5 answers

##### The point $(2,3)$ undergoes the following three transformations successively(i) reflection about the line $y=x$(ii) translation through a distance 2 units along the positive direction of $y$-axis(iii) rotation through an angle of $45^{circ}$ about the origin in the anti-clockwise direction. The final coordinates of the point are(A) $left(frac{1}{sqrt{2}}, frac{7}{sqrt{2}}ight)$(B) $left(-frac{1}{sqrt{2}}, frac{7}{sqrt{2}}ight)$(C) $left(frac{1}{sqrt{2}},-frac{7}{sqrt{2}}ight)$(D) none of these

The point $(2,3)$ undergoes the following three transformations successively (i) reflection about the line $y=x$ (ii) translation through a distance 2 units along the positive direction of $y$-axis (iii) rotation through an angle of $45^{circ}$ about the origin in the anti-clockwise direction. The f...

5 answers

##### Lines $L_{1}=a x+b y+c=0$ and $L_{2}=L x+m y+n=0$intersect at the point $P$ and make an angle $heta$ with each other. The equation of line $L$ different from $L_{2}$ which passes through $mathrm{P}$ and makes the same angle $heta$ with $L_{1}$ is(A) $2(a l+b m)(a x+b y+c)-left(a^{2}+b^{2}ight)(l x+m y+n)$$=0$(B) $2(a l+b m)(a x+b y+c)+left(a^{2}+b^{2}ight)(l x+m y+n)$$=0$(C) $2left(a^{2}+b^{2}ight)(a x+b y+c)-(a l+b m)(l x+m y+n)$$=0$(D) none of these

Lines $L_{1}=a x+b y+c=0$ and $L_{2}=L x+m y+n=0$ intersect at the point $P$ and make an angle $ heta$ with each other. The equation of line $L$ different from $L_{2}$ which passes through $mathrm{P}$ and makes the same angle $ heta$ with $L_{1}$ is (A) $2(a l+b m)(a x+b y+c)-left(a^{2}+b^{2} ight)(...

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##### The equations of the perpendicular bisector of the sides $A B$ and $A C$ of a $Delta A B C$ are $x-y+5=0$ and $x+$ $2 y=0$, respectively. If the point $A$ is $(1,-2)$ then the equation of the line $B C$ is(A) $14 x+23 y=40$(B) $14 x-23 y=40$(C) $23 x+14 y=40$(D) $23 x-14 y=40$

The equations of the perpendicular bisector of the sides $A B$ and $A C$ of a $Delta A B C$ are $x-y+5=0$ and $x+$ $2 y=0$, respectively. If the point $A$ is $(1,-2)$ then the equation of the line $B C$ is (A) $14 x+23 y=40$ (B) $14 x-23 y=40$ (C) $23 x+14 y=40$ (D) $23 x-14 y=40$...

4 answers

##### 1. The equation of a family of lines is given by $(2+3 t)$ $x+(1-2 t) y+4=0$, where $t$ is the parameter. The equation of a straight line, belonging to this family, at the maximum distance from the point $(2,3)$ is(A) $21 x+14 y=0$(B) $21 x-14 y=0$(C) $14 x-21 y=0$(D) none of these

1. The equation of a family of lines is given by $(2+3 t)$ $x+(1-2 t) y+4=0$, where $t$ is the parameter. The equation of a straight line, belonging to this family, at the maximum distance from the point $(2,3)$ is (A) $21 x+14 y=0$ (B) $21 x-14 y=0$ (C) $14 x-21 y=0$ (D) none of these...

4 answers

##### $A B C D$ is a square whose vertices $A, B, C$ and $D$ are $(0,0),(2,0),(2,2)$ and $(0,2)$, respectively. This square is rotated in the $X-Y$ plane with an angle of $30^{circ}$ in anti-clockwise direction about an axis passing through the vertex $A$. The equation of the diagonal $B D$ of this rotated square is(A) $sqrt{3} x+(1-sqrt{3}) y=sqrt{3}$(B) $(1+sqrt{3}) x-(1-sqrt{2})=2$(C) $(2-sqrt{3}) x+y=2(sqrt{3}-1)$(D) none of these

$A B C D$ is a square whose vertices $A, B, C$ and $D$ are $(0,0),(2,0),(2,2)$ and $(0,2)$, respectively. This square is rotated in the $X-Y$ plane with an angle of $30^{circ}$ in anti-clockwise direction about an axis passing through the vertex $A$. The equation of the diagonal $B D$ of this rotate...

5 answers

##### The equations of the straight lines passing through $(-2,-7)$ and cutting an intercept of length three units between the straight lines $4 x+3 y=12$ and $4 x+3 y=$ 3 are(A) $x+2=0, y+7=frac{7}{24}(x+2)$(B) $x-2=0, y+7=-frac{7}{24}(x+2)$(C) $x+2=0, y+7=-frac{7}{24}(x+2)$(D) $x+2=0, y+7=-frac{7}{12}(x+2)$

The equations of the straight lines passing through $(-2,-7)$ and cutting an intercept of length three units between the straight lines $4 x+3 y=12$ and $4 x+3 y=$ 3 are (A) $x+2=0, y+7=frac{7}{24}(x+2)$ (B) $x-2=0, y+7=-frac{7}{24}(x+2)$ (C) $x+2=0, y+7=-frac{7}{24}(x+2)$ (D) $x+2=0, y+7=-frac{7}{1...

5 answers

##### The coordinates of the point which is at unit distance from the lines $L_{1} equiv 3 x-4 y+1=0$ and $L_{2} equiv 8 x+6 y+$ $1=0$ and lies below $L_{1}$ and above $L_{2}$ are(A) $left(frac{6}{5}, frac{1}{10}ight)$(B) $left(frac{6}{5},-frac{1}{10}ight)$(C) $left(frac{6}{5}, frac{1}{5}ight)$(D) $left(frac{6}{5},-frac{1}{5}ight)$

The coordinates of the point which is at unit distance from the lines $L_{1} equiv 3 x-4 y+1=0$ and $L_{2} equiv 8 x+6 y+$ $1=0$ and lies below $L_{1}$ and above $L_{2}$ are (A) $left(frac{6}{5}, frac{1}{10} ight)$ (B) $left(frac{6}{5},-frac{1}{10} ight)$ (C) $left(frac{6}{5}, frac{1}{5} ight)$ (D) ...

5 answers

##### The vertices of a triangle are $Aleft(x_{1}, x_{1} an alphaight), Bleft(x_{2}, x_{2}ight.$$an eta$ ) and $Cleft(x_{3}, x_{3} an gammaight)$. If the circumcentre of triangle $A B C$ coincides with the origin and $H(a, b)$ be its orthocentre then $frac{a}{h}=$(A) $frac{cos alpha+cos eta+cos gamma}{cos alpha cdot cos eta cdot cos gamma}$(B) $frac{sin alpha+sin eta+sin gamma}{sin alpha cdot sin eta cdot sin gamma}$(C) $frac{an alpha+an eta+an gamma}{an alpha cdot an eta cdot an gamma}$(D) $frac{cos

The vertices of a triangle are $Aleft(x_{1}, x_{1} an alpha ight), Bleft(x_{2}, x_{2} ight.$ $ an eta$ ) and $Cleft(x_{3}, x_{3} an gamma ight)$. If the circumcentre of triangle $A B C$ coincides with the origin and $H(a, b)$ be its orthocentre then $frac{a}{h}=$ (A) $frac{cos alpha+cos eta+cos ...

5 answers

##### $O X$ and $O Y$ are two coordinate axes. On $O Y$ is taken a fixed point $P$ and on $O X$ any point $Q .$ On $P Q$ an equilateral triangle is described, its vertex $R$ being on the side of $P Q$ away from $O$, then the locus of $R$ will be(A) straight line(B) circle(C) ellipse(D) parabola

$O X$ and $O Y$ are two coordinate axes. On $O Y$ is taken a fixed point $P$ and on $O X$ any point $Q .$ On $P Q$ an equilateral triangle is described, its vertex $R$ being on the side of $P Q$ away from $O$, then the locus of $R$ will be (A) straight line (B) circle (C) ellipse (D) parabola...

5 answers

##### If the vertices of a variable triangle are $(3,4)$, ( $5 mathrm{cos}$ $heta, 5 sin heta$ ) and $(5 sin heta,-5 cos heta)$, then the locus of itsorthocentre is(A) $(x+y-1)^{2}+(x-y-7)^{2}=100$(B) $(x+y-7)^{2}+(x-y+1)^{2}=100$(C) $(x+y-7)^{2}+(x-y-1)^{2}=100$(D) $(x+y+7)^{2}+(x+y-1)^{2}=100$

If the vertices of a variable triangle are $(3,4)$, ( $5 mathrm{cos}$ $ heta, 5 sin heta$ ) and $(5 sin heta,-5 cos heta)$, then the locus of its orthocentre is (A) $(x+y-1)^{2}+(x-y-7)^{2}=100$ (B) $(x+y-7)^{2}+(x-y+1)^{2}=100$ (C) $(x+y-7)^{2}+(x-y-1)^{2}=100$ (D) $(x+y+7)^{2}+(x+y-1)^{2}=100$...

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5 answers

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5 answers

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