1. Which rule does MATLAB use while differentiating a set of functions?

a) u-v rule

b) by parts

c) no pre-defined rule

d) not possible

Explanation: If we give an argument within our command diff() which is a product of multiple functions or division of two functions; we will get the result that will be generated according to the u-v rule. This makes MATLAB very versatile for the applications concerning differentiation.

2. There is no difference between a difference equation and a differential equation.

a) True

b) False

Explanation: There are many differences between a difference equation and a differential equation. But the most important would be that a difference equation takes finite steps of changes of our changing variable while a differential equation takes an infinitesimal change in our changing variable.

3. For the existence of the n^{th} (n is varying from 1 to until the derivative is becoming 0) derivative of an equation, the equation should have __________

a) Initial values

b) At least one independent variable

c) At least one dependent variable

d) No such condition

Explanation: Derivatives are calculated with respect to a change in an independent variable. Hence for deriving a derivative- the equation should have at least one independent variable so that we can find the derivative with respect to a change in that independent variable.

4. What will be the output of the following code?

syms x;diff(sin(x)\x^{2})

a) (2*x)/sin(x) – (x^{2}*cos(x))/sin(x)^{2}

b) cos(x)/x^{2} – (2*sin(x))/x^{3}

c) x^{2}*cos(x) + 2*x*sin(x)

d) Error

Explanation: We observe that sin(x)\x

^{2}has a back slash. This, in MATLAB, implies that x

^{2}is divided by sin(x). Hence the answer is (2*x)/sin(x) – (x

^{2}*cos(x))/sin(x)

^{2}. If it would have been a front slash, the answer would have been cos(x)/x

^{2}– (2*sin(x))/x

^{3}. If there was a ‘*’ sign, the answer would have been ‘x

^{2}*cos(x) + 2*x*sin(x)’.

5. What is the data type of y?

y=diff(x^{2}*cos(x) + 2*x*sin(x))

a) Symbolic

b) Double

c) Array

d) Symbolic Array

Explanation: Every element saved in the workspace is stored as an array. The class of the array will be symbolic for y since we haven’t specified a value for x. If we give a value of x, y will be stored as Double.

6. The output for diff(p^{2},q) is _______

a) 0

b) 2*p

c) 2 dp/dq

d) Error

Explanation: We are differentiating the function ‘p

^{2}’ with respect to q. Hence the value will be 0. The 2

^{nd}argument in the diff() command is the variable, with respect to which- we differentiate our function.

7. What does the following code do?

syms m,y,x,c;

y=mx+c;

diff(y)

a) Calculate m

b) Calculate slope

c) Error

d) Calculate divergence

Explanation: While using syms, we can’t instantiate multiple symbolic variables using a comma. We will have to enter them with space in between. Hence MATLAB returns an error. If we remove the comma, the code will calculate the slope of ‘y=mx+c’.

8. What is the nature of ode45 solver?

a) 2^{nd} ordered R-K solver

b) 4^{th} ordered R-K solver

c) 1^{st} order R-K solver

d) Adams solver

Explanation: The ode45 solver is an Ordinary Differential Equation solver in MATLAB which is used to solve a differential equation using the Runga-Kutta or R-K method upto 4

^{th}order. This is an inbuilt ODE solver in MATLAB.

9. Ordinary differential equations having initial values ____________

a) Can be solved

b) Cannot be solved

c) Can be modelled

d) Has a trivial solution

Explanation: We have 8 different Ordinary differential equations solvers in MATLAB. They take the initial values, if at all present, into account while solving the Differential equation of interest. Hence, systems which follow a differential equation can be modelled and observed using MATLAB.

10. The current characteristics of RC networks are better analyzed by Laplace than differentiation methods.

a) True

b) False

Explanation: We use the Laplace method to ease the process of solving a differential equation. But, with the help of MATLAB- we can solve them very fast. So, it is obvious to use the ODE solver to calculate the current through the capacitor in RC networks and get a time response.