Incentre of a Triangle

Q.

The equation of the incircle fonned by the coordinate axes and the line $4x+3y=6$ is

1. $x^2+y^2-6x-6y+9=0$

2. $4(x^2+y^2-x-y)+1=0$

3. $4(x^2+y^2+x+y)+1=0$

4. none of these

Q. If the points $A(2,-1,1),B(1,-3,-5)$and$C(3,-4,-4)$ form a triangle, find the circum radius for this triangle.

1. 

2. 

3. 

4. 

Q. Circumcenter of a right angled triangle lies outside the triangle.

1. True
2. False

Q. If $A(1,2,3),B(2,3,1)$ and $C(3,1,2$) are the vertices of the triangle. Find the coordinates of its orthocenter $\left(O\right)$ and In center $\left(I\right)$.

1. O((3, 3, 3), I(3, 3, 2)

2. O(2, 2, 3), I(2, 2, 2)

3. O(4, 4, 4), I(1, 2, 3)

4. O(1, 1, 1), I(1, 1, 1)

Q. The plane $4x+4y+8z=16$ meets the coordinate axes $x,y$ and $z$ at $A,B$ and $C$ respectively. Then the area of the $\Delta ABC$ is equal to $k\sqrt{6}.$ The value of k is

Q. Let $A(2,-3)$ and $B(-2,1)$ be two angular points of $△ABC.$ If the centroid of the triangle moves on the line $2x+3y=1,$ then the locus of the angular point $C$ is given by

1. $2x-3y=9$
2. $3x+2y=5$
3. $3x-2y=3$
4. $2x+3y=9$

Q. Circumcenter of a right angled triangle lies outside the triangle.

1. True

2. False

Q. If the points $A(2,-1,1),B(1,-3,-5)$and$C(3,-4,-4)$ form a triangle, find the circum radius for this triangle.

1. $\sqrt{41}$

2. $\frac{\sqrt{41}}{2}$

3. $\sqrt{35}$

4. $\sqrt{6}$

Q. A variable line passes through a fixed point $(a,b)$ and meets the coordinates axes in $A$ and $B.$ The locus of the point of intersection of lines through A, B parallel to coordinate axes is-

1. $\frac{x}{a}+\frac{y}{b}=2$
2. $\frac{a}{x}+\frac{b}{y}=1$
3. $\frac{x}{a}+\frac{y}{b}=1$
4. $\frac{x}{a}+\frac{y}{b}=3$

Q. If the points $A(2,-1,1),B(1,-3,-5)$and$C(3,-4,-4)$ form a triangle, find the circum radius for this triangle.

1. $\sqrt{41}$

2. $\frac{\sqrt{41}}{2}$

3. $\sqrt{35}$

4. $\sqrt{6}$

Q. The circum radius of the triangle formed by the points $(2,-1,1),(1,-3,-5)$ and $(3,-4,-4)$ is

1. $\frac{\sqrt{6}}{2}$
2. $\frac{\sqrt{41}}{2}$
3. $\sqrt{41}$
4. $\frac{\sqrt{35}}{2}$

Q. If $f\left(x\right)=\{\begin{array}{c}p{x}^2-q,xϵ[0,1)\\ x+1,xϵ(1,2]\end{array}$
and $f\left(1\right)=2$ then the value of the pair $(p,q)$ for which $f\left(x\right)$ cannot be continuous at $x=1$ is

1. $(2,0)$
2. $(1,-1)$
3. $(4,2)$
4. $(1,1)$