List of top Mathematics Questions on Straight lines asked in WBJEE

A rectangle ABCD has its side parallel to the line y=2x and vertices A,B,D are on y=1,x=1 and x=-1 respectively. The coordinate of C can be

If 4a²+9b²-c²+12ab=0, then the family of straight lines ax+by+c=0 is concurrent at 

A letter lock consists of three rings with 15 different letters. If N denotes the number of ways in which it is possible to make unsuccessful attempts to open the lock, Then 

The straight lines x+2y-9=0, 3x+5y-5=0, and ax+by-1=0 are concurrent if the straight line 35x-22y+1=0 passes through the point:

A variable line passes through the fixed point ($\alpha,\,\beta$). The locus of the foot of the perpendicular from the origin on the line is,

Let $d_1$ and $d_2$ be the lengths of the perpendiculars drawn from any point of the line $7x - 9y + 10 = 0$ upon the lines $3x + 4y = 5$ and $12x + 5y = 7$ respectively. Then

The point $P \,(3, 6)$ is first reflected on the line $y = x$ and then the image point $Q$ is again reflected on the line $y = - x$ to get the image point $Q'$. Then the circumcentre of the $\Delta PQQ'$ is

Let $A(2, -3)$ and $B (-2, 1)$ be two angular points of $\Delta ABC$. If the centroid of the triangle moves on the line $2x + 3y = 1$, then the locus of the angular point $C$ is given by

Transforming to parallel axes through a point $(p, q)$, the equation $2x^2 + 3xy + 4y^2 + x + 18y + 25 = 0$ becomes $2x^2 + 3xy + 4y^2 = 1$. Then

A point moves so that the sum of squares of its distances from the points (1,2) and (-2,1) is always 6. Then its locus is

The number of integer values of $m$, for which the $x$-coordinate of the point of intersection of the lines $3x + 4y = 9$ and $y = mx + 1$ is also an integer, is

If the three points $A(1,6), B(3, -4)$ and $C(x, y)$ are collinear then the equation satisfying by $x$ and $y$ is

A line through the point $A(2, 0)$ which makes an angle of $30^{\circ}$ with the positive direction of $x$-axis is rotated about $A$ in clockwise direction through an angle $15^{\circ}$. Then, the equation of the straight line in the new position is

The coordinates of the foot of the perpendicular from $(0,0)$ upon the line $x + y = 2$ are

The equation  8x²+ 12y²– 4x + 4y – 1 = 0  represents 

If  A and B are two matrices such that A+B and AB are both defined, then 

The equation of the locus of the point of intersection of the straight lines x sin θ + (1 – cos θ) y = a sin θ  and x sin θ – (1 + cos θ) y + a sin θ = 0 is 

The angle between the straight lines $x-y\sqrt{3}=5$ and $\sqrt{3}x+y=7$ is

${\int }_0^{\pi /2}\frac{\sqrt{\cot x}}{\sqrt{\cot x}+\sqrt{\tan x}}$dx is equal to

If [x] denotes the greatest integer x, then $\left[\frac{2}{3}\right]+[\frac{2}{3}+\frac{1}{99}]+[\frac{2}{3}+\frac{2}{99}]+\dots ..+[\frac{2}{3}+\frac{98}{99}]$is equal to