Straight Lines and Pair of Straight Lines
5 Questions
MSQ (Multiple Correct)
2008
JEE Advanced
MSQ
IIT-JEE 2008 Paper 1 Offline
A straight line through the vertex p of a triangle PQR intersects the side QR at the point S and the circumcircle of the triangle PQR at the point T. If S is not the centre of the circumcircle, then :
A.
${1 \over {PS}} + {1 \over {ST}} < {2 \over {\sqrt {QS \times SR} }}$
B.
${1 \over {PS}} + {1 \over {ST}} > {2 \over {\sqrt {QS \times SR} }}$
C.
${1 \over {PS}} + {1 \over {ST}} < {4 \over {QR}}$
D.
${1 \over {PS}} + {1 \over {ST}} > {4 \over {QR}}$
1999
JEE Advanced
MSQ
IIT-JEE 1999
Let ${L_1}$ be a straight line passing through the origin and ${L_2}$ be the straight line $x + y = 1$. If the intercepts made by the circle ${x^2} + {y^2} - x + 3y = 0$ on ${L_1}$ and ${L_2}$ are equal, then which of the following equations can represent ${L_1}$?
A.
$x + y = 0$
B.
$x -y = 0$
C.
$x + 7y = 0$
D.
$x - 7y = 0$
1998
JEE Advanced
MSQ
IIT-JEE 1998
If the vertices $P, Q, R$ of a triangle $PQR$ are rational points, which of the following points of the triangle $PQR$ is (are) always rational point(s)?
A.
centroid ( A rational point is a point both of whose co-ordinates are rational numbers.)
B.
incentre. ( A rational point is a point both of whose co-ordinates are rational numbers.)
C.
circumcentre ( A rational point is a point both of whose co-ordinates are rational numbers.)
D.
orthocentre ( A rational point is a point both of whose co-ordinates are rational numbers.)
1986
JEE Advanced
MSQ
IIT-JEE 1986
All points lying inside the triangle formed by the points $\left( {1,\,3} \right),\,\left( {5,\,0} \right)$ and $\left( { - 1,\,2} \right)$ satisfy
A.
$3x + 2y \ge 0$
B.
$2x + y - 13 \ge 0$
C.
$2x - 3y - 12 \le 0$
D.
$ - 2x + y \ge 0$
1985
JEE Advanced
MSQ
IIT-JEE 1985
Three lines $px + qy + r = 0$, $qx + ry + p = 0$ and $rx + py + q = 0$ are concurrent if
A.
$p + q + r = 0$
B.
${p^2} + {q^2} + {r^2} = qr + rp + pq$
C.
${p^3} + {q^3} + {r^3} = 3pqr$
D.
none of these.