Area of Polygon Using Coordinates

Q. A system of line is given as $y=m_{i}x+c_i,$ where $m_i$ can take any value out of 0, 1, -1 and when $m_i$ is positive then $c_i$ can be 1 or -1 when $m_i$ equal 0, $c_i$ can be 0 or 1 and when $m_i$ equals -1, $c_i$ can take 0 or 2. Then the area enclosed by all these straight lines is

1. sq. units
2. sq. units
3. sq. untis
4. sq. units

Q.

The area enclosed by 2|x| + 3|y| $\le$ 6 is

1. 4 sq units

2. 24 sq units

3. 3 sq units

4. 12 sq unit

Q. If the vertices of a quadrilateral are $A(-3,1),$ $B(-1,4),$ $C(3,2)$ and $D(t_1,-2)$ and the area of the quadrilateral is $19\text{sq. units}$, then which of the following is/are correct?

1. $t_1=1$
2. $t_1=-75$
3. $t_1=75$
4. $t_1=-1$

Q. The area (in sq. units) of the quadrilateral whose vertices are $A(1,1),$ $B(3,4),$ $C(5,-2)$ and $D(4,-7)$ is

1. $41$
2. $64$
3. $\frac{37}{4}$
4. $\frac{41}{2}$

Q. The volume of water to be added to $100c{m}^3$ of a $0.5$ N $H_{2}S{O}_4$ to get a decinormal solution is:

1. $200c{m}^3$
2. $300c{m}^3$
3. $500c{m}^3$
4. $400c{m}^3$

Q. 10 mL of a strong acid solution of pH = 2 is mixed with 990 mL of another strong acid solution of pH = 4. The pH of resulting solution will be :

1. 4.002
2. 3.7
3. 4
4. 4.2

Q.

The half life of a ratio active source is T. If radio activities of the samples are $R_1-R_2$ at time

$T_{1}and{T}_2$ Respectively, then the number of atoms disintegrated in time $(T_2-T_1)$ is proportional to

1. 

2. 

3. 

4. 

Q. If Y = SX, Z = tX all the variables being differentiable functions of x and lower suffices denote the derivative with respect to x and $\left|\begin{array}{ccc}X& Y& Z\\ X_1& Y_1& Z_1\\ X_2& Y_2& Z_2\end{array}\right|÷\left|\begin{array}{cc}{S}_1& t_1\\ S_2& t_2\end{array}\right|=X^n,thenn=$

1. 3
2. 4
3. 1
4. 2

Q.

Find the value of K if $(\frac{-3k+1}{k+1},\frac{4k+2}{k+1})$ lies on x + y - 5 = 0

1. 2

2. -2

3. 

4. 

Q.

Prove that the area of the parallelogram formed by the lines.

$a_{1}x+b_{1}y+c_1=0,a_{1}x+b_{1}y+d_1=0,a_{2}x+b_{2}y+c_2=0,a_{2}x+b_{2}y+d_2=0$ is $\left|\frac{(d_1-c_1)(d_2-c_2)}{a_1{b}_2-a_2{b}_1}\right|$ sq. units.

Deduce the condition for these lines to form a rhombus.