Expression 'T'

Q. The tangent and the normal lines at the point $(\sqrt{3},1)$ to the circle $x^2+y^2=4$ and the $x$-axis forms a triangle. The area of this triangle (in square units) is :

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

Q. Let the tangents drawn to the circle, $x^2+y^2=16$ from the point $P(0,h)$ meet the x-axis at points $A$ and $B$. If the area of $△APB$ is minimum, then $h$ is equal to:

1. $4\sqrt{2}$
2. $4\sqrt{3}$
3. $3\sqrt{2}$
4. $3\sqrt{3}$

Q. A variable circle is described to pass through the point $(2,3)$ and is tangent to the line $y=x.$ The locus of the center of the circle is a conic whose:

1. length of latus rectum is $\sqrt{2}$
2. axis of symmetry has the equation $x+y=5$
3. vertex has the coordinates $(\frac{9}{4},\frac{11}{4})$
4. distance between focus and (nearest) vertex is $\sqrt{2}-1$

Q. $C_1\text{and}{C}_2$ are circles of unit radius with centres at $(0,0)\text{and}(1,0)$ respectively. $C_3$ is a circle of radius $r(r\in N)$. It passes through the centres of the circles $C_1\text{and}{C}_2$ and has its center above the $x-$axis. If the common tangent of $C_1\text{and}{C}_3$ is $\sqrt{3}x-y+c=0$. Then maximum value of $c+r=$

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

Q. The area of the triangle formed by the positive x-axis, and the normal and tangent to the circle $x^2+y^2=4$ at $(1,\sqrt{3})$

1. None of these
2. $\sqrt{3}$ sq unit
3. $2\sqrt{3}$ sq unit
4. $4\sqrt{3}$ sq unit

Q. If $\Delta$ is the area of the triangle formed by the positive x-axis and the normal and tangent to the circle $x^2+y^2=4$ at $(1,\sqrt{3})$, then $\Delta =$

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

Q. The area bounded by$(y-2{)}^2=x-1$ the tangent to it at the point whose ordinate is 3 and the x – axis is (in sq.units)___

Q. The tangent and the normal lines at the point $(\sqrt{3},1)$ to the circle $x^2+y^2=4$ and the $x$-axis forms a triangle. The area of this triangle (in square units) is :

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

Q. Let the tangents drawn to the circle, $x^2+y^2=16$ from the point $P(0,h)$ meet the x-axis at points $A$ and $B$. If the area of $△APB$ is minimum, then $h$ is equal to:

1. $4\sqrt{2}$
2. $4\sqrt{3}$
3. $3\sqrt{2}$
4. $3\sqrt{3}$

Q. Area of the triangle formed by the tangent, normal at $(1,1)$ on the curve $\sqrt{x}+\sqrt{y}=2$ and the y axis is (in sq. units)

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

Q. Let the tangents drawn to the circle, $x^2+y^2=16$ from the point $P(0,h)$ meet the x-axis at points $A$ and $B$. If the area of $△APB$ is minimum, then $h$ is equal to:

1. $4\sqrt{2}$
2. $4\sqrt{3}$
3. $3\sqrt{2}$
4. $3\sqrt{3}$

Q. Area lying in the first quadrant and bounded by the circle $x^2+y^2=4$ and the lines $x=0$ and $x=2$ is :

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