Arts (English Medium) इयत्ता ११ - CBSE Question Bank Solutions

In a potato race 20 potatoes are placed in a line at intervals of 4 metres with the first potato 24 metres from the starting point. A contestant is required to bring the potatoes back to the starting place one at a time. How far would he run in bringing back all the potatoes?

In a cricket tournament 16 school teams participated. A sum of Rs 8000 is to be awarded among themselves as prize money. If the last-placed team is awarded Rs 275 in prize money and the award increases by the same amount for successive finishing places, how much amount will the first-place team receive?

Find the equation of lines passing through (1, 2) and making angle 30° with y-axis.

Find the equation of the line passing through the point of intersection of 2x + y = 5 and x + 3y + 8 = 0 and parallel to the line 3x + 4y = 7.

In what direction should a line be drawn through the point (1, 2) so that its point of intersection with the line x + y = 4 is at a distance `sqrt(6)/3` from the given point.

A straight line moves so that the sum of the reciprocals of its intercepts made on axes is constant. Show that the line passes through a fixed point.

Find the equations of the lines through the point of intersection of the lines x – y + 1 = 0 and 2x – 3y + 5 = 0 and whose distance from the point (3, 2) is `7/5`

The equation of the line passing through the point (1, 2) and perpendicular to the line x + y + 1 = 0 is ______.

The equations of the lines which pass through the point (3, –2) and are inclined at 60° to the line `sqrt(3)  x + y` = 1 is ______.

If a, b, c are in A.P., then the straight lines ax + by + c = 0 will always pass through ______.

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 ______.