List of top Mathematics Questions on Slope of a line

A line passing through the point \( A(9, 0) \) makes an angle of \( 30^\circ \) with the positive direction of the x-axis. If this line is rotated about \( A \) through an angle of \( 15^\circ \) in the clockwise direction, then its equation in the new position is:

If points \( (5, 5) \), \( (10, k) \), and \( (-5, 1) \) are collinear, then the value of \( k \) is:

Let the slope of the line \( 45x + 5y + 3 = 0 \) be \( 27r_1 + \frac{9r_2}{2} \) for some \( r_1, r_2 \in \mathbb{R} \).Then\[\lim_{x \to 3} \left( \int_3^x \frac{8t^2}{\frac{3r_1 x}{2} - r_2 x^2 - r_1 x^3 - 3x} \, dt \right)\]is equal to _____.

If the slope of the line joining the points (4,2) and (3,-k) is -2, then the value of k is

The slope of the normal to the curve y = 2x² + 3sinx at x = 0, is :

The angle of elevation of the top of the tower, whose height is 15 mts, at a point whose distance from the base of the tower is 15 mts is

A thin particle moves from \((0,1)\) and gets reflected upon hitting the x-axis at \((√3,0)\). Then the slope of the reflected line is ?

The slope of normal at any point \((x, y), x > 0, y > 0\) on the curve \(y = y(x)\) is given by \(\frac{x^2}{xy-x^2y2^-1}\) If the curve passes through the point (1, 1), then \(e · y(e)\) is equal to

A line, with a slope greater than one, passes through point A(4, 3) and intersects the line x – y – 2 = 0 at the point B. If the length of the line segment AB is \(\frac{\sqrt{29}}{3}\) then B also lies on the line :

The slope of the line which makes \(\frac {3\pi}{4}\)angle with the positive direction of x-axis is

If the slope of the line joining the two points P(2,5) and Q(x, 3) is 2, then the value of x is

The radius of a cone is 7 m and its height is 10 m. Then its slant height is______

The distance between the points (0, 0) and (5, 12) is

If the slope of the line through (x, 5) and (5, 2) is 3, then the value of x is

If the slope of the line through (2, -7) and (x, 5) is 3 then x =

The two lines $l x+my=n$ and $l'x+m'y=n'$ are perpendicular if

A line $y = mx + 1$ intersects the circle $(x ? 3)^2 + (y + 2)^2 = 25$ at the points $P$ and $Q$ If the midpoint of the line segment $PQ$ has $x$-coordinate $-\frac{3}{5}$, then which one of the following options is correct?

The slope of the straight line$\frac{ x}{10 }$-$\frac{y }{4 }$ = 3 is

The medians $AD$ and $BE$ of a triangle with vertices $A(0, b), B(0, 0) $ & $C(a, 0)$ are perpendicular to each other, if

The line joining two points $A(2,0), B(3,1)$ is rotated about $A$ in anti-clockwise direction through an angle of $15^{\circ}$. The equation of the line in the now position,is

Form the differential equation of $y=a{e}^{3x}\cos (x+b)$ Where $y^{\prime }=\frac{dy}{dx}$ and $y^n=\frac{d^{2}y}{d{x}^2}$?