HSC Science (General) इयत्ता ११ वी - Maharashtra State Board Question Bank Solutions

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

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

C: Odd number on the first die.

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

D: Even number on the first die.

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

Check whether events A and B are mutually exclusive and exhaustive.

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

B: Sum of numbers on two dice is 7.

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

Check whether events C and D are mutually exclusive and exhaustive

C: Odd number on the first die.

D: Even number on the first die.

A bag contains four cards marked as 5, 6, 7, and 8. Find the sample space if two cards are drawn at random with replacement.

A bag contains four cards marked as 5, 6, 7, and 8. Find the sample space if two cards are drawn at random without replacement.

From a bag containing 10 red, 4 blue and 6 black balls, a ball is drawn at random. Find the probability of drawing a red ball.