Explore topic-wise MCQs in Engineering Mathematics.

This section includes 9 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.

f(x, y) = sin(y/x)x3 + x2y find the value of fx + fy at (x,y)=(4,4).

A. 0
B. 78
C. 4<sup>2</sup> . 3(sin(1) + 1)
D. -12
Answer» D. -12
Discussion
2.

A foil is to be put as shield over a cake (circular) in a shape such that the heat is even along any diameter of the cake.
Given that the heat on cake is proportional to the height of foil over cake, the shape of the foil is given by

A. f(x, y) = sin(y/x)x<sup>2</sup> + xy
B. f(x, y) = x<sup>2</sup> + y<sup>3</sup>
C. f(x, y) = x<sup>2</sup>y<sup>2</sup> + x<sup>3</sup>y<sup>3</sup>
D. not possible by any analytical function
Answer» C. f(x, y) = x<sup>2</sup>y<sup>2</sup> + x<sup>3</sup>y<sup>3</sup>
Discussion
3.

For homogeneous function the linear combination of rates of independent change along x and y axes is __________

A. Integral multiple of function value
B. no relation to function value
C. real multiple of function value
D. depends if the function is a polynomial
Answer» D. depends if the function is a polynomial
Discussion
4.

For homogeneous function with no saddle points we must have the minimum value as _____________

A. 90
B. 1
C. equal to degree
D. 0
Answer» E.
Discussion
5.

For a homogeneous function if critical points exist the value at critical points is?

A. 1
B. equal to its degree
C. 0
D. -1
Answer» D. -1
Discussion
6.

(f(x, y)=x^9.y^8sin( frac{x^2+y^2}{xy})+cos( frac{x^3}{x^2y+yx^2})x^{11}.y^6 ) Find the value of fx at (1,0).

A. 23
B. 16
C. 17(sin(2) + cos(1 2))
D. 90
Answer» D. 90
Discussion
7.

A non-polynomial function can never agree with euler s theorem.

A. True
B. false
Answer» C.
Discussion
8.

f(x, y)= ( frac{x^3+y^3}{x^{99}+y^{98}x+y^{99}} ) find the value of fy at (x,y) = (0,1).

A. 101
B. -96
C. 210
D. 0
Answer» C. 210
Discussion
9.

f(x, y) = x3 + xy2 + 901 satisfies the Euler s theorem.

A. True
B. False
Answer» C.
Discussion