HSC Commerce (English Medium) 11th Standard - Maharashtra State Board Question Bank Solutions

A bag contains 50 tickets, numbered from 1 to 50. One ticket is drawn at random. What is the probability that, number on the ticket is a prime number or greater than 30?

Hundred students appeared for two examinations. 60 passed the first, 50 passed the second and 30 passed in both. Find the probability that student selected at random passed in at least one examination.

Hundred students appeared for two examinations. 60 passed the first, 50 passed the second, and 30 passed in both. Find the probability that student selected at random passed in exactly one examination.

Hundred students appeared for two examinations. 60 passed the first, 50 passed the second, and 30 passed in both. Find the probability that student selected at random failed in both the examinations.

If P(A) = `1/4`, `"P"("B") = 2/5` and `"P"("A" ∪ "B") = 1/2` Find the value of the following probability: P(A ∩ B)

If P(A) = `1/4`, P(B) = `2/5` and P(A ∪ B) = `1/2` Find the value of the following probability: P(A ∩ B')

If P(A) = `1/4`, P(B) = `2/5` and P(A ∪ B) = `1/2` Find the value of the following probability: P(A' ∩ B)

If P(A) = `1/4`, P(B) = `2/5` and P(A ∪ B) = `1/2` Find the value of the following probability: P(A' ∪ B')

If P(A) = `1/4`, P(B) = `2/5` and P(A ∪ B) = `1/2` Find the value of the following probability: P(A' ∩ B')

A computer software company is bidding for computer programs A and B. The probability that the company will get software A is `3/5`, the probability that the company will get software B is `1/3`, and the probability that the company will get both A and B is `1/8`. What is the probability that the company will get at least one software?

A card is drawn from a well shuffled pack of 52 cards. Find the probability of it being a heart or a queen.

In a group of students, there are 3 boys and 4 girls. Four students are to be selected at random from the group. Find the probability that either 3 boys and 1 girl or 3 girls and 1 boy are selected.

Find the graphical solution of the following system of linear inequations:
x – y ≤ 0, 2x – y ≥ − 2

Find the graphical solution of the following system of linear inequations:
2x + 3y ≥ 12, – x + y ≤ 3, x ≤ 4, y ≥ 3

Find the graphical solution of the following system of linear inequations:
3x + 2y ≤ 1800, 2x + 7y ≤ 1400

Find the graphical solution of the following system of linear inequations:
`"x"/60 + "y"/90 ≤ 1`, `"x"/120 + "y"/75 ≤ 1`, y ≥ 0, x ≥ 0

Solve the following system of inequalities graphically.
3x + 2y ≤ 12, x ≥ 1, y ≥ 2

Solve the following system of inequalities graphically.
2x – y ≥ 1, x – 2y ≤ – 1

If f(x) = 3x + 5, `"g"(x)` = 6x − 1, then find `("f" + "g") (x)`

If f(x) = 3x + 5, g(x) = 6x − 1, then find (f - g) (2).