Arts (English Medium) Class 11 - CBSE Question Bank Solutions for Mathematics

Equation of the line passing through the point (a cos³θ, a sin³θ) and perpendicular to the line x sec θ + y cosec θ = a is x cos θ – y sin θ = a sin 2θ.

The straight line 5x + 4y = 0 passes through the point of intersection of the straight lines x + 2y – 10 = 0 and 2x + y + 5 = 0.

The equation of the line joining the point (3, 5) to the point of intersection of the lines 4x + y – 1 = 0 and 7x – 3y – 35 = 0 is equidistant from the points (0, 0) and (8, 34).

The lines ax + 2y + 1 = 0, bx + 3y + 1 = 0 and cx + 4y + 1 = 0 are concurrent if a, b, c are in G.P.

Given the ellipse with equation 9x² + 25y² = 225, find the major and minor axes, eccentricity, foci and vertices.

Find the equation of the ellipse with foci at (± 5, 0) and x = `36/5` as one of the directrices.

The equation of the circle in the first quadrant touching each coordinate axis at a distance of one unit from the origin is ______.

The equation of the circle having centre (1, –2) and passing through the point of intersection of the lines 3x + y = 14 and 2x + 5y = 18 is ______.

The equation of the ellipse whose centre is at the origin and the x-axis, the major axis, which passes through the points (–3, 1) and (2, –2) is ______.

The equation of the circle which passes through the point (4, 5) and has its centre at (2, 2) is ______.

If the lines 3x – 4y + 4 = 0 and 6x – 8y – 7 = 0 are tangents to a circle, then find the radius of the circle.

Find the equation of a circle which touches both the axes and the line 3x – 4y + 8 = 0 and lies in the third quadrant.

Find the distance between the directrices of the ellipse `x^2/36 + y^2/20` = 1

The shortest distance from the point (2, –7) to the circle x² + y² – 14x – 10y – 151 = 0 is equal to 5.

Draw appropriate Venn diagram for the following:

(A ∪ B)'

Draw appropriate Venn diagram for the following:

A' ∩ B'

Draw appropriate Venn diagram for the following:

(A ∩ B)'

Draw appropriate Venn diagram for the following:

A' ∪ B'

In a survey it was found that 21 people liked product A, 26 liked product B and 29 liked product C. If 14 people liked products A and B, 12 people liked products C and A, 14 people liked products B and C and 8 liked all the three products. Find how many liked product C only.

Find the derivative of x² – 2 at x = 10.