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

A sample of boys and girls were asked to choose their favourite sport, with the following results. Find the value of the χ² statistic.

A box contains 25 tickets numbered 1 to 25. Two tickets are drawn at random. What is the probability that the product on the numbers is even?

Two throws are made, the first with 3 dice and the second with 2 dice. The faces of each die are marked with the number 1 to 6. What is the probability that the total in first throw is not less than 15 and at the same time the total in the second throw is not less than 8?

A number of two digits is formed using the digits 1, 2, 3, ….., 9. What is the probability that the number so chosen is even and less than 60?

A bag contains 8 red balls and 5 white balls. Two successive draws of 3 balls are made without replacement. Find the probability that the first drawing will give 3 white balls and second drawing will give 3 red balls.

Find the values of x and y which satisfy the following equations (x, y ∈ R): (x + 2y) + (2x – 3y i + 4i = 5

Find the values of x and y which satisfy the following equations (x, y ∈ R):

`(x + 1)/(1 + "i") + (y - 1)/(1 - "i")` = i

Solve the following quadratic equation: 

8x² + 2x + 1 = 0

Solve the following quadratic equation:

`2x^2 - sqrt(3)  x + 1` = 0

Solve the following quadratic equation:

3x² – 7x + 5 = 0

Solve the following quadratic equation:

x² – 4x + 13 = 0

Solve the following quadratic equation:

x² + 3ix + 10 = 0

Solve the following quadratic equation:

2x² + 3ix + 2 = 0

Solve the following quadratic equation:

x² + 4ix – 4 = 0

Solve the following quadratic equation:

ix² – 4x – 4i = 0

Solve the following quadratic equation:

x² – (2 + i) x – (1 – 7i) = 0

Find k if the following function is continuous at the points indicated against them:

`f(x) = ((5x - 8)/(8 - 3x))^(3/(2x - 4)`  for x ≠ 2
         = k                           for x = 2 at x = 2.

Solve the following quadratic equation:

`x^2 - (3 sqrt(2) + 2"i") x + 6 sqrt(2)"i"` = 0

Find k if the following function is continuous at the points indicated against them:

`f(x) = (45^x - 9^x - 5^x + 1)/((k^x - 1)(3^x - 1))`  for x ≠ 0

         = `2/3`                  for x = 0, at x = 0

Find k if the following function is continuous at the points indicated against them:

`f(x) = (1 + kx)^(1/x)`  , for x ≠ 0

       = `e^(3/2)`                  ,  for x = 0, at x = 0