computing the integral

Consider the differential equation (dy / dx) = (1 + y )x. The general solution with constant c is

Using a unit step size, the volume of integral

If x is the mean of data 3, x, 2 and 4, then the mode is

Let X

The function y = |2 3x|

A machine produces 0, 1 or 2 defective pieces in a day with associated probability of 1/6, 2/3 and 1/6, respectively. The mean value and the variance of the number of defective pieces produced by the machine in a day, respectively, are

If x dy+ 2xy =2ln(x), and y(1) = 0, then what is y(e)?dxx

The solution of xdy+ y = x4 with the condition y(1) =6isdx5

The solution of dy/dx = y with initial value y(0) = 1 bounded in the interval

Which one of the following equations is a correct identity for arbitrary 3 3 real matrices P, Q and R?

Match the items in columns I and II

The integral ∮_c(ydx - xdy) is evaluated along the circle x + y = 1/4 traversed in counter clockwise direction. The integral is equal to

Consider the continuous random variable with probability density function
f(t) = 1 + t for 1 t 0
= 1 t for 0 t 5 1
The standard deviation of the random variable is

The value of the integral
² ₀ (x - 1) sin(x - 1) dx is
(x - 1) + cos(x - 1)

The value of the following definite integral is _____ (round off to there decimal places).
^e ₁(xInx)dx

Given a vector U = 1 (-y + x &jcirc; + z k)
3
and n as the unit normal vector to the surface of the hemisphere (x + y + z = 1; z 0), the value of integral ( u) n dS evaluated on the curved surface of the hemisphere S is

Consider the differential equation x d y + x dy - 4y = 0
dx dx

with the boundary conditions of y(0) with the boundary conditions of y(0) = 0 and y(1) = 1. The complete solution of the differential equation is

The solution to the differential equation d u - k du = 0
dx dx

is where k is constant, subjected to the boundary conditions u(0) = 0 and u(L) = U, is

If y = f(x) is the solution of d y = 0
dx

with the boundary conditions y = 5 at x = 0, and dy = 2
dx

at x = 10, f(15) = _______.

Finding the solution of d y + 16y = 0 for y(x) with the two boundary
dx

conditions dy |_x=0 = 1 and dy |_{x= /2} = - 1 has
dx dx

The set of equations
x + y + z = 1
a ay + 3z = 5
5x 3y + az = 6
has infinite solution, if a =

The value of the definite integral ^e ₁ x In (x)dx is

Consider a spatial curve in three-dimensional space given in parametric form by x(t) = cos t, y(t) = sin t,
z(t) = 2 t , 0 t The length of the curve is ___________.
2

Consider the system of simultaneous equations
x + 2y + z = 6
2x + y + 2z = 6
x + y + z = 5
This system has

Consider the following system of equations
2x₁ + x₂ + x₃ = 0
x₂ x₃ = 0
x₁ + x₂ = 0
this system has

x + 2y + z = 4
2x + y + 2z = 5
x y + z = 1
The system of algebraic given below has

For what value of a, if any, will the following system of equation in x, y and z have a solution?
2x + 3y = 4
x + y + z = 4
x + 2y z = a

Equation of the line normal to function f(x) = (x 8)^{2 / 3} + 1 at P(0, 5) is

The best approximation of the minimum value attained by e^x sin (100 x) for x > 0 is ______.

At x = 0, the function f(x) = x³ + 1 has

For the equation dy + 7x²y = 0 , if y(0) = 3 / 7 ,
dx

then the value of y(1) is

If y is the solution of the differential equation y³ dy + x³ = 0 ,
dx

y(0) = 1 the value of y( 1) is

Consider the following differential equation :
dy = -5y ; initial condition; y = 2 at t = 0 The value of y at t = 3 is
dt

The distance between the origin and the point nearest it on the surface z² = 1 + xy is

The root of the function f(x) = x³ + x 1 obtained after first iteration on application of Newton Raphson scheme using an initial guess of x₀ = 1 is

Newton-Raphson method is used to find the roots of the equation, x³ + 2x² + 3x 1 = 0. If the initial guess is x₀ = 1, then the value of x after 2nd iteration is ________.

If x dy + 2xy =
2ln(x) , and y(1) = 0, then what is y(e)?
dx x

The solution of x dy + y = x⁴ with the condition y(1) = 6 is
dx 5