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question_answer1) A square of area 25 sq. unit is formed by taking two sides as \[3x+4y={{k}_{1}}\] and \[3x+4y={{k}_{2}}\], then find value of \[\left| {{k}_{1}}-{{k}_{2}} \right|\].
question_answer2) If the lines \[3y+4x=1,y=x+5\] and \[5y+bx=3\] are concurrent, then find the value of b.
question_answer3) A straight line passing through P (3, 1) meet the coordinate axes at A and B. It is given that distance of this straight line from the origin 'O' is maximum. Then find area of triangle OAB.
question_answer4) A variable line \[x/a+y/b=1\] moves in such a way that harmonic mean of a and b is 8. Then find the least area of triangle made by the line with the coordinate axes.
question_answer5) Let ABC be a triangle. Let A be the point \[\left( 1,\text{ }2 \right).\text{ }y=\text{ }x\] is the perpendicular bisector of AB and \[x-2y+1=0\] is the angle bisector of \[\angle C\]. If equation of BC is given by \[ax+by-5=0\], then find the value of \[a+b.\]
question_answer6) Find the number of straight lines parallel to \[3x+6y+7=0\] & have intercept of length 10 between the coordinate axes.
question_answer7) Find the distance of origin from line \[\left( 1+\sqrt{3} \right)y+\left( 1-\sqrt{3} \right)x=10\] along the line \[y=\sqrt{3}x+k\].
question_answer8) If the distance between the parallel lines \[y=2x+4\] and \[6x=3y+5\] is \[\frac{k\sqrt{5}}{15}\] then find k.
question_answer9) If the lines \[x=a+m,\text{ }y=-2\] and \[y=mx\] are concurrent, then find the least value of \[{{a}^{2}}\].
question_answer10) Reflection of a point \[\left( t-1,2t+2 \right)\]in a line is \[\left( 2t+1,t \right),\]then find the slope of line.
question_answer11) The acute angle bisector between the lines \[2x-y+4=0\] and \[x-2y-1=0\] is \[y-x=k,\] then find value of 'k'.
question_answer12) Find the sum of the abscissas of the points lying on the line \[x-y=3,\]which lies at a unit distance from\[4x-3y=12\].
question_answer13) If \[(\text{sin}\theta ,\text{ cos}\theta ),\text{ }\theta \in \left[ 0,\text{ 2}\pi \text{ }\!\!~\!\!\text{ } \right]\] and (1, 4) lie on the same side or on the line \[\sqrt{3}x-y+1=0,\] then find the maximum value of \[\sin \theta \].
question_answer14) If all lines given by the equation \[\left( 3\,sin\,\theta +5\,cos\,\theta \right)x+\left( 7sin\,\theta -3\,cos\,\theta \right)\]\[y+11(sin\,\theta -\cos \,\theta )=0\] Pass through a fixed point P for all \[\theta \in \,\,R,\] then find the half distance of P from Q (7, - 10).
question_answer15) Let \[A=(3,4)\]and B is a variable point on the lines\[\left| \,x\, \right|=6\]. If\[AB\,\,\le \,\,4\], then find the number of position of B with integral coordinates.
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