Vector Calculus: PYQ | Engineering Mathematics - Civil Engineering (CE) PDF Download

Q.1. If the vector function Vector Calculus: PYQ | Engineering Mathematics - Civil Engineering (CE) is irrotational, then the values of the constants k1, k2 and k3 respectively, are
(a) 0.3, –2.5, 0.5
(b) 0.0, 3.0, 2.0
(c) 0.3, 0.33, 0.5
(d) 4.0, 3.0, 2.0

Correct Answer is option (b)
Vector Calculus: PYQ | Engineering Mathematics - Civil Engineering (CE)


Q.2. The magnitude of the gradient for the function f(x, y, z) = x2 + 3y2 + z3 at the point (1, 1, 1) is
(a) 7
(b) 9
(c) 12
(d) 5

Correct Answer is option (a) 
Gradient of function f is
Vector Calculus: PYQ | Engineering Mathematics - Civil Engineering (CE)
Gradient at P(1, 1, 1) is = Vector Calculus: PYQ | Engineering Mathematics - Civil Engineering (CE)
Magnitude of gradient
= Vector Calculus: PYQ | Engineering Mathematics - Civil Engineering (CE)


Q.3. For a right angled triangle, if the sum of the lengths of the hypotenuse and a side is kept constant, in order to have maximum area of the triangle, the angle between the hypotenuse and the side is________(o)
(a) 12
(b) 36
(c) 30
(d) 45

Correct Answer is option (c)
Le
x (opposite side
y (adjacent side
z (hypotenuse) of a right angled triangle
Given Z + y = K(constant) ......(1) and angle between them say θ then Area,
Vector Calculus: PYQ | Engineering Mathematics - Civil Engineering (CE)
In order to have maximum area, Vector Calculus: PYQ | Engineering Mathematics - Civil Engineering (CE)
Vector Calculus: PYQ | Engineering Mathematics - Civil Engineering (CE)


Q.4. The directional derivative of Vector Calculus: PYQ | Engineering Mathematics - Civil Engineering (CE) in the direction of the unit vector at an angle of π/4 with y-axis at point (1,1), is given by _____.
(a) 3
(b) 5
(c) 8
(d) 4

Correct Answer is option (a)
Gradient of function is :
Vector Calculus: PYQ | Engineering Mathematics - Civil Engineering (CE)
Gradient at (1, 1), Vector Calculus: PYQ | Engineering Mathematics - Civil Engineering (CE)
So, representation of unit vector in cartesion is,
= Vector Calculus: PYQ | Engineering Mathematics - Civil Engineering (CE)
∴ Directions of derivative = Vector Calculus: PYQ | Engineering Mathematics - Civil Engineering (CE)
Vector Calculus: PYQ | Engineering Mathematics - Civil Engineering (CE)


Q.5. If Vector Calculus: PYQ | Engineering Mathematics - Civil Engineering (CE)
(a) 1
(b) 2

(c) 3

(d) 4

Correct Answer is option (c)
Given , the vector field
Vector Calculus: PYQ | Engineering Mathematics - Civil Engineering (CE)
Divergence of Vector Vector Calculus: PYQ | Engineering Mathematics - Civil Engineering (CE) is
Vector Calculus: PYQ | Engineering Mathematics - Civil Engineering (CE)
Vector Calculus: PYQ | Engineering Mathematics - Civil Engineering (CE)


Q.6. A vector field D = Vector Calculus: PYQ | Engineering Mathematics - Civil Engineering (CE) exists inside a cylindrical region enclosed by the surfaces p = 1, z = 0 and z = 5. Let S be the surface bounding this cylindrical region. The surface integral of this field on S Vector Calculus: PYQ | Engineering Mathematics - Civil Engineering (CE) is _____. (Fill in the Blank Type Question)

In the given vector field,
Vector Calculus: PYQ | Engineering Mathematics - Civil Engineering (CE)
By using divergence theorem
Vector Calculus: PYQ | Engineering Mathematics - Civil Engineering (CE)
Vector Calculus: PYQ | Engineering Mathematics - Civil Engineering (CE)
Vector Calculus: PYQ | Engineering Mathematics - Civil Engineering (CE)

The document Vector Calculus: PYQ | Engineering Mathematics - Civil Engineering (CE) is a part of the Civil Engineering (CE) Course Engineering Mathematics.
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