f(x) Transforms to Its Inverse

Q.

A line meets the co-ordinate axes in A & B, a circle is circumscribed about the triangle OAB. If $d_{1}and{d}_2$ are the distances of the tangent to the circle at the origin O from the points A and B respectively the diameter of the circle is:

1. 

2. 

3. 

4. 

Q. The maximum area of a rectangle whose two vertices lie on the x-axis and two on the curve $y=3-\left|x\right|,-3\le x\le 3$ , is

1. 9
2. 3
3. $\frac{9}{4}$
4. $\frac{9}{2}$

Q. The graph of the function $y=f\left(x\right)$ is symmetrical about line $x=2,$ then

1. $f\left(x\right)=f(-x)$
2. $f(2+x)=f(2-x)$
3. $f\left(2\right)=f(2-x)$
4. $f(2+x)=f(x-2)$

Q.

The graph of the function $y=f\left(x\right)$ is symmertical about the line $x=2$ , then

1. f(x) = -f(-x)

2. f(2+x) =f(2-x)

3. f(x) = f(-x)

4. f(x + 2) = f(x=2)

Q. The area bounded by $y=-|x|+3,x=0,y=0$ and $x=2,$ is

1. $\frac{7}{2}\text{sq. units}$
2. $\frac{11}{2}\text{sq. units}$
3. $6\text{sq. units}$
4. $4\text{sq. units}$

Q. The two points on the line 2x + 3y + 4 = 0 which are at distance 2 unit from the line 3x + 4y - 6 = 0 are

1. (-8, -8) and (-16, -16)
2. (-44, 64) and (-5, 2)
3. (-5.5, 1) and (-5, 2)
4. (64, -44) and (4, -4)

Q. Let $f\left(x\right)=min\{x+1,\sqrt{1-x}\}$, then the area bounded by $y=f\left(x\right)$ and $x$-axis is:

1. $\frac{5}{6}$
2. $\frac{1}{6}$
3. $\frac{7}{6}$
4. $\frac{11}{6}$

Q. Area of the region $\left\{\right(x,y)\in R^2:y\ge \sqrt{|x+3|},5y\le x+9\le 15\}$ is equal to

1. $\frac{1}{6}$
2. $\frac{4}{3}$
3. $\frac{3}{2}$
4. $\frac{5}{3}$

Q. The graph of the function $y=f\left(x\right)$ is symmetrical about the line $x=2$. Then,

1. $f(x+2)=f(x-2)$
2. $f(2+x)=f(2-x)$
3. $f\left(x\right)=-f(-x)$
4. $f\left(x\right)=f(-x)$

Q. If length of perpendicular from origin to line $\frac{x}{a}+\frac{y}{b}=1$ is p, then prove that
$\frac{1}{p^2}=\frac{1}{a^2}+\frac{1}{b^2}$ ?

Q. The equation of line passing through $(3,-1,2)$ and perpendicular to the lines
$\overline{r}=(\hat{i}+\hat{j}-\hat{k})+\lambda (2\hat{i}-2\hat{j}+\hat{k})$ and $\overline{r}=(2\hat{i}+\hat{j}-3\hat{k})+\mu (\hat{i}-2\hat{j}+2\hat{k})$ is

1. $\frac{x+3}{2}=\frac{y+1}{3}=\frac{z-2}{2}$
2. $\frac{x-3}{3}=\frac{y+1}{2}=\frac{z-2}{2}$
3. $\frac{x-3}{2}=\frac{y+1}{3}=\frac{z-2}{2}$
4. $\frac{x-3}{2}=\frac{y+1}{2}=\frac{z-2}{2}$

Q. Find the direction cosines $l,m,n$ of a line which are connected by the relation $l+m-n=0$ and $2ml-2mn+nl=0$

1. $\frac{-2}{\sqrt{6}},\frac{1}{\sqrt{6}},\frac{-1}{\sqrt{6}}$
2. $\frac{2}{\sqrt{6}},\frac{-1}{\sqrt{6}},\frac{1}{\sqrt{6}}$
3. $\frac{-2}{\sqrt{6}},\frac{-1}{\sqrt{6}},\frac{-1}{\sqrt{6}}$
4. $\frac{2}{\sqrt{6}},\frac{1}{\sqrt{6}},\frac{1}{\sqrt{6}}$

Q. The number of lines that can be drawn through the point $(4,-5)$ at distance of 12 units from the point $(-2,3)$ is

1. 0
2. 1
3. 2
4. infinite

Q. The graph of $y=f\left(x\right)$ is symmetrical about the line $x=1,$ then

1. $f(-x)=f\left(x\right)$
2. $f(1+x)=f(1-x)$
3. $f(x+1)=f(x-1)$
4. None of these

Q. In given figure trapezoid $ABCD$ is graphed in the standard $(x,y)$ coordinate plane. Which of the following vertical line cuts $ABCD$ into $2$ trapezoids with equal areas

1. $x=2.5$
2. $x=3.5$
3. $x=4.5$
4. $x=6.5$
5. $x=5.5$

Q. Find the area under the curve $y=\sqrt{6x+4}$ above $x$-axis from $x=0$ to $x=2.$

Q. Draw the graph of the following function given by $\{\begin{array}{c}\frac{x}{\left|x\right|}ifx\ne 0\\ 0ifx=0\end{array}$

Q. The graph of the function $y=f\left(x\right)$ is symmetrical about line $x=2,$ then

1. $f\left(x\right)=f(-x)$
2. $f(2+x)=f(2-x)$
3. $f\left(2\right)=f(2-x)$
4. $f(2+x)=f(x-2)$

Q. The area bounded by $y=-|x|+3,x=0,y=0$ and $x=2,$ is

1. $\frac{7}{2}\text{sq. units}$
2. $4\text{sq. units}$
3. $\frac{11}{2}\text{sq. units}$
4. $6\text{sq. units}$

Q. The area bounded by $y=-|x|+3,x=0,y=0$ and $x=2,$ is

1. $\frac{7}{2}\text{sq. units}$
2. $4\text{sq. units}$
3. $\frac{11}{2}\text{sq. units}$
4. $6\text{sq. units}$

Q. Square $OABC$ is drawn with vertex $O$ as origin, vertex $A$ on the positive side of $x-$axis and vertex $C$ on the positive side of y-axis. If each side of the square $OABC$ is of length $6$ units, draw $OABC$ on a graph paper and then use the graph to find the co-ordinates of vertices $A,B$ and $C.$

Q. The number of lines that can be drawn through the point $(4,-5)$ at a distance $12$ from the point $(-2,3)$ is :

1. $0$
2. $1$
3. $2$
4. Infinite

Q. The graph of the function $y=f\left(x\right)$ is symmetrical about line $x=2,$ then

1. $f\left(x\right)=f(-x)$
2. $f(2+x)=f(2-x)$
3. $f\left(2\right)=f(2-x)$
4. $f(2+x)=f(x-2)$

Q. On the graph above, when $x=\frac{1}{2},y=2$ and when $x=1,y=1$. The graph is symmetric with respect to the vertical line at $x=2$. According to the graph, when $x=3,y=$

1. $-1$
2. $-\frac{1}{2}$
3. $0$
4. $\frac{1}{2}$
5. $1$