Question 1 :
For non zero vectors $a,b$ and $c$, if $a+b+c=0$ then which relation true:-

Question 3 :
Two vectors $a$ and $b$ are said to be equal, if<br>I. $|a| = |b|$<br>II. they have same or parallel support.<br>III. the same sense.<br>Which of the following is true?

Question 4 :
Let $\vec{a}=3\hat{i}+2\hat{j}+2\hat{k}, b=\hat{i}+2\hat{j}-2\hat{k}$. Then a unit vector perpendicular to both $\vec{a}-\vec{b}$ and $\vec{a}+\vec{b}$ is :

Question 5 :
If $p=\hat {i} + \hat{j}, q=4\hat{k}-\hat{j}$ and $r=\hat{i}+\hat{k}$, then the unit vector in the direction of $3p+q-2r$ is

Question 6 :
Cosine of an angle between the vectors $\vec{a}+\vec{b}$ and $\vec{a}-\vec{b}$ if $|\vec{a}|=2, |\vec{b}|=1$ and $\vec{a}$ ^ $\vec{b}=60^o$ is?

Question 7 :
If A and B are two events such that $P\left ( A \right )&gt; 0$ and $P\left ( B \right )\neq 1$, then $P\left ( \bar{A}/\bar{B} \right )= $

Question 8 :
A four-digit number is formed by using the digits 1, 2, 4, 8 and 9 without repitition. If one number is selected from those numbers, then what is the probability that it will be an odd number ?

Question 9 :
If $P(A) + P(B) = 1$; then which of the following option explains the event $A$ and $B$ correctly ?

Question 10 :
One percent of the population suffers from a certain disease. There is blood test for this disease, and it is $99\%$ accurate, in other words, the probability that is gives the correct answer is $0.99$, regardless of whether the person is sick or healthy. A person takes the blood test, and the result says that he has the disease. The probability that he actually has the disease, is?

Question 11 :
For two independent events $A$ and $B$, which of the following pair of events need not be independent?<br/>

Question 12 :
For two events $A$ and $B$, if $\displaystyle&#160;P\left( A \right) =P\left( \frac { A }{ B } &#160;\right) =\frac { 1 }{ 4 } $ and $\displaystyle&#160;P\left( \frac { B }{ A } &#160;\right) =\frac { 1 }{ 2 } $, then

Question 13 :
A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is :

Question 14 :
$P(A) =3/8; P(B)=1/2; P( A \cup B)=5/8$, which of the following do/does hold good?