List of top Mathematics Questions asked in CBSE Class XI

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.

Find angles between the lines \(\sqrt3x+y=1\) and \(x+\sqrt3y=1.\)

Find the distance of the point (–1, 1) from the line \(12(x + 6) = 5(y – 2)\)

Find the points on the x-axis, whose distances from the line \(\frac{ x}{3}+\frac{y}{4}=1\) are 4 units.

By using the concept of equation of a line, prove that the three points (3, 0), (– 2, – 2) and (8, 2) are collinear.

Reduce the following equations into slope-intercept form and find their slopes and the y-intercepts. 
(i) \(x + 7y = 0 \)
(ii) \(6x + 3y - 5 = 0 \)
(iii) \(y = 0\)

P (a,b) is the mid-point of a line segment between axes. Show that equation of the line is \(\frac{x}{a}+\frac{y}{b}=2\)

Point R (h, k) divides a line segment between the axes in the ratio 1: 2. Find equation of the line.

The owner of a milk store finds that, he can sell 980 litres of milk each week at Rs 14/litre and 1220 litres of milk each week at Rs 16/litre. Assuming a linear relationship between selling price and demand, how many litres could he sell weekly at Rs 17/litre?

The perpendicular from the origin to a line meets it at the point (–2, 9), find the equation of the line.

The length L (in centimetre) of a copper rod is a linear function of its Celsius temperature C. In an experiment, if L = 124.942 when C = 20 and L= 125.134 when C = 110, express L in terms of C.

Prove that the product of the lengths of the perpendiculars drawn from the points \(\left(\sqrt{a^2-b^2},0\right)\) and \(\left(-\sqrt{a^2-b^2},0\right)\) to the line \(\frac{x}{a}cosθ+\frac{y}{b}sinθ=1\) is \(b^2\).

A person standing at the junction (crossing) of two straight paths represented by the equations 2x - 3y + 4 = 0 and 3x + 4y - 5 = 0 wants to reach the path whose equation is 6x - 7y + 8 = 0 in the least time. Find equation of the path that he should follow.

A ray of light passing through the point (1, 2) reflects on the x-axis at point A and the reflected ray passes through the point (5, 3). Find the coordinates of A.

If sum of the perpendicular distances of a variable point P (x, y) from the lines x + y - 5 = 0 and 3x - 2y + 7 = 0 is always 10. Show that P must move on a line.

The given figure shows a relationship between the sets P and Q. Write this relation

1. in set-builder form
2. in roster form.

What is its domain and range?

Write the relation R = {(x, x³ ): x is a prime number less than 10} in roster form.

Determine the domain and range of the relation R defined by R = {(x, x + 5): x ∈ {0, 1, 2, 3, 4, 5}}.

Let A = {1, 2, 3, 4, 6}. Let R be the relation on A defined by 
{(a, b): a, b ∈ A, b is exactly divisible by a}.

1. Write R in roster form
2. Find the domain of R
3. Find the range of R

A = {1, 2, 3, 5} and B = {4, 6, 9}. Define a relation R from A to B by R = {(x, y): the difference between x and y is odd; x ∈A, y ∈B}. Write R in roster form.

Define a relation R on the set Non natural numbers by R = {(x, y): y= x+ 5, x is a natural number less than 4; x, y ∈ N}. Depict this relationship using roster form. Write down the domain and the range.

Let A = {1, 2, 3, ... ,14}. Define a relation R from A to A by R = {(x, y): 3x - y = 0, where x, y ∈ A}. Write down its domain, codomain and range.