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Test: Differential Calculus - Civil Engineering (CE) MCQ


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20 Questions MCQ Test Engineering Mathematics - Test: Differential Calculus

Test: Differential Calculus for Civil Engineering (CE) 2024 is part of Engineering Mathematics preparation. The Test: Differential Calculus questions and answers have been prepared according to the Civil Engineering (CE) exam syllabus.The Test: Differential Calculus MCQs are made for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Differential Calculus below.
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Test: Differential Calculus - Question 1

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Test: Differential Calculus - Question 2

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Test: Differential Calculus - Question 3

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f is a homogeneous function of degree one

Test: Differential Calculus - Question 4

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It is a homogeneous function of degree n

Test: Differential Calculus - Question 5

Match the List–I with List–II.

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It is a homogeneous function of
degree 2.

Test: Differential Calculus - Question 6

If an error of 1% is made in measuring the major and minor axes of an ellipse, then the percentage error in the area is approximately equal to

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Let 2 a and 2 b be the major and minor axes of the ellipse

Test: Differential Calculus - Question 7

Consider the Assertion (A) and Reason (R) given below:

Reason (R): Given function u is homogeneous of degree 2 in x and y.
Of these statements

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Given that  u = xyf(y/x) Since it is a homogeneous function of degree 2.

Test: Differential Calculus - Question 8

If u = x log xy, where x3 + y3 + 3xy = 1, then du/dx is equal to

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Given that u = x log xy ... (i)

Test: Differential Calculus - Question 9

f(x) = x2e-x is increasing in the interval

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Test: Differential Calculus - Question 10

The minimum distance from the point (4, 2) to the parabola y2 =​ 8x is

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Let the point closest to (4, 2) be (2t2,4)

Test: Differential Calculus - Question 11

The co-ordinates of the point on the parabola y = x2 + 7x + 2 which is closest to the straight line y = 3x - 3, are

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Let the required point be P(x, y). Then, perpendicular distance of P(x, y) from y -  3x - 3 = 0 is

Test: Differential Calculus - Question 12

The shortest distance of the point (0, c), where 0 ≤ c ≤ 5, from the parabola y = x2 is 

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Let A (0,c) be the given point and P (x, y) be any point on y = x2

Test: Differential Calculus - Question 13

The set of equations

has infinite solutions, if a=

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The given system of equations can be expressed in the matrix form:

The augmented matrix is

For infinite solutions

Test: Differential Calculus - Question 14

The maximum value of ( 1/x)x is 

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f (x) = (1 / x)x

f’ (x) = (1 / x)x (log (1 / x) – 1))

f’ (x) = 0

log (1 / x) – 1 = log e

1 / x = e

x = 1 / e

The maximum value of function is e1/e.

Test: Differential Calculus - Question 15

The minimum value of 3x+5y such that:

is ___________.

Detailed Solution for Test: Differential Calculus - Question 15

Comparing (ii) and (iii)

Hence, Checking at corner points:

At (0, 0) Z=0 so minimum value will be 0

Test: Differential Calculus - Question 16

The condition for which the eigenvalues of the matrix

are positive, is

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All Eigen values of  are positive

2 > 0

∴2 × 2 leading minor must be greater than zero

Test: Differential Calculus - Question 17

The maximum value of f ( x) = (1 + cos x) sin x is

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Test: Differential Calculus - Question 18

The solution to the system of equations

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Test: Differential Calculus - Question 19

The greatest value of

on the interval [0, π/2] is 

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Test: Differential Calculus - Question 20

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

Detailed Solution for Test: Differential Calculus - Question 20

Augmented matrix is

will have solution if a=0 as Rank A= Rank (aug. A)

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