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.

1.

Consider the function f(x) = 2x<3 3x in the domain [ 1, 2]. The global minimum of f(x) is

A. -5
B. -4
C. 5
D. 4
Answer» B. -4
Discussion
2.

The solution of the differential equation (dy / dx) + 2xy = e-x with y(0) = 1 is

A. (1 + x) e
B. (1 + x) e
C. (1 - x) e
D. (1 - x) e
Answer» C. (1 - x) e
Discussion
3.

The solution of the initial value problem (dy / dx) = 2xy; y(0) = 2 is

A. 1 + e
B. 2e
C. 1 + e
D. 2e
Answer» C. 1 + e
Discussion
4.

A box contains 20 defective items and 80 nondefective items. If two items are selected at random without replacement, what will be the probability that both items are defective?

A.
B.
Answer» E.
Discussion
5.

A single die is thrown twice. What is the probability that the sum is neither 8 nor 9?

A.
B.
Answer» E.
Discussion
6.

The argument of the complex number {(1 + i) / (1 - i)} , where i = -1 is

A. -
B. - / 2
C. / 2
D.
Answer» D.
Discussion
7.

The following surface integral is to be evaluated over a sphere for the given steady velocity vector field F = x + yĵ + zk defined with respect to a Cartesian coordinate system having i, j and k as unit base vectors.
∬s ( F.n )dA
where S is the sphere, x2 + y2 + z3 = 1 and n is the outward unit normal vector to the sphere. The value of the surface integral is

A.
B. 2
C. 3 /4
D. 4
Answer» B. 2
Discussion
8.

The divergence of the vector field 3xz + 2xyĵ - yz2k at a point (1, 1, 1) is equal to

A. 7
B. 4
C. 3
D. 0
Answer» D. 0
Discussion
9.

The directional derivative of the scalar function f(x, y, z) = x2 + 2y2 + z at the point P = (1, 1, 2) in the direction of the vector a = 3 - 4ĵ is

A. 4
B. 2
C. 1
D. 1
Answer» C. 1
Discussion
10.

Divergence of the vector field
x2z + xyĵ - yz2k at (1, -1, 1) is

A. 0
B. 3
C. 5
D. 6
Answer» D. 6
Discussion
11.

For the vector V = 2yz + 3xzĵ + 4xyk of ( V) is _________.

A. -0
B. -1
C. 1
D. 0
Answer» E.
Discussion
12.

The value of the line integral ∮F . rds , where C is a circle of radius units is ________
Here, F ( x, y ) = y + 2xĵ and r is the UNIT tangent vector on the curve C at an arc length s from a reference point on the curve and are the basis vectors in the x y Cartesian reference. In evaluating the line integral, the curve has to be traversed in the counterclockwise direction.

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

Given the ordinary differential equation
d2y
+
dy
= 0
dx2dx

with(0) = 0 and
dy
(0) = 1, the value of y(1) is
dx

_______ (correct to two decimal places).

A. 1.4678
B. 1.4628
C. 1.4698
D. 1.46
Answer» B. 1.4628
Discussion
14.

Let z be a complex variable. For a counterclockwise integration around a unit circle C, centred at origin.
&conint;c
1
dz = A i the value of A is
5z - 4
A. 2/5
B. 1/2
C. 2
D. 4/5
Answer» B. 1/2
Discussion
15.

F(z) is a function of the complex variable z = x + iy given by
F(z) = iz + k Re(z) + i Im(z)
For what value of k will F(z) satisfy the Cauchy Riemann equations?

A. 0
B. 1
C. 1
D. y
Answer» C. 1
Discussion
16.

If f(z) = (x2 + ay2) + ibxy is a complex analytic function of z = x + iy, where i = - 1, then

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
17.

Using a unit step size, the volume of integral 21 xlnxdx by trapezoidal rule is ______

A. 0.693
B. 0.669
C. 0.653
D. 0.623
Answer» B. 0.669
Discussion
18.

The inverse Laplace transform of 1/(s2 + s) is

A. 1 + e
B.
C. 1 e
D. 1 e
E. 1 + e
Answer» D. 1 e
Discussion
19.

Evaluation of 42 x3 dx using a 2-equal-segment trapezoidal rule gives value of _______.

A. 63
B. 55
C. 45
D. 51
Answer» B. 55
Discussion
20.

The value of &conint;r
3z - 5
dz
(z - 1)(z - 2)

along a closed path R is is equal to (4 i), where z = x + iy and i
= - 1 . The correct path r is

A.
B.
Answer» C.
Discussion
21.

Consider the following partial differential equation u(x, y) with the constant c > 1:
u
+ c
u
= 0
y x

Solution of this equation is

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
22.

Consider a function u which depends on position x and time t. The partial differential equation
u
=
2u
 is known as the
t x2
A. Wave equation
B. Heat equation
C. Laplace's equation
D. Elasticity equation
Answer» C. Laplace's equation
Discussion
23.

The partial differential equation
u
+ u
u
=
2u
is
t x x2
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
24.

The Blasius equation,
d3f
+
f
d2f
= 0, is a
d 32d 2
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
25.

Match the items in columns I and II
Column I
P. Singular matrix
Q. Non-square matrix
R. Real symmetric
S. Orthogonal matrix
Column II
1. Determinant is not defined
2. Determinant is always one
3. Determinant is zero
4. Eigenvalues are always real
5. Eigenvalues are not defined

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
26.

Let X1 and X2 be two independent exponentially distributed random variables with means 0.5 and 0.25 respectively. Then Y = min (X1, X2) is

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
27.

The error in numerically computing the integral 0 (sinx + cosx) dx using the trapezoidal rule with three intervals of equal length between 0 and is _________.

A. 0.1860
B. 0.1863
C. 0.18
D. 0.1163
Answer» C. 0.18
Discussion
28.

Let X1, X2 be two independent normal random variables with means 1, 2 and standard deviations 1, 2 respectively. Consider Y = X1 X2; 1 = 2 = 1, 1 = 1, 2 = 2, Then,

A. Y is normal distributed with mean 0 and variance 1
B. Y is normally distributed with mean 0 and variance 5
C. Y has mean 0 and variance 5, but is NOT normally distributed
D. Y has mean 0 and variance 1, but is NOT normally distributed
Answer» C. Y has mean 0 and variance 5, but is NOT normally distributed
Discussion
29.

Consider a Poisson distribution for the tossing of a biased coin. The mean for this distribution is . The standard deviation for this distribution is given by

A.
B.
C.
D.
Answer» B.
Discussion
30.

For a position vector r = x + yĵ + zk the norm of the vector can be defined as
| r | = x2 + y2 + z2 . Given a function = In | r |, its gradient is

A.
Answer» D.
Discussion
31.

The line integral V . dr of the vector V(r)
= 2xyz + x2z + x2ĵ + xyk from the origin to the point P(1, 1, 1)

A. is 1
B. is zero
C. is 1
D. cannot be determined without specifying the path
Answer» B. is zero
Discussion
32.

The Laplace transform of ei5t where i = -1, is

A.
B.
C.
Answer» C.
Discussion
33.

Laplace transform of cos( t) is
s
s2 + 2

The laplace transform of e 2t cos(4t) is

A.
B.
C.
D.
Answer» E.
Discussion
34.

Laplace transform of cos ( t) is

A.
B.
C.
D.
Answer» B.
Discussion
35.

An explicit forward Euler method is used to numerically integrate the differential equation
dy
 = y
dt

using a time step of 0.1. With the initial condition y(0) = 1, the value of y(10) computed by this method is ______ (correct to two decimal places).

A. 21.5937
B. 25.937
C. 2.5937
D. 1 21.15937
Answer» D. 1 21.15937
Discussion
36.

Gauss seidel method is used to solve the following equations (as per the given order):
x1 + 2x2 + 3x3 = 1
2x1 + 3x2 + x3 = 1
3x1 + 2x2 + x3 = 1
Assuming initial guess as x1 = x2 = x3 = 0, the value of x3 after the first iteration is ______.

A. 1.555
B. 15.555
C. 10.555
D. None of the above
Answer» B. 15.555
Discussion
37.

Consider an ordinary differential equation
dw
 = 0 - iz
dz

If x = x0 at t = 0 , the increment in x calculated using Runge-Kutta fourth order multi-step method with a step size of t = 0.2 is

A. 0.22
B. 0.44
C. 0.66
D. 0.88
Answer» E.
Discussion
38.

Match the items in columns I and II.
Column I
P. Gauss-Seidel method
Q. Forward Newton-Gauss method
R. Runge-Kutta method
S. Trapezoidal Rule
Column II
1. Interpolation
2. Non-linear differential equations
3. Numerical integration
4. Linear algebraic equations

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
39.

The probability of obtaining at least two "SIX" in throwing a fair dice 4 times is

A.
B.
C.
D.
Answer» C.
Discussion
40.

The chance of a student passing an exam is 20%. The chance of a student passing the exam and getting above 90% marks in it is 5%, Given that a student passes the examination, the probability that the student gets above 90% marks is

A.
B.
C.
D.
Answer» C.
Discussion
41.

If P(X) =
1
, P(Y) =
1
and P(X Y) =
1
,the value of P(Y/X) is
4312
A.
B.
C.
D.
Answer» D.
Discussion
42.

The probability that a student knows the correct answer to a multiple choice question is 2/3. If the student does not known the answer, then the student guesses the answer. The probability of the guessed answer being correct is 1/4. Given that the student has answered the question correctly, the conditional probability that the student known the correct answer is

A.
B.
C.
D.
Answer» E.
Discussion
43.

F(s) is the Laplace transform of the function f(t) = 2t e t
F(1) is _______(correct to two decimal places.)

A. 0.4
B. 0.5
C. 1.5
D. 0.9
Answer» C. 1.5
Discussion
44.

An analytic function of a complex variable z = x + iy is expressed as f(z) = u(x, y)+ iv(x, y), where i = -1. If u(x, y) = x2 - y2, then expression for v(x, y) in terms of x, y and a general constant c would be

A. xy + c
B.
C. 2xy + c
Answer» D.
Discussion
45.

Match the correct pairs
Numerical Integration SchemeOrder of Fitting Polynomial
P. Simpson's 3/8 Rule1. First
Q. Trapezoidal Rule2. Second
R. Simpson's 1/3 Rule3. Third
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
46.

An analytic function of a complex variable z = x + iy is expressed as f(z) = u(x, y) + i v(x, y) where i = -1. If u = xy, the expression for v should be

A.
B.
C.
Answer» D.
Discussion
47.

By a change of variable x(u, y) = uv, y(u, v) = v/u is double integral, the integrand f(x, y) changes to f(uv, v/u) (u, v). Then, (u, v) is

A. 2 v / u
B. 2 uv
C. v
D.
E. 1
Answer» B. 2 uv
Discussion
48.

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 b af(x)dx

A. f( )(b a)
B. f(b)( a)
C. f(a)(b )
D. 0
Answer» B. f(b)( a)
Discussion
49.

The value of the integral
-
sin x
dx is
x + 2x + 2

evaluated using contour integration and the residue theorem is

A.
Answer» B.
Discussion
50.

The value of the integral 2 0x 0dydx

A.
Answer» C.
Discussion