1. Let $S$= $(0,1) \cup (1,2) \cup (3,4)$ and $T$={0,1, 2,3} . Then which of the following statements is(are) true?
   1. There are infinitely many functions from $S$ to $T$
   2. There are infinitely many strictly increasing functions from $S$ to $T$
   3. The number of continuous functions from $S$ to $T$ is at most 120
   4. Every continuous function from $S$ to $T$ is differentiable
2. Let $T_1$ and $T_2$ be two distinct common tangents to the ellipse $E$:$\frac{x^2}{6}$+$\frac{y^2}{3}$=1 and the parabola $P$:$y^2$=$12x$ . Suppose that the tangent $T_1$ touches $P$ and $E$ at the points $A_1$ and $A_2$, respectively and the tangent $T_2$ touches $P$ and $E$ at the points $A_4$ and $A_3$, respectively. Then which of the following statements is(are) true?
   1. The area of the quadrilateral $A_1$$A_2$$A_3$$A_4$ is 35 square units
   2. The area of the quadrilateral $A_1$$A_2$$A_3$$A_4$ is 36 square units
   3. The tangents $T_1$ and $T_2$ meet the $x$ -axis at the point ( -3,0)
   4. The tangents $T_1$ and $T_2$ meet the $x$ -axis at the point ( -6,0)
3. Let $\alpha$, $\beta$ and $\gamma$ be real numbers. Consider the following system of linear equations
   $x$+$2y$+$z$=7
   $x$+$\alpha z$=11
   $2x-$$3y$+$\beta z$=$\gamma$
   
   Match each entry in List-I to the correct entries in List-II
   • Project: Intimate House
   • Location: Pulau Putri, Puri - West Jakarta - Indonesia
   • Site Area: 160 sqm
   • Building Area: 210 sqm
   • Design Phase: 2016
   • Construction Period: April 2016 - July 2017