Question : The area of the triangle formed by the graph of the straight lines $x-y=0$, $x+y=2$, and the $x$-axis is:

Option 1: 1 sq. unit

Option 2: 2 sq. units

Option 3: 4 sq. units

Option 4: 5 sq. units

Question : If $x^4+y^4+x^2 y^2=17 \frac{1}{16}$ and $x^2-x y+y^2=5 \frac{1}{4}$, then one of the values of $(x-y)$ is:

Option 1: $\frac{5}{2}$

Option 2: $\frac{3}{4}$

Option 3: $\frac{5}{4}$

Option 4: $\frac{3}{2}$

Question : If $2^x+3^y=17$ and $2^{x+2}-3^{y+1}=5$, then:

Option 1: $x= 1, y = 3$

Option 2: $x = 3, y = 3$

Option 3: $x = 3, y = 2$

Option 4: $x = 1, y = 2$

Question : Let $x, y, z$ be fractions such that $x<y<z$. If $z$ is divided by $x$, the result is $\frac{5}{2}$, which exceeds $y$ by $\frac{7}{4}$. If $x+y+z=1 \frac{11}{12}$, then the ratio of $(z-x):(y-x)$ is:

Option 1: 6 : 5

Option 2: 9 : 5

Option 3: 5 : 6

Option 4: 5 : 9

Question : The third proportional of the following numbers $(x-y)^2, (x^2-y^2)^2$ is:

Option 1: $(x+y)^3(x-y)^2$

Option 2: $(x+y)^4(x-y)^2$

Option 3: $(x+y)^2(x-y)^2$

Option 4: $(x+y)^2(x-y)^3$