2nd Year Mathematics Chapter 11 TestUNIT 11: VECTOR VALUED FUNCTIONS AND THEIR DERIVATIVES

Q1. Multiple choice questions (Attempt all · 10 × 1 = 10)

1. A scalar function assigns a ...... to each point in its domain.

   1. Vector

   2. Single real number

   3. Matrix

   4. Complex vector

2. Vector-valued functions are useful in:

   1. Engineering

   2. Physics

   3. Computer graphics

   4. All of these

3. Vector-valued functions can be used to model:

   1. Position

   2. Velocity

   3. Force

   4. All of these

4. Which of the following mathematical functions is classified as a scalar function?

   1. f(t)=(3t²-5)²

   2. f(t)=(3t²+5)²

   3. f(t)=(3t²-4)²

   4. f(t)=(3t²-3)²

5. The derivative of a vector-valued function provides the instantaneous:

   1. Position

   2. Rate of change

   3. Temperature

   4. Distance only

6. In the satellite example, the x-coordinate is:

   1. 4000 sint

   2. 3000t

   3. 4000 cos t

   4. 3000 cos t

7. A vector-valued function takes ...... as input and returns ...... as output.

   1. Vector, scalar

   2. Scalar, vector

   3. Scalar, scalar

   4. Vector, vector

8. To construct a vector-valued function, the first step is to:

   1. Differentiate the function

   2. Determine the components

   3. Find the magnitude

   4. Find the inverse

9. In the satellite example, the z-coordinate is:

   1. 4000 cos t

   2. 4000 sin t

   3. 3000 t

   4. 3000 cos t

10. The components of a vector-valued function are themselves:

    1. Vector functions

    2. Constant vectors

    3. Scalar functions

    4. Matrices