$\begin{align}  & \text{The }nth\text{ term of the progression }\tfrac{4}{2},\tfrac{7}{3},\tfrac{10}{4},\tfrac{13}{4},\cdot \cdot \cdot \text{ is} \\ & (A)\text{ }\tfrac{3n-1}{n+1}\text{ }(B)\text{ }\tfrac{1-3n}{n+1}\text{ }(C)\text{ }\tfrac{3n+1}{n+1}\text{  (D) }\tfrac{3n+1}{n-1} \\\end{align}$

$\begin{align}  & \text{If the sum of the first term of G}\text{.P is 3, and the sum of the second  and} \\ & \text{the  third term is }-6,\text{ find the sum of the first term and the common ratio} \\ & \text{(A) 5 (B) }-2\text{  (C) }-3\text{  }(D)\text{ }-5 \\\end{align}$

$\begin{align}  & \text{Solve for }x:\text{ }\left| x-2 \right|<3 \\ & \text{(}A)\text{ }x<1\text{  }(B)\text{ }x<5\text{ }(C)\text{ }-2<x<3\text{  (D) }-1<x<5 \\\end{align}$

$\begin{align}  & \text{Evaluate }3(x+2)>6(x+3) \\ & (A)\text{ }x>4\text{  }(B)\text{  }x<4\text{  }(C)\text{ }x>-4\text{ }(D)\text{ }x<-4 \\\end{align}$

$\begin{align}  & \text{If }r\text{ varies inversely as the square root of }s\text{ and }t\text{ how does }s\text{ vary with }r\text{ and }t. \\ & (A)\text{ }s\text{ varies directly as }r\text{ and }t \\ & (B)\text{ }s\text{ varies inversely as }r\text{ and }{{t}^{2}} \\ & (C)\text{ }s\text{ varies inversely as }{{r}^{2}}\text{ and }t \\ & (D)\text{ }s\text{ varies directly as }{{r}^{2}}\text{ and }{{t}^{2}} \\\end{align}$

$\begin{align}  & P\text{ varies jointly as }m\text{ and }u,\text{ varies inversely as }q.\text{ Given that }p=4,\text{ }m=3\text{ } \\ & \text{and }u=2\text{ when }q=1,\text{find  the value of }p\text{ when }m=6,u=4\text{ and }q=\tfrac{8}{5} \\ & (A)\text{  }\tfrac{128}{5}\text{  (B) }15\text{  (C) 10  (D)  }\tfrac{288}{5} \\\end{align}$

$\begin{align}  & \text{The remainder when }6{{p}^{3}}-{{p}^{2}}-47p+30\text{ is divided by }p-3\text{ is } \\ & \text{(A) }21\text{  (B)  42  (C)  63  (D) 18} \\\end{align}$

$\begin{align}  & \text{If }x-4\text{ is a factor of }{{x}^{2}}-x-k,\text{ then }k\text{ is } \\ & \text{(A) 4  (B) 12 (C) 20  (D) 2} \\\end{align}$

$\begin{align}  & \text{If }S=\sqrt{{{t}^{2}}-4t+4},\text{ find }t\text{ in terms of }S \\ & \text{(A)  }{{S}^{2}}-2\text{  (B) }S+2\text{  (C) }S-2\text{ (D) }{{S}^{2}}+2 \\\end{align}$