MTH301 Midterm Solved MCQs by Junaid

5

Q1. Every point in three dimensional space can be described by -------- coordinates.

1. Two
2. Three
3. Four
4. Eight

Correct answer: Three

Q2. What are the direction cosines for the line joining the points (1, 3, 2) and (7, -2, 3)?

1. 1 , 3 and 2
2. 7 , 6 and 6

and

and

Q3. The angles which a line makes with positive x ,y and z-axis are known as ------------

1. Direction cosines
2. Direction ratios
3. Direction angles

Correct answer: Direction angles

Q4. Which of the following is geometrical representation of the equation dimensional space?

1. A point on y-axis (Farhan)
2. Plane parallel to xy-plane
3. Plane parallel to yz-axis
4. Plane parallel to xz-plane (Ali)

Correct answer: Plane parallel to xz-plane (Ali)

y  4 , in three

1. df

dt  10t 2  8t 1

Q8. For a function

f (x, y, z) , the equation 2 f 2 x  2 f

2 y  2 f

2z  0 is known as -------------

1. Gauss Equation
2. Euler’s equation
3. Laplace’s Equation
4. Stoke's Equation

Correct answer: Laplace’s Equation

Q9. Magnitude of vector  is 2, magnitude of vector  is 3 and angle between them when a

b

placed tail to tail is 45 degrees. What is a . b ?

1. 4.5
2. 6.2
3. 5.1
4. 4.2

Correct answer: 4.2

Q10. Is the function f (x, y) continuous at origin? If not, why?

f (x, y)  xy x2  y2

1. f (x, y) is continuous at origin

lim ( x, y)(0, 0) f (x, y) does not exist

equal. f (0, 0) is defined and lim ( x, y)(0, 0) f (x, y) exists but these two numbers are not

Q11. Let R be a closed region in two dimensional space. What does the double integral over R calculates?

1. Area of R.??(ali)
2. Radius of inscribed circle in R
3. Distance between two endpoints of R.
4. None of these

Correct answer: Radius of inscribed circle in R

Q12. Which of the following formula can be used to find the Volume of a parallelepiped with adjacent edges formed by the vectors a , b and c ?

a  b  c

a g b gc

a g b  c

a  b gc