Question 1 :
Formulate the equations for the above problem.<br>($x$ and $y$ are the number of units of $A$ and $B$ manufactured in a day respectively)

Question 2 :
The sum of four numbers in AP is $20.$ The numbers are such that the ratio of the product of first and fourth is to the product of second and third as $2 : 3.$ The greatest number is:-

Question 3 :
A pack of coffee powder contains a mixture of x&#160;gms of coffee and y gms of choco. The amount of coffee powder is greater than that of chocolate and each pack weights at least 10 g. Which of the following inequalities describe the given&#160;condition?

Question 5 :
The function $f(x)\, =\, \sqrt{\log_x^2\, (x)}$ is defined for x belonging to

Question 6 :
Write explicitly, functions of $y$ defined by the following equations and also find the domains of definition of the given implicit functions:<br/>$x + \mid y \mid = 2y$

Question 8 :
If $A=\left \{ 1,2,3 \right \} $ and $B=\left \{ 4,5,6 \right \}$ then which of the following sets are relation from $A$ to $B$<br>(i) $\displaystyle R_{1}=\left \{ (4,2) (2,6)(5,1)(2,4)\right \}$<br>(ii) $\displaystyle R_{2}=\left \{ (1,4) (1,5)(3,6)(2,6) (3,4)\right \}$<br>(iii) $\displaystyle R_{3}=\left \{ (1,5) (2,4)(3,6)\right \}$<br>(iv) $\displaystyle R_{4}=\left \{ (1,4) (1,5)(1,6)\right \}$<br>

Question 9 :
If $A$ is the set of even natural numbers less than $8$ and $B$ is the set of prime numbers less than $7$, then the number of relations from $A$ to $B$ is

Question 10 :
If $f:R\rightarrow R,g\quad :R\rightarrow R$ are defined by $f\left( x \right) =5x-3,g(x)={ x }^{ 2 }+3,$ then $\left( { gof }^{ -1 } \right) \left( 3 \right) =$

Question 11 :
Identify the type of Set$A = \{x|x \epsilon N,x &lt;1 \}$

Question 12 :
If $X = \left \{1, 2, 3, ..., 10\right \}$ and $A = \left \{1, 2, 3, 4, 5\right \}$. Then, the number of subsets $B$ of $X$ such that $A - B = \left \{4\right \}$ is

Question 13 :
{$x \epsilon R : \dfrac{14x}{x+1} - \dfrac{9x-30}{x-4} &lt;0$ } is equal to

Question 14 :
Find out the truth sets of the following open sentences replacement sets are given against them.<br>$x^2=9; \{-3, -2, -1, 0, 1, 2, 3\}$

Question 15 :
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 17 :
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

Question 18 :
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?