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

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

Solve the following quadratic equation:

x² – (5 – i)x + (18 + i) = 0

Solve the following quadratic equation:

(2 + i) x² – (5 – i) x + 2(1 – i) = 0

Find a and b if the following function is continuous at the point indicated against them.

`f(x) = (32^x - 1)/(8^x - 1) + a` , for x > 0
         = 2                      , for x = 0
         = x + 5 − 2b       , for x < 0
is continuous at x = 0