Question 2 :
Suman is given an aptitude test containing 80 problems, each carrying I mark to be tackled in 60 minutes. The problems are of 2 types; the easy ones and the difficult ones. Suman can solve the easy problems in half a minute each and the difficult ones in 2 minutes each. (The two type of problems alternate in the test). Before solving a problem, Suman must spend one-fourth of a minute for reading it. What is the maximum score that Suman can get if he solves all the problems that he attempts?

Question 3 :
Suppose $A_1 , A_2,... A_{30}$ are thirty sets each having 5 elements and $B_1, B_2,..., B_n$ are n sets each with 3 elements , let $\underset{i = 1}{\overset{30}{\cup}} A_i = \underset{j = 1}{\overset{n}{\cup}} B_j = S$ and each element of S belongs to exactly 10 of the $A_i's$ and exactly 9 of the $B_j'S$. then n is equal to

Question 4 :
If $X=\left\{ { 4 }^{ n }-3n-1;n\in R \right\} $ and $Y=\left\{ 9\left( n-1 \right) ;n\in N \right\} $, then $X\cap Y=$

Question 5 :
Let A and B be two sets containing four and two elements respectively. Then the number of subsets of the set $A \times B$, each having at least three elements is............

Question 6 :
Consider the non-empty set consisting of children in a family and a relation $R$ defined as a $Rb$ if $a$ is brother of $b$. Then $R$ is

Question 8 :
Set of all real value of a such that $f(x) = \frac {(2a - 1)x^2(a + 1)x + (2a - 1)}{x^2 2x + 40}$ always negative is

Question 9 :
Suppose ${ A }_{ 1 },{ A }_{ 2 },,{A }_{ 30 }$ are thirty sets each having $5$ elements and ${ B }_{ 1 },{ B }_{ 2 },..,{B}_{ n }$ are $n$ sets each with $3$ elements, let $\displaystyle \bigcup _{ i=1 }^{ 30 }{ { A }_{ i } } =\bigcup _{ j=1 }^{ n }{ { B }_{ j } =S}$ and each element of $S$ belongs to exactly $10$ of the ${A}_{i}s$ and exactly $9$ of the ${B}_{j}s.$ Then $n$ is equal to