MTH301 Midterm Past Paper 2010 Session 3

Q1. Which of the following number is associated to each point on a co-ordinate line? (1 marks)

1. An integer
2. A real number
3. A rational number
4. A natural number

Correct answer: A real number

Q2. If (1 marks)

a > , then the parabola y ax bx c opens in which of the following direction?

1. Positive x - direction
2. Negative x - direction
3. Positive

Correct answer: Positive x - direction

y

direction

1. Negative

y - direction

Q3. Rectangular co-ordinate of a point is (1 marks)

(1, 3, 2) . What is its spherical co-

ordinate?

2 2, π π

2 2, π π

2 2, π π

2, π π

Q4. If a function is not defined at some point, then its limit ----------- exist at that point. (1 marks)

1. 
2. Always
3. 
4. Never
5. 
6. May

Q5. Suppose (1 marks)

xy f x y x e . Which one of the statements is correct?

xy f x e y

xy f x e y

xy f x e y

xy f x ye y

Q6. If (1 marks)

ln f x y x y y x

then f

x

2xy x

2 y x

2xy x

2 y x

Q7. Suppose (1 marks)

f x y xy y where x t and y t . Which one of the following

is true?

df t dt = −

df t t dt = −

df t dt =

df t t dt = −

Q8. Is the function (1 marks)

f x y continuous at origin? If not, why?

If x and y f x y Otherwise

f x y is continuous at origin (0, 0) f is not defined

(0, 0) f is defined but (0, 0) lim x y f x y

does not exist

(0, 0) f is defined and (0, 0) lim x y f x y

exists but these two numbers are not equal.

Q9. What is the relation between the direction of gradient at any point on the surface to the tangent plane at that point ? (1 marks)

1. 
2. parallel
3. 
4. perpendicular
5. 
6. opposite direction
7. 
8. No relation between them.

Correct answer: perpendicular

Q10. Two surfaces are said to intersect orthogonally if their normals at every point common to them are ---------- (1 marks)

1. perpendicular
2. parallel
3. in opposite direction

Correct answer: in opposite direction