SSC (English Medium) 9th Standard - Maharashtra State Board Question Bank Solutions

 If `[by + cz ]/[b^2 + c^2] = [cz + ax]/[c^2 + a^2] = [ax + by]/[a^2 + b^2]` then prove that `x/a= y/b = z/c`

Complete the following cumulative frequency table:

Complete the following Cumulative Frequency Table:

The data is given for 62 students in a certain class regarding their mathematics marks out of 100. Take the classes 0-10, 10-20.. and prepare frequency distribution table and cumulative frequency table more than or equal to type.

55, 60, 81, 90, 45, 65, 45, 52, 30, 85, 20, 10, 75, 95, 09, 20, 25, 39, 45, 50, 78, 70, 46, 64, 42, 58, 31, 82, 27, 11, 78, 97, 07, 22, 27, 36, 35, 40, 75, 80, 47, 69, 48, 59, 32, 83, 23, 17, 77, 45, 05, 23, 37, 38, 35, 25, 46, 57, 68, 45, 47, 49.

1. How many students obtained marks 40 or above 40?
2. How many students obtained marks 90 or above 90?
3. How many students obtained marks 60 or above 60?
4. What is the cumulative frequency of equal to or more than type of the class 0-10?

The data is given for 62 students in a certain class regarding their mathematics marks out of 100. Take the classes 0-10, 10-20.. and prepare less than type cumulative frequency table and answer the following questions.

55, 60, 81, 90, 45, 65, 45, 52, 30, 85, 20, 10, 75, 95, 09, 20, 25, 39, 45, 50, 78, 70, 46, 64, 42, 58, 31, 82, 27, 11, 78, 97, 07, 22, 27, 36, 35, 40, 75, 80, 47, 69, 48, 59, 32, 83, 23, 17, 77, 45, 05, 23, 37, 38, 35, 25, 46, 57, 68, 45, 47, 49.

1. How many students obtained less than 40 marks?
2. How many students obtained less than 10 marks?
3. How many students obtained less than 60 marks?
4. Find the cumulative frequency of the class 50-60.

From following table, what is the cumulative frequency of less than type for the class 30-40?

There are 68 students of 9th standard from model Highschool, Nandpur. They have scored following marks out of 80, in written exam of mathematics.

70, 50, 60, 66, 45, 46, 38, 30, 40, 47, 56, 68, 80, 79, 39, 43, 57, 61, 51, 32, 42, 43, 75, 43, 36, 37, 61, 71, 32, 40, 45, 32, 36, 42, 43, 55, 56, 62, 66, 72, 73, 78, 36, 46, 47, 52, 68, 78, 80, 49, 59, 69, 65, 35, 46, 56, 57, 60, 36, 37, 45, 42, 70, 37, 45, 66, 56, 47

By taking classes 30-40, 40-50, .... prepare the less than type cumulative frequency table

1. How many students, have scored marks less than 80?
2. How many students have scored marks less than 40?
3. How many students have scored marks less than 60?

Write the following number in `bb("p"/"q")` form.

9.315315...

Use factor theorem to determine whether x + 3 is factor of x ² + 2x − 3 or not. 

If (x - 2) is a factor of x³ − mx² + 10x − 20 then find the value of m.

By using factor theorem in the following example, determine whether q(x) is a factor p(x) or not.

p(x) = x³ − x² − x − 1, q(x) = x − 1

By using factor theorem in the following example, determine whether q(x) is a factor p(x) or not.

p(x) = 2x³ − x² − 45, q(x) = x − 3

Show that m − 1 is a factor of m²¹ − 1 and m²² − 1.

If x - 2 and  `x - 1/2` both are the factors of the polynomial  nx² − 5x + m, then show that  m = n = 2

There are 68 students of 9th standard from model Highschool, Nandpur. They have scored following marks out of 80, in written exam of mathematics.

70, 50, 60, 66, 45, 46, 38, 30, 40, 47, 56, 68, 80, 79, 39, 43, 57, 61, 51, 32, 42, 43, 75, 43, 36, 37, 61, 71, 32, 40, 45, 32, 36, 42, 43, 55, 56, 62, 66, 72, 73, 78, 36, 46, 47, 52, 68, 78, 80, 49, 59, 69, 65, 35, 46, 56, 57, 60, 36, 37, 45, 42, 70, 37, 45, 66, 56, 47

By taking classes 30-40, 40-50 ... prepare equal to or more than type cumulative frequency table and answer the following questions based on it.

1. How many students have scored marks 70 or more than 70?
2. How many students have scored marks 30 or more than 30?

Find the Factors of the Polynomial Given Below.

2x² + x – 1

Find the factor of the polynomial given below.

2m² + 5m – 3

Find the factor of the polynomial given below.

12x² + 61x + 77

Find the factor of the polynomial given below.

3y² – 2y – 1

Find the factor of the polynomial given below.

`sqrt 3 x^2 + 4x + sqrt 3`