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##### If a right-angled isosceles triangle right-angled at origin has $3 x+4 y=6$ as its base, then the area of the triangle is(A) 7(B) $frac{11}{25}$(C) $frac{36}{25}$(D) $frac{12}{25}$
If a right-angled isosceles triangle right-angled at origin has $3 x+4 y=6$ as its base, then the area of the triangle is (A) 7 (B) $frac{11}{25}$ (C) $frac{36}{25}$ (D) $frac{12}{25}$...
##### The line $x+y=1$ meets $mathrm{x}$-axis at $A$ and $mathrm{y}$-axis at $B . P$ is the mid-point of $A B cdot P_{1}$ is the foot of the perpendicular from $P$ to $O A ; M_{1}$ is that from $P_{1}$ to $O P ; P_{2}$ is that from $M_{1}$ to $O A$ and so on. If $P_{n}$ denotes the foot of the $n$th perpendicular on $O A$ from $M_{n-1}$, then $O P_{n}$ is equal to(A) $frac{1}{2^{n}}$(B) $frac{1}{2^{n-1}}$(C) $frac{1}{2^{n-2}}$(D) none of these
The line $x+y=1$ meets $mathrm{x}$-axis at $A$ and $mathrm{y}$-axis at $B . P$ is the mid-point of $A B cdot P_{1}$ is the foot of the perpendicular from $P$ to $O A ; M_{1}$ is that from $P_{1}$ to $O P ; P_{2}$ is that from $M_{1}$ to $O A$ and so on. If $P_{n}$ denotes the foot of the $n$th perpe...
##### The line $x+y=a$ meets $x$-axis at $A$. $A$ triangle $A M N$ is inscribed in the triangle $O A B, O$ being the origin with right angle at $N ; M$ and $N$ lie respectively on $O B$ and $A B$. If area of $riangle A M N$ is $frac{3}{8}$ of the area of triangle $O A B$, then $frac{A N}{B N}$ is equal to(A) 3(B) $frac{1}{3}$(C) 2(D) $frac{2}{3}$
The line $x+y=a$ meets $x$-axis at $A$. $A$ triangle $A M N$ is inscribed in the triangle $O A B, O$ being the origin with right angle at $N ; M$ and $N$ lie respectively on $O B$ and $A B$. If area of $riangle A M N$ is $frac{3}{8}$ of the area of triangle $O A B$, then $frac{A N}{B N}$ is equal t...
##### Straight lines $3 x+4 y=5$ and $4 x-3 y=15$ intersect at $A$. Points $B$ and $C$ are choosen on these lines such that $A B=A C$. The equation of the line $B C$ passing through the point $(1,2)$ is(A) $x+7 y+13=0$(B) $x-7 y+13=0$(C) $7 x+y-9=0$(D) none of these
Straight lines $3 x+4 y=5$ and $4 x-3 y=15$ intersect at $A$. Points $B$ and $C$ are choosen on these lines such that $A B=A C$. The equation of the line $B C$ passing through the point $(1,2)$ is (A) $x+7 y+13=0$ (B) $x-7 y+13=0$ (C) $7 x+y-9=0$ (D) none of these...
##### The equation of the straight line passing through the point $(4,5)$ and making equal angles with the two straight lines given by the equations $3 x-4 y-7=0$ and $12 x-5 y+6=0$, is(A) $9 x-7 y-1=0$(B) $9 x+7 y-1=0$(C) $7 x+9 y-73=0$(D) $7 x+9 y+73=0$
The equation of the straight line passing through the point $(4,5)$ and making equal angles with the two straight lines given by the equations $3 x-4 y-7=0$ and $12 x-5 y+6=0$, is (A) $9 x-7 y-1=0$ (B) $9 x+7 y-1=0$ (C) $7 x+9 y-73=0$ (D) $7 x+9 y+73=0$...
##### Let the algebraic sum of the perpendicular distances from the points $A(2,0), B(0,2), C(1,1)$ to a variable line be zero. Then, all such lines(A) are concurrent(B) pass through the fixed point $(1,1)$(C) touch some fixed circle(D) pass through the centroid of $riangle A B C$
Let the algebraic sum of the perpendicular distances from the points $A(2,0), B(0,2), C(1,1)$ to a variable line be zero. Then, all such lines (A) are concurrent (B) pass through the fixed point $(1,1)$ (C) touch some fixed circle (D) pass through the centroid of $riangle A B C$...
##### The equation of the line passing through the point ( 2 , 3) and making intercept of length 2 units between the lines $y+2 x=3$ and $y+2 x=5$, is(A) $x=2$(B) $3 x+4 y=18$(C) $4 x+3 y=18$(D) none of these
The equation of the line passing through the point ( 2 , 3) and making intercept of length 2 units between the lines $y+2 x=3$ and $y+2 x=5$, is (A) $x=2$ (B) $3 x+4 y=18$ (C) $4 x+3 y=18$ (D) none of these...
##### Two sides of a rhombus $A B C D$ are parallel to the lines $y=x+2$ and $y=7 x+3$. If the diagonals of the rhombus intersect at the point $(1,2)$ and the vertex $A$ is on the $y$-axis, then the possible coordinates of $A$ are(A) $(0,0)$(B) $left(0, frac{5}{2}ight)$(C) $left(0,-frac{5}{2}ight)$(D) none of these
Two sides of a rhombus $A B C D$ are parallel to the lines $y=x+2$ and $y=7 x+3$. If the diagonals of the rhombus intersect at the point $(1,2)$ and the vertex $A$ is on the $y$-axis, then the possible coordinates of $A$ are (A) $(0,0)$ (B) $left(0, frac{5}{2} ight)$ (C) $left(0,-frac{5}{2} ight)$ (...

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