The span of a Astroid is increased along both the x and y axes equally. Then the maximum value of: z = x + y along the Astroid is?

The scaling of Astroid is irrelevant

Consider the points closest to the origin on the planes x + y + z = a.

The closest point travels nearer as a is increased

The closest point travels farther as a is increased

The closest point travels nearer as a is increased

The closest point is independent of a as a is not there in the expression of the gradient.

Varies as a2, away from the origin.

Maximum value of a 3-d plane is to be found over a circular region. Which of the following happens if we increase the radius of the circular region.

Maximum value increases and minimum value goes lesser

Which one of these is the right formula for the Lagrange multiplier with more than one constraint?

Cannot be applied to more than one constraint function.

Explore topic-wise MCQs in Engineering Mathematics.

This section includes 8 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.	The extreme value of the function f(x₁, x₂, .. x_n)= ( frac{x_1}{2^0}+ frac{x_2}{2^1}+ + frac{x_n}{2^{n-1}} ) With respect to the constraint ^m_i=1 (x_i)² = 1 where m always stays lesser than n and as m,n tends to infinity is?
A.	1
B.	( frac{2}{3 sqrt{3}} )
C.	2
D.	1 2
Answer» C. 2

Discussion

2.	The span of a Astroid is increased along both the x and y axes equally. Then the maximum value of: z = x + y along the Astroid is?
A.	Increases
B.	Decreases
C.	Invariant
D.	The scaling of Astroid is irrelevant
Answer» B. Decreases

Discussion

3.	Consider the points closest to the origin on the planes x + y + z = a.
A.	The closest point travels farther as <b>a</b> is increased
B.	The closest point travels nearer as <b>a</b> is increased
C.	The closest point is independent of <b>a</b> as <b>a</b> is not there in the expression of the gradient.
D.	Varies as <b>a<sup>2</sup></b>, away from the origin.
Answer» B. The closest point travels nearer as <b>a</b> is increased

Discussion

4.	Find the points on the plane x + y + z = 9 which are closest to origin.
A.	(3,3,3)
B.	(2,1,3)
C.	(2,2,2)
D.	(3,4,1)
Answer» B. (2,1,3)

Discussion

5.	Maximum value of a 3-d plane is to be found over a circular region. Which of the following happens if we increase the radius of the circular region.
A.	Maximum value is invariant
B.	Maximum value decreases
C.	Maximum value increases and minimum value goes lesser
D.	minimum value goes higher
Answer» D. minimum value goes higher

Discussion

6.	Which one of these is the right formula for the Lagrange multiplier with more than one constraint?
A.	f = ( )<sup>2</sup> * <sub>g1</sub> + <sub>g2</sub>
B.	Cannot be applied to more than one constraint function.
C.	f = * <sub>g1</sub> + * <sub>g2</sub>
D.	f = * <sub>g1</sub> + <sub>g2</sub>
Answer» D. f = * <sub>g1</sub> + <sub>g2</sub>

Discussion

7.	Maximize the function x + y z = 1 with respect to the constraint xy=36.
A.	0
B.	-8
C.	8
D.	No Maxima exists
Answer» E.

Discussion

8.	In a simple one-constraint Lagrange multiplier setup, the constraint has to be always one dimension lesser than the objective function.
A.	True
B.	False
Answer» C.

Discussion

Explore topic-wise MCQs in Engineering Mathematics.

The extreme value of the function f(x1, x2, .. xn)= ( frac{x_1}{2^0}+ frac{x_2}{2^1}+ + frac{x_n}{2^{n-1}} ) With respect to the constraint mi=1 (xi)2 = 1 where m always stays lesser than n and as m,n tends to infinity is?

The span of a Astroid is increased along both the x and y axes equally. Then the maximum value of: z = x + y along the Astroid is?

Consider the points closest to the origin on the planes x + y + z = a.

Find the points on the plane x + y + z = 9 which are closest to origin.

Maximum value of a 3-d plane is to be found over a circular region. Which of the following happens if we increase the radius of the circular region.

Which one of these is the right formula for the Lagrange multiplier with more than one constraint?

Maximize the function x + y z = 1 with respect to the constraint xy=36.

In a simple one-constraint Lagrange multiplier setup, the constraint has to be always one dimension lesser than the objective function.

The extreme value of the function f(x₁, x₂, .. x_n)= ( frac{x_1}{2^0}+ frac{x_2}{2^1}+ + frac{x_n}{2^{n-1}} ) With respect to the constraint ^m_i=1 (x_i)² = 1 where m always stays lesser than n and as m,n tends to infinity is?