HSC Science (General) ११ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

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

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

B: Getting a prime number

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

C: Getting a head and a perfect square.

Find n(S) of the following random experiment.

From an urn containing 5 gold and 3 silver coins, 3 coins are drawn at random

Find n(S) of the following random experiment.

5 letters are to be placed into 5 envelopes such that no envelope is empty.

Find n(S) of the following random experiment.

6 books of different subjects arranged on a shelf.

Find n(S) of the following random experiment.

3 tickets are drawn from a box containing 20 lottery tickets.

Two fair dice are thrown. State the sample space and write favorable outcomes for the following event:

A: Sum of numbers on two dice is divisible by 3 or 4

Two fair dice are thrown. State the sample space and write favorable outcomes for the following event:

B: Sum of numbers on two dice is 7