MCQOPTIONS

Explore topic-wise MCQs in Engineering Mathematics.

This section includes 14 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.	Observe the figure. It is given that the function has no limit as (x, y) (0 ,0) along the paths given in the figure. Then which of the following could be f(x, y)
A.	(f(x,y) = frac{x^7.y^8}{(x+y)} )
B.	f(x,y) = x<sup>2</sup>y<sup>7</sup>
C.	(f(x,y) = frac{xy^2}{(x^2+y^2)} )
D.	(f(x,y) = frac{x^6.y^2}{(y^5+x^{10})} )
Answer» E.

2.	Two men on a 3-D surface want to meet each other. The surface is given by (f(x,y)= frac{x^6.y^7}{x^{13}+y^{13}} ). They make their move horizontally or vertically with the X-Y plane as their reference. It was observed that one man was initially at (400, 1600) and the other at (897, 897). Their meet point is decided as (0, 0). Given that they travel in straight lines, will they meet?
A.	They will meet
B.	They will not meet
C.	They meet with probability <sup>1</sup> <sub>2</sub>
D.	Insufficient information
Answer» C. They meet with probability <sup>1</sup> <sub>2</sub>

3.	Two men on a 3-D surface want to meet each other. The surface is given by (f(x,y)= frac{x^{-6}.y^7}{x+y} ). They make their move horizontally or vertically with the X-Y plane as their reference. It was observed that one man was initially at (200, 400) and the other at (100, 100). Their meet point is decided as (0, 0). Given that they travel in straight lines, will they meet?
A.	They will meet
B.	They Will not meet
C.	They meet with probability <sup>1</sup> <sub>2</sub>
D.	Insufficient information
Answer» C. They meet with probability <sup>1</sup> <sub>2</sub>

4.	Given that limit exists (lt_{(x,y,z) rightarrow(0,0,0)} left ( frac{cos( frac{ pi}{2}-x).tan(y).cot( frac{ pi}{2}-z)}{sin(x).sin(y).sin(z)} right ) )
A.	99
B.	0
C.	1
D.	100
Answer» D. 100

5.	Given that limit exists find (lt_{(x,y,z) rightarrow(2,2,2)} left ( frac{ln(1+ frac{xy-2x-y+z}{xz-2x-6z+12}+ frac{xz-5x-2z+10}{xy-7y-2x+14}}{(x-2)(y-2)(z-2)} right ) )
A.
B.	1
C.	0
D.	ln(<sup>4</sup> <sub>5</sub>)
Answer» B. 1

6.	Given that limit exists find (lt_{(x,y,z) rightarrow(-1,-1,-1)} frac{tan((x-1)(y-2)(z-3))}{(x-1)(y-6)(z+7)} )
A.	1
B.	<sup>1</sup> <sub>2</sub>
C.	<sup>1</sup> <sub>7</sub>
D.	<sup>2</sup> <sub>7</sub>
Answer» E.

7.	Given that limit exist find (lt_{(x,y,z) rightarrow(-9,-9,-9)} frac{tan((x+9)(y+11)(z+7))}{(x+9)(y+10)} )
A.	2
B.	1
C.	4
D.	3
Answer» D. 3

8.	Given that limit exists find (lt_{(x,y,z) rightarrow(-2,-2,-2)} frac{sin((x+2)(y+5)(z+1))}{(x+2)(y+7)} )
A.	1
B.	<sup>3</sup> <sub>5</sub>
C.	<sup>1</sup> <sub>2</sub>
D.	0
Answer» C. <sup>1</sup> <sub>2</sub>

9.	Find (lt_{(x,y,z,w) rightarrow(3,1,1,11)} frac{x^4+y^2+z^2+2x^2y+2yz+2x^2z-(w)^2}{x^2+y+z-w} )
A.	700
B.	701
C.	699
D.	22
Answer» E.

10.	Find (lt_{(x,y,z,w) rightarrow(0,0,0,0)} frac{x^{-6}.y^2.(z.w)^3}{x+y^2+z-w} )
A.	1990
B.
C.	Does Not Exist
D.	0
Answer» D. 0

11.	Find (lt_{(x,y,z) rightarrow(2,2,4)} frac{x^2+y^2-z^2+2xy}{x+y-z} )
A.
B.	123
C.	9098
D.	8
Answer» E.

12.	Find (lt_{(x,y,z) rightarrow(0,0,0)} frac{sin(x).sin(y)}{x.z} )
A.
B.	<sup>1</sup> <sub>3</sub>
C.	1
D.	Does Not Exist
Answer» E.

13.	Find (lt_{(x,y,z) rightarrow(0,0,0)} frac{y^2.z^2}{x^3+x^2.(y)^{ frac{4}{3}}+x^2.(z)^{ frac{4}{3}}} )
A.	1
B.	0
C.
D.	Does Not Exist
Answer» E.

14.	Two men on a surface want to meet each other. They have taken the point (0, 0) as meeting point. The surface is 3-D and its equation is f(x,y) = ( frac{x^{ frac{-23}{4}}y^9}{x+(y)^{ frac{4}{3}}} ). Given that they both play this game infinite number of times with their starting point as (908, 908) and (90, 180) (choosing a different path every time they play the game). Will they always meet?
A.	They will not meet every time
B.	They will meet every time
C.	Insufficient information
D.	They meet with probability <sup>1</sup> <sub>2</sub>
Answer» B. They will meet every time