List of top Mathematics Questions asked in CBSE Class XI

Find the distance of the line \(4x + 7y + 5 = 0\)  from the point (1, 2) along the line  \(2x - y = 0\)

The hypotenuse of a right-angled triangle has its ends at the points (1, 3) and (-4, 1). Find the equation of the legs (perpendicular sides) of the triangle.

Find the image of the point (3, 8) with respect to the line x + 3y = 7 assuming the line to be a plane mirror.

If the lines y = 3x + 1 and 2y = x + 3 are equally inclined to the line y = mx + 4, find the value of m.

If three lines whose equations are y = m₁x + c₁, y = m₂x + c₂ and y = m₃x + c₃ are concurrent, then show that m₁ (c₂ – c₃) + m₂ (c₃ – c₁) + m₃ (c₁ – c₂) = 0.

Find the equation of the lines through the point (3, 2) which make an angle of 45° with the line  \(x -2y = 3.\)

Find the equation of the line passing through the point of intersection of the lines \(4x + 7y - 3 = 0\) and \(2x - 3y+ 1 = 0\)  that has equal intercepts on the axes.

Show that the equation of the line passing through the origin and making an angle θ with the line \(y=mx+c\) is \(\frac{y}{x}=\frac{m±tanθ}{1-+mtanθ}\)

In what ratio, the line joining (-1, 1) and (5, 7) is divided by the line x + y = 4?

Find the perpendicular distance from the origin to the line joining the points \((cosθ,sinθ) \) and \((cos\phi,sin\phi).\)

Find the equation of the line parallel to y-axis and drawn through the point of intersection of the lines  \(x - 7y+ 5 = 0\) and \(3x + y = 0.\)

Find the equation of a line drawn perpendicular to the line \(\frac{x}{4} +\frac{ y}{6} = 1 \) through the point where it meets the y-axis

Find the area of the triangle formed by the lines  \(y -x = 0, x + y = 0\) and \(x - k = 0.\)

If p is the length of perpendicular from the origin to the line whose intercepts on the axes are a and b, then show that  \(\frac{1}{p^2}=\frac{1}{a^2}+\frac{1}{b^2}.\)

Find the equations of the lines, which cut-off intercepts on the axes whose sum and product are 1 and – 6, respectively.

What are the points on the y-axis whose distance from the line  \(\frac{ x}{3} +\frac{ y}{4} = 1\) is 4 units?

Find the equation of the right bisector of the line segment joining the points (3,4) and (–1,2).

Find the coordinates of the foot of perpendicular from the point \( (–1, 3) \) to the line \(3x – 4y – 16 = 0.\)

The perpendicular from the origin to the line  \(y = mx + c\)  meets it at the point \((-1, 2)\). Find the values of m and c.

If p and q are the lengths of perpendiculars from the origin to the lines  \(x \space cos θ − y \space sin θ = k\space  cos 2θ\) and \(x \space sec θ + y\space cosec θ = k\), respectively, prove that  \(p^2 + 4q^2 = k^2\)

The line through the points (h, 3) and (4, 1) intersects the line \(7x - 9y - 19 = 0\). at right angle. Find the value of h.

Prove that the line through the point \((x_1, y_1)\) and parallel to the line \(Ax + By + C = 0 \) is \(A (x -x_1) + B (y - y_1) = 0.\)

Two lines passing through the point (2, 3) intersects each other at an angle of \(60º .\) If slope of one line is 2, find equation of the other line.

Find equation of the line parallel to the line \(3x - 4y + 2 = 0\) and passing through the point (-2, 3).

Find equation of the line perpendicular to the line \(x – 7y + 5 = 0\) and having x intercept 3.