List of top Mathematics Questions on Straight lines asked in MHT CET

If slope of two lines represented by \( \dfrac{x^2}{a}+\dfrac{2xy}{h}+\dfrac{y^2}{b}=0 \) is twice the other, then \(ab:h^2=\ ?\)
The distance between the lines represented by \[ 16x^2 + 9y^2 + 48x - 24xy - 36y + 35 = 0 \] is ......... units
The slopes of the lines represented by $6x^2 + 2hxy + y^2 = 0$ are in the ratio 2 : 3, then $h = \dots$
The straight line passing through $(-3, 6)$ and midpoint of the line segment joining the points $(4, -5)$ and $(-2, 9)$ have inclination ______.
The line MN whose equation is $x - y - 2 = 0$ cuts the X-axis at M and coordinates of N are (4, 2). The line MN is rotated about M through $45^{\circ}$ in anticlockwise direction. The equation of the line MN in the new position is ______.
The acute angle between the line $4x-2y+13=0$ and the line which makes equal intercepts with the co-ordinate axes is
The integrating factor of \( y + \frac{d}{dx}(xy) = x(\sin x + \log x) \) is
The equation $x^2 - 3xy + 2y^2 + 3x - 5y + 2 = 0$ represents a pair of straight lines. If $\theta$ is the angle between them, then the value of $\cos \theta$ is equal to
If the line $3x + 4y - 24 = 0$ intersects X and Y axes in points A and B respectively then incentre of the triangle OAB where O is origin is
The derivative of $\tan^{-1} \left(\sqrt{1+x^2}-1\right)$ is
The value of $\int_1^4 \log[x]\text{d}x$, where $[x]$ is the greatest integer function is equal to
If the pair of straight lines \(xy - x + y - 1 = 0\) and the line \(x + ky - 3 = 0\) are concurrent, then the value of \(k\) is equal to
From the following options, the nearest line to the origin is ....
The equation $x^2 - 3xy + 2y^2 + 3x - 5y + 2 = 0$ represents a pair of straight lines. If $\theta$ is the angle between them, then the value of $\cos \theta$ is equal to
If the line $3x + 4y - 24 = 0$ intersects X and Y axes in points A and B respectively then incentre of the triangle OAB where O is origin is
If a random variable $X$ has p.d.f. $f(x) = \begin{cases} \frac{ax^2}{2} + bx & , \text{if } 1 \leq x \leq 3 \\ 0 & , \text{otherwise} \end{cases}$ and $f(2) = 2$, then the values of $a$ and $b$ are, respectively}
The equation $x^2 - 3xy + 2y^2 + 3x - 5y + 2 = 0$ represents a pair of straight lines. If $\theta$ is the angle between them, then the value of $\cos \theta$ is equal to
If the line $3x + 4y - 24 = 0$ intersects X and Y axes in points A and B respectively then incentre of the triangle OAB where O is origin is
If \( x = a(\cos \theta + \theta \sin \theta), \, y = a(\sin \theta - \theta \cos \theta) \), then \( \frac{d^2 y}{dx^2} \) equals
The distance of a point (2, 5) from the line $3x+y+4=0$ measured along the line $L_{1}$ and $L_{2}$ are same. If slope of line $L_{1}$ is $\frac{3}{4}$, then slope of the line $L_{2}$ is
If the distance between the parallel lines given by the equation $x^{2}+4xy+py^{2}+3x+qy-4=0$ is $\lambda$, then $\lambda^{2}=$
The centroid of the triangle formed by the lines $x + 3y = 10$ and $6x^2 + xy - y^2 = 0$ is
Let $P = (-3, 0)$, $Q = (0,0)$ and $R = (3,3\sqrt{3})$ be three points. Then the equation of the bisector of the angle PQR is
The equation of the perpendicular bisector of the line segment joining $A(-2, 3)$ and $B(6, -5)$ is
Area of the triangle formed by the lines $y^2 - 9xy + 18x^2 = 0$ and $y = 9$ is