Explore topic-wise MCQs in Engineering Mathematics.

This section includes 218 Mcqs, each offering curated multiple-choice questions to sharpen your Engineering Mathematics knowledge and support exam preparation. Choose a topic below to get started.

101.

The minimum value of function y = x in the interval [1, 5] is

A. 0
B. 1
C. 25
D. undefined
Answer» C. 25
Discussion
102.

If a function is continuous at a point,

A. the limit of the function may not exist at the point.
B. the function must be derivable at the point.
C. the limit of the function at the point tends to infinity.
D. the limit must exist at the point and the value of limit should be same as the value of the function at that point.
Answer» E.
Discussion
103.

The matrix form of the linear system
dx
= 3x - 5y and
dy
= 4x + 8y is
dtdt
A. <img src="http://images.interviewmania.com/wp-content/uploads/2019/10/10op1.png%20">
B. <img src="http://images.interviewmania.com/wp-content/uploads/2019/10/10op2.png">
C. <img src="http://images.interviewmania.com/wp-content/uploads/2019/10/10op3.png%20">
D. <img src="http://images.interviewmania.com/wp-content/uploads/2019/10/10op4.png%20">
Answer» B. <img src="http://images.interviewmania.com/wp-content/uploads/2019/10/10op2.png">
Discussion
104.

The solution of the differential equation
dy
+ y = 0 is
dx
A. <table><tr><td rowspan="2">y =</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td><td rowspan="2"></td></tr><td align="center">x + c</td></table>
B. <table><tr><td rowspan="2">y =</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>- x <sup>3</sup></center></td><td rowspan="2"> + c</td></tr><td align="center">3</td></table>
C. ce
D. <sup>x</sup>
E. unsolvable as equation is non-linear
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>3</sup></center></td><td rowspan="2"> + c</td></tr><td align="center">3</td></table>
Discussion
105.

Consider the function f(x) = 2x<

A. -5
B. -4
C. 5
D. 4
Answer» B. -4
Discussion
106.

Let z be a complex variable. For a counterclockwise integration around a unit circle C, centred at origin.

A. 2/5
B. 1/2
C. 2
D. 4/5
Answer» B. 1/2
Discussion
107.

For a position vector r = x + yĵ + zk the norm of the vector can be defined as

A. <span style="text-decoration:overline;">r</span>
B. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center><span style="text-decoration:overline;">r</span></center></td><td rowspan="2"></td></tr><td align="center">| <span style="text-decoration:overline;">r</span> |</td></table>
C.
D. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center><span style="text-decoration:overline;">r</span></center></td><td rowspan="2"></td></tr><td align="center"> <span style="text-decoration:overline;">r</span>.<span style="text-decoration:overline;">r</span> </td></table>
E. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center><span style="text-decoration:overline;">r</span></center></td><td rowspan="2"></td></tr><td align="center">| <span style="text-decoration:overline;">r</span> |<sup>3</sup></td></table>
Answer» D. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center><span style="text-decoration:overline;">r</span></center></td><td rowspan="2"></td></tr><td align="center"> <span style="text-decoration:overline;">r</span>.<span style="text-decoration:overline;">r</span> </td></table>
Discussion
108.

The variable x takes a value between 0 and 10 with uniform probability distribution. The variable y takes a value between 0 and 20 with uniform probability distribution. The probability of the sum of variables (x + y) being greater than 20 is

A. 0.33
B. 0.25
C. 0
D. 0.50
Answer» C. 0
Discussion
109.

Given the ordinary differential equation

A. 1.4678
B. 1.4628
C. 1.4698
D. 1.46
Answer» B. 1.4628
Discussion
110.

Consider the differential equation 3y"(x) + 27y(x) = 0 with initial conditions y(0) and y'(0) = 2000. The value of y at x = 1 is _________.

A. 94.08
B. 95
C. 94.58
D. 94
Answer» B. 95
Discussion
111.

Match the items in columns I and II.

A. P-1, Q-4, R-3, S-2
B. P-1, Q-4, R-2, S-3
C. P-1, Q-3, R-2, S-4
D. P-4, Q-1, R-2, S-3
Answer» E.
Discussion
112.

Three vendors were asked to supply a very high precision component. The respective probabilities of their meeting the strict design specifications are 0.8, 0.7 and 0.5. Each vendor supplies one component. The probability that out of total three components supplied by the vendors, at least one will meet the design specification is ______.

A. 0.97
B. 0.99
C. 0.92
D. 0.91
Answer» B. 0.99
Discussion
113.

The divergence of the vector yi + xj is _____

A. 0
B. 1
C. 2
D. 3
Answer» B. 1
Discussion
114.

Consider the following partial differential equation u(x, y) with the constant c > 1:

A. u(x, y) = f(x + cy)
B. u(x, y) = f(x cy)
C. u(x, y) = f(cx + y)
D. u(x, y) = f(cx y)
Answer» C. u(x, y) = f(cx + y)
Discussion
115.

The probability that a screw manufactured by a company is defective is 0.1. The company sells screws in packets containing 5 screws and gives a guarantee of replacement if one or more screws in the packet are found to be defective. The probability that a packet would have to be replaced is ___.

A. 1.41
B. 0.141
C. 0.41
D. 10.41
Answer» D. 10.41
Discussion
116.

Consider a function u which depends on position x and time t. The partial differential equation

A. Wave equation
B. Heat equation
C. Laplace's equation
D. Elasticity equation
Answer» C. Laplace's equation
Discussion
117.

The derivative of f(x) = cos(x) can be estimated using the approximation

A. < 0.1%
B. > 1% and < 5%
C. > 0.1% and < 1%
D. > 5%
Answer» D. > 5%
Discussion
118.

The partial differential equation

A. linear equation of order 2
B. non-linear equation of order 1
C. linear equation of order 1
D. non-linear equation of order 2
Answer» E.
Discussion
119.

F(z) is a function of the complex variable z = x + iy given by

A. 0
B. 1
C. 1
D. y
Answer» C. 1
Discussion
120.

If f(z) = (x

A. a = 1, b = 1
B. a= 1, b = 2
C. a = 1, b = 2
D. a = 2, b = 2
Answer» C. a = 1, b = 2
Discussion
121.

The Blasius equation,

A. second order nonlinear ordinary differential equation
B. third order nonlinear ordinary differential equation
C. third order linear ordinary differential equation
D. mixed order nonlinear ordinary differential equation
Answer» C. third order linear ordinary differential equation
Discussion
122.

Consider an ordinary differential equation
dw
 = 0 - iz
dz
A. 0.22
B. 0.44
C. 0.66
D. 0.88
Answer» E.
Discussion
123.

For the vector

A. -0
B. -1
C. 1
D. 0
Answer» E.
Discussion
124.

Laplace transform of the function sin t is

A. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>s</center></td><td rowspan="2"></td></tr><td align="center">s + </td></table>
B. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> </center></td><td rowspan="2"></td></tr><td align="center">s + </td></table>
C. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>s</center></td><td rowspan="2"></td></tr><td align="center">s - </td></table>
D. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> </center></td><td rowspan="2"></td></tr><td align="center">s - </td></table>
Answer» C. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>s</center></td><td rowspan="2"></td></tr><td align="center">s - </td></table>
Discussion
125.

Gauss seidel method is used to solve the following equations (as per the given order):

A. 1.555
B. 15.555
C. 10.555
D. None of the above
Answer» B. 15.555
Discussion
126.

The Laplace transform of tet is

A. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>s</center></td></tr><tr><td style="text-align: center;">(s + 1) </td></tr></table>
B. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td></tr><tr><td style="text-align: center;">(s - 1) </td></tr></table>
C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td></tr><tr><td style="text-align: center;">(s + 1) </td></tr></table>
D. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>s</center></td></tr><tr><td style="text-align: center;">s - 1</td></tr></table>
Answer» C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td></tr><tr><td style="text-align: center;">(s + 1) </td></tr></table>
Discussion
127.

Solutions of Laplace's equation having continuous second-order partial derivatives are called

A. biharmonic functions
B. harmonic functions
C. conjugate harmonic functions
D. error functions
Answer» C. conjugate harmonic functions
Discussion
128.

If f(t) is a function defined for all t > 0, its Laplace transform F(s) is defined as

A. <img src="http://images.interviewmania.com/wp-content/uploads/2019/10/A.jpg">
B. <img src="http://images.interviewmania.com/wp-content/uploads/2019/10/B.jpg">
C. <img src="http://images.interviewmania.com/wp-content/uploads/2019/10/C.jpg">
D. <img src="http://images.interviewmania.com/wp-content/uploads/2019/10/D.jpg">
Answer» C. <img src="http://images.interviewmania.com/wp-content/uploads/2019/10/C.jpg">
Discussion
129.

Simpson's 1/3 rule is used to integrate the function f(x) = 3/5 x + 9/5 between x = 0 and x = 1 using the least number of equal sub-intervals. The value of the integral is ______.

A. 5
B. 3
C. 2
D. 6
Answer» D. 6
Discussion
130.

F(s) is the Laplace transform of the function f(t) = 2t e

A. 0.4
B. 0.5
C. 1.5
D. 0.9
Answer» C. 1.5
Discussion
131.

The value of the line integral ∮

A. 18
B. 13
C. 16
D. 15
Answer» D. 15
Discussion
132.

Match the correct pairs

A. P-2, Q-1, R-3
B. P-3, Q-2, R-1
C. P-1, Q-2, R-3
D. P-3, Q-1, R-2
Answer» E.
Discussion
133.

Consider an unbiased cubic dice with opposite faces coloured identically and each face coloured red, blue or green such that each colour appears only two times on the dice. If the dice is thrown thrice, the probability of obtaining red colour on top face of the dice at least twice is _____.

A. 27 /2
B. 7 /21
C. 27 /21
D. 7 /27
Answer» E.
Discussion
134.

An explicit forward Euler method is used to numerically integrate the differential equation

A. 21.5937
B. 25.937
C. 2.5937
D. 1 21.15937
Answer» D. 1 21.15937
Discussion
135.

The probability that a part manufactured by a company will be defective is 0.05. If such parts are selected randomly and inspected, then the probabilit y that at least t wo par ts will be defective is ____ (round off to two decimal places).

A. 2.17
B. 0.17
C. 1.25
D. 1.17
Answer» C. 1.25
Discussion
136.

According to Mean Value Theorem, for a continuous function f(x) in the interval [a, b], there exists a value in this interval such that

A. f( )(b a)
B. f(b)( a)
C. f(a)(b )
D. 0
Answer» B. f(b)( a)
Discussion
137.

A function f of the complex variable z = x + iy, is given as f(x, y) = u(x, y) + iv(x, y), where u(x, y) = 2 kxy and v(x, y) = x y . The value of k, for which the function is analytic, is_____

A. - 1
B. - 2
C. - 3
D. - 4
Answer» B. - 2
Discussion
138.

It is given that y + 2 y' = 0, y = 0, y(0) = 0, y(1)= 0. What is y(0.5)?

A. 0
B. 0.37
C. 0.62
D. 1.13
Answer» B. 0.37
Discussion
139.

A box contains 4 red balls and 6 black balls. Three balls are selected randomly from the box one after another, without replacement. The probability that the selected set contains one, red ball and two black balls is

A. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td></tr><td align="center">20</td></table>
B. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td></tr><td align="center">12</td></table>
C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>3</center></td></tr><td align="center">10</td></table>
D. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td></tr><td align="center">2</td></table>
Answer» E.
Discussion
140.

The integral ∮ f (z) dz evaluated around the unit circle on the complex plane for f(z) = cosz/z is

A. 2 i
B. 4 i
C. 2 i
D. 0
Answer» B. 4 i
Discussion
141.

An analytic function f(z) of complex variable z = x + iy may be written as f(z) = u(x, y) + iv(x, y). Then u(x, y) and v(x, y) must satisfy

A. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> u</center></td><td rowspan="2"> = - </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> v</center></td><td rowspan="2"> and </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> u</center></td><td rowspan="2"> = </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> v</center></td></tr><tr><td style="text-align: center;"> x</td><td style="text-align: center;"> y</td><td style="text-align: center;"> y</td><td style="text-align: center;"> x</td></tr></table>
B. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> u</center></td><td rowspan="2"> = </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> v</center></td><td rowspan="2"> and </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> u</center></td><td rowspan="2"> = - </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> v</center></td></tr><tr><td style="text-align: center;"> x</td><td style="text-align: center;"> y</td><td style="text-align: center;"> y</td><td style="text-align: center;"> x</td></tr></table>
C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> u</center></td><td rowspan="2"> = - </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> v</center></td><td rowspan="2"> and </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> u</center></td><td rowspan="2"> = - </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> v</center></td></tr><tr><td style="text-align: center;"> x</td><td style="text-align: center;"> y</td><td style="text-align: center;"> y</td><td style="text-align: center;"> x</td></tr></table>
D. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> u</center></td><td rowspan="2"> = </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> v</center></td><td rowspan="2"> and </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> u</center></td><td rowspan="2"> = </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> v</center></td></tr><tr><td style="text-align: center;"> x</td><td style="text-align: center;"> y</td><td style="text-align: center;"> y</td><td style="text-align: center;"> x</td></tr></table>
Answer» C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> u</center></td><td rowspan="2"> = - </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> v</center></td><td rowspan="2"> and </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> u</center></td><td rowspan="2"> = - </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> v</center></td></tr><tr><td style="text-align: center;"> x</td><td style="text-align: center;"> y</td><td style="text-align: center;"> y</td><td style="text-align: center;"> x</td></tr></table>
Discussion
142.

A harmonic function is analytic if it satisfies the Laplace equation. If u(x, y) = 2x 2y + 4xy is a harmonic function, t hen its conjugate harmonic function v (x, y) is

A. 4y 4xy + constant
B. 4xy 2x + 2y + constant
C. 2x 2y + xy + constant
D. 4xy + 2y 2x + constant
Answer» C. 2x 2y + xy + constant
Discussion
143.

The integral ∮

A. 0
B. - /4
C. - /2
D. /4
Answer» D. /4
Discussion
144.

Consider an ant crawling along the curve (x 2) + y = 4, where x and y are in meters. The ant starts at the point (4, 0) and moves counter clockwise with a speed of 1.57 meters per second. The time taken by the ant to reach the point (2, 2) is (in seconds) ________.

A. 3 sec
B. 3.5 sec
C. 2 sec
D. 2.5sec
Answer» D. 2.5sec
Discussion
145.

The value of the integral

A. 3
B. 0
C. 1
D. 2
Answer» C. 1
Discussion
146.

The value of the integral -
dx
is
1 + x

A.
B. /2
C. /2
D.
Answer» E.
Discussion
147.

If y = f(x) satisfies the boundary value problem

A. -1
B. -2
C. -3
D. -4
Answer» B. -2
Discussion
148.

The number of linearly independent eigenvectors or

A. 0
B. 1
C. 2
D. infinite
Answer» D. infinite
Discussion
149.

The parabolic arc y =

A. /4
B. /2
C. 3 /4
D. 3 /2
Answer» E.
Discussion
150.

Consider the differential equation x
d y
 + x
dy
 - 4y = 0
dx dx
A. x
B. <table><tr><td rowspan="2">sin</td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-oparen-h1.gif"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> x</center></td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-cparen-h1.gif"></td></tr><tr><td style="text-align: center;">2</td></tr></table>
C. <table><tr><td rowspan="2">e<sup>x</sup>sin</td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-oparen-h1.gif"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> x</center></td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-cparen-h1.gif"></td></tr><tr><td style="text-align: center;">2</td></tr></table>
D. <table><tr><td rowspan="2">e<sup>-x</sup>sin</td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-oparen-h1.gif"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> x</center></td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-cparen-h1.gif"></td></tr><tr><td style="text-align: center;">2</td></tr></table>
Answer» B. <table><tr><td rowspan="2">sin</td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-oparen-h1.gif"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> x</center></td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-cparen-h1.gif"></td></tr><tr><td style="text-align: center;">2</td></tr></table>
Discussion