$P(A'|B) = 1 - P(A|B)$

• A) False
• B) True
• C)
• D)

If B is a subset of A then $$P(A|B) = 1$$ .

• A) Flase
• B) True
• C)
• D)

Among 20 people, 15 either swim or jog or both. If 5 swim and 6 swim and jog, how many jog ?

• A) 46
• B) 16
• C) 24
• D) 6

An urn contains six red and nine blue balls. What is the probability that a ball chosen from the urn is blue?

• A) 9/15
• B) 15/9
• C) 15/6
• D) 6/15

There are 5 girls students and 20 boys students in a class. How many students are there in total ?

• A) 25
• B) 15
• C) 4
• D) 100

Suppose that A and B are events in a sample space S. If A and B are disjoint, could P(A)=0.6 and P(B)=0.5?

• A) No
• B) Yes
• C)
• D)

[Math Processing Error]$P(A|B) = \frac{{P(A \cap B)}}{{P(B)}},\,\,\,\,\,where\,\,.............$

• A) [Math Processing Error]$P(B) > 0$
• B) [Math Processing Error]$P(B) < 0$
• C) [Math Processing Error]$P(B) > 1$
• D) [Math Processing Error]$P(B) = 0$

If A is a subset of B then [Math Processing Error]$$P(A|B) = \frac{{P(A)}}{{P(B)}}$$ .

• A) False
• B) True
• C)
• D)

If one event can occur in {n_1} ways, a second event can occur in {n_2} ways, a third event can occur in {n_3} ways, how ways all of the events can occur in the order?

• A) {n_1} + {n_2} + {n_3}
• B) {n_1}.{n_2}.{n_3}
• C)
• D)

If one event can occur in {n_1} ways, a second event can occur in {n_2} ways, a third event can occur in {n_3} ways, how ways in which exactly one of the events can occur?

• A) {n_1}.{n_2}.{n_3}
• B) {n_1} + {n_2} + {n_3}
• C)
• D)

If A and B are finite sets then \[n(A \cup \,B) = \_\_\_\_\_\_.\]

• A) \[n(A) + n(B) - n(A \cap \,B)\]
• B) \[n(A) + n(B) + n(A \cap \,B)\]
• C) \[n(A) + n(B)\]
• D) \[n(A) + n(B) - n(A \cup \,B)\]

There are three bus lines between A and B, and two bus lines between B and C. Find the number of ways a person can travel round trip by bus from A to C by way of B ?

• A) 36
• B) 6
• C) 5
• D) 10

If there are 5 different optional courses in English and 3 different optional courses in Maths. Choices for a student who wants to take one optional course _____?

• A) 7
• B) 9
• C) 8
• D) 5

A student can choose a computer project from one of the two lists. The two lists contain 12 and 18 possible projects, respectively. How many possible projects are there to choose from ?

• A) 30
• B) 18
• C) 216
• D) 12

The last step of describing algorithms formally is?

• A) An end statement.
• B) The output variable names.
• C) The input variable names.
• D) The name of the algorithm.

$${\text{The graph of the equation }}r\, = \,a(1 - \cos \,\theta ){\text{ is symmetric about - - - - - - - - - }}{\text{.}}$$

• A) $${\text{None of these}}{\text{.}}$$
• B) $${\text{pole}}$$
• C) $${\text{initial line}}$$
• D) $${\text{y - axis}}$$

$${\text{For a vector valued function }}\vec r(t){\text{ }} = {\text{ }}\sqrt 2 t{\text{ }}i + (t + 1){\text{ }}j - k{\text{ then lenght of }}\vec r(t){\text{ }}$$

• A) $$\left\| {r(t)} \right\| = \sqrt {2{t^2} + {{(t + 1)}^2} + 1}$$
• B) $$\left\| {r(t)} \right\| = \sqrt {{t^2} + {{(t + 1)}^2} + 1}$$
• C) $$\left\| {r(t)} \right\| = \sqrt {4{t^2} - {{(t + 1)}^2} - 1}$$
• D) $$\left\| {r(t)} \right\| = \sqrt {4{t^2} + {{(t + 1)}^2} - 1}$$

$\begin{gathered} {\text{Let }}\bar r(t)\,\, = \,\,2{t^2}\,\hat i\,\, + \,\,3{t^3}\,\,\hat j,\,\,{\text{then}}\,\,\bar r'(1)\,\, = \,\,4\,\hat i\,\, + \,\,9\,\hat j. \hfill \ \hfill \\ \end{gathered}$

• A) $True$
• B) $False$
• C)
• D)

$$The\,point\,( - \,42,\,\,{35^0}\,\,)\,\,{\text{and the point - - - - - - - - - - - - - - }}\,{\text{are the same in polar system}}{\text{.}}$$

• A) $$(\,42,\,\,{215^0}\,)$$
• B) $$(\,\,42,\,\,{35^0}\,\,)$$
• C) $$(\,122,\,\,{215^0}\,\,)$$
• D) $$(122,\,\,{35^0}\,\,)$$

$${\text{In polar coordinates, }}\iint\limits_R {f(x,\,\,y)\,\,dx\,dy\,\, = \,\, - - - - - - }\,$$

• A) $$\iint\limits_G {f(r\,\cos \theta ,\,r\,\sin \,\theta )\,rdr\,d\theta }\,$$
• B) $$\int\limits_G {f(r\,\cos \theta ,\,r\,\sin \,\theta )\,rdr\,d\theta }$$
• C) $$\iint\limits_G {f(r\,\cos \theta ,\,r\,\sin \,\theta )\,dr\,d\theta }\,\,$$
• D) $$\iint\limits_G {f(r\,\sin \,\theta ,\,\,r\,\cos \theta )\,rdr\,d\theta }$$