HSC Arts (English Medium) इयत्ता ११ वी - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Choose the correct alternative:

Find the equation of the circle which passes through the points (2, 3) and (4, 5) and the centre lies on the straight line y − 4x + 3 = 0

Choose the correct alternative:

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

Choose the correct alternative:

Area of the circle centre at (1, 2) and passing through (4, 6) is

Choose the correct alternative:

If a circle passes through the point (0, 0), (a, 0) and (0, b) then find the co-ordinates of its centre

Choose the correct alternative:

The equation of a circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length 3a is

Answer the following :

Find the centre and radius of the circle x² + y² − x +2y − 3 = 0

Answer the following :

Find the centre and radius of the circle x = 3 – 4 sinθ, y = 2 – 4cosθ

Answer the following :

Find the equation of circle passing through the point of intersection of the lines x + 3y = 0 and 2x − 7y = 0 whose centre is the point of intersection of lines x + y + 1 = 0 and x − 2y + 4 = 0

Answer the following :

Find the equation of circle which passes through the origin and cuts of chords of length 4 and 6 on the positive side of x-axis and y-axis respectively

Answer the following :

Show that the points (9, 1), (7, 9), (−2, 12) and (6, 10) are concyclic

The line 2x − y + 6 = 0 meets the circle x² + y² + 10x + 9 = 0 at A and B. Find the equation of circle on AB as diameter.

Answer the following :

Find the equation of the circle concentric with x² + y² – 4x + 6y = 1 and having radius 4 units

Answer the following :

Show that the circles touch each other externally. Find their point of contact and the equation of their common tangent:

x² + y² – 4x + 10y +20 = 0,

x² + y² + 8x – 6y – 24 = 0.

Answer the following :

Show that the circles touch each other externally. Find their point of contact and the equation of their common tangent:

x² + y² – 4x – 10y + 19 = 0,

x² + y² + 2x + 8y – 23 = 0.

Answer the following :

Show that the circles touch each other internally. Find their point of contact and the equation of their common tangent:

x² + y² – 4x – 4y – 28 = 0,

x² + y² – 4x – 12 = 0

Answer the following :

Show that the circles touch each other internally. Find their point of contact and the equation of their common tangent:

x² + y² + 4x – 12y + 4 = 0,

x² + y² – 2x – 4y + 4 = 0

Answer the following :

Find the length of the tangent segment drawn from the point (5, 3) to the circle x² + y² + 10x – 6y – 17 = 0

There are four pens: Red, Green, Blue, and Purple in a desk drawer of which two pens are selected at random one after the other with replacement. State the sample space and the following event.

A: Selecting at least one red pen.

There are four pens: Red, Green, Blue, and Purple in a desk drawer of which two pens are selected at random one after the other with replacement. State the sample space and the following event.

B: Two pens of the same color are not selected.

A coin and a die are tossed simultaneously. Enumerate the sample space and the following event.

A: Getting a Tail and an Odd number