Related InterviewSolutions

• Let a,b, c and d be non-zero numbers. If the point of intersection of the lines `4ax + 2ay+c=0` and `5bx+2by +d=0` lies in the fourth quadrant and is equidistant from the two axes, thenA. `2bc-3ad=0`B. `2bc+3ad=0`C. `2ad-3bc=0`D. `3bc+2ad=0`
• Three lines `px+qy+r=0`, `qx+ry+p=0` and `rx+py+q=0` are concurrent , ifA. `p+q+r=0`B. `p^(2)+q^(2)+r^(2)=pr+rq`C. `p^(3)+q^(3)+r^(3)=3pqr`D. None of these
• If `px+qx+r=0` represent a family fo staright lines such that `3p+2q+4r=0` then (a) All lines are parallel (b) All lines are incosistance (c) All lines are concurrent at `((3)/(4),(1)/(2))` (d) All lines are concurrent at `(3,2)`A. Each lines passes through the origin.B. The lines are concurrent at the point `((3)/(4),(1)/(2))`C. The lines are all parallelD. The lines are not concurrent
• The equation of the line which bisects the obtuse angle between the line `x-2y+4=0` and `4x-3y+2=0` is
• The number of integer values of `m ,`for which the x-coordinate of the point of intersection of the lines, `3x+4y=9`and `y=x m+1`is also an integer is2 (b) 0 (c) 4(d) 1A. `2`B. `0`C. `4`D. `1`
• For `a gt b gt c gt 0`, if the distance between `(1,1)` and the point of intersection of the line `ax+by-c=0` and `bx+ay+c=0` is less than `2sqrt2` then,(A) `a+b-cgt0` (B) `a-b+clt0` (C) `a-b+cgt0` (D) `a+b-clt0`A. `a+b-c gt 0`B. `a-b+c lt 0`C. `a-b+c gt 0`D. `a+b-c lt 0`
• The coordinates of `A,B,C` are `(6,3)`, `(-3,5)`, `(4,-2)` respectively and `P` is any point `(x,y)` . Show that the ratio of the areas of the triangles `DeltaPBC` and `DeltaABC` is `|(x+y-2)/(7)|`.
• The vertices of a triangle are `[at_(1)t_(2),a(t_(1)+t_(2))]`,`[at_(2)t_(3),a(t_(2)+t_(3))]`, `[at_(3)t_(1),a(t_(3)+t_(1))]`. Find the orthocentre of the triangle.
• Find the incentre of the triangle with vertices `(1, sqrt3), (0, 0)` and `(2, 0)`A. `(1,(sqrt(3))/(2))`B. `((2)/(3),(1)/(sqrt(3)))`C. `((2)/(3),(sqrt(3))/(2))`D. `(1,(1)/(sqrt(3)))`
• Suppose that the points `(h,k)`, `(1,2)` and `(-3,4)` lie on the line `L_(1)`. If a line `L_(2)` passing through the points `(h,k)` and `(4,3)` is perpendicular to `L_(1)`, then `k//h` equalsA. `-(1)/(7)`B. `(1)/(3)`C. `3`D. `0`