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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) $frac{12}{25}$...

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##### 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...

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##### 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...

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##### Let $S_{1}, S_{2}, ldots$ be squares such that for each $n geq 1$, the length of a side of $S_{n}$ equals the length of a diagonal of $S_{n+1}$. If the length of a side of $S_{1}$ is $10 mathrm{~cm}$, then for which of the following values of $n$ is the area of $S_{s}$ less than 1 square $mathrm{cm} ?$(A) 7(B) 8(C) 9(D) 10

Let $S_{1}, S_{2}, ldots$ be squares such that for each $n geq 1$, the length of a side of $S_{n}$ equals the length of a diagonal of $S_{n+1}$. If the length of a side of $S_{1}$ is $10 mathrm{~cm}$, then for which of the following values of $n$ is the area of $S_{s}$ less than 1 square $mathrm{cm}...

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##### A line which makes an acute angle $heta$ with the positive direction of $x$-axis is drawn through the point $P(3,4)$ to meet the line $x=6$ at $R$ and $y=8$ at $S$, then(A) $P R=3 sec heta$(B) $P S=4 operatorname{cosec} heta$(C) $P R+P S=frac{2(3 sin heta+4 cos heta)}{sin 2 heta}$(D) $frac{9}{(P R)^{2}}+frac{16}{(P S)^{2}}=1$

A line which makes an acute angle $ heta$ with the positive direction of $x$-axis is drawn through the point $P(3,4)$ to meet the line $x=6$ at $R$ and $y=8$ at $S$, then (A) $P R=3 sec heta$ (B) $P S=4 operatorname{cosec} heta$ (C) $P R+P S=frac{2(3 sin heta+4 cos heta)}{sin 2 heta}$ (D) $frac...

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##### 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...

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##### 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) $7 x+9 y+73=0$...

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##### 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$...

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##### 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...

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##### 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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